2 wires help support a tall pole. 1 wire forms an angle of 48 degrees with the ground and the other wire forms an angle of 72 degrees with the ground The wires are 20 meters apart. How tall is the pole?

Answers

Answer 1

Answer:

the height of the pole is 24.48 m

What is the concept of heights and distances?

The concept of heights and distances is the use of right triangles in real-world examples and solving for missing components using trigonometric ratios in a right triangle.

The scenario is illustrated below :

let triangle form with wire of angle 48 degree be BCD and that with angle 72 degree is ACD,

with, distance AB equals to = 20 m

Let AD be = y

the height of the pole CD = x

y represents the distance from the foot of one stabilizing wire to the foot of the pole.

In solving the triangles, we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side.

Considering triangle ACD,

Tan 72 = x/y

x = ytan72° = y ×3.077

x = 3.077y- - - - - - - - -(1)

Considering triangle BCD,

Tan48 = x/(20 - y)

x = (20 - y)tan48 = 1.11(30 - y)

x = 33.31 - 1.11y- - - - - - - - -(2)

Substituting equation 1 into equation 2, it becomes

3.077y= 33.31 - 1.11y

3.077y+ 1.11y = 33.31

4.187y = 33.31

y = 7.95 m

x = 3.077y

x = 3.077 x 7.95

x = 24.48 m

Therefore, the height of the pole is 24.48 m.

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Answer 2

Answer: First you'll want to draw your triangles (2 right triangles with the pole running through the middle). The angles you know are 72 degrees on the bottom left corner and 48 degrees on the bottom right corner. With this, you can figure out what the remaining angles are.
Angles of a triangle add up to 180 degrees so the missing top angle for the first triangle is 18 degrees (180 - (90 + 72)) and the missing top angle for the second triangle is 42 degrees.

You can now set up a ratio since angles are directly proportional to their opposite side. You know that the bottom is 20 meters. This means that 18/(18+42) = x/20, which simplifies to x = 6. This means the bottom of the first triangle is 6 meters, and it follows that the bottom of the second triangle is 12 meters (although you don't really need this information).

Now comes the trig. You need to figure out the length of the hypotenuse of one of the triangles so that you can use the Pythagorean Theorem to figure out the height of the pole. You can set up tan(72) = (6/x) - tangent is opposite over adjacent - which simplifies to x = 6/tan(72). You can plug this into your calculator (make sure you're in degrees mode) and you'll get x = 5.4024. This is the length of your hypotenuse.

Now plug this value into the Pythagorean Theorem (a^2+b^2=c^2) to get 6^2 + b^2 = (5.4024)^2 = c^2, c^2 = 65.1862, and c is approximately 8.0738!

8.0738 meters tall.

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school x and school y play eachother in a competition school x has eight more points than school y school x has three times as many points as school y. how many points does each school have?

Answers

Answer:

3y+8=x

Step-by-step explanation:

School X School Y

y+8=x

3y=x

3y+8=x

3/4 (6x + 1) - 3x = 1/4 (2x - 1)

Answers

3/4 (6x + 1) - 3x = 1/4 (2x - 1) . The purpose of this question is to solve for x.

$\mathbf{x = (-4)/(13)}$

Given that:

3/4 (6x + 1) - 3x = 1/4 (2x - 1)

When calculating algebraic expression, we take note of integers in bracket first, then we collect the like terms in order to find the value of x.

$\mathbf{(3)/(4) (6x + 1) - 3x =(1)/(4) (2x - 1) }$

Let's multiply both sides by 4 to eliminate the fraction.

$\mathbf{((3)/(4) * 4) (6x + 1) - 3x =((1)/(4) * 4 ) (2x - 1) }$

$\mathbf{(3) (6x + 1) - 3x =(1 ) (2x - 1) }$

Open brackets;

18x + 3 - 3x = 2x - 1

By rearrangement;

18x - 3x + 3 = 2x - 1

15x + 3 = 2x - 1

Collect like terms

15x - 2x = - 3 - 1

13x = - 4

Divide both sides by 13

$\mathbf{(13x)/(13) = (-4)/(13)}$

$\mathbf{x = (-4)/(13)}$

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3/4*(6x+1)-3*x-(1/4*(2*x-1))=0
X=1

Subtract 3x^2 - 2x + 1 from 5x^2 + 3x -7

Answers

$(5x^2 + 3x -7) - (3x^2 - 2x + 1)$

$5x^2 + 3x -7 - 3x^2 + 2x - 1$

$5x^2 - 3x^2 + 3x +2x - 7 - 1$

$2x^2 + 5x - 8$

$5x^2 + 3x -7-(3x^2 - 2x + 1)=\n 5x^2+3x-7-3x^2+2x-1=\n 2x^2+5x-8$

How do I figure out expressions for example -4×4×4×4×4×4×4×4?

Answers

-4x4x4x4x4x4x4x4 simplified would be -4^8

Answer:

-4x4x4x4x4x4x4x4 simplified would be -4^8

Step-by-step explanation:

If n=24, x=31, and s = 3 find the margin of error at a 95% confidence level. Give your answer to two decimal places. A) 0.59 B) 1.23 C) 1.96 D) 2.73

Answers

Answer:the correct answer is A) 0.59.

To find the margin of error at a 95% confidence level, we can use the formula:

Margin of Error = Critical Value * Standard Deviation

First, let's find the critical value. Since we are working with a 95% confidence level, we can use a z-score table to find the corresponding critical value.

For a 95% confidence level, the critical value is approximately 1.96.

Next, we need to find the standard deviation. In this case, the standard deviation is represented by "s" which is given as 3.

Now we can calculate the margin of error:

Margin of Error = 1.96 * 3 = 5.88

Rounding this to two decimal places, the margin of error is approximately 5.88.

Therefore, the correct answer is A) 0.59.

Final answer:

The margin of error for a 95% confidence interval with a sample size of 24 and a standard deviation of 3 is approximately 1.2 (or 1.23 when rounding up to the next available answer). This is calculated using the formula M = Z * (s/√n), where M is the margin of error, Z is the z-score, s denotes standard deviation, and n represents the sample size.

Explanation:

The formula for calculating the margin of error at a 95% confidence level is M = Z * (s/√n), where M is the margin of error, Z is the z-score, s is the standard deviation, and n is the sample size.

Since we're finding the margin of error for the 95% confidence level, we use a z-score of 1.96: the value that corresponds to 95% confidence in a standard normal distribution. In your case, n=24, s=3, and z=1.96. Thus, the margin of error is M = 1.96 * (3/√24).

After performing the arithmetic, you'll find that the margin of error, rounded to two decimal places, is approximately 1.2 (1.21 to be more accurate). Thus, the closest answer is B) 1.23.

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What is the sum of a 6-term geometric series if the first term is 24 and the last term is 1,417,176?