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anastassius [24]
3 years ago
12

Given the following right triangle, what is the measure of angle B?

Mathematics
1 answer:
Pepsi [2]3 years ago
5 0

Answer:

A. 55 degrees

Step-by-step explanation:

We are given a right angled triangle ABC having the horizontal length = 10 units and vertical length = 7 units.

Now, the trigonometric form for angles of a right angled triangle gives,

\tan B=\frac{opposite}{adjacent}

i.e. \tan B=\frac{10}{7}

i.e. \tan B=1.42857

i.e. B=\arctan 1.42857

i.e. B=55.03

Hence, the measure of angle B is 55°

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Lim x->pi/3 ((2cosx-1)/(tan^2x-3))
beks73 [17]

You can check that the limit comes in an undefined form:

\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\dfrac{0}{0}

In these cases, we can use de l'Hospital rule, and evaluate the limit of the ratio of the derivatives. We have:

\dfrac{\text{d}}{\text{d}x}2\cos(x)-1 = -2\sin(x)

and

\dfrac{\text{d}}{\text{d}x}\tan^2(x)-3 = 2\dfrac{\tan(x)}{\cos^2(x)}=\dfrac{2\sin(x)}{\cos^3(x)}

So, we have

\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\lim_{x\to\frac{\pi}{3}} \dfrac{-2\sin(x)}{\frac{2\sin(x)}{\cos^3(x)}}=\lim_{x\to\frac{\pi}{3}}-\cos^3(x)=-\cos^3\left(\dfrac{\pi}{3}\right)

6 0
3 years ago
The distance between two points on a number line can be found by taking the ____A_____ of the ____B_____ of the coordinates. Fil
xeze [42]

Answer:

The distance between two points on a number line can be found by taking the <u>absolute value</u> of the <u>difference</u> of the coordinates.

Step-by-step explanation:

  • Every point can be paired with a number on a number line
  • The coordinate is the number associated with a point
  • To find the distance between point A and B you subtract the coordinates in any order you like and take the absolute value.
6 0
3 years ago
Does this graph show a function? Explain how you know.
Lera25 [3.4K]

Answer: D) No. The graph fails the vertical line test.

Explanation:

We are able to draw a single vertical line that passes through more than one point on the red curve. For example, we could draw a vertical line through x = 5 and have it cross the red curve at (5,4) and (5,-4).

So this is one example where the graph fails the vertical line test. It passes this test when such a thing doesn't happen. In other words, a function is only possible if any x input leads to exactly one and only one y output.

In this case, x = 5 leads to multiple outputs y = 4 and y = -4 at the same time. There are other x values which this occurs as well (any x values such that x > 1). So this is why we don't have a function.

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A research company found that 11% of the people that they called agreed to participate in a survey. If the company called 196 pe
natita [175]

Answer:

B

Step-by-step explanation:

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