A woman looking out from the window of a height of 30m, observed that the angle of depression of the top of a flag pole was 44 degrees. If the foot of the pole is 25m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the angle of depression of the foot of the pole from the woman and the height of the flag pole

The electric field intensity at the center of the equilateral triangle is given by -q * L / (πε₀r), considering the contributions of the line charge ℓ₃.

Let's calculate the electric field intensity at the center of the equilateral triangle formed by the three line charges.

Given:
Length of each line charge: L
ℓ₁ = ℓ₂
ℓ₃ = -2ℓ₁

We need to calculate the electric field intensity created by ℓ₃ at the center of the triangle. The formula for electric field intensity created by a line charge is E = (ρ * L) / (2πε₀r), where ρ is the charge density, L is the length of the line charge, ε₀ is the permittivity of free space, and r is the distance from the charge to the point where the electric field is being measured.

Since ℓ₃ = -2ℓ₁, let's assume ℓ₁ = q, where q is the charge density of ℓ₁. Therefore, ℓ₃ = -2q.

To find the electric field intensity at the center, we need to calculate the individual electric field intensities created by ℓ₃ at the center and then sum them up.

For ℓ₃:
Electric field intensity at the center (E₃) = (ℓ₃ * L) / (2πε₀r)
= (-2q * L) / (2πε₀r)
= (-q * L) / (πε₀r)

Hence, the electric field intensity at the center of the equilateral triangle is given by -q * L / (πε₀r).

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Answer:

Substitute x = 5 into the function machine 4x = y:

4(5) = y

y = 20

Therefore, if 5 is inputted into the function machine, the output will be 20.

Answer:

1 gallon

Step-by-step explanation:

Answer:

Since the Independent variable is something that is modified or controlled in a scientific experiment, it is his age.

Answer:

The GCF of the terms of the polynomial 52x^8 + 12x^3 is 4x^3.

Step-by-step explanation:

Answer: the first option

Step-by-step explanation: if you dont want to spend more than 65 $ it is less than or equal to 65

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.

This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.

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Answer: 0.3

Step-by-step explanation:

3/10 = 30/100 = 0.3

Answer:

0.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

You simply need to assign 1 to n if you wanna know what is a1. Then, a1 turns to 6 cuz a1 means 3×1 + 3. Step by step, assign 2,3,4,5 to n and you'll get the right answers!

Answer:

126

Step-by-step explanation:

Vertical angles are congruent, as the two pairs of non-adjacent angles formed by intersecting two lines superimpose on each other.

Therefore, the other angle in the set of vertical angles measures 63 degrees as well.

63 + 63 gives us the sum of the angles, which is equal to 126.

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Answer:

Right handed 41

Right handed male 18

Right handed female 23

Male employees 22

Female employees 32

Left handed 13

Left handed male 4

Left handed female 9

One of the variables that is categorical in the survey is the type of operating system used by the students.

This variable categorizes the students' responses into different categories based on the type of operating system they have on their personal computers.

Categorical variables are qualitative and represent characteristics or attributes that cannot be measured numerically.

In this case, the categories for the operating system variable might include options such as Windows, Mac, Linux, or Other.

Other variables in the survey may include numerical or quantitative data, such as the amount of RAM or the storage capacity of the students' computers.

These variables can be measured and expressed numerically.

However, since you asked for a variable that is categorical, the type of operating system is the relevant variable in this case.

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Answer:

fesgqwa

Step-by-step explanation:

Answer:

254 cm

Step-by-step explanation:

multiply the 100 by the 2.54

the trick being, you flip the ratio as needed, hmmm in this case we want 750 oz converted to lbs, so hmmm we'd want to cancel out the "oz" part and only leave the "lbs" part,

\(750~~~\begin{matrix} oz \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cfrac{1lbs}{16~~\begin{matrix} oz \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{750}{16}lbs\implies 46.875lbs\)

notice, to cancel out the "oz", we placed the 16 at the bottom.

The coordinates of the midpoints of the sides of the triangle are: Midpoint of AB: (1/2, 1) Midpoint of BC: (-2, -1) and Midpoint of AC: (2, -2).

To find the coordinates of the midpoints of the sides of the triangle, we can average the coordinates of the endpoints of each side.

Let's label the vertices of the triangle as A(5, 0), B(-3, 2), and C(-1, -4).

To find the midpoint of side AB, we average the x-coordinates and the y-coordinates separately:

Midpoint of AB:

x-coordinate = (5 + (-3))/2 = 1/2

y-coordinate = (0 + 2)/2 = 1

Therefore, the midpoint of side AB is (1/2, 1).

To find the midpoint of side BC, we again average the x-coordinates and the y-coordinates:

Midpoint of BC:

x-coordinate = (-3 + (-1))/2 = -2

y-coordinate = (2 + (-4))/2 = -1

So, the midpoint of side BC is (-2, -1).

Finally, for the midpoint of side AC, we average the x-coordinates and the y-coordinates:

Midpoint of AC:

x-coordinate = (5 + (-1))/2 = 2

y-coordinate = (0 + (-4))/2 = -2

Thus, the midpoint of side AC is (2, -2).

To summarize, the coordinates of the midpoints of the sides of the triangle are:

Midpoint of AB: (1/2, 1)

Midpoint of BC: (-2, -1)

Midpoint of AC: (2, -2)

The midpoint of a line segment is the point that is exactly halfway between the two endpoints. In this case, we have a triangle with vertices A(5, 0), B(-3, 2), and C(-1, -4). To find the midpoints of the sides of the triangle, we need to calculate the average of the coordinates of the endpoints of each side.

Let's label the vertices as A(5, 0), B(-3, 2), and C(-1, -4).

To find the midpoint of side AB, we average the x-coordinates and the y-coordinates separately. The x-coordinate is (5 + (-3))/2 = 1/2, and the y-coordinate is (0 + 2)/2 = 1. So the midpoint of AB is (1/2, 1).

Similarly, for side BC, the x-coordinate is (-3 + (-1))/2 = -2, and the y-coordinate is (2 + (-4))/2 = -1. Hence, the midpoint of BC is (-2, -1).

For side AC, the x-coordinate is (5 + (-1))/2 = 2, and the y-coordinate is (0 + (-4))/2 = -2. Therefore, the midpoint of AC is (2, -2).

In summary, the coordinates of the midpoints of the sides of the triangle are:

Midpoint of AB: (1/2, 1)

Midpoint of BC: (-2, -1)

Midpoint of AC: (2, -2)

These midpoints divide the sides of the triangle into equal segments, representing the halfway point along each side.

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The coordinates of the midpoints of the sides of the triangle are: Midpoint of AB: (1/2, 1) Midpoint of BC: (-2, -1) and Midpoint of AC: (2, -2).

To find the coordinates of the midpoints of the sides of the triangle, we can average the coordinates of the endpoints of each side.

Let's label the vertices of the triangle as A(5, 0), B(-3, 2), and C(-1, -4).

To find the midpoint of side AB, we average the x-coordinates and the y-coordinates separately:

Midpoint of AB:

x-coordinate = (5 + (-3))/2 = 1/2

y-coordinate = (0 + 2)/2 = 1

Therefore, the midpoint of side AB is (1/2, 1).

To find the midpoint of side BC, we again average the x-coordinates and the y-coordinates:

Midpoint of BC:

x-coordinate = (-3 + (-1))/2 = -2

y-coordinate = (2 + (-4))/2 = -1

So, the midpoint of side BC is (-2, -1).

Finally, for the midpoint of side AC, we average the x-coordinates and the y-coordinates:

Midpoint of AC:

x-coordinate = (5 + (-1))/2 = 2

y-coordinate = (0 + (-4))/2 = -2

Thus, the midpoint of side AC is (2, -2).

Therefore, the coordinates of the midpoints of the sides of the triangle are:

Midpoint of AB: (1/2, 1)

Midpoint of BC: (-2, -1)

Midpoint of AC: (2, -2)

The midpoint of a line segment is the point that is exactly halfway between the two endpoints. In this case, we have a triangle with vertices A(5, 0), B(-3, 2), and C(-1, -4). To find the midpoints of the sides of the triangle, we need to calculate the average of the coordinates of the endpoints of each side.

Let's label the vertices as A(5, 0), B(-3, 2), and C(-1, -4).

To find the midpoint of side AB, we average the x-coordinates and the y-coordinates separately. The x-coordinate is (5 + (-3))/2 = 1/2, and the y-coordinate is (0 + 2)/2 = 1. So the midpoint of AB is (1/2, 1).

Similarly, for side BC, the x-coordinate is (-3 + (-1))/2 = -2, and the y-coordinate is (2 + (-4))/2 = -1. Hence, the midpoint of BC is (-2, -1).

For side AC, the x-coordinate is (5 + (-1))/2 = 2, and the y-coordinate is (0 + (-4))/2 = -2. Therefore, the midpoint of AC is (2, -2).

In summary, the coordinates of the midpoints of the sides of the triangle are:

Midpoint of AB: (1/2, 1)

Midpoint of BC: (-2, -1)

Midpoint of AC: (2, -2)

These midpoints divide the sides of the triangle into equal segments, representing the halfway point along each side.

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Answer: x > 3

Step-by-step explanation:

Answer:

To determine whether a decimal is rational or not, you need to know that...

Irrational numbers don't end and have no pattern whereas rational numbers are the complete opposite. Rational numbers end and have a repeating pattern.

Step-by-step explanation:

Here are examples of irrational numbers:

0.9384903204..... , π , √2

Examples of rational numbers:

0.777777... (is rational because it has a repeating pattern of 7) , √49

Hope this helps :)

To solve this problem, we need to set up a system of equations based on the given information. Let's assume that the farmer needs x cubic yards of mix a and y cubic yards of mix b.

For phosphoric acid, the equation would be:
x * pounds of phosphoric acid in mix a + y * pounds of phosphoric acid in mix b = pounds of phosphoric acid required

For nitrogen, the equation would be:
x * pounds of nitrogen in mix a + y * pounds of nitrogen in mix b = pounds of nitrogen required

For potash, the equation would be:
x * pounds of potash in mix a + y * pounds of potash in mix b = pounds of potash required

We can solve this system of equations using substitution or elimination method. Once we find the values of x and y, we can calculate the total cost.

Since the question asks for the answer in more than 100 words, I'll provide an explanation for the solution process.

1. Set up the equations using the given information.
2. Solve the system of equations to find the values of x and y.
3. Substitute the values of x and y into the cost equation to find the total cost.

The solution to the problem is to blend x cubic yards of mix a and y cubic yards of mix b to meet the minimum monthly requirements at a minimum cost. The total cost can be calculated by substituting the values of x and y into the cost equation.

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To find the measure of angle P in triangle PQR, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, the measure of angle P in triangle PQR is 47.5 degrees.

Given that angle R is 97.5 degrees, we can start by subtracting this angle from 180 degrees to find the sum of angles P and Q:

180° - 97.5° = 82.5°

Since we know the measures of angles R and Q, we can subtract these angles from the sum we just calculated to find the measure of angle P:

82.5° - m ∠ Q = m ∠ P

We are given that m ∠ Q is 35 degrees, so we substitute this value into the equation:
82.5° - 35° = m ∠ P

Simplifying the equation, we have:

47.5° = m ∠ P

Therefore, the measure of angle P in triangle PQR is 47.5 degrees.

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*Complete question

In ΔPQR, m ∠ R=97.5°, r=80 , q=35 and p=75 . What is the measure of m ∠ P ?

Answer: -19.2

Step-by-step explanation:

Answer:

this triangle is soo mathematically incorrect but x = 90°

Step-by-step explanation:

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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The steady-state response yss(t) can be determined by evaluating the transfer function T(s) at the frequency of the input function f(t) and multiplying it by the Laplace transform of f(t).

To find the steady-state response yss(t), we first need to find the Laplace transform of the input function f(t). In this case, f(t) = 30sin(2t), so its Laplace transform F(s) can be calculated using the Laplace transform properties. Once we have F(s), we can substitute it into the transfer function T(s) = Y(s) / F(s) and solve for Y(s), which represents the Laplace transform of the steady-state response yss(t). Finally, we can use the inverse Laplace transform to obtain the expression for yss(t). By evaluating this expression at different time points, we can determine the steady-state response of the system to the given input function.

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Answer:

7:42

Step-by-step explanation:

Answer:

If you start at 7:12 and add 30 minutes it would be 7:42

Step-by-step explanation:

dont count the hour and just add the minutes

12 + 30 = 42

Answer:

63 m^2 would be your answer

Step-by-step explanation:

finding the area is preety easy

look at pic

Option A is correct,  The slope is -1, and the y-intercept is (0,6)

A line's slope is defined as the ratio of the change in y coordinates to the change in x coordinates.

Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate.

Given coordinates (-2, 8) and (0, 6)

the slope is given by,

m = (y₂ - y₁)/(x₂ - x₁)

x₁ = -2, x₂ = 0

y₁ = 8, y₂ = 6

m = (6 - 8)/(0 - (-2))

m = 1

and the y-intercept is the point where x is 0,

the y-intercept is (0, 6)

Hence option A is correct.

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Answer:

Step-by-step explanation:

How do you solve 2x+7= −17?

2x + 7 = -17

2x = -17 - 7

2x = -24

x = -12

------------

check

2 × (-12) + 7 = -17

-24 + 7 = -17

-17 = -17

The answer is good