How is the graph of y = 7x2 + 4 different from the graph of y = 7x2?

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

3 years ago

Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are

viktelen [127]

Using the normal distribution, it is found that due to the greater z-score, Stewart caught the longer fish relative to the same specie.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

To find who caught the longer fish relative to the same specie, we need to find out who had the higher z-score.

Stewart caught a bluefish with a length of 322 mm, hence the parameters are as follows:

$X = 322, \mu = 267, \sigma = 39$

The z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{322 - 267}{39}$

Z = 1.41

Gina caught a pompano with a length of 176 mm, hence the parameters are as follows:

$X = 176, \mu = 155, \sigma = 28$

The z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{176 - 155}{28}$

Z = 0.75.

Hence Stewart caught the longer fish relative to the same specie.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

8 0

2 years ago

What is the circumference of a circle with radius pi?

vfiekz [6]

Answer:

2π² or 19.74

Step-by-step explanation:

<em>Circumference of a circle is C = 2πr</em>

Given r = π

<u>Then</u>:

C= 2π*π = 2π²

or

≈19.74

6 0

3 years ago

Bonds from the U.S. Treasury are selling at 102.293, bonds from Alachua County are selling at 85.681, and bonds from the city of

Anestetic [448]

Answer:

a. $3000

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Compare 8.25 and 8.250

GenaCL600 [577]

The answer is = because of you take away the 0 in the decimal 8.250 it's the same decimal as 8.25 and in decimals the zeros farthest to the right don't matter.
8.25 = 8.250

3 0

3 years ago