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3 years ago

Find the exact value of cos(arcsin(one fourth)). For full credit, explain your reasoning.

1 answer:

5 0

We are asked to give the exact value of <span>cos(arcsin(one fourth)). In this case, we shift first the setting to degrees since this involves angles. we determine first arc sin of one fourth equal to 14.48 degrees. then we take the cos of 14.48 degrees equal to 0.9682. Answer is 0.9682.</span>

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A wire b units long is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle.

mezya [45]

1. Divide wire b in parts x and b-x.

2. Bend the b-x piece to form a triangle with side (b-x)/3

There are many ways to find the area of the equilateral triangle. One is by the formula A= $\frac{1}{2}sin60^{o}side*side= \frac{1}{2} \frac{ \sqrt{3} }{2} (\frac{b-x}{3}) ^{2}= \frac{ \sqrt{3} }{36}(b-x)^{2}$
A= $\frac{ \sqrt{3} }{36}(b-x)^{2}=\frac{ \sqrt{3} }{36}( b^{2}-2bx+ x^{2} )=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}$

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6

3. Let x be the circumference of the circle.

$2 \pi r=x$

so $r= \frac{x}{2 \pi }$

Area of circle = $\pi r^{2}= \pi ( \frac{x}{2 \pi } )^{2} = \frac{ \pi }{ 4 \pi ^{2} }* x^{2} = \frac{1}{4 \pi } x^{2}$

4. Let f(x)= $\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}+\frac{1}{4 \pi } x^{2}$

be the function of the sum of the areas of the triangle and circle.

5. f(x) is a minimum means f'(x)=0

f'(x)= $\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x$ =0

$\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0$

$(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) x=\frac{ \sqrt{3} }{18}b$

$x= \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

6. So one part is $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$ and the other part is b- $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

4 0

3 years ago

Read 2 more answers

Is 4x positive or negative?

Nikolay [14]

Answer:

if x is positive, the answer is positive. If x is negative, the answer is negative.

7 0

3 years ago

The expressions that are equivalent to 9(5v+4)

DiKsa [7]

Answer:

45v+36

Step-by-step explanation:

9•5v= 45v

9•4= 36

45v+36

6 0

3 years ago

In a manufacturing process, for every 465 items assembled, 4 are defective. at this rate, if 5,115 items are assembled, how many

7nadin3 [17]

The expected number that will be defective is:
$5115\times\frac{4}{465}=44\ items$

5 0

3 years ago

Read 2 more answers

How do you know if 2x+3y=9xy is linear or nonlinear.

Advocard [28]

We are given equation 2x+3y=9xy.

A linear equation is a equation that has maximum degree of the equation as 1.

Degree is the maximum power(exponent) of the variables.

If two variables are being multiplied together in a term, we can find power of the that term by adding powers of those variables.

In the given equation, on the left side we have two terms 2x and 3y, each opf the variable x, and y has power 1 and right side of the eqaution we have term 9xy. There x and y variables are being multiplied together.

So, the total power of the term would be 1+1=2.

So, the degree of the given equation would be 2.

Because degree of the given equation is not 1. Therefore, given equation is not a linear eqaution and it is a non-linear equation.

6 0

3 years ago

Read 2 more answers