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julia-pushkina [17]
3 years ago
12

A banner is in the shape of a right triangle. the area is 63 inches. The height of the banner is 4 in less than twice the width

of the banner. Find the height and width of the banner. Please show all work
Mathematics
1 answer:
Blizzard [7]3 years ago
5 0
Area=1/2 times base times height
note:bh=base times height

a=1/2bh
b=width

h=-4+2w
h=2w-4
subsitute
a=1/2w(2w-4)
a=1/2(2s^2-4w)
a=w^2-2w
a=63
63=w^2-2w
subtract 63 from both sdies
0=w^2-2w-63
factor
find what 2 numbers multiply to get -63 and add to get -2
the numbers are -9 and 7
so
0=(w-9)(w+7)
if xy=0 then x and/or y=0

so
w-9=0
w+7=0

solve each
w-9=0
add 9 to both sdies
w=9

w+7=0
subtract 7 from both sides
w=-7
width cannot be negative so this can be discarded

width=9

subsitute
l=2w-4
l=2(9)-4
l=18-4
l=14


legnth=14 in
width/base=9 in
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Answer:

<h3>A production level that will minimize the average cost of making x items is x=5.</h3>

Step-by-step explanation:

Given that

c(x)=7x^3-70x^2+13,000x

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<h3>To find a production level that will minimize the average cost of making x items:</h3>

The average cost per item is f(x)=\frac{c(x)}{x}

Now  we get f(x)= 7x^2-70x+13000

<h3> f(x) is continuously differentiable for all x</h3>

Here x≥0 since it represents the number of items.,

Put x=0 in 7x^2-70x+13000

For x=0 the average cost becomes 13000

f(0)=7(0)^2-70(0)+13000

=13000

<h3>∴ f(0)=13000</h3><h3>To find Local extrema :</h3>

Differentiating f(x) with respect to x

f^{\prime} (x)=14x-70=0

14x=70

x=\frac{70}{14}

<h3>∴  x=5 gives the minimum average cost .</h3><h3>At x=5 the average cost is </h3>

f(5)=7(5)^2-70(5)+13000

=12825

<h3>∴ f(5)=12825 which is smaller than for x=0 is 13000</h3><h3>∴ f(x) is decreasing between 0 and 5 and it is increasing after 5.</h3>
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Bro that stuff is really hard is this rocket science

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Answer:

Angle C

Step-by-step explanation:

By applying sine rule in the given triangle,

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