A graphing utility such as Desmos or Wolfram Alpha can be used to graph the function. The graph shows that the maximum value occurs at t = 13 and the minimum value occurs at t = 7, which confirms our calculations.
To find the absolute extrema of the function h(t) = t^2 - 6 on the closed interval [7, 13], we can start by taking the derivative of the function and setting it equal to zero to find any critical points:
h'(t) = 2t = 0
t = 0
However, t = 0 is not in the interval [7, 13], so we only need to check the endpoints of the interval and any other critical points that may lie within the interval.
Since there are no critical points in the interval, we only need to evaluate the function at the endpoints:
h(7) = 7^2 - 6 = 43
h(13) = 13^2 - 6 = 163
Thus, the absolute maximum of h(t) on the interval [7, 13] is 163, which occurs at t = 13, and the absolute minimum is 43, which occurs at t = 7.
To verify our results using a graphing utility, we can graph the function h(t) = t^2 - 6 on the interval [7, 13] and visually observe the maximum and minimum values.
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50 POINTS PLEASE HELP SOLVE
Currencies in U.S. Dollars
giving money to Margaret, h
§ that Tobias exchanged?
- 15.75x = 41.87
+ 15.75x = 41.87
x + 15.75 = 41.87
ur answer and then click Check Answer.
Currency
1 Canadian Dollar
1 British Pound
1 Euro
1 Japanese Yen
1 Brazilian Real
Value in U.S. Dollars
0.7386
1.5395
1.0982
0.0093
0.2547
The correct equation is option (A): 0.7386x - 15.75 = 41.87 equation can be used to find the quantity of Canadian dollars that Tobias exchanged .
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to obtain a value. An expression can contain constants, variables, and operators such as addition, subtraction, multiplication, division, and exponentiation, as well as functions and parentheses to control the order of operations.
According to the given information :Let x be the quantity of Canadian dollars that Tobias exchanged. According to the problem statement, he received 0.7386 U.S. dollars for each Canadian dollar exchanged, and he gave away $15.75, leaving him with $41.87. We can use this information to set up the equation:
0.7386x - 15.75 = 41.87
Therefore, the correct equation is option (A):
0.7386x - 15.75 = 41.87 equation can be used to find the quantity of Canadian dollars that Tobias exchanged .
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Katie made a bag of trail mix with1/2 cup of raisins, 3/5 cup of banana chips, and 3/8 cup of peanuts. How much trail mix did she make
So, Katie made 1 19/40 number cups of trail mix.
What is denominator?In mathematics, the denominator is the bottom number in a fraction, and it represents the total number of equal parts into which the whole has been divided. The denominator is written below the numerator, which is the top number in a fraction, and it indicates the number of those equal parts that are being considered or used in the fraction.
given by the question.
To find the total amount of trail mix Katie made, we need to add up the amounts of each ingredient:
1/2 cup of raisins +
3/5 cup of banana chips +
3/8 cup of peanuts
To add these fractions, we need to find a common denominator. The smallest number that all the denominators (2, 5, and 8) divide into evenly is 40. We can convert each fraction to have a denominator of 40:
1/2 cup of raisins = 20/40 cup
3/5 cup of banana chips = 24/40 cup
3/8 cup of peanuts = 15/40 cup
Now we can add them up:
20/40 cup + 24/40 cup + 15/40 cup = 59/40 cup
So, Katie made 59/40 cup of trail mix. However, we can simplify this fraction:
59/40 cup = 1 19/40 cup
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Given: hypotenuse = 5
adjacent = 3
Find Find opposite =
Answer:
Opposite is = 4
Step-by-step explanation:
Fromthe question Hypotenuse = 5
Adjacent = 3
opposite = ?
Let opposite = x
Hypotenuse² = adjacent² + opposite²
5² = 3² + x²
25 = 9 + x²
25 - 9 = x²
16 = x²
[tex] \sqrt{16} = \sqrt{ {x}^{2} } \\ = \sqrt{16} = x \\ = 4 = x [/tex]
Therefore opposite is = 4.
The average cost per item, C, of manufacturing a quantity q of cell phones is given by C = (a/q) +b. Find the rate of change of C as q increases. if production increases at a rate of 100 cell phones per week, how fast is the average cost changing?
Answer: The average cost per item is given by the equation C = (a/q) + b. To find the rate of change of C as q increases, we need to take the derivative of this equation with respect to q.
dC/dq = -(a/q^2)
So, the rate of change of C with respect to q is proportional to -1/q^2.
If production increases at a rate of 100 cell phones per week, the rate of change of q is 100. But we need to convert this to units of items per hour or per second, depending on the context.
Let's assume the rate of increase of q is in items per hour. Then the rate of change of C with respect to time t (in hours) is given by:
dC/dt = (dC/dq) * (dq/dt) = (-(a/q^2)) * (100) = -100a/q^2
So, the rate at which the average cost is changing depends on the value of a and q. If we knew the values of a and q, we could calculate the specific rate at which the average cost is changing.
Step-by-step explanation:
Combine like terms:
5y - 2+4+3y
Answer:
8y+2
Step-by-step explanation:
5y+3y=8y
-2+4=2
Since it's positive two we add them together.
8y+2
Can I get help please
Answer:
B. Vertex
Step-by-step explanation:
The midpoint between the two x-intercepts of a parabola will provide the x-coordinate of the vertex. Line of symmetry is drawn along this particular x-coordinate. This x-coordinate is substituted into the equation of the graph to find its corresponding y-coordinate.
2/3 divided by 13/ 4
Calculate the monthly payment and total interest for a loan of $89,000 at 5.7% for 30 years.
Monthly Payment:
Total Interest:
To calculate the monthly payment and total interest for a loan of $89,000 at 5.7% for 30 years, we can use the formula for the monthly payment of a fixed-rate mortgage loan:
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of monthly payments (which is the number of years multiplied by 12).
Plugging in the given values, we have:
L = $89,000
r = 5.7% = 0.057 (monthly interest rate)
n = 30 years * 12 months/year = 360 months
P = ($89,000)[0.057(1 + 0.057)^360]/[(1 + 0.057)^360 - 1]
P = $515.92 (rounded to the nearest cent)
Therefore, the monthly payment is $515.92.
To calculate the total interest, we can subtract the loan amount from the total amount paid over the life of the loan. The total amount paid is equal to the monthly payment times the total number of payments:
Total amount paid = P * n = $515.92 * 360 = $185,731.20
Total interest = Total amount paid - Loan amount = $185,731.20 - $89,000 = $96,731.20
Therefore, the total interest paid over the life of the loan is $96,731.20.
Identify the base: "Automobiles are 97% cleaner than they were 30 years ago
(97x/100) represents the total number of cleaner automobiles.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that automobiles are 97% cleaner than they were 30 years ago.
Assume that the total number of automobiles 30 years ago were {x}. Then, the total number of clean automobiles will be -
97% of {x} = 97x/100
Therefore, (97x/100) represents the total number of cleaner automobiles.
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. payroll mix-up five paychecks and envelopes are addressed to five different people. the paychecks are randomly inserted into the envelopes. what are the probabilities that (a) exactly one paycheck will be inserted in the correct envelope and (b) at least one paycheck will be inserted in the correct envelope? 43. game show on a game show, you are gi
The probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.
The probability of exactly one paycheck being in the correct envelope can be calculated by taking the number of possible outcomes where one paycheck is in the correct envelope (1) and dividing it by the total number of possible outcomes (5). This yields a probability of 1 in 5. The probability of at least one paycheck being in the correct envelope is calculated by taking the total number of possible outcomes where at least one paycheck is in the correct envelope (4) and dividing it by the total number of possible outcomes (5). This yields a probability of 4 in 5. Thus, the probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.
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Find mangleCHF when mangleBGE = 120°.
mangleCHF = ___°
Answer:
120°
Step-by-step explanation:
AB //CD and EF is transversal. When two parallel lines are cut by a transversal, the alternate exterior angles are congruent.
∠CHF = ∠BGE
= 120°
Consider a one-sample two-sided z-test for a population proportion. Given that conditions for inference are met, which of the following is closest to the p-value for a test statistic of z=−1.86 ?
Answer: 0.0628
Step-by-step explanation:
The closest answer to the p-value for a test statistic of z = -1.86 is 0.0614.
To calculate the p-value for a one-sample two-sided z-test on a population proportion, we must first calculate the area under the standard normal distribution curve that corresponds to the test statistic z = -1.86.
Because this is a two-sided test, we must find the area of the distribution in both tails that is more extreme than the test statistic. We can do this by using a standard normal distribution table or calculator, or by exploiting the distribution's symmetry.
We can calculate the area to the left of z = -1.86 using a standard normal distribution table or calculator. Because this is a two-sided test, the area in the distribution's right tail is also 0.0307.As a result, the p-value for this test statistic is as follows:
2(0.0307) = 0.0614 p-value
So 0.0614 is the closest answer to the p-value for a test statistic of z = -1.86.
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The manager of a furniture factory finds that it costs $2,200 to manufacture 100 chairs in one day and $4,800 to produce 300 chairs in one day.
a) Express the cost as a function of the number of chairs produced, assuming that it is linear.
b) Sketch the graph of the function obtained in part (a).
c) What is the slope of the graph and what does it represent?
d) What is the y-intercept of the graph and what does it represent?
a) C(x) = 0.02x + 2200, b) A straight line with positive slope, c) Slope is 0.02, represents cost per chair, d) Y-intercept is 2200, represents fixed cost.
a) The cost C(x) can be expressed as a linear function of the number of chairs x produced. We can solve for the slope and y-intercept using the two points (100, 2200) and (300, 4800). First, calculate the slope of the line using the formula (y2 - y1)/(x2 - x1). This gives us (4800 - 2200)/(300 - 100) = 0.02. Then, we can use the slope and one of the points to solve for the y-intercept using the equation y = mx + b, where m is the slope and b is the y-intercept. Substituting the values from the first point (100, 2200) into the equation gives us 2200 = 0.02(100) + b, so the y-intercept is 2200. Therefore, the cost function can be expressed as C(x) = 0.02x + 2200.
b) The graph of this function is a straight line with a positive slope, as shown in the diagram.
c) The slope of the graph is 0.02, which represents the cost per chair.
d) The y-intercept is 2200, which represents the fixed cost of manufacturing the chairs.
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Question 12
A homeowner is planning to build a concrete sidewalk that will require 1 3/4 cubic yards of concrete.
She also will build a small patio requiring 2 1/3 cubic yards of concrete. The two projects are in the
backyard, so the concrete will be carried in a wheelbarrow. The wheelbarrow will comfortably hold
1/6 of cubic yard of concrete. How many wheelbarrow loads will be required for the entire job?
The total number of wheelbarrow loads required to complete both the projects 25.
What are Fractions?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. In ordinary English, a fraction refers to the number of parts of a specific size.
The combined volume of concrete needed for the patio and walkway is 1 3/4 + 2 1/3 = 7/4 + 7/3 = 21/12 + 28/12 = 49/12 cubic yards
The entire volume of concrete can be divided by the capacity of a wheelbarrow to determine the necessary number of wheelbarrow loads: (49/12 )/( 1/6) = 49/12* 6/1 = 49/2 = 24.5
We round up to 25 because we can't have half a wheelbarrow load. The homeowner will therefore require 25 wheelbarrow loads to finish both projects.
Hence, The total number of wheelbarrow loads required to complete both the projects 25.
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Peter travels at an average speed of 98km/h for 3 hours.he then travels at an average speed of 105km/h for 2 Hours
Answer:
Assuming that Peter travels at a constant speed, then he would have travelled a total distance of (98 * 3) + (105 * 2) = 531 km.
Thomas is finding the coordinates of the image of a polygon with vertices W(2, 2), X(2, 4), Y(4, 4), and Z(4, 2) after a reflection across the y-axis. Describe his error.
The coordinates of W′X′Y′Z′ are W′(2, –2), X′(2, –4), Y′(4, –4), and Z′(4, –2).
After reflection, Coordinates of W'X'Y'Z' are
W'(-2, 2), X'(-2 , 4), Y' (-4, 4), and Z' (-4, 2)
What is reflection?
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure. The reflected image should have the same shape and size, but the image faces in the opposite direction.
Given,
Vertices of a polygon WXYZ
W(2, 2), X(2, 4), Y(4, 4), and Z(4, 2)
There is reflection over y-axis
For reflection over y - axis , y=f(-x)
Thomas reflected y coordinate y → -y
but x coordinate should be reflected, then x → -x
W(2, 2) → W'(-2, 2)
X(2, 4) → X'(-2 , 4)
Y(4, 4) → Y' (-4, 4)
Z(4, 2) → Z' (-4, 2)
Hence, W'(-2, 2), X'(-2 , 4), Y' (-4, 4), and Z' (-4, 2) are coordinates of W'X'Y'Z'
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consider the discrete random variable x given in the table below calculate the mean variance and standard deviation of X.
Answer:
Expected value E(x)
= 2 x 0.11 + 11 x 0.09 + 12 x 0.08 + 13 x 0.58 + 19 x 0.14
= 12.37
Variance
= E( X^2 ) - (E(X))^2
= (2^2 x 0.11 + 11^2 x 0.09 + 12^2 x 0.08 + 13^2 x 0.58 + 19^2 x 0.14) - (12.37)^2
= 171.41 - 153.0169
= 18.393 (cor to 3 dp)
Standard deviation
= [tex]\sqrt{variance}[/tex]
=[tex]\sqrt{18.3931}[/tex]
= 4.289 (cor to 3 dp)
Mean should be ( [tex]\frac{2+11+12+13+19}{5}[/tex] ) = 11.4 but i am not very sure
Mean, variance and the standard deviation of the discrete random variable are 12.37, 18.3931 and 4.2887 respectively.
What is Expected Value in Probability?Expected value in probability is defined as the sum of the product of each of the variable and probability corresponding to the variable.
Expected value is same as the mean of a discrete random variable.
Mean, μ = Σ x. P(x)
= (2 × 0.11) + (11 × 0.09) + (12 × 0.08) + (13 × 0.58) + (19 × 0.14)
= 12.37
Variance, σ² = Σx² P(x) - μ²
= [(2² × 0.11) + (11² × 0.09) + (12² × 0.08) + (13² × 0.58) + (19² ×
0.14)]- [ 12.37²]
= 18.3931
Standard Deviation, σ = √Variance
= 4.2887
Hence the mean is 12.37, Variance is 18.3931 and Standard deviation is 4.2887.
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1 in a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer. a blank answer scores 0. mike scored a total of 0 and he did not leave all of the answers blank
a) Either 3 or 4 questions did Mike answer correctly.
b) Either 7 or 8 questions did Sheila answer correctly.
What is a equation in math?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
a) Let mike did x correct
then, incorrect will be (10- x)
The equation is:
Now, 5x + (10 - x) (-3) = 0
=> 5x - 30 + 3x = 0
=> 8x = 30
=> x = 30/8
=> x > 3 and x < 4
b) Let Sheila did y correct
then, incorrect = (10 - y)
Now, 5y + (10 - y) (-3) = 32
=> 5y - 30 + 3y = 32
=> 8y = 62
=> y > 7 and y< 8
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The given question is incomplete, complete question is:
In a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer.
A blank answer scores (). Mike scored a total of () and he did not leave all of the answers blank. (a) How many questions did Mike answer correctly? _ _ _ _ _ _ _ _ Sheila scored a total of 32. (b) How many questions did Sheila answer correctly?
If Q-E-R, and if QE = 8x + 3, QR = 64, and
ER = 4x+1, then find ER.
The measure of ER given by the equation ER = 21
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The measure of QE = 8x + 3 be equation (1)
The measure of ER = 4x + 1 be equation (2)
The measure of QR = 64
Now , QR = QE + ER be equation (3)
Substituting the values of QE and ER in the equation (3) , we get
8x + 3 + 4x + 1 = 64
On simplifying the equation , we get
12x + 4 = 64
Subtracting 4 on both sides of the equation , we get
12x = 60
Divide by 12 on both sides of the equation , we get
x = 5
Substitute the value of x in equation (2) , we get
The measure of ER = 4 ( 5 ) + 1
The measure of ER = 21
Hence , the equation is ER = 21
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Rework Cantor’s proof from the beginning. This time, however, if the digit under consideration is 4, then make the corresponding digit of M an 8; and if the digit is not 4, make the associated digit of M a 4.
M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
Here,
Georg Cantor's diagonal argument is proof by contradiction that shows that there are more real numbers than natural numbers. Here's how the proof can be reworked with the given modification:
Suppose that we have a list of all real numbers between 0 and 1, written in decimal form. We will show that this list cannot be a complete listing of all real numbers between 0 and 1.
Let M be a new real number whose decimal expansion is obtained by following the following rule: if the nth digit of the nth number on the list is 4, then the nth digit of M is 8; if the nth digit of the nth number on the list is not 4, then the nth digit of M is 4.
Since each number on the list has a unique decimal expansion, M is a real number between 0 and 1, and its decimal expansion is different from the nth number on the list in the nth digit for all n.
Therefore, M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.
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Determine if the following equation is linear. If the equation is linear, convert it to standard form: ax+by=c
.
−2x+11(y+x)=2
Step-by-step explanation:
-2x + 11(y+x) = 2
-2x + 11y + 11x = 2
-2x + 11x +11y = 2
9x + 11y = 2
where a = 9, b= 11 and c= 2
the graph is provided for questions a-h
The probability that a randomly selected medical student who took the test had a total score that was less than 480 is 0.49, which means that approximately 49% of medical students had a score lower than 480.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
To calculate the probability that a randomly selected medical student who took the test had a total score that was less than 480, we need to start by looking at the data given.
In this case, the data tells us that the mean score was 500 and the standard deviation was 50.
This means that the scores are normally distributed, which means that the probability of finding a score lower than 480 can be calculated using the normal distribution formula.
We can use this formula to calculate the area under the curve (or probability) below the score of 480.
The result of this calculation is 0.49, which means that approximately 49% of medical students had a score lower than 480.
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Find the volume of the right cone below. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
the volume of such a cone is
pi×r² × h / 3
r is the radius of the ground circle, h is the straight inner height.
the radius is as always half of the diameter, so in our case
6/2 = 3 units.
so, the volume is
pi×3² × 11 / 3 = pi×9×11/3 = pi×3×11 = 33pi =
= 103.6725576... units³ ≈
≈ 103.7 units³
7. Serena bought a scarf for $16.99 and was charged 7.5% tax on her purchase. Which of the
following was the amount of sales tax that Serena had to pay?
(1) $1.19
(3) $1.36
(2) $1.27
(4) $1.51
Answer:
$1.27
Step-by-step explanation:
We know
The tax is 7.5%
7.5% = 0.075
Which of the following was the sales tax Serena had to pay?
We take
16.99 times 0.075 = $1.27
So, the answer is $1.27
need help with my misisng he asap plss 30 points
Answer:
y=4
x=3
Step-by-step explanation:
2y-4=y
y=4
4x=x+9
3x=9
x=3
using the washer method, determine the volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle , on the right by the line , and above by the line about the -axis.
The volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle , on the right by the line , and above by the line about the x-axis is (47/3)π.
To use the washer method, we need to consider the solid as a stack of thin washers, each with a hole in the center. We will integrate along the axis of revolution (in this case, the x-axis).
First, let's sketch the region we're revolving:
The circle has equation x^2 + y^2 = 1, so its radius is r = 1 when y = 0. The line has equation x = 4, so its distance from the axis of revolution is R = 4. The region we're revolving is bounded by y = 0 and y = √(1 - x^2), which we can rewrite as x = √(1 - y^2).
We can now set up the integral for the volume of the solid:
V = [tex]\int\limits^1_0[/tex] π(R^2 - r^2) dy
= [tex]\int\limits^1_0[/tex] π(4^2 - x^2) dy
= π[tex]\int\limits^1_0[/tex] (16 - y^2) dy
= π [16y - (1/3)y^3] |₀¹
= π (16 - 1/3)
= (47/3)π
Therefore, the volume of the solid is (47/3)π cubic units.
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Complete question is:
Using the washer method, determine the volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle x^2+y^2=1, on the right by the line x = 4, and above by the line x=4 about the x-axis.
A grocer can buy raspberries from a local farmer for $1.04 per pound (lb). Her last raspberry order from the farmer cost $171.08 How many pounds of raspberries did
the grocer order? Round your answer to the nearest tenth if needed
Answer
Duration: 0010:10
f(x) pounds of raspberries from the local farmer
The grocer ordered approximately 164.3 pounds of raspberries from the local farmer. We can round this to the nearest tenth if needed, which would give us an answer of 164.3 pounds.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given,
o determine how many pounds of raspberries the grocer ordered, we can use the formula:
Total cost = Price per pound x Number of pounds
We know that the price per pound is $1.04, and the total cost of the last order was $171.08. Let's use "x" to represent the number of pounds of raspberries the grocer ordered:
$171.08 = $1.04 x
To solve for x, we can divide both sides by $1.04:
x = $171.08 / $1.04
x ≈ 164.3
Therefore, The grocer ordered approximately 164.3 pounds of raspberries from the local farmer. We can round this to the nearest tenth if needed, which would give us an answer of 164.3 pounds.
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Two fractions are equal. They also have the same denominator. What must be true of the numerators of the fractions? Explain.
Answer: The numerators must be the same for the fractions to be equal.
The denominator of a fraction is the bottom number. Take a look at these two fractions.
¾ & ¾
The numbers at the bottom are the same. If I eat ¾ of an apple and you eat ¾ of an apple, we both eat the same amount.
Now look at these fractions.
⅗ & ¾
They both have the same top number (numerator), but they have different denominators. If I eat ¾ of an apple and you eat ⅗ of an apple, we both do not eat the same amount.
So if both the numerator and denominator are the same they are equal.
This means that the numerators must be the same for the fractions to be equal.
I hope this helps & Good Luck <3 !!!
Let C1be the circle radius 2 centered at the origin, oriented counterclockwise, let C2 be the
center radisus 1 and center at the origin, oriented clockwise and let C= C1 U C2. Use Green’s
theorem to evaluate the line integral H
C(4x2 y3)dx+ ( x3 + y2)dy
Using Green's theorem the line integral H C(4x2 y3)dx+ ( x3 + y2)dy is 70.6858.
Step: 1
Given
[tex]\int\limi {4x2 - y3} \, dx + (x3+y2) dy[/tex]
Formula for Greens theorem
δQ/δx = 3x2
Explanation:
partial derivative w.r.t x i . e y is constant
partial derivative w.r.t y i. e x is constant
power rule of derivative is
d/dx Xn = nXⁿ⁻¹
Step: 2
[tex]\int\limits\int\li {dQ/dy + dP/dx dA} \, dx = \int \int {3(x2+y2)} \, dx[/tex]
Explanation:
in polar coordinates x2 + y2 = r2 and dA = radθ
Step: 3
given
C1 = r1 = 2
C2 = r2 = 1
the limits for r is 1 ≤ r ≤ 2
since it is a circle the limits for θ
0 ≤ θ ≤ 2π
Explanation: Please refer to solution,
now integrate w.rt θ
= 45/4[θ] 2π
= 45/4[2π - 0]
= 45/4(2π)
= 45/2(π)
= 45π/2 ≈ 70.6858.
by greens theorem,
[tex]\int 4x2 y3)dx+ ( x3 + y2)dy \, dx[/tex] is 70.6858.
Green’s theorem is substantially used for the integration of the line combined with a twisted aeroplane . This theorem shows the relationship between a line integral and a face integral. It's related to numerous theorems similar as Gauss theorem, Stokes theorem.
Green’s theorem is used to integrate the derivations in a particular plane. However, it's converted into a face integral or the double integral or vice versa using this theorem, If a line integral is given.
Learn more about Line integral:
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