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Sholpan [36]
3 years ago
7

Find the tangent for angle A

Mathematics
1 answer:
TEA [102]3 years ago
8 0

12^2+b^2=40^2

144+b^2= 1600

b^2 =1456

√b2= √1456

b = 38.2

tan = 12/38.2

Or .31

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The width of a box in the shape of a rectangular prism is 4 inches more than the height h . The length is the difference of 9 in
Doss [256]

Answer:

(a) V = -H^3+ 5H^2 + 36H

(b) Length = 5in; Width = 9in; Height = 5in or Length = 3in; Width = 10in; Height = 6in

Step-by-step explanation:

Let:

W=Width; L = Length; H = Height

Given

W = 4 + H

L = 9 - H

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

V = L * W * H

V = (9 - H) * (4 + H) * H

Expand

V = (9 - H) * (4H + H^2)

Open brackets

V = 36H + 9H^2 - 4H^2 - H^3

V = 36H + 5H^2 - H^3

Rewrite as:

V = -H^3+ 5H^2 + 36H

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in: V = -H^3+ 5H^2 + 36H

180 = -H^3+ 5H^2 + 36H

Rewrite as:

H^3 - 5H^2 - 36H + 180 = 0

Factorize:

H^2(H - 5) - 36(H - 5) = 0

(H^2 - 36)(H - 5) = 0

Express H^2 - 36 as difference of two squares

(H - 6)(H + 6)(H - 5) =0

This gives:

H - 6 =0==> H = 6

H + 6 =0==> H = -6

H - 5 =0==> H = 5

Since the height can not be negative, then H = 5 or H = 6

Recall that:

W = 4 + H

L = 9 - H

When H = 5

W = 4 + 5 = 9

L = 9 - 5 = 4

When H = 6

W = 4 + 6 = 10

L = 9 - 6 = 3

Hence, the dimensions of the box are:

Length = 5in; Width = 9in; Height = 5in

or

Length = 3in; Width = 10in; Height = 6in

3 0
3 years ago
Simplify . need help
mezya [45]
I hope this helps you

3 0
3 years ago
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• Since January 1980, the population, P, of the city of Brownville has increased closely modeling the
igomit [66]

Answer:

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Step-by-step explanation:

1.022 times 100 equals 102.2% (a number in the decimals place times 100 give you the percent).

6 0
3 years ago
6% of 124 =<br> 7.44<br> 0.744<br> 74.4<br> 744<br> If you could explain would be great
Nezavi [6.7K]
To turn a percentage into a decimal, divide it by a hundred. So, 6% --> 6/100 which is 0.06.  To find a percentage of a number, multiply the number by the percent in decimal form. In this case, 124 x 0.06. The answer is 7.44. So 6% of 124 is 7.44
8 0
4 years ago
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ikadub [295]

Answer:

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Step-by-step explanation:

6/5 of 7003

= 6/5 × 7003

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Hence 6/5 of 7003 is 8,403.6

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3 years ago
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