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3 years ago

10

Secθ= a. (sqrt tan^2 + 1) b. 1/sinθ c. (sqrt cos^2 + 1)

1 answer:

Dmitry_Shevchenko [17]3 years ago

6 0

Answer:

secθ= $\sqrt{ \tan^{2} θ - 1 }$

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What is the answer for #7?

Karo-lina-s [1.5K]

Answer:

radius: 1.84 in
height: 3.68 in

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

S = 2πr² + 2πrh

For a given volume, V, this becomes ...

S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

0 = 2πr³ -V

r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

__

If we substitute the equation for V into the equation just above this last one, we have ...

0 = 2πr³ - πr²·h

Dividing by πr² gives ...

0 = 2r - h

h = 2r . . . . . generic solution for cylinder optimization problems

3 0

3 years ago

Amanda has 72 baseball cards this is eight times as many cards as John has how many baseball cards does John have

SVETLANKA909090 [29]

576 because 72×8=576

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3 years ago

Answer this volume based Question. I will make uh brainliest + 50 points

Harlamova29_29 [7]

Answer:

$\huge{\purple {r= 2\times\sqrt[3]3}}$

$\huge 2\times \sqrt [3]3 = 2.88$

Step-by-step explanation:

For solid iron sphere:
radius (r) = 2 cm (Given)

Formula for $V_{sphere}$ is given as:

$V_{sphere} =\frac{4}{3}\pi r^3$

$\implies V_{sphere} =\frac{4}{3}\pi (2)^3$

$\implies V_{sphere} =\frac{32}{3}\pi \:cm^3$

For cone:
r : h = 3 : 4 (Given)
Let r = 3x & h = 4x

Formula for $V_{cone}$ is given as:

$V_{cone} =\frac{1}{3}\pi r^2h$

$\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)$

$\implies V_{cone} =\frac{1}{3}\pi (36x^3)$

$\implies V_{cone} =12\pi x^3\: cm^3$

It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume
$\implies V_{cone} = V_{sphere}$

$\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}$

$\implies 12x^3= \frac{32}{3}$

$\implies x^3= \frac{32}{36}$

$\implies x^3= \frac{8}{9}$

$\implies x= \sqrt[3]{\frac{8}{3^2}}$

$\implies x={\frac{2}{ \sqrt[3]{3^2}}}$

$\because r = 3x$

$\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}$

$\implies r=3\times 2(3)^{-\frac{2}{3}}$

$\implies r= 2\times (3)^{1-\frac{2}{3}}$

$\implies r= 2\times (3)^{\frac{1}{3}}$

$\implies \huge{\purple {r= 2\times\sqrt[3]3}}$
Assuming log on both sides, we find:

$log r = log (2\times \sqrt [3]3)$

$log r = log (2\times 3^{\frac{1}{3}})$

$log r = log 2+ log 3^{\frac{1}{3}}$

$log r = log 2+ \frac{1}{3}log 3$

$log r = 0.4600704139$

Taking antilog on both sides, we find:

$antilog(log r )= antilog(0.4600704139)$

$\implies r = 2.8844991406$

$\implies \huge \red{r = 2.88\: cm}$

$\implies 2\times \sqrt [3]3 = 2.88$

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2 years ago

List 4 rational numbers between-4 and -3?

lana [24]

-3.1, -3.5, -3.9, -3.8

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4 years ago

What is smallest number that is divisible by 20 ,48and 72

Katyanochek1 [597]

Answer:

2

Step-by-step explanation:all of them can be divided by 2 and it is the smallest number.

7 0

3 years ago

Read 2 more answers