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3 years ago

Determine whether or not this is a function. Explain why it is or not is. Thank you!

Mathematics

1 answer:

emmasim [6.3K]3 years ago

6 0

Here you have black dots at x = {0, 1, 2, 4, 4.5, 5}.

For each of these x-values, there is one and only one associated y-value. This fact tells us that the graph does represent a function.

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For positive acute angles A and B, it is known that cos A= 60/61 and tan B= 45/28. Find the value of sin(A+B) in simplest form

inna [77]

Answer:

$\displaystyle \sin(A+B)=\frac{3008}{3233}$

Step-by-step explanation:

We are given that:

$\displaystyle \cos(A)=\frac{60}{61}\text{ and } \tan(B)=\frac{45}{28}$

And that the two angles A and B are both in QI (positive acute angles).

Given this, we want to determine the value of sin(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, we can determine the opposite side with respect to A:

$\displaystyle o=\sqrt{61^2-60^2}=\sqrt{121}=11$

Likewise, for B, tangent gives the ratio of the opposite side to the adjacent. Using this information, we can determine the hypotenuse of B:

$h=\sqrt{45^2+28^2}=\sqrt{2809}=53$

In conclusion:

With respect to A, the adjacent side is 60, the opposite side is 11, and the hypotenuse is 61.

With respect to B, the adjacent side is 28, the opposite side is 45, and the hypotenuse is 53.

We can rewrite our original expression as:

$\sin(A+B)=\sin(A)\cos(B)+\sin(B)\cos(A)$

And since A and B are both in QI, all trigonometric ratios will be positive.

Using the above conclusions, substitute:

$\displaystyle \sin(A+B)=\left(\frac{11}{61}\right)\left(\frac{28}{53}\right)+\left(\frac{45}{53}\right)\left(\frac{60}{61}\right)$

Simplify. Hence:

$\displaystyle \sin(A+B)=\frac{308+2700}{3233} = \frac{3008}{3233}$

7 0

3 years ago

A factory makes circular rugs with a radius of 6.5 feet. How much braid do

Igoryamba

The answer is A, or 40.82 ft. This can be found using the formula for finding the perimeter of a circle: 2pir (2 x pi x radius). 2 x 3.14 = 6.28, and 6.28 x 6.5 = 40.82 ft. Hope this helps!

6 0

2 years ago

Solve for x. The triangles in each pair are similar I need help! (´༎ຶོρ༎ຶོ`)

Taya2010 [7]

The answer is D) 12
If you need proof, just comment.

5 0

3 years ago

What is the following number in decimal form? 8.49 x10^-7

guajiro [1.7K]

8.49 x 10⁻⁷ = 0.000000849

7 0

3 years ago

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How do I solve for x? (the picture has the problem)

max2010maxim [7]

Answer:

x = 21.013155617496

Step-by-step explanation:

we have a right triangle then ,

$\cos \left( 36\right) =\frac{17}{x}$

Then

$x=\frac{17}{\cos \left( 36\right) } = 21.013155617496$

Then

x ≈ 21

5 0

2 years ago

Read 2 more answers