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Rasek [7]
2 years ago
9

What is the volume of the square pyramid with base edges 54 yd and slant height 45 yd?

Mathematics
1 answer:
Effectus [21]2 years ago
7 0
The answer is V = 34,992 y^3

You can answer this using an online calculator - calculator soup dot com under geometry then pyramid. Select given a (side length) and s (slant height). Enter the amounts to find V (volume).

To manually compute, get the h (height) first before computing for V (volume).

h^2 = l^2 - (s/2)^2  :  l (slant height), s (base edge/side)
h = √((45^2) - (54/2)^2)
h = 36

Then find V (volume) : s (side), h (height)

V = 1/3 (s^2)(h)
V = 1/3 (54^2)(36)
V = 34,992 y^3

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Apply the distributive property to factor out the greatest common factor. 44h-33=
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A manufacturer has been selling 1000 flat-screen TVs a week at $500 each. A market survey indicates that for A manufacturer has
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Answer:

a) Demand function: q=6000-10\cdot p

b) The rebate should be of $200, so the sale price becomes $300 per unit.

c) The rebate should be of $150, so the sale price becomes $350 per unit.

Step-by-step explanation:

a) In this case, we have a known point of the demand function (1000 units sold at $500), and the slope of a linear function (increase by 100 units fora decrease in $10).

We can express the demand function (linear) as:

q=b+m\cdot p

To calculate the slope m, we use:

m=\Delta q/\Delta p=(+100)/(-10)=-10

To calculate b, we use the known point and the calculated slope:

q=b+m\cdot p\\\\b=q-m\cdot p=1000-(-10)\cdot (500)=1000+5000=6000

Then the demand function is:

q=6000-10\cdot p

b) The revenue can be expressed as:

R=q\cdot p = (6000-10p)\cdot p=6000p-10p^2

To maximize, we can derive and equal to zero

dR/dp=6000-2*10p=0\\\\20p=6000\\\\p=300

The rebate should be of $200, so the sale price becomes $300 per unit.

c) If we take into account the cost, we have that

R=q\cdot p-C=(6000p-10p^2)-(68000+100q)\\\\R=(6000p-10p^2)-(68000+100(6000-10p))\\\\R=6000p-10p^2-(68000+600000-1000p)\\\\R=-10p^2+7000p-668000

To maximize, we can derive and equal to zero

dR/dp=-20p+7000=0\\\\p=7000/20=350

The rebate should be of $150, so the sale price becomes $350 per unit.

5 0
3 years ago
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