P(x) = √x
for x = 0 → √0 = 0 and p(0) = 0
for x = 1.44 → √1.44 =1.2 and p(1.44) = 1.2
for x = 2.25 → √2.25 = 1.5 and p(2.25) = 1.5
for x = 3.24 → √3.24 = 1.8 and p(3.24) = 1.8
for x = 4.41 → √4.41= 2.1 and p(4.41) = 2.1
for x = 5.29 → √5.29 = 2.3 and p(5.29) = 2.3
Answer:
28.27
Step-by-step explanation:
Answer:
- y = 81-x
- the domain of P(x) is [0, 81]
- P is maximized at (x, y) = (54, 27)
Step-by-step explanation:
<u>Given</u>
- x plus y equals 81
- x and y are non-negative
<u>Find</u>
- P equals x squared y is maximized
<u>Solution</u>
a. Solve x plus y equals 81 for y.
y equals 81 minus x
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b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.
P equals x squared left parenthesis 81 minus x right parenthesis
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c. Find the domain of the function P found in part b.
left bracket 0 comma 81 right bracket
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d. Find dP/dx. Solve the equation dP/dx = 0.
P = 81x² -x³
dP/dx = 162x -3x² = 3x(54 -x) = 0
The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...
P is maximized at (x, y) = (54, 27).
The formula for the volume of a cylinder is V=πr²h. Substituting the information we have, we get 1470=(3.14)(6²)<span>h
</span>1470=113.04h
Divide both sides by 113.04:
1470/113.04 = 113.04h/113.04
13 ≈ h
The height of the cylinder is 13 inches. We know that the height of the cone is 1/2 the height of the cylinder; 1/2(13) = 6.5 inches. The formula for the volume of a cone is:
V=1/3πr²h
The cone and the cylinder have the same radius, and we now know that the height of the cone is 6.5. Substituting this information in we have:
V=1/3(3.14)(6²)(6.5) = 244.92 in³
The total volume of the cake would be the volume of the cylinder added to the volume of the cone:
1470+244.92 = 1714.92 in³.
The formula for the volume of a sphere, for the ball cake, is
<em /><em>V</em>=4/3πr³. Using the radius of 3 we have:
<span><em>V</em>=4/3(3.14)(3</span>³)=113.04 for the volume of the circus ball cake.
The formula for the area of the cone-shaped hat cake is <em>V</em>=1/3π<em>r</em>²<em>h</em>. We want it to have the same volume as the circus ball cake, and we know the radius is still 3:
<em />113.04=1/3(3.14)(3²)<em>h</em>
This simplifies to
113.04=9.42<em>h</em>
Divide both sides by 9.42:
113.04/9.42 = 9.42<em>h</em>/9.42
The hat cake would have to have a height of 12 inches to have the same volume.
⓵ Write down your complete equation:
x + ¾ = 9/8
⓶ Solve the equation in order to find the value of “x”:
x + ¾ = 9/8
- ¾ - ¾
x = 9/8 - ¾
There a 3 simple steps to subtract fractions:
⒈ Make sure the bottom numbers (the denominators) are the same.
9/8 - ¾ → They don’t have the same denominator.
You need to multiply the top number and the bottom number of ¾ by 2 :
3 (x2) 6
—- = ——
4 (x2) 8
So now you are left with : 9/8 - 6/8
⒉ Subtract the top numbers (the numerators). Put the answer over the same denominator :
9 - 6 = 3 → ⅜
⒊ Simplify the fraction (if needed) :
⅜ → The fraction is already simplified.
⇨ Your answer is: x = ⅜
There you go! I really hope this helped, if there’s anything just let me know! ☻
