Which equation represents a nonlinear function?

the angle of elevation of the top of a tower from a point 42m away from the base on level ground is 36 find the height of the to

Tcecarenko [31]

Answer:

30.51 meters

Step-by-step explanation:

Given that:

The distance from the point to the base of the tower = 42 m, the angle of elevation = 36°.

According to sine rule if a,b,c are the sides of a triangle and its respective opposite angles are A, B, C. Therefore:

$\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}$

Let the height of the tower be a and the angle opposite the height be A = angle of elevation = 36°

Also let the distance from the point to the base of the tower be b = 42 m, and the angle opposite the base of the tower be B

To find B, since the angle between the height of the tower and the base is 90°, we use:

B + 36° + 90° = 180° (sum of angles in a triangle)

B + 126 = 180

B = 180 - 126

B = 54°

Therefore using sine rule:

$\frac{a}{sin(A)} =\frac{b}{sin(B)}\\\\\frac{a}{sin(36)}=\frac{42}{sin(54)}\\\\ a=\frac{42*sin(36)}{sin(54)}\\ \\a=30.51\ meters$

The height of the tower is 30.51 meters

6 0

3 years ago

The heights of 40 randomly chosen men are measured and found to follow a normal distribution. An average height of 175 cm is obt

AVprozaik [17]

Answer:

95% two-sided confidence interval for the true mean heights of men is [168.8 cm , 181.2 cm].

Step-by-step explanation:

We are given that the heights of 40 randomly chosen men are measured and found to follow a normal distribution.

An average height of 175 cm is obtained. The standard deviation of men's heights is 20 cm.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average height = 175 cm

$\sigma$ = population standard deviation = 20 cm

n = sample of men = 40

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the true mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ]

= [ $175-1.96 \times }{\frac{20}{\sqrt{40} } }$ , $175+1.96 \times }{\frac{20}{\sqrt{40} } }$ ]

= [168.8 cm , 181.2 cm]

Therefore, 95% confidence interval for the true mean height of men is [168.8 cm , 181.2 cm].

The interpretation of the above interval is that we are 95% confident that the true mean height of men will be between 168.8 cm and 181.2 cm.

3 0

3 years ago

What is the perimeter, in units, of polygon UVWXYZ? Enter your answer in the box.

nikitadnepr [17]

Given:

Consider the below figure attached with this question.

To find:

The perimeter of the polygon UVWXYZ.

Solution:

All sides and vertical and horizontal. So, we can easily find the side lengths of the given polygon by counting the boxes between two points.

From the figure it is clear that,

UV = 9 units

VW = 2 units

WX = 3 units

XY = 3 units

YZ = 6 units

ZU = 5 units

Now, perimeter is the sum of all the sides.

$Perimeter=UV+VW+WX+XY+YZ+ZU$

$Perimeter=9+2+3+3+6+5$

$Perimeter=28$

Therefore, the perimeter of UVWXYZ is 28 units.

6 0

3 years ago

A triangle has sides with lengths of 26 meters, 39 meters, and 43 meters. Is it a right triangle?

Ivanshal [37]

Answer: No

Step-by-step explanation:

This triangle is not a right triangle because:

A right triangle must have one side that is exactly 90°.

A triangle with sides 26, 39, and 43 do not have any sides that total 90.

The answer to your question is no.

Best of Luck!

4 0

3 years ago

Read 2 more answers

The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2 + 4x – 60. The cost, in dollars,

sladkih [1.3K]

That would be

3x^2 + 4x - 60 - (3x^2 - x + 200)

= 4x - 60 + x - 200

= 5x - 260 Answer

6 0

4 years ago