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3 years ago

12

Do you know why when dividing a fraction by a fraction, you flip and multiple? What does dividing a fraction by a fraction reall

y mean?

1 answer:

lilavasa [31]3 years ago

8 0

Answer:

Because dividing is basically multiply by the inverse.

Step-by-step explanation:

Much like negating a number from a number is adding the later one to the flipped sign of the earlier number, dividing a fraction by a fraction means you multiply the later by the inverse of the earlier. To find the inverse of a fraction, you flip it upside down.

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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

3 years ago

How do i solve this

MAXImum [283]

Answer:

x = 0, x = 3

Step-by-step explanation:

Given

- 4x² = - 12x ( add 12x to both sides )

- 4x² + 12x = 0 ← factor out - 4x from each term

- 4x(x - 3) = 0

Equate each factor to zero and solve for x

- 4x = 0 ⇒ x = 0

x - 3 = 0 ⇒ x = 3

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=g%28t%29%20%3D%20%20%7Bt%7D%5E%7B3%7D%20%20%2B%20%20%7B2t%7D%5E%7B2%7D%20%20-%2010t%20-%208" i

-Dominant- [34]

Answer:

Step-by-step explanation:

for example

We have to write the polynomial P(x) = 5x^3 -2x^2 + 5x - 2 as a product of linear factors.

P(x) = 5x^3 -2x^2 + 5x - 2

=> P(x) = x^2( 5x - 2) + 1( 5x - 2)

=> P(x) = (x^2 + 1)(5x - 2)

4 0

3 years ago

A line that includes the point (0, 3) has a slope of 8. What is its equation in slope-intercept

iris [78.8K]

Point Slope Intercept
8x - y + 3 = 0

8 0

4 years ago

Read 2 more answers

3<br><br><br> math geniuses help please!!<br><br><br> math

dedylja [7]

Answer:

A or C ( they are the same answer in your Q)

Step-by-step explanation:

3 cos (theta)

6 0

2 years ago