The volume of the solid is given by the equation V = 36π (√2 - 1) using the triple integral.
A three-dimensional object's volume in three-dimensional space may be determined using the triple integral. The three-variable function is represented by the triple integral. If in space is a closed region, the region's entire volume may be expressed as V = Ddv, which is equivalent to V = D d x d y d z.
Cone: z = [tex]\sqrt{x^2+y^2}[/tex]
sphere: x² + y² + z² = 18
Here, we will use cylindrical coordinates to evaluate volume:
x = rcosθ , y = rsinθ, z = z
so, z = [tex]\sqrt{r^2cos^2\theta+r^2sin^2\theta} =r[/tex]
z = [tex]\sqrt{18-(x^2+y^2)} =\sqrt{18-r^2}[/tex]
r = [tex]\sqrt{18-r^2}[/tex]
r = 3
Finding limits,
[tex]Volume = \int\limits^2_0 \int\limits^3_0\int\limits^a_r {rdzdrd\theta} \, \\\\= \int\limits^2_0 \int\limits^3_0rz \ drd\theta\\\\= \int\limits^2_0 \int\limits^3_0 r(\sqrt{18-r^2}-r ) \ drd\theta\\\\[/tex]
Now, we have
[tex]\int\limits^3_0 {r\sqrt{18-r^2} } \, dr = -(9-18\sqrt{2} ) = 18\sqrt{2} -9[/tex]
Now the integral becomes,
Volume = 2π [(18√2-9) - 9]
= 2π x 18√2 - 18
V = 36π (√2 - 1)
Therefore, the volume of the solid is given by V = 36π (√2 - 1).
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The result of adding 15 to x and dividing the answer by 4 is the same as taking x from 80. a Express this statement as an algebraic equation. b Hence find the value of x.
Answer:
(15+x)÷4 = 80-x
by criss cross we'll get:
15+x = 4(80-x)
15+x = 320-4x
x+4x=320-15
5x = 305
x = 61
Which expressions are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1
Answer:
8(3/4y - 2) + 6(-1/2x + 4) + 1 can be simplified as:
6(-1/2x) = -3x
8(3/4y) = 6y
8(-2) = -16
6(4) = 24
1 remains as 1.
So the expression becomes:
6y - 3x - 16 + 24 + 1
which simplifies to:
6y - 3x + 9
Therefore, the expressions that are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1 are:
6y - 3x + 9
Question 2 of 3
Which subtraction equation shows how to subtract
4
2
12
−
2
8
12
using equivalent fractions? i need help
Answer:
Step-by-step explanation:
your given is not cleared repost it then post
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formula.
In response to the stated question, we may state that Therefore, the trigonometry exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Using the given triangle, we can find the values of sin(u), cos(u), and tan(u) as follows:
sin(u) = opposite / hypotenuse = 4 / 5
cos(u) = adjacent / hypotenuse = 3 / 5
tan(u) = opposite / adjacent = 4 / 3
To find the values of sin(2u) and cos(2u), we can use the double angle formulas:
[tex]sin(2u) = 2 sin(u) cos(u)\\cos(2u) = cos^2(u) - sin^2(u)\\sin(2u) = 2 (4/5) (3/5) = 24/25\\cos(2u) = (3/5)^2 - (4/5)^2 = -7/25[/tex]
sin(t/2) = ± [tex]\sqrt((1 - cos(t)) / 2)[/tex]
We need to determine the sign of the square root based on the quadrant in which t/2 lies. Since 7t/2 is in the second quadrant (between pi and 3pi/2), t/2 is in the second quadrant as well (between pi/2 and pi). In the second quadrant, sine is positive and cosine is negative. Therefore, we take the positive square root:
[tex]sin(t/2) = \sqrt((1 - cos(t)) / 2)\\= \sqrt((1 - (-3/5)) / 2)\\= \sqrt(8/10)\\= \sqrt(4/5)\\[/tex]
= 2/√5
= 2√5 / 5
Therefore, the exact values of sin(u), cos(u), sin(2u), and cos(2u) are 4/5, 3/5, 24/25, and -7/25, respectively. The exact value of sin(t/2) is 2√5 / 5.
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What is the solution of
O x≤-3 or 2
Ox<-3 or 2
O-3≤x≤2
or x > 7
O-3 7
x²+x-6
<0?
X-7 50₂
Answer:
[-3, 7].
Step-by-step explanation:
do i need to explain all that?
Answer:
The inequality can be rewritten as x-7 ≤ 50, which we can solve by adding 7 to both sides to get x ≤ 57.
Step-by-step explanation:
It seems like there are multiple questions combined in this one prompt. I will break them down and provide solutions for each one.
Solution for O x≤-3 or 2 Ox<-3 or 2 O-3≤x≤2 or x > 7:
To find the solution for this inequality, we need to solve each part separately and then combine the solutions using the union (OR) operation.
a) x ≤ -3: This part is already solved for x. The solution is x ≤ -3.
b) 2x < -3: We divide both sides by 2 to isolate x and get x < -3/2.
c) 2 ≤ x ≤ -3: This is not possible as there is no number that is both greater than or equal to 2 and less than or equal to -3.
d) x > 7: This part is already solved for x. The solution is x > 7.
The solution to the entire inequality is the union of these solutions: x ≤ -3 OR x < -3/2 OR x > 7.
Solution for x²+x-6 < 0
To solve this quadratic inequality, we can factor it as (x-2)(x+3) < 0 and use the sign chart method.
We create a sign chart for the expression (x-2)(x+3) and test the sign of the expression in each interval
-3 2
---|-------|---
- +
(x-2) - 0 + +
(x+3) - - - 0 +
-------------
- + - 0 +
The sign chart tells us that the expression is negative when x is between -3 and 2. Therefore, the solution to the inequality is -3 < x < 2.
Solution for x-7 ≤ 50₂
It seems like the expression "50₂" is intended to represent the number 50 in base 2 (binary). To convert this number to base 10 (decimal), we can write 50₂ as
50₂ = 12^5 + 12^4 + 02^3 + 02^2 + 12^1 + 02^0 = 32 + 16 + 2 = 50
Therefore, the inequality can be rewritten as x-7 ≤ 50, which we can solve by adding 7 to both sides to get x ≤ 57.
6. Deepa's age is three times that of her brother Devan. After 2 years Deepa's age would
be two times that of Devan. How old are they now?
Answer:
Devan's age = 2 years.
Deepa's age = 6 years.
Step-by-step explanation:
Framing and solving algebraic equation:Present age:
Let the present age of Devan = x
Present age of Deepa = 3x
After 2 years:
Age of Devan = x + 2
Age of Deepa = 3x + 2
Deepa's age = 2* Devan's age
3x + 2 = 2 *(x + 2)
3x + 2 = 2x + 2*2 {Use distributive property}
3x + 2 = 2x + 4
Subtract '2' from both sides,
3x = 2x + 4 - 2
3x = 2x + 2
Subtract '2x' from both sides,
3x - 2x = 2
x = 2
Devan's age = 2 years.
Deepa's age = 3*2
= 6 years
Answer the question attached above. The first person who gets it right will be given brainly.
Answer:
Step-by-step explanation:
a) One possible function that satisfies the conditions is:
f(x) = (x^2 - 25) / (x - 5)
This function is undefined when x = 5, but it is defined for all other real numbers.
b) One possible function that satisfies the conditions is:
g(x) = 1 / (x - 1)
This function is undefined when x = 1, but it is defined for all other positive numbers greater than 1.
c) One possible function that satisfies the conditions is:
h(x) = ln(x - 1)
This function is undefined when x = 1, but it is defined for all other positive numbers greater than 1. The range of this function is all real numbers.
A spinner with 10 equally sized slices has 5 red slices, 3 yellow slices, and 2 blue slices. Ann spun the dial 25 times. It landed on red 12 times, landed on yellow 10 times, and landed on blue 3 times. From Ann's results, compute the experimental probability of landing on blue or yellow
Answer:
0.600 or 600, 0.500 or 500, select option 2
Step-by-step explanation:
Hydrogen produced from a hydrolysis reaction was collected over water. The data is compiled in the table.
Total volume of H2(g) collected 94.00 mL
Temperature 26.0 °C
Barometric pressure 745 mmHg
Vapor pressure of water at 26.0 °
25.5 mmHg
Calculate the moles of hydrogen gas produced by the reaction.
moles:
Answer:
To calculate the moles of hydrogen gas produced, we need to use the ideal gas law equation:
PV = nRT
where P is the total pressure, V is the volume of the gas, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature to Kelvin by adding 273.15:
T = 26.0 + 273.15 = 299.15 K
Next, we need to calculate the pressure of the hydrogen gas by subtracting the vapor pressure of water from the barometric pressure:
P(H2) = P(total) - P(vapor) = 745 - 25.5 = 719.5 mmHg
Now we can plug in the values into the ideal gas law equation and solve for n:
n = PV/RT
n = (719.5 mmHg)(94.00 mL)/(62.3637 L mmHg/K mol)(299.15 K)
n = 0.00384 mol
Therefore, the moles of hydrogen gas produced by the reaction is 0.00384 mol.
Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.
a. How much time do students at your school spend on the Internet? You collect data from the members of your AP Statistics class and calculate the mean amount of time that these students spent on the Internet yesterday.
b. Is the real-estate market heating up? To estimate the mean sales price, a realtor in a large city randomly selected home sales from the previous months in her city. These sales prices are displayed in the boxplot.
Conditions for constructing a confidence interval for the population mean are met in first scenario. Conditions are generally met for population mean sales price, but potential outliers and non-normality need to be checked.
Yes, the conditions are met for constructing a confidence interval for the population mean in first scenario. The sample is randomly selected and independent, and we can also assume that the sample size is sufficiently large due to the Central Limit Theorem.
The sample comes from a normal population, or use a t-distribution if the sample size is small and the population standard deviation is unknown.
Yes, the conditions are generally met for constructing a confidence interval for the population mean sales price. We can assume that the sample is randomly selected and independent, and we can also assume that the sample size is sufficiently large due to the Central Limit Theorem.
However, we may want to check for these issues and consider using a non-parametric method, such as a confidence interval based on the median or the bootstrap, if there are concerns.
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Which of the following statements must be true based on the diagram below? Select
all that apply. (Diagram is not to scale.)
P
R
N
OOR is a segment bisector.
OOR is a perpendicular bisector.
□ O is the vertex of a pair of congruent angles in the diagram.
OR is the vertex of a pair of congruent angles in the diagram.
□ O is the vertex of a right angle.
None of the above.
OR is the perpendicular bisector and R is the vertex of a pair of congruent angles in the diagram.
What is perpendicular bisector and a pair of congruent angles ?
A perpendicular bisector is a geometric tool that is commonly used in mathematics and geometry. It is used to divide a line segment into two equal parts and is constructed by first finding the midpoint of the line segment. The perpendicular bisector is then constructed by drawing a line perpendicular to the line segment at its midpoint.
In geometry, two angles are said to be congruent if they have the same measure. This means that they have the same size and shape, even if they are oriented differently. In other words, if you were to place one angle on top of the other, they would perfectly overlap.
Explanation of the true statements:
In the given diagram ,
PR=RN and OR is perpendicular .
Hence, OR is the perpendicular bisector because a perpendicular bisector is a line that passes through the midpoint of a line segment and intersects it at a right angle, dividing the segment into two equal parts.
The vertex of a pair of congruent angles is the point where the two angle bisectors intersect.
Hence, R is the vertex of a pair of congruent angles in the diagram.
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I'm not sure where I'm going wrong here and need a detailed explanation with a full answer please.
Answer:
g(x) = 1/2|x - 1| + 2
Step-by-step explanation:
You were almost there, you just got the slope wrong.
original vertex (h, k): (0, 0)
transformed vertex (h', k'): (1, 2)
original slope: 1
transformed slope: m = (3-2)/(3-1) = 1/2 pick any 2 points to find the slope
equation for the transformed function shown in the graph:
g(x) = 1/2|x - h'| + k'
g(x) = 1/2|x - 1| + 2
(pls help need answer by 10pm) Given that AC = DC and BC = CE, how do you write a two column proof to prove that angle A equals angle D?
Answer:
look at the explanation
Step-by-step explanation:
okay so here if AC is equals to DC and BC is equals to CE then AB is equals to DE as well hence, angle A would be equals to angle D.
The second reason that prove that angle A is a angle D is that angle A and angle D are alternate angles
I am also in ninth grade so do recheck yourself
HELP PLEASEEE 30 POINTS!!
Answer:
m<1 = 63° (Exterior alternating Angles)
m<2 = 62°
m<3 = 118°
Step-by-step explanation:
[tex]{ \tt{m \angle 2 + 63 \degree + 55 \degree = 180 \degree}} \\ { \sf{(exterior \: corresponding \: angles)}} \\ { \tt{m \angle 2 = 180 - (63 + 55)}} \\ { \tt{ \underline{ \: m \angle 2 = 62 \degree \: }}}[/tex]
[tex]{ \tt{m \angle 3 = m \angle 1 + 55 \degree}} \\ { \tt{m \angle 3 = 63 + 55}} \\ { \tt{ \underline{ \: m \angle 3 = 118 \degree \: }}}[/tex]
Old Navy is having a 25% off sale on all dresses. Nala sees a dress for 60$. what is the discount rate? What is the sale price of the dress?
Answer: The sale price of the dress is $45.
Step-by-step explanation:
To find the discount rate, we need to calculate the amount of the discount first. Since the dress is on sale for 25% off, the discount amount is:
Discount = 25% x $60 = $15
The discount rate is then calculated by dividing the discount amount by the original price of the dress and multiplying by 100:
Discount rate = ($15 / $60) x 100% = 25%
To find the sale price of the dress, we need to subtract the discount amount from the original price:
Sale price = $60 - $15 = $45
Therefore, the sale price of the dress is $45.
Petra has a jar full of marbles. It has 30 blue marbles and 70 red marbles. She randomly chooses one marble, replaces it and then chooses a second marble. What is the probability Petra chose two blue marbles? What is the probability Petra chose two red marbles?
the lotka-volterra prey-predator equations with self-limitation ofprey are given in non-dimensional form by dt
The parameter an in the Lotka-Volterra predator-prey model denotes the capture efficiency (alpha).
The lotka-Volterra predator-prey model is what.
The Lotka-Volterra model makes the assumption that a predator's rate of prey consumption is inversely related to its abundance.
The parameter an in the Lotka-Volterra predator-prey model denotes the capture efficiency (alpha).
In conclusion, the lotka-volterra predator-prey model aids in estimating the rate at which prey is consumed.
We possess that
The predator population is x.
y is the number of prey.
The dy/dt equation contains the coefficient c. Hence, this coefficient is correlated with the prey population. The presence of a minus sign indicates a decline in the population of prey. It multiplies x as well, indicating a connection to the predator population.
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place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
The correct order of the steps to test the general hypothesis is given as B, A, E, C, D, F.
A hypothesis is basically a uncertain fact that is backed by some logical and solid information. While using the hypothesis, it s important that we use the correct method to verify the credibility of the hypothesis in the system.
So, as per the given option, the correct sequence should be, B, A, E, C, D, F.
We first set up the null hypothesis and the alternative hypothesis, and then we choose the degree of significance. The next phases in hypothesis testing are choosing the test statistics and creating the decision-making rule.
When we get to a conclusion based on the hypothesis after carefully calculating and computing the hypothesis' performance, the procedure is said to be finished.
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Complete question - place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
A. Select the level of significance
B. setup null and alternative hypothesis
C. Establish the decision rule
D. performance computation
E. select the test statistics
F. Draw conclusions
PLS HELP FAST IM GIVING 50 POINTS
Answer:
4 + - 6 = -2
Hope this helps!
Step-by-step explanation:
The arrow closest to the line shows going forward 4 or + 4
The second arrow shows going back 6 or -6
+ 4 - 6 = -6 + 4 = -2
main Street tea company blends black tea that sells for $3.45 a pound with Earl Gray tea that sells for $2.15 a pound to produce 80 lb of mixture that they sell for $2.75 a pound how much of each kind of tea does the mixture contain rounding to the nearest pound
36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.
Let x and y be the amount of tea that sells fo 3.45 and 2.15 a pound respectively:
x+y=80....................eq 1
3.45x+2.15y=2.75(80)......eq 2
:
rewrite eq 1 to x=80-y and plug that value into eq 2
:
3.45(80-y) +2.15y=2.75(80)
:
276-3.45y+2.15y=220
:
-1.3y=56
:
y=43.07 pounds of $2.15 tea
:
28x=80-43.07=36.93 pounds of $3.45 tea
Let a= the pounds of the more expensive tea needed
Let b= the pounds of the less expensive tea needed
(1) a+%2B+b+=+80
(2) 345a+%2B+215b+=+80%2A275 (in cents)
--------------------------
In words, (2) says.
(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =
(lbs of mixture x price/lb of mixture)
-------
Multiply both sides of (1) by 215 and then.
subtract from (2)
345a+%2B+215b+=+80%2A275
-215a+-+215b+=+-80%2A215
130a+=+80%2A60
130a+=+4800
a+=+36.92
and, from (1)
(1) a+%2B+b+=+80
36.92+%2B+b+=+80
b+=+80+-+36.92
b+=+43.08
36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.
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The mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations.
Let's denote the amount of black tea in pounds by "x" and the amount of Earl Gray tea in pounds by "y".
Since the total amount of mixture is 80 lb, we have:
x + y = 80 ----(1)
We also know that the mixture sells for $2.75 a pound, so the total revenue from selling 80 lb of mixture is:
80 x $2.75 = $220
On the other hand, the cost of the mixture is the sum of the costs of the black tea and the Earl Gray tea, which is:
3.45x + 2.15y
Since the company wants to make a profit, the revenue must be greater than the cost, so we have:
3.45x + 2.15y < $220
We can simplify this inequality by dividing both sides by 0.1:
34.5x + 21.5y < 2200 ----(2)
Now we have two equations with two unknowns (equations (1) and (2)), which we can solve using substitution or elimination.
Substitution method:
From equation (1), we have:
y = 80 - x
Substituting this into equation (2), we get:
34.5x + 21.5(80 - x) < 2200
Simplifying and solving for x, we get:
x < 34.5
Rounding x to the nearest pound, we get x = 34.
Substituting this value into y = 80 - x, we get y = 46.
Therefore, the mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.
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f(x)
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Answer:
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Step-by-step explanation:
Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).
Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:
f(x) = x^2 - 2x + 1
Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:
g(f(x)) = 6f(x) - 4
= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))
= 6x^2 - 12x + 2
Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.
Between 11pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
A. Find the probability that at least 3 minutes will elapse before the next telephone order
B. Find the probability that less then 15 minutes will elapse
C. Find the probability that between 15 and 30 minutes will elapse
Answer all please URGENT
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
The probability that less than 15 minutes will elapse between orders is 0.677.
The probability that between 15 and 30 minutes will elapse between orders is 0.2275
Using Poisson distribution:To solve the following problem, we need to use the Poisson distribution, which is a probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average rate of occurrence of those events.
The Poisson distribution has the following formula:
[tex]P(X = k) = (\lambda\times ex^{-\lambda}) / k![/tex]
Where:
P(X = k) is the probability that there are exactly k events in the interval
λ is the average rate of occurrence of events in the interval
e is the mathematical constant e (approximately 2.71828)
k! is the factorial of k (i.e., k * (k-1) * (k-2) * ... * 2 * 1)
Here we have
Between 11 pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
A. The probability that at least 3 minutes will elapse before the next telephone order, using the complement rule:
=> P(at least 3 minutes) = 1 - P(less than 3 minutes)
Assume that the time between telephone orders follows an exponential distribution with a mean of 1/4.2 = 0.2381 hours (or 14.28 minutes).
Therefore, the Poisson distribution is λ = 1/0.2381 = 4.2/1.0 = 4.2.
Using the exponential distribution, we can find the probability of less than 3 minutes elapsing between orders as follows:
P(less than 3 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]
Where t = 3/60 = 0.05 hours
P(less than 3 minutes) = [tex]1 - e^{(-4.2\times 0.05) } = 0.203[/tex]
Therefore,
P(at least 3 minutes) = 1 - 0.203 = 0.797
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
B. To find the probability that less than 15 minutes will elapse between orders, we can use the same exponential distribution as before and set t = 15/60 = 0.25 hours:
P(less than 15 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]
P(less than 15 minutes) = [tex]1 - e^{(-4.2 \times 0.25)} = 0.677[/tex]
Hence, The probability that less than 15 minutes will elapse between orders is 0.677.
C. To find the probability that between 15 and 30 minutes will elapse between orders, we can subtract the probabilities found in less than 15 minutes and less than 30 minutes.
P(15 to 30 minutes) = P(less than 15 minutes) - P(less than 30 minutes) -
P(15 to 30 minutes) = [tex]e^{ (-\lambda0.5)} - e^{ (-\lambda 0.25)}[/tex]
= 0.3499 - 0.1224 = 0.2275
Therefore,
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
The probability that less than 15 minutes will elapse between orders is 0.677.
The probability that between 15 and 30 minutes will elapse between orders is 0.2275
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a delivery truck driver charges a fixed base price of $6 for 2 miles. after 2 miles, he charges an additional $2 for every mile after 6 miles he charges an additional $4 for every mile
The analysis of the relationship in the question and the graph of the relationship indicates that the cost of the delivery truck between 1 mile and 2 miles is a constant, therefore;
The cost of the delivery truck between 1 mile and 2 miles is constant.What is the graph of a dataset?The graph of a dataset displays the relationship, between the variables in the dataset. It is a visual representation of the connection between the variables.
The fixed base price of the delivery truck for (the first) 2 miles = $6
The additional amount the delivery truck charges after 2 miles = $2 per mile
The additional amount charged by the delivery truck after 6 miles = $4 per mile
The part of the question obtained from a similar question posted on the website, includes;
The description of the cost of the delivery truck between 1 mile and 2 milesThe cost of the delivery truck, between 1 mile and 2 miles based on the graph is an horizontal line.
The horizontal line of a graph, indicates that the relationship between the input and output is a constant, such that the output of the relationship, within the interval of the horizontal line is a constant. The correct option is therefore;
b). The cost of the delivery truck between 1 mile and 2 miles is constant
The possible question options includes;
a) More information is required to determine the cost of the delivery truck between 1 mile and 2 miles
b) The cost of the delivery truck between 1 mile and 2 miles, is constant
c) The cost of the delivery truck is decreasing between 1 mile and 2 miles
d) The cost of the delivery truck is increasing between 1 mile and 2 miles
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the car drives at an average speed of 106 km per hour for 2 hours for 45 minutes at which constant speed must the car drive to travel the same distance in 2 hours 35 minutes
The car must drive at a constant speed of approximately 112.89 km/hr to cover the same distance in 2 hours 35 minutes.
What is the formula for Time?The formula for time is: time = distance / speed
where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.
What is the formula for Speed?The formula for speed is: speed = distance / time
where "distance" is the distance traveled by an object and "time" is the duration of travel.
This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.
In the given question,
Let's first calculate the distance traveled in 2 hours 45 minutes (2.75 hours) at an average speed of 106 km/hr.
distance = speed × time
distance = 106 × 2.75
distance = 291.5 km
Now, we need to find at which constant speed the car must drive to cover the same distance in 2 hours 35 minutes (2.5833 hours). Let's call this speed "x".
distance = speed × time
291.5 = x × 2.5833
x = 291.5 / 2.5833
x ≈ 112.89 km/hr
Therefore, the car must drive at a constant speed of approximately 112.89 km/hr to cover the same distance in 2 hours 35 minutes.
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xfind the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y
The volume of the solid obtained by rotating the region bounded by the curves y = x and y = √x about the line x = 6 is (128π/15) - (13π/3), or approximately 3.013 cubic units.
To find the volume of the solid obtained by rotating the region bounded by the curves y = x and y = √x about the line x = 6, we can use the method of cylindrical shells.
First, we need to determine the limits of integration. Since the curves intersect at (0,0) and (1,1), we can integrate with respect to y from 0 to 1.
The radius of each cylindrical shell is the distance from the line x = 6 to the curve y = x or y = √x. We can express this distance as r = 6 - x or r = 6 - y^2, depending on which curve we are using.
The height of each cylindrical shell is the difference between the two curves at the given y-value. This is given by h = y - √x for y = x, and h = y^2 - x for y = √x.
Therefore, the volume of the solid is:
V = ∫(2πrh) dy from 0 to 1
Substituting r and h, we get:
V = ∫(2π(6 - x)(y - √x)) dy from 0 to 1 (for y = x)
V = ∫(2π(6 - y^2)(y^2 - x)) dy from 0 to 1 (for y = √x)
Evaluating these integrals using u-substitution and simplifying, we get:
V = (128π/15) - (13π/3)
Therefore, the volume of the solid is (128π/15) - (13π/3), or approximately 3.013 cubic units
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_____The given question is incomplete, the complete question is given below:
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified in y = x, y = sqrt(x) ; about x = 6
A company makes wax candles shaped like rectangular prisms. Each candle is 4 cm long, 3 cm wide, and 10 cm tall. If the company used 4080^3 cm of wax, how many candles did they make?
Answer:
87
Step-by-step explanation:
87
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
help me pls D;
please !!!!
In linear equatiοn, the bοοkcase shοuld be apprοximately 12.2 inches in οrder tο give Bria's sοap carving cοllectiοn a 300-square-inch area.
What in mathematics is a linear equatiοn?An algebraic equatiοn with simply a cοnstant and a first-οrder (linear) term, such as y=mx+b, where m is the slοpe and b is the y-intercept, is knοwn as a linear equatiοn.
Sοmetimes, the afοrementiοned is referred tο as a "linear equatiοn οf twο variables," where x and y are the variables. Equatiοns with variables οf pοwer 1 are referred tο as linear equatiοns. One example with οnly οne variable is where ax+b = 0, where a and b are real values and x is the variable.
the bοοkcase's tοp is rectangular, with length "L" and width "b". Because the area οf a rectangle is the prοduct οf its length and width, we get:
L * b = 300
Tο find "b," we can rearrange the equatiοn as fοllοws:
b = 300 / L
L ≈ 2b
When we plug this intο the equatiοn abοve, we get:
b = 300 / (2b) (2b)
Tο simplify, we have:
b² = 150
When we take the square rοοt οf bοth sides, we get:
b ≈ 12.2
We have, rοunded tο the nearest tenth οf an inch:
b ≈ 12.2 inches
the width οf the tοp οf the bοοkcase shοuld be apprοximately 12.2 inches in οrder tο give Bria's sοap carving cοllectiοn a 300-square-inch area.
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A regular hexagon is inscribed into a circle. Find the length of the side of the hexagon, if the radius of the circle is 12 cm.
A. 20 cm
B. 18 cm
C. 16 cm
D. 12 cm
E. None of these
The length of the side of the hexagon is 12 cm and option d is the correct answer.
What is a regular polygon?A regular polygon is a closed shape made up of straight line segments with sides and angles that are all of the same length. For instance, a regular hexagon is a polygon having six equal-length sides and six equal-sized angles. Regular polygons have a variety of intriguing characteristics. For instance, their diagonals (lines connecting non-adjacent vertices) all intersect at a single point, and their centre of symmetry is located at the centre of the polygon's circumscribed circle (the circle that passes through all of the polygon's vertices).
Given that, regular hexagon is inscribed into a circle.
The radius of a circle enclosing a regular hexagon is the same as the length of the hexagon's sides.
Hence, the length of the side of the hexagon is 12 cm and option d is the correct answer.
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a. Multiples of: 7: {_ 6: { LCM:
The least common multiple (LCM) of 6 and 7 is 42. To find the LCM, we must first list out all the multiples of 6 and 7.
What is number?Number is a mathematical object used to count, measure, and label. It is also commonly used to represent a certain quantity. Numbers are a fundamental part of mathematics, and they can be used in a variety of ways. From basic arithmetic operations to complex equations, numbers are essential in the field of mathematics. Numbers can be used to represent any quantity, such as distance, size, time, or money. Numbers can also be used to represent abstract concepts, such as emotions or thoughts.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
The LCM is the smallest number that is a multiple of both numbers. In this case, the LCM of 6 and 7 is 42. This can be seen because both 6 and 7 have 42 as a multiple and no other number is smaller.
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The least common multiple (LCM) of 6 and 7 is 42. To find the LCM, we must first list out all the multiples of 6 and 7.
What is number?Number is a mathematical object used to count, measure, and label. It is also commonly used to represent a certain quantity. Numbers are a fundamental part of mathematics, and they can be used in a variety of ways. From basic arithmetic operations to complex equations, numbers are essential in the field of mathematics. Numbers can be used to represent any quantity, such as distance, size, time, or money. Numbers can also be used to represent abstract concepts, such as emotions or thoughts.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
The LCM is the smallest number that is a multiple of both numbers. In this case, the LCM of 6 and 7 is 42. This can be seen because both 6 and 7 have 42 as a multiple and no other number is smaller.
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Complete questions as follows-
How to find LCM of 6 and 7.
Multiply: (–4 + i)(2 – 3i)
Answer:
Step-by-step explanation:
We can use the distributive property and FOIL method to multiply these two complex numbers:
(-4 + i)(2 - 3i) = -4(2) + (-4)(-3i) + (i)(2) + (i)(-3i)
Simplifying each term, we get:
(-4 + i)(2 - 3i) = -8 + 12i + 2i - 3i^2
Since i^2 = -1, we can replace it with -1:
(-4 + i)(2 - 3i) = -8 + 12i + 2i - 3(-1)
Simplifying further, we get:
(-4 + i)(2 - 3i) = -5 + 14i
Therefore, the product of (-4 + i) and (2 - 3i) is -5 + 14i.