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3 years ago

What is the value of the angle to 2 decimal places? Help please

Mathematics

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

The COS of the angle is 60

Step-by-step explanation:

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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago

Luke is going to a carnival that has games and rides. Each game costs $3.50 and each ride costs $4.50. How much would Luke have

Svetach [21]

Answer:

28$ games and 45$ for rides so 73$

Step-by-step explanation:

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3 years ago

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Which expression is equivalent to 5 (w + 4) when w = 9?

larisa [96]

Answer:

I think it's 5(9)+20

Step-by-step explanation:

5(9+4) can be expanded to get 5(9)+5(4). And 5(4)=20

4 0

3 years ago

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Solve this please, and quick

rosijanka [135]

Error: They subtracted 9x from both sides when they should have subtracted 12. You can’t subtract unlike terms
Correct: x=-5/16
Subtract 12 from both sides to get -5 on the left and add 7x and 9x to get 16x. Divide both sides by 16 to isolate x.

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3 years ago

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13w-8w =20 ??????????

Nookie1986 [14]

Answer:

w = 4

Step-by-step explanation:

13w-8w =20

Combine like terms

5w = 20

Divide each side by 5

5w/5 = 20/5

w = 4

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3 years ago

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