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3 years ago

10

Jessica invests $250 each quarter in an ordinary annuity with a 5% interest rate compounded quarterly. Determine the accumulat

ed amount in Jessica's annuity after 25 years.

1 answer:

madam [21]3 years ago

4 0

Answer:

Step-by-step explanation:

Usimg formula for calculating compound interest.

A = P(1+r/n)^nt

P is the principal =$250

r is the rate = 5%

t is the time = 25years

n = 1/4(compounded quarterly)

Substituting to get the amount A.

A = 250(1+5/25)^25/4

A = 250(1+0.2)^6.25

A = 250(1.2)^6.25

A = 250(3.125)

A = $781.31

Hence the accumulated amount in Jessica's annuity after 25 years is $781.31

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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

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3 years ago

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professor190 [17]

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Step-by-step explanation:

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beks73 [17]

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

6, 6, 6, 7, 8, 8, 29

We will calculate the measures of central tendency:

1) Mode - the most occurring element in the data set.

So, Mode = 6

2) Median - the middle value of organised data set

So, Median = 7

3) Mean - the average of all data set

So, Mean = $\dfrac{6+6+6+7+8+8+29}{7}=\dfrac{70}{7}=10$

So, we can see that Mode and Median are giving the closest value to each other, whereas Mean is giving the farthest value as compared to rest.

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Vilka [71]

Answer:

88.5

Step-by-step explanation:

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⇒ 0.75 × 118 = y

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Hope this helps! Good Luck!

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3 years ago

What is the y-intercept of this line?

Brilliant_brown [7]

Answer:

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We can see that the coefficient on the x-term is $-\frac{4}{3}$ and the constant being added to it is 5.

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4 years ago

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