37. A company is choosing between two tanks for mixing chemicals Bothhave the same price, so the company plans to choose the one thatcan holdtanksthemost chemicals. The first tank conical with a diameter of 10 feet anda heightof 15 feet. The second tank is a hemisphere with a radius of 5.5 feetOne cubic foot 7.48 gallons

Answers

Answer 1

Answer: Volume of the conical tank = 1/3pi*r^2 * h = 1/3pi * (10/2)^2 * 15 = 125pi cubic feet or 392.7 cubic feet = 392.7 * 7.48 gallons = 2937 gallons.

Volume of the hemispherical tank = 2/3pi * r^3 = 2/3pi * (5.5)^3 = 348.5 cubic feet = 348.5 * 7.8 gallons = 2606 gallons

Hence the conical tank will contain more chemicals

Answer 2

Answer: Given:
1st tank: conical with diameter of 10 feet and height of 15 feet.
2nd tank: hemisphere with a radius of 5.5 feet

volume of a cone = πr² h/3
V = 3.14 * (5ft)² * 15ft/3
V = 3.14 * 25ft² * 5ft
V = 392.5 ft³

392.5 ft³ * 7.48 gallons/ft³ = 2,935.9 gallons

volume of a hemisphere = (2πr³)/3
V = [2 * 3.14 * (5.5ft)³]/3
V = (2 * 3.14 * 166.375 ft³)/3
V = 1,044.835 ft³/3
V = 348.28 ft³

348.28 ft³ * 7.48 gallons/ft³ = 2,605.13 gallons

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There's nothing there to solve. But you can simplify the expression.

-- The difference of two logs is the log of the quotient.

log₆(25) - log₆(5)

= log₆(25/5) = log₆(5) .

That may be all you can do with it.
If they want you to go ahead and actually find the value of log₆(5) ...
I don't remember how to do that. If it was log₁₀(5) or ln(5) ,
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Answers

For given functions f(x) and g(x) the composite function f(g(x)) is $f(g(x))=4x^4+22x^2+32$

What is function?

"It defines a relation between input values and output values."
"In function, for each input there is exactly one output."

What is composition of function?

"It is applying one function to the results of another."
"It is written is $\( f\circ g(x)=f(g(x))$ "
"First apply function f, then apply function g on the result of function f "

For given question,

We have been given two functions,

$f(x) = x^2 + x + 2,~g(x) = 2x^2 + 5.$

We need to find f(g(x))

This means we need to find composite function $\( f\circ g(x)=f(g(x))$

We have, $g(x) = 2x^2 + 5$

We find the value of f(x) for x = g(x)

$f(g(x))\n\n=f(2x^2 + 5)\n\n=(2x^2 + 5)^2 + (2x^2 + 5) + 2\n\n=[(2x^2)^2+2(2x^2)(5)+5^2]+2x^2+5+2\n\n=[4x^4+20x^2+25]+2x^2+7\n\n=4x^4+20x^2+2x^2+25+7\n\n=4x^4+22x^2+32$

Therefore, for given functions f(x) and g(x) the composite function f(g(x)) is $f(g(x))=4x^4+22x^2+32$

Learn more about compositefunction here:

brainly.com/question/20379727

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$f(g(x))=(2x^2+5)^2+2x^2+5+2\nf(g(x))=4x^4+20x^2+25+2x^2+7\nf(g(x))=4x^4+22x^2+32$

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Answers

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Answers

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Step-by-step explanation:

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