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Andrew [12]
2 years ago
15

Slope: 1.5, y-intercept: -1

Mathematics
1 answer:
madreJ [45]2 years ago
3 0

Option 1 is the correct answer

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A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 8 marbles, each of diameter 3 inches. The va
DIA [1.3K]

Answer:

  π(3 in)²(10 in) -8(4/3)(1.5 in)³

Step-by-step explanation:

The volume of a cylinder with a radius of 3 inches and a height of 10 inches is ...

  V = πr²h = π(3 in)²(10 in)

The volume of 8 spheres with a radius of 1.5 inches is ...

  V = 8(4/3)πr³ = 8(4/3)π(1.5 in)³

The volume occupied by the water is the volume of the cylinder not occupied by the spheres. So, it is ...

  V = π(3 in)²(10 in) -8(4/3)(1.5 in)³ . . . . . . matches the 4th choice

5 0
3 years ago
Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and
Nadusha1986 [10]
Call the surface S; then the area of S is given by the surface integral

\displaystyle\iint_S\mathrm d\mathbf S

Parameterize the surface by

\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}

with 2\le u\le4 and 0\le v\le2\pi. The surface element is given by

\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv
\mathrm d\mathbf S=u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv

So the area is

\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv
=\displaystyle2\pi\int_{w=17}^{w=65}\sqrt w\,\frac{\mathrm dw}8

where w=1+4u^2\implies\mathrm dw=8u\,\mathrm du

=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}
=\dfrac\pi6\left(65^{3/2}-17^{3/2}\right)\approx237.69
8 0
3 years ago
How to find the area of a segment of a circle if r=8 and central angle =120 degrees. Please explain clearly and thoroughly. Will
bekas [8.4K]
First you need to find the area of the circle, which is πr^2
With a radius of 8 inches, the area of the circle will be π*8^2 or 64π.
Next you want to find the area of the 120 degree section of that circle.
120 degrees is 1/3 of a circle, so all you have to do next is multiply the are of the circle by 1/3 (because 360/120= 1/3).
(1/3)(64π) --> All you really have to do here is multiply 64 by 1/3 or divide it by 3 (because to divide by a number is the same a multiplying by it's reciprocal) so you get (64/3)(π).
64/3 is 21 and 1/3 or 21.333..., so however you choose to write it, I will leave the answer as (64/3)π squared inches.
5 0
3 years ago
how do theme and tone work together? a. theme involves characters, and tone involves the historical context of those characters.
ahrayia [7]
Theme and tone work together in that B) theme is a poem's main idea, and tone is the writer's attitude toward that idea. 
4 0
3 years ago
Margo borrows $900, agreeing to pay it back with 7% annual interest after 9 months. How much interest will she pay? Round your a
Veronika [31]

Answer:

I=\$47.25

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest Value

P is the amount of money borrowed

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=9/12\ years\\ P=\$900\\r=0.07

substitute in the formula above

I=900(0.07(9/12))

I=\$47.25

3 0
3 years ago
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