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nataly862011 [7]
3 years ago
13

Help me please asap I need to know fully how to solve this problem

Mathematics
1 answer:
vivado [14]3 years ago
7 0
Consider the absolute value, because we only worry about the quadrant later.

\text{Consider: } sin(A) = |-\frac{\sqrt{3}}{4}|
sin(A) = \frac{\sqrt{3}}{4}

Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.

The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13

\therefore tan(A) = \pm \sqrt{\frac{3}{13}}

Since angle A is in the third quadrant, the tangent function will produce a positive angle.

tan(A) = \sqrt{\frac{3}{13}}
\text{Rationalise the denominator: } \frac{\sqrt{3}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}

tan(A) = \frac{\sqrt{39}}{13}
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A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formu
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Questions:

A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

Answer:

32 units of fabrics

Step-by-step explanation:

Given

a = \sqrt{f + 4} - \sqrt{36 - f}

Required

Find f when a  = 4

Substitute 4 for a

4 = \sqrt{f + 4} - \sqrt{36 - f}

Rewrite as:

\sqrt{36 - f} + 4 = \sqrt{f + 4}

Square both sides

(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2

(\sqrt{36 - f} + 4)^2 = f + 4

36 - f + 8\sqrt{36 - f} + 16 = f + 4

Collect Like Terms

8\sqrt{36 - f}= f +f+ 4 - 36 -16

8\sqrt{36 - f}= 2f -48

Divide through by 2

4\sqrt{36 - f}= f -24

Square both sides

16(36-f) = (f - 24)^2

16(36-f) = f^2 - 48f + 576

576-16f = f^2 - 48f + 576

-16f = f^2 - 48f

Collect like terms

f^2 - 48f + 16f = 0

f^2 -32f = 0

Factorize

f(f - 32) = 0

f = 0 or f = 32

f can not be 0 because some units must be ordered.

So, f = 32

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