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3 years ago

3? Choose the THREE correct answers.

Mathematics

1 answer:

Eduardwww [97]3 years ago

8 0

None of them have a solution of x, but 5x=15, 7x-2=19, and 5x+6=21 all have the same answer of x=3

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a. Calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x bet

miskamm [114]

Answer:

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is $\dfrac{4}{3}\pi r^3$

a = -r , b = r , $f(x)=\sqrt{r^2-x^2}$ and $V=\dfrac{4}{3}\pi r^3$

Solution A)

The given curve, $y=3+3e^{-5x}$ rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

$V=\int_a^b\pi R^2dx$

where, a = 2, b= 4 , $R=y=3+3e^{-5x}$ and dx is thickness of disk.

$V=\int_2^4\pi (3+3e^{-5x})^2dx$

$V=9\pi\int_2^4(1+e^{-10x}+2e^{-5x})dx$

$V=9\pi(x-\dfrac{1}{10}e^{-10x}-\dfrac{2}{5}e^{-5x})|_2^4)$

$V=9\pi(4-\dfrac{1}{10}e^{-40}-\dfrac{2}{5}e^{-20}-2+\dfrac{1}{10}e^{-20}-\dfrac{2}{5}e^{-10}))$

$V=9\pi (2-0)$

$V=18\pi$

Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

$x^2+y^2=r^2$

$y=\sqrt{r^2-x^2}$

The solid form is sphere of radius r.

Using disk method, to find volume of solid

$V=\int_a^b\pi R^2dx$

where, a = -r, b = r , $R=y=\sqrt{r^2-x^2}$ and dx is thickness of disk.

$V=\int_{-r}^r\pi (r^2-x^2)dx$

$V=\pi(r^2x-\dfrac{x^3}{3})|_{-r}^r$

$V=\pi(2r^3-\dfrac{2r^3}{3})$

$V=\dfrac{4}{3}\pi r^3$

Hence, the volume of sphere is $\dfrac{4}{3}\pi r^3$

4 0

4 years ago

what is the amount returned on a deposit of $1,000 held for 2 years at 10% interest compound annually?

pickupchik [31]

Answer:

since its 10%percent annualy(compound interest),at the end of 1year it would be 1000+(1/10 *1000)that is 1100,then for the second year it would be 1100+(1/10 * 1100)that is 1210.please mark me as brainliest

3 0

3 years ago

Find the slope of the blue line

Ierofanga [76]

The answer is B.) 1/4 because it goes 1 up and 4 right.

7 0

3 years ago

Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the fiv

Nesterboy [21]

Answer:

a) It is probability distribution

b) mean = 2.5

c) Standard Deviation = 1.11

Step-by-step explanation:

We are given the following in the question:

x 0 1 2 3 4 5

P(x) 0.033 0.149 0.318 0.318 0.149 0.033

Probability distribution:

$\displaystyle\sum P_i(x_i) = 0.033+ 0.149 +0.318+ 0.318+ 0.149 +0.033 = 1$

Since, the summation of all the probabilities is 1 and each value of probability is between 0 and 1, the given is a probability distribution.

Mean of probability distribution:

$E(x) = \displaystyle\sumx_iP(x_i)\\E(x) = 0(0.033)+ 1(0.149)+2(0.318)+3(0.318) +4(0.149) + 5(0.033)\\E(x) = 2.5$

Thus, the mean of distribution is 2.5

Standard deviation of probability distribution:

$E(x^2) = 0^2(0.033)+ 1^2(0.149)+2^2(0.318)+3^2(0.318) +4^2(0.149) + 5^2(0.033)\\E(x^2) = 7.492\\\sigma^2 = E(x^2) - (E(x))^2\\\sigma^2 = 7.492 - (2.5)^2 = 1.242\\\sigma= \sqrt{1.242} = 1.11$

Thus, the standard deviation of the probability distribution is 1.11

5 0

4 years ago

Can you help me??please?!?

enyata [817]

The numbers inside the circles are the number for each one. Where the circles overlap means it is in both.

See attached picture:

8 0

3 years ago