I need this one done too! Really need help, big brain fart.

For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Fi

MrRa [10]

Answer:

$\cos(A + B) = \frac{23}{265}$

Step-by-step explanation:

Given

$\tan A=\frac{28}{45}$

$\cos B=\frac{3}{5}$

Required

$\cos(A+B)$

In trigonometry:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

We need to solve for cosA, sinA and sinB

Given that:

$\tan A=\frac{28}{45}$ and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

$x =28$ and $y = 45$

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

$z^2 = x^2 + y^2$

$z = \sqrt{x^2 + y^2$

$z = \sqrt{28^2 + 45^2$

$z = \sqrt{2809$

$z = 53$

From here, we can calculate sin and cos A

$\sin A= \frac{opposite}{hypotenuse}$ and $\cos A= \frac{adjacent}{hypotenuse}$

$\sin A= \frac{x}{z}$

$\sin A= \frac{28}{53}$

$\cos A= \frac{y}{z}$

$\cos A= \frac{45}{53}$

To angle B.

Give that

$\cos B=\frac{3}{5}$ and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

$a = 3$ and $b = 5$

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

$c^2 = a^2 + b^2$

$5^2 = 3^2 + b^2$

$25 = 9 + b^2$

Collect like terms

$b^2 = 25 - 9$

$b^2 = 16$

$b = \sqrt{16$

$b = 4$

From here, we can calculate sin B

$\sin B= \frac{opposite}{hypotenuse}$

$\sin B = \frac{b}{c}$

$\sin B = \frac{4}{5}$

Recall that:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

and

$\cos B=\frac{3}{5}$ $\sin B = \frac{4}{5}$ $\sin A= \frac{28}{53}$ $\cos A= \frac{45}{53}$

$\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}$

$\cos(A + B) = \frac{135}{265} - \frac{112}{265}$

$\cos(A + B) = \frac{135-112}{265}$

$\cos(A + B) = \frac{23}{265}$

7 0

2 years ago

Which statements are true about the median of a data set?

Leto [7]

Answer: Third and fifth option

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Step-by-step explanation:

Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.

For example, for the following set of 7 data:

2, 3, [5], 8, 13

the median is 5.

If the data number is even, for example 10 data:

3, 5, 9, 12, [19, 21], 33, 35, 40, 69

The median is the average between the two data that are in the middle

$\frac{19 +21}{2} = \frac{40}{2} = 20$

Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example

2, 4, 4.5, 4.8, 5 Median = 4.5

2, 4, 4.5, 67, 1506 Median = 4.5

The median does not represent the difference between the highest and the lowest data.

Therefore the correct affirmations are:

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

8 0

3 years ago

Read 2 more answers

I need help in this!

In-s [12.5K]

For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that $a$ is such that

$\displaystyle\lim_{x\to0^-}g(x)=\lim_{x\to0^+}g(x)\iff\lim_{x\to0}ax=\lim_{x\to0}x^2-3x$

Obviously, both limits are 0, so $g$ is indeed continuous at $x=0$ .

Now, for $g$ to be differentiable everywhere, its derivative $g'$ must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:

$g'(x)=\begin{cases}a&\text{for }x0\end{cases}$

and at this time, we don't know what's going on at $x=0$ , so we omit that case. We want $g'$ to be continuous, so we require that

$\displaystyle\lim_{x\to0^-}g'(x)=\lim_{x\to0^+}g'(x)\iff\lim_{x\to0}a=\lim_{x\to0}2x-3$

from which it follows that $a=-3$ .

3 0

3 years ago

Could someone confirm if I was correct?

mart [117]

compare to the correct answer on the picture. If not helped you can use a graph calculator and it should let you know wether or not you’re correct

3 0

3 years ago

There are 11 people in a room. Are there any outliers in the room? If

Katarina [22]

Answer:

D

Step-by-step explanation:

1, 17, and 20 are very different from the average numbers in this list.

6 0

3 years ago

Read 2 more answers