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3 years ago

15

Combine the like terms to create an equivalent expression: -2x-x+8

1 answer:

lara31 [8.8K]3 years ago

7 0

Answer:

-3x+8

Step-by-step explanation:

-2x-x+8=

-3x+8

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An artist creates a right prism whose base are regular pentagons. He wants to paints the lateral surfaces of the prism. One can

Usimov [2.4K]

He needs 13 cans of paint.

The lateral area is given by the area of 5 rectangles, whose dimensions are 15 by 5:
5(15)(5) = 375

Divide this by 30:
375/30 = 12.5 ≈ 13

6 0

3 years ago

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

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3 years ago

In Mona’s new video game she earns 30 points for each fish caught and 80 points for each octopus captured, but she loses 15 poin

beks73 [17]

Answer:

Third one

Step-by-step explanation:

30x would be 30 times the amount of fish (x)

+ 80y would be 80 times the amount of octopus captured (y)

- 15z would be subtracting 15 times the amount of crabs she captures

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2 years ago

What is f(x)= 13,500 (times) 0.89^4?

SOVA2 [1]

Solution : 8470.202535

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3 years ago

The ratio of students to adults on a field trip is 8 to 1. Which table correctly shows this ratio for each grade?

iogann1982 [59]

The answer would be b hope this helps :)

5 0

3 years ago