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3 years ago

11

Find the slope and the y-intercept of the line. y=7x-3

1 answer:

Ivanshal [37]3 years ago

7 0

Answer:

(0, -3) is the y intercept

the slope is equal to 7

Step-by-step explanation:

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If BC=CD=94 and AD=59, what is AB?

Novay_Z [31]

Answer: I do not know

Step-by-step explanation:

7 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,

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

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

$=2\pi \sqrt{16}$

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

4 0

2 years ago

What is the answer to 14n- 7= 49

finlep [7]

<span>14n- 7= 49
Add 7 to both sides
14n=56
Divide 14 on both sides
Final Answer: n=4</span>

8 0

3 years ago

Read 2 more answers

What is the measure of each interior angle of a regular decagon (10 sides)?

bixtya [17]

6)a

if we put n as the number of sides in a regular polygon, the formula to find the measure of each angle is
$\frac{(n - 2) \times 180}{n}$
so the answer will be
$\frac{(10 - 2) \times 180 }{10} = \frac{1440}{10} = 144$
they each measures 144 degrees

good luck

7 0

3 years ago

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What is the value of k?<br><br> -3(k+7)-5k + 4 = 23

melamori03 [73]

Answer:

k=-5

Step-by-step explanation:

you can use Photomath to solve problems like these

3 0

3 years ago

Read 2 more answers