a. The simple interest for 4 years would be $960.
b. The amount at the end of the 4 years would be $2160.$
A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
a. For calculating simple interest for the 4 years
We have been given data as:
Principal (P) = $1200
Rate of Interest (R) = 20%
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
The simple interest for 4 years would be:
⇒ 1200 x 20% x 4 = 960
b. For calculating the amount at the end of the 4 years
The amount at the end of the 4 years would be:
1200 + 960 = 2160
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Which equation describes how the parent function, y = x cubed, is vertically stretched by a factor of 4?
The equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 is y = 4x³.
We can find how the equation is vertically stretched below:When an equation is vertically stretched, it means that the parent equation has been multiplied by a number that is more than one.
This means that the equation is multiplied by some factor.
It is given that we should describe how the parent function is vertically stretched by a factor of 4.
The parent function is given as y = x³.
Since the equation is said to be vertically stretched by a factor of 4, we must multiply the parent equation by 4 to stretch it.
Therefore, we have found the equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 to be y = 4x³.
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Answer: C
Step-by-step explanation:
Just C
Penny attended a four year state college. she took out a student loan to pay for her tuition and room & board for the four years she was attending the college. her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. now that she has graduated, she will have to start paying back her loan. fortunately, penny has a grace period of one year before she has to start paying back the loan. her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. during her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. her goal is to be able to payoff the loan in 10 years. what is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? this is the amount that she will be responsible for paying back. (round your answer to the nearest whole dollar)
The new loan amount is $113,797
What is compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
We can find new loan amount as shown below:
Total amount of loan=4*6,970+4*11,320
=27,880+45,280
=$73,160
Now, we will find new loan amount using compound interest formula.
Amount=[tex]P(1+\frac{r}{n})^{nt}[/tex]
P=$73,160
n=12
t=1 year
r=4.5%=0.045
Putting in formula
Amount[tex]=73,160(1+\frac{0.045}{12})^{12}[/tex]
=$113,797.039
Rounding to nearest dollar
=$ 113,797
Hence, new loan amount after one-year grace period is $113.797.
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Find the value of x in the given figure
Step-by-step explanation:
3x° + 2x° = 180° ( supplementary angle )
5x° = 180°
x = 180° / 5
x = 36°
[tex]...[/tex]
The perimeter of a deck is 33 at the length of the deck is 10 feet what is the width of the deck
The width of the deck is 6.5 feet.
The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc.
Assuming the deck is rectangle
Perimeter = 2(length + width)
33ft = 2 (10 + width)
16.5 = 10 + width
width = 6.5 ft
Thus the width of the deck is 6.5 feet.
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Select the correct answer from each drop-down menu.
Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated
units
, and g(x) =
.
there are two correct options:
A translation of 6 units down: g(x) = f(x) - 6A translation of 2 units to the right: g(x) = f(x - 2).How to relate the function g(x) to the function f(x)?
We know that:
f(x) = 3x + 1
Now, if we look at the graph of f(x), we can see that the y-intercept is at y = -5, and for each increase in one unit in the x-variable, there is an increase of 3 units in the y-variable.
Then the equation of g(x) is:
g(x) = 3*x - 5
Then g(x) is a translation downwards of 6 units, such that:
g(x) = f(x) - 6 = (3x + 1) - 6 = 3x - 5
And we also could write it as a horizontal translation of 2 units to the right:
g(x) = f(x - 2) = 3*(x - 2) + 1 = 3*x - 3*2 + 1 = 3x - 5
So there are two correct options:
A translation of 6 units down: g(x) = f(x) - 6A translation of 2 units to the right: g(x) = f(x - 2).If you want to learn more about translations:
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the base of an isosceles triangle is 4/3 cm . the perimeter of the triangle is 4 2/15 cm.
Answer:
[tex]\sf 1\dfrac{2}{5} \ cm[/tex]
Step-by-step explanation:
Isosceles triangle:If two sides of the triangle are equal, then the triangle is called isosceles triangle.
Let the two equal sides = x cm
Perimeter of the triangle = [tex]\sf 4\dfrac{2}{15}[/tex] cm
[tex]\sf x + x + \dfrac{4}{3}=4\dfrac{2}{15}\\\\[/tex]
[tex]\sf 2x +\dfrac{4}{3}=\dfrac{62}{15}[/tex]
[tex]\sf 2x = \dfrac{62}{15}-\dfrac{4}{3} \ [\text{\bf LCM of 15 , 3 = 15}]\\\\2x = \dfrac{62}{15}-\dfrac{4*5}{3*5}\\\\2x = \dfrac{62}{15}-\dfrac{20}{15}\\\\2x = \dfrac{42}{15} \ [\text{\bf Divide both sides by 2}]\\\\ x = \dfrac{42}{15*2}\\\\ x = \dfrac{7}{5}\\\\ x = 1\dfrac{2}{5}[/tex]
[tex]\sf \boxed{\text{Equal sides of isosceles triangle = $1\dfrac{2}{5}$ cm}}[/tex]
Please help me!!! due today. Pls show work thank youuu!
Answer: D
Step-by-step explanation:
As the circumference of a circle is 360 degrees, this means arc BC is 64 degrees.
So, we can conclude that arc AB measures 180-64=116 degrees.
Thus, angle AOB is also 116 degrees.
Answer:
D) 116°
Step-by-step explanation:
If arcBAC measure 296°,
And arcAC measure 180°,
You can get arcAB measure 116°,
Because the arc equals the measure of the central angle,
<AOB=116°
Hope this helps <3
(-1,1) (0,-1) (5,-11) (10,-21) what is the domain of the set of ordered pairs above?
Answer:
domain =(-1,0,5,10)to find domain just take the first values of each ordered pairs.
range=(1,-1,-11,-21)to find range take the second values of the ordered pairs.
Help pls, it’s urgent!! ASAP! (Geometry)
“Compete the proof”
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)
2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)
3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)
4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)
5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)
6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)
7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)
8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)
find the area of following figure...?
Answer:
33600 m²
Step-by-step explanation:
The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.
area of trapezoid = (a + b)h/2
where a and b are the lengths of the bases, and h is the height.
We need to find the height, BC.
Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.
DE + EC = DC
EC = AB = 360 m
DC = 600 m
DE + 360 m = 600 m
DE = 240 m
Use right triangle ADE to find AE. Then BC = AE.
DE² + AE² = AD²
DE² + 240² = 250²
DE² = 62500 - 57600
DE² = 4900
DE = √4900
DE = 70
BC = 70 = h
area = (a + b)h/2
area = (600 m + 360 m)(70 m)/2
area = 33600 m²
Answer:
33,600 m^2.
Step-by-step explanation:
This is a trapezium, so
Area = (h/2)(a + b)
= (h/2) ( 360 + 600)
= 960h / 2
= 480h,
We find the value of h using Pythagoras:
250^2 = h^2 + (600-360)^2
h^2 = 250^2 - 240^2 = 4900
h = 70.
So the Area = 70 * 480
= 33,600 m^2
he section of paper shown in the pattern below is 1/4 of a circle. It will be wrapped around a cone. The wrapper will then be painted.
The volume of the cone based on the figure illustrated wil be 196cm³.
Host illustrate the information?The information is incomplete and the complete question wast found online. An overview will be given.
Let's assume that the height is 4cm and the radius of the cone is 7cm. The volume of the cone will be:
= 1/3πr²h
= 1/3 × 3.14 × 7² × 4
= 196cm³
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the graph of y =-3x+4 is
Answer:
Step-by-step explanation:
hello :
The graph of y =-3x+4 is the line
what operation is evaluated first in the expression 4 + 9 2 /3 x 2 - 2 =
Answer:
You add the numerator
multiply the denominator and substract
then you can divide the expression.
Step-by-step explanation:
According to BODMAS
division comes before multiplication, addition and subtraction.
but in some cases like this, it's difficult to follow that procedure
A cube with side length is stacked on another cube with side length . What is the total volume of the cubes in factored form
The total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
What is the volume of a figure?The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape
How to determine the total volume?The two cubes are stacked upon one another, so they form a composite figure.
The side lengths of the cubes are given as
Cube 1 = 4p
Cube 2 = 2q^2
The volume of each cube is calculated as:
Volume = Side length^3
So, the total volume is
Total = (4p)^3 + (2q^2)^3
Evaluate the exponents
Total = 64p^3 + 8q^6
Using the sum of cubes, we have the factored form to be
Total = (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
Hence, the total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
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Complete question
A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?
Nora works at a retail store. She earns a commission of $5.50 on each item she sells. If she sells 17 items, how much does she earn from commissions?
The total earnings in commission is $93.50
How to determine the total commission?The given parameters are:
Commission = $5.50
Items = 17
The total commission is:
Total = $5.5 0 * 17
Evaluate
Total = $93.50
Hence, the total earnings in commission is $93.50
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Ian is borrowing $1000 from his parents to buy a notebook computer. he plans to pay them back at the rate of $60 per month. ken is borrowing $600 from his parents to purchase a snowboard. he plans to pay his parents back at the rate of $20 per month. write a system equations that can be used to determine after how many months the boys will owe the same amount.
A system equations that can be used to determine after how many months the boys will owe the same amount is
60 x = $ 1000
20 y = $ 600
In mathematics, a system of equations, also known as a system of simultaneous or systems of equations, is a finite system of equations for which we have sought common solutions. A system of equations can be classified in a similar way to simple equations. A system of equations finds application in our everyday life in modeling problems where unknown values can be represented in the form of variables.
In algebra, a system of equations contains two or more equations and looks for common solutions to the equations. "A system of linear equations is a set of equations that are satisfied by the same set of variables."
We need to find a system equations that can be used to determine after how many months the boys will owe the same amount
Let lan take x months to pay $ 1000 to his parents
In 1 month Ian pays $60
In x months Ian pays =
60 x= $ 1000
Let Ken take y months to pay $ 600 to his parents
In 1 month Ian pays $20
In y months Ian pays =
20 y= $ 600
Hence 60 x= $ 1000 and 20 y= $ 600 are the system of equations
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If she was vaping every 15 minutes, assuming she was awake from 7 am- 11 pm (16 hours) how many times in a day would she vape?
Answer:
64 times
Step-by-step explanation:
16 hours to minutes: 16*60 = 960 minutes
vaping every 15 minutes: 960/15 = 64
Change y = − 3x² + 36x - 73 to standard form, y = a (x - h)² + k.
The standard form of the given equation is: y = -3(x-6)²+35.
In mathematics, the most typical way to represent a specific element is called standard form.
A standard form is a way to express a particular mathematical idea, such as an equation, number, or expression, in prose that adheres to a set of criteria.
Given equation is: y = − 3x² + 36x - 73
In order to convert to the standard form,
y+73 = −3x² +36x
Subtract 108 from both the sides,
y+73-108 = −3x² +36x-108
y-35 = -3(x² -12x+36)
y-35 = -3(x-6)²
y = -3(x-6)²+35
This is the required standard form, corresponding to the given equation.
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what type of correlation relationship is "the number of fire stations in a city is positively correlated with the number of parks"
The type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.
What is Accidental Correlation Relationship?Accidental relationship is a type of correlation relationship whereby there is a strong correlation between two variables without a logical explanation for such relationship. It is often regarded as coincidental.
Therefore, the type of correlation relationship that exists between the number of fire stations in a city and the number of parks is: accidental correlation relationship.
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please help
Which reason completes the proof for step 6?
The reason that completes the proof for step 6 is (a) Definition of median
How to complete step 6?From the graph, point R' to be the midpoint of points M' and O'
Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively
This means that the three points are the median of the sides of the triangle
The line drawn through the three medians meet at point S
Hence, the reason that completes the proof for step 6 is (a) Definition of median
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Answer: median
Step-by-step explanation:
Simplify the expression below. Then classify the resulting expression
as a monomial, binomial, or trinomial.
3x²+6x+5-3x(2+x)
Which of the following represents the simplified expression and its
polynomial classification?
Answer:
Simplified = 5
Classification = Monomial
Step-by-step explanation:
PART I: Simplify the expressionGiven expression:
3x² + 6x + 5 - 3x (2 + x)
Expand parenthesis by distributive property:
= 3x² + 6x + 5 - 3x (2) - 3x (x)
= 3x² +6x + 5 - 6x - 3x²
Put like terms together:
= 3x² - 3x² + 6x - 6x + 5
= 0 + 0 + 5
= [tex]\boxed{5}[/tex]
PART II: Classify polynomialConcept:
Polynomial is classified by the number of terms a polynomial has.
Monomial: a polynomial with only one termBinomial: a polynomial with two terms...Classify the given expression:
Original = 3x² + 6x + 5 - 3x (2 + x)
Simplified = 5
5 is a constant and it has only one term
Therefore, it is a monomial.
Hope this helps!! :)
Please let me know if you have any questions
The answer is 5, which is a monomial.
Let's simplify using the distributive property.
3x² + 6x + 5 - 3x(2) - 3x(x)3x² + 6x + 5 - 6x - 3x²5If the resulting expression has only one term, it is classified as a monomial.
Let z = 3(cos(15°) + i sin(15°)) and w = 5(cos(90°) + i sin(90°)). What best describes the geometric construction of the quotient z/w on the complex plane?
z is scaled by a factor of One-fifth and rotated 90 degrees clockwise.
z is scaled by a factor of 1 and rotated 90 degrees clockwise.
z is scaled by a factor of 1 and rotated 90 degrees counterclockwise.
z is scaled by a factor of One-fifth and rotated 90 degrees counterclockwise.
The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise
How to find Complex Trigonometric numbers?
We are given;
z = 3(cos(15°) + i sin(15°))
w = 5(cos(90°) + i sin(90°))
Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.
Thus, option A is the correct answer.
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Solve the equation by completing the square.
0 = x²14x + 46
a x = 7 ± √3
b x = -7 ± √3
c 14 ± √3
d -14 ± √3
Answer:
[tex]0 = {x}^{2} + 14x + 46[/tex]
[tex] \boxed{ {x}^{2} - 14x - 46 = 0}[/tex]
[tex]x1.2 = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]x1.2 = \frac{ - 14 ± \sqrt{ { - 14}^{2} - 4(1 \times 46) } }{2 (1)} [/tex]
[tex]x1.2 = \frac{ - 14 ± \sqrt{196 - 184} }{2} [/tex]
[tex]x1.2 = \frac{ - 14 ± \sqrt{12} }{2} [/tex]
[tex]x1.2 = \frac{ \cancel{ - 14} ± \sqrt{12} }{ \cancel{2} } [/tex]
[tex]x1.2 = - 7 ± \sqrt{12} [/tex]
[tex]x1.2 = - 7 ± \sqrt{4 \times 3} [/tex]
[tex] \boxed{ \bold{ - 7 ± 2 \sqrt{3}}} [/tex]
Answer:
its a I hope it's helps you
A public health organization reports that 40%of baby boys 6-8 months old in the United
States weigh more than 20 pounds. A sample of 10 babies is studied. Round the answers to three decimal places.
what is the probability that more than 4 weigh more than 20 pounds
What is the probability that fewer than 3 weigh more than 20 pounds?
Would it be unusual if more than 7 of them weigh more than 20 pounds?
Using the binomial distribution, the probabilities are given as follows:
0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters for this problem are:
n = 10, p = 0.4.
The probability that more than 4 weigh more than 20 pounds is:
[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]
In which:
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061[/tex]
[tex]P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403[/tex]
[tex]P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209[/tex]
[tex]P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150[/tex]
[tex]P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502[/tex]
Hence:
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325[/tex]
[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675[/tex]
0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.
The probability that fewer than 3 weigh more than 20 pounds is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673
0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.
For more than 7, the probability is:
[tex]P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106[/tex]
[tex]P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016[/tex]
[tex]P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001[/tex]
Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.
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Please help me im stuckkm
Answer:
Below in bold.
Step-by-step explanation:
(a) Using the Pythagoras theorem:
30^2 = 21^2 + p^2
p^2 = 30^2 - 21^2 = 459
p = √459
= 21.4 cm to nearest tenth.
(b) cos P = 21/30 = 0.70
m < P = 45.57 degrees to nearest hundredth.
Answer:
a) p = 21.4 cm (nearest tenth)
B) P = 45.6° (nearest tenth)
Step-by-step explanation:
As triangle PQR is a right triangle, we can use Pythagoras Theorem to find the length of p.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleFrom inspection of the triangle:
a = PQ = 21b = QR = pc = PR = 30Substitute the given values into the formula and solve for p:
[tex]\implies 21^2+p^2=30^2[/tex]
[tex]\implies 441+p^2=900[/tex]
[tex]\implies 441+p^2-441=900-441[/tex]
[tex]\implies p^2=459[/tex]
[tex]\implies \sqrt{p^2}=\sqrt{459}[/tex]
[tex]\implies p=\pm 3\sqrt{51}[/tex]
As p is the length, p can be positive only.
Therefore, p = 21.4 cm (nearest tenth)
To find the angle P, use the cosine trigonometric ratio.
Cosine trigonometric ratio
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)From inspection of the triangle:
[tex]\theta[/tex] = PA = PQ = 21H = PR = 30Substitute the given values into the formula and solve for P:
[tex]\implies \sf \cos P=\dfrac{21}{30}[/tex]
[tex]\implies \sf P=\cos^{-1}\left(\dfrac{21}{30}\right)[/tex]
[tex]\implies \sf P=45.572996^{\circ}[/tex]
Therefore, the measure of angle P is 45.6° (nearest tenth).
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A rectangle is reduced by a scale factor of One-fourth.
A large rectangle has a length of 16 and width of 12. A smaller rectangle has length of 4 and width of 3.
Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options.
The ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16
Area of a rectangle
The formula for calculating the area of a rectangle is expressed as:
A = length * width
For the large triangle
Area = 16 * 12
Area of large triangle = 192 square units
For the smaller rectangle
Area = 4 * 3
Area. of small rectangle = 12 square units
Ratio = 12/192 = 1:16
Hence the ratio of the area of the smaller rectangle to the area of the larger rectangle is 1:16
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Explain how to find the 41st term of the arithmetic sequence where a1 = 5 and a7 = 34.
The 41th term of the arithmetic sequence is 66.
What is arithmetic sequence in math's ?Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence.
[tex]a_1[/tex] = the first term in the sequence.
d = the common difference between terms.
According to the given information:Finding arithmetic sequence for the nth term:
aₙ = a₁ + (n-1)d
d = the common difference
a₇ = a₁ + (7-1)d
34 = 5 + 6d
29 = 6d
d = 29/6
Now ,
Finding the 41st term of the arithmetic sequence.
a₄₁ = a₁ + (n-1)d
= 5 + (41-1)d
= 5 + 40d
= 5 + 40(29/6)
= (198)* 1/3
= 66
The 41th term of the arithmetic sequence is 66.
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A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 3 feet per minute. Find the rate at which the area is changing at the instant the radius is 4 feet.
The rate of change of area when radius = 4feet is 75.36 feet²/min.
What is area?Area definition, any particular extent of space or surface.
Area of circle = πr²
Let the area of the circle be πr²
dr/dt = 3feet/min (GIVEN)
Differentiating both sides with respect to time:
A = πr²
dA/dt = π(2r).(dr/dt)
dA/dt = (2 * 3.14 * r).(dr/dt)
The rate of change of area when radius = 4feet
dA/dt = (2 * 3.14 * 4).(3)
dA/dt = 75.36
Hence, the rate of change of area is 75.36feet²/min.
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Which best describes the function on the graph?
A) Direct Variation; k=3
B) Direct Variation; k=1/3
C) Inverse Variation; k=3
D) Inverse Variation; k=1/3
Please answer quickly! <3
Direct Variation; k=3 best describes the function on the graph
Option A)
Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant. In direct variation, as one number increases, so does the other. This is also called direct proportion: they're the same thing. An example of this is relationship between age and height. As the age in years of a child increases, the height will also increase. In inverse variation, it's exactly the opposite: as one number increases, the other decreases. This is also called inverse proportion. An example would be the relationship between time spent goofing off in class and your grade on the midterm. The more you goof off, the lower your score on the test
The given equation is a Straight line with equation y = 3x.
Thus the given graph is direct Variation graph with k=3.
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What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: (0, one-half); directrix: y = negative one-half focus: (8,0); directrix: x = –8 focus: (one-half, 0); directrix: x = negative one-half
The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.
How do you get the Parabola?Since we were given Parabola x² = 2 y
Then one has to compare and and so it will be x² = 4 a y
4 a = 2
Make a the subject of the formula:
a = 2/4
= 1/2
Therefore, Focus ( 0,a) = (0, 1/2 )
To solve for directrix:
Note that the equation of the directrix is:
y = -a or y +a=0
Then the equation of the directrix is:
y = - 1/2 or
y = + 1/2 = 0
Then the equation of the directrix will be 2 y +1 =0.
Therefore, The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.
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A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: (0, one-half); directrix: y = negative one-half focus: (8,0); directrix: x = –8 focus: (one-half, 0); directrix: x = negative one-half
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