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3 years ago

What is the answer for #7?

Mathematics

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

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

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For which inequality would x = 8 not be a solution?

Naya [18.7K]

Put the value of x to the inequality:

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A hiker travels 45 degrees north of east for 30 km. What is his NORTH (or y) displacement component? Round your answer and inclu

miv72 [106K]

consider X-axis along the east-west direction and north-south direction along Y-axis

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θ = angle of direction of displacement of the hiker relative to x-axis or east direction = 45 degree counterclockwise

A' = component of distance traveled by the hiker along the east direction.

Since the angle is given with the x-axis, the Sin provides the component in Y-direction. hence

Using the equation

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If x = 4y + 21y and y = 14 + 5, what is 3x × 7? No need to show your work.

podryga [215]

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9975 <--- answer.

Hope this helped!

Nate

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3 years ago

Read 2 more answers

Test the set of polynomials for linear independence. If it is linearly dependent, express one of the polynomials as a linear com

aliina [53]

Answer:

The set of polynomial is Linearly Independent.

Step-by-step explanation:

Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2

To find - Test the set of polynomials for linear independence.

Definition used -

A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.

The set is dependent if the determinant is zero.

Solution -

Given that,

f(x) =7 + x,

g(x) = 7 +x^2,

h(x)=7 - x + x^2

Now,

We can also write them as

f(x) = 7 + 1.x + 0.x²

g(x) = 7 + 0.x + 1.x²

h(x) = 7 - 1.x + 1.x²

Now,

The coefficient matrix becomes

A = $\left[\begin{array}{ccc}7&1&0\\7&0&1\\7&-1&1\end{array}\right]$

Now,

Det(A) = 7(0 + 1) - 1(7 - 7) + 0

= 7(1) - 1(0)

= 7 - 0 = 7

⇒Det(A) = 7 ≠ 0

As the determinant is non- zero ,

So, The set of polynomial is Linearly Independent.

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babunello [35]

Answer: i believe its rhombus rectangle quadrilateral

Step-by-step explanation:

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