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3 years ago

How do you do these questions?

Mathematics

1 answer:

Sophie [7]3 years ago

3 0

Answer:

f(x) = 2π (11 + sin x) √(1 + cos²x)

Step-by-step explanation:

Surface area of a curve rotated about y = a is:

S = ∫ 2π (y − a) ds,

where ds = √(1 + (dy/dx)²) dx.

y = 6 + sin x, and a = -5. dy/dx = cos x. Plugging in:

S = ∫₀²ᵖⁱ 2π (6 + sin x − -5) √(1 + cos²x) dx

S = ∫₀²ᵖⁱ 2π (11 + sin x) √(1 + cos²x) dx

Therefore, f(x) = 2π (11 + sin x) √(1 + cos²x).

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Solve for <br> x<br> x and graph the solution on the number line below.<br> −14<7x

yanalaym [24]

Answer:

Step-by-step explanation:

-14<7x

-14/7<7/7x

2<x

7 0

3 years ago

What is the 8th term of the geometric sequence a2 = 20 and r = 5

algol [13]

Answer:

8th term of geometric sequence is 312500

Step-by-step explanation:

Given : $a_2=20$ and common ratio (r) = 5

We have to find the 8th term of the geometric sequence whose $a_2=20$ and common ratio (r) = 5

Geometric sequence is a sequence of numbers in which next term is found by multiplying by a constant called the common ratio (r).

$a_n=ar^{n-1}$ ......(1)

where $a_n$ is nth term and a is first term.

For given sequence

a can be find using $a_2=20$ and r = 5

Substitute in (1) , we get,

$a_2=ar^{2-1}$

$\Rightarrow 20=a(5)$

$\Rightarrow a=4$

Thus, 8th term of the sequence denoted as $a_8$

Substitute n= 8 in (1) , we get,

$a_8=ar^{8-1} \\\\a_8=(4)r_{7} \\\\a_8=4(5)^7=4 \times 78125=312500$

Thus 8th term of geometric sequence is 312500

8 0

3 years ago

At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temp

kiruha [24]

Answer:

Zero

Step-by-step explanation:

The temperature will remain constant over time. This means the slope of the graph will be constant from one point of the graph to the other, which cancels out to zero.

8 0

3 years ago

Find the volume of the solid generated by revolving the region bounded by

Rama09 [41]

Answer:

$V =\dfrac{25\pi}{\sqrt{2}}$

Step-by-step explanation:

given,

y=5√sinx

Volume of the solid by revolving

$V = \int_a^b(\pi y^2)dx$

a and b are the limits of the integrals

now,

$V = \int_a^b(\pi (5\sqrt{sinx})^2)dx$

$V =25\pi \int_{\pi/4}^{\pi/2}sinxdx$

$\int sin x = - cos x$

$V =25\pi [-cos x]_{\pi/4}^{\pi/2}$

$V =25\pi [-cos (\pi/2)+cos(\pi/4)]$

$V =25\pi [0+\dfrac{1}{\sqrt{2}}]$

$V =\dfrac{25\pi}{\sqrt{2}}$

volume of the solid generated is equal to $V =\dfrac{25\pi}{\sqrt{2}}$

4 0

3 years ago

Lillianne made 6 out of every 10 baskets she attempted during basketball practice. If she attempted to make 25 baskets, how many

patriot [66]

Answer:

15.

Step-by-step explanation:

(6/ 10) * 25

= 0.6 * 25

= 15.

3 0

3 years ago