Warren measured a rectangular window
to find out how much wood he would
need for a new frame. What is the total
length of wood that Warren needs? Write
your answer in feet and inches.
2 feet 9 inches
5 feet 6 inches

Answer:

a. The amount borrowed is $95,000. The annual interest rate is 5%. The number of payments per year is 12 (monthly payments). The loan term in years is 25, and the payment amount is $450.

b. The loan requires a total of 25 x 12 = 300 payments over the full term.

To calculate the total amount paid over the full term of the loan, we can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where PV is the present value (the amount borrowed), PMT is the payment amount, r is the monthly interest rate (5% / 12 = 0.004167), and n is the total number of payments (300).

Plugging in the values, we get:PV = $95,000

PMT = $450

r = 0.004167

n = 300PV = $450 x [(1 - (1 + 0.004167)^-300) / 0.004167] = $144,781.92

Therefore, the total amount paid over the full term of the loan is $144,781.92.

The measure of the segment OD is same as OE. Hence , OD = DE.

A straight line that only touches a circle once is said to be tangent to it. The term "point of tangency" refers to this point. At the point of tangency, the tangent to a circle is perpendicular to the radius.

Given: XY is the tangent to the circle with centre O at A and

∠CAX=∠BAY=60°

By Alternate Segment Theorem

∠BCA=∠BAY=60°

Similarly,

∠ABC=∠CAX=60°

Therefore, ΔABC is an equilateral triangle circumscribing the circle with centre O.

Thus, centre O is also the centroid.

⇒OA:OD=2:1

Also,

OA=OE            (Radii)

∴ OD=DE

Hence , OD = DE

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The solution for x in the given equation (x-c)/2 = d is x = 2d + c.

What is the solution for x in the given equation?

Given the equation in the question;

(x-c)/2 = d

x = ?

To solve for x, cross multiply and simplify.

(x-c)/2 = d

x - c = d × 2

x - c = 2d

Add +c to both sides

x - c + c = 2d + c

x = 2d + c

Therefore, the solution for x in the given equation (x-c)/2 = d is x = 2d + c.

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The measure of angle 1 and the measure of angle 2 are 45° and 90°.

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other.

Given is a square,

We are asked to find the missing angles,

We know that, The diagonals of the square bisect each other at 90°,

The diagonal of a square bisects its internal angle,

Therefore, the measure of angle 1 = 45°

And,

The measure of angle 2 = 90°

Hence, the measure of angle 1 and the measure of angle 2 are 45° and 90°.

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The required length of the parking lot is 75 meters.

Perimeter is the measure of the figure on its circumference.

Here,
Let's call the length of the parking lot "L". The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (length + width)

We know that the width is 62 m and the perimeter is 274 m, so we can plug these values into the formula and solve for the length:

274 = 2 × (L + 62)

Dividing both sides by 2, we get:

137 = L + 62

Subtracting 62 from both sides, we get:

L = 137 - 62

L = 75

Therefore, the length of the parking lot is 75 meters.

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Note that the equation for the parent function y=x² stretched horizontally by a factor of 4 and shifted down 5 units is given as follows: y = (1/16)x² - 5

Note that a parent function is a simple, basic function from which other more complex functions can be derived by applying transformations.

To stretch the graph horizontally by a factor of 4, we divide x by 4, which gives:

y = (1/16)x²

To shift the graph down 5 units, we subtract 5 from the whole function, which gives:

y = (1/16)x² - 5

Therefore, the equation for the parent function y=x^2 stretched horizontally by a factor of 4 and shifted down 5 units is:

y = (1/16)x² - 5

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Answer:

The answer to this question would be A

Step-by-step explanation:

I took the test one time before .

Primary data is usually designed to collect original data which is required for a specific kind of research. This data is tailored according to what is the focus of the research and what outcome are the people looking for.

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Complete Question:

A marketing manager tells her assistant that she wants to use only primary data in her market research. Which of the following data would be most applicable for this research?

Interviews

Observation

Focus groups

Experiment

Surveys and Questionnaire

qualitative research

market research

we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

What is ratio ?

Ratio can be defined as given value divided by total value.

Let's assume that we have x liters of milk and y liters of water. We want to find the ratio in which water must be mixed with milk to gain 25% on selling the mixture at cost price.

If we sell the mixture at cost price, we will not make any profit or loss. So, let's first calculate the cost price of the mixture.

Assuming that the cost price of milk is the same as the cost price of water, the cost price of x liters of milk and y liters of water is:

Cost price = Cost price of milk + Cost price of water

= x * cost price of milk + y * cost price of water

Since we are not making any profit or loss, the selling price of the mixture will be the same as the cost price.

Now, to gain a profit of 25%, the selling price must be 125% of the cost price. So, we have:

Selling price = 125% of cost price

= 1.25 * (x * cost price of milk + y * cost price of water)

We know that the mixture contains only milk and water, so the total volume of the mixture is x + y liters.

Now, we can set up an equation to find the ratio of water to milk:

y/x = (1 - 1.25) / (1.25 - 0)

y/x = -0.2

Simplifying this equation, we get:

y = -0.2x

This means that for every 1 liter of milk, we need to mix it with 0.2 liters of water in order to gain a 25% profit when selling the mixture at cost price.

In terms of ratio, the ratio of water to milk is:

0.2 : 1

or

1 : 5 (by simplifying the ratio by multiplying both sides by 5)

Hence, we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

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So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.

Let c be the number of cars that Mr. Diaz sold.

According to the problem statement, Ms. Wong sold 8 fewer cars than 34 times the number of cars Mr. Diaz sold, which can be written as:

Ms. Wong's cars sold = 34c - 8

We also know that Ms. Wong sold 28 cars, so we can set this expression equal to 28 to get:

34c - 8 = 28

To solve for c, we can add 8 to both sides and then divide both sides by 34:

34c - 8 + 8 = 28 + 8

34c = 36

c = 36/34

So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

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Answer:

y = x + 3 --- 1

y = 4x + 9 --- 2

By combining 1 and 2, we have

x + 3 = 4x + 9

3-9 = 4x-x

-6 = 3x

x = -2

Sub x = -2 into 1

y = (-2) + 3 = 1

Intersection = (-2,1)

Answer:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}=\dfrac{6\sqrt{61}}{61}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Use Pythagoras Theorem to calculate the length of the hypotenuse of the given right triangle:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies 5^2+6^2=c^2[/tex]

[tex]\implies 25+36=c^2[/tex]

[tex]\implies c^2=61[/tex]

[tex]\implies c=\sqrt{61}[/tex]

Therefore:

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric ratios}\\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\\\$\sf\csc(\theta)=\dfrac{H}{O}\quad\sec(\theta)=\dfrac{H}{A}\quad\cot(\theta)=\dfrac{A}{O}$\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Substitute the given values into each ratio:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Note: The sin θ ratio can also be written as:

[tex]\implies \sin \theta=\dfrac{6}{\sqrt{61}}\cdot \dfrac{\sqrt{61}}{\sqrt{61}}[/tex]

[tex]\implies \sin \theta=\dfrac{6\sqrt{61}}{61}[/tex]

By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.

What is integration ?

Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.

Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.

Given by the question:

The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:

[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]

To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):

[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]

= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]

= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]

=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12

=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]

= [tex]51600[/tex]

Therefore, the total revenue of the shop for a year is $51,600.

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The percentage of the normal oxygen level after 4 weeks is 52.2%

At week 4, the percentage of the normal oxygen level in the pond is increasing at a rate of 96% per week.

The percentage of the normal oxygen level after 5 weeks is 41.9%

At week 5, the percentage of the normal oxygen level in the pond is increasing at a rate of 60% per week.

What is the increasing rate of a function?

The increasing rate of a function is the rate at which the function is increasing at a specific point in its domain. It tells us how fast the function is increasing, or how quickly its output values are getting larger, at that particular point.

The increasing rate can be determined using the derivative of the function. Specifically, if the derivative of a function is positive at a certain point, then the function is increasing at that point, and the magnitude of the derivative gives us the rate of increase. If the derivative is negative at a point, then the function is decreasing at that point, and the magnitude of the derivative gives us the rate of decrease.

In general, the sign of the derivative indicates the direction of change of the function, while the magnitude of the derivative indicates the rate of change. So, when we take the derivative of a function, we can use it to analyse how the function is changing and how quickly it is changing at each point in its domain.

The given model is:

o(t) = [0.6t² - t + 2] / [t² + 2]

(a) To find the percentage of the normal oxygen level after 4 weeks, we need to evaluate o(4) and multiply it by 100:

o(4) = [0.6(4²) - 4 + 2] / [4² + 2] = 9.4 / 18 = 0.522

So the percentage of the normal oxygen level after 4 weeks is:

0.522 * 100% = 52.2%

(b) To find how quickly the percentage of the normal oxygen level is changing after 4 weeks, we need to find the derivative of o(t) with respect to t and evaluate it at t = 4:

o'(t) = [1.2t(t²+ 2) - (2t)(0.6t² - t + 2)] / (t² + 2)²

o'(4) = [1.2(4)(4² + 2) - (2)(4)(0.6(4²) - 4 + 2)] / (4² + 2)² = 0.96

So the rate of change of the percentage of the normal oxygen level after 4 weeks is:

0.96 * 100% per week = 96% per week

This means that at week 4, the percentage of the normal oxygen level in the pond is increasing at a rate of 96% per week.

(c) To find the percentage of the normal oxygen level after 5 weeks, we need to evaluate o(5) and multiply it by 100:

o(5) = [0.6(5²) - 5 + 2] / [5² + 2] = 11.3 / 27 = 0.419

So the percentage of the normal oxygen level after 5 weeks is:

0.419 * 100% = 41.9%

(d) To find o'(5), we can use the same formula for the derivative of o(t) that we found in part (b), but evaluate it at t = 5:

o'(5) = [1.2(5)(5² + 2) - (2)(5)(0.6(5²) - 5 + 2)] / (5² + 2)² = 0.60

So at week 5, the percentage of the normal oxygen level in the pond is increasing at a rate of 0.60 * 100% per week, which is approximately 60% per week.

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Answer:

16Ft

Step-by-step explanation:

We can use proportions to solve this problem.

Let's let "x" be the height of the flagpole. We know that the sign is 4 feet high, and it casts a shadow of 1 1/4 feet. So we can set up the proportion:

4/1.25 = x/5

Simplifying the left side of the equation, we get:

4/1.25 = 16/5

Substituting into the original equation, we have:

16/5 = x/5

Multiplying both sides by 5, we get:

16 = x

Therefore, the height of the flagpole is 16 feet.

The statement that are true are:

a) (Vx) (x+xzx). (R)

c) (3x) (3*=x²). (R)

d) (3) (3x). (R)

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R)

a) (Vx) (x+xzx). (R) - This statement is true. It is a vacuously true statement, meaning it is true because the predicate (x+xzx) is never satisfied for any element x in the universe (R).

b) (3x) (2x+3=6x+7). (N) - This statement is false. There is no value of x in the universe (N) that satisfies the equation 2x+3=6x+7.

c) (3x) (3*=x²). (R) - This statement is true. For every value of x in the universe (R), 3 times x is equal to x squared.

d) (3) (3x). (R) - This statement is true. For any value of x in the universe (R), multiplying x by 3 will always result in a real number, which means 3x is also in the universe (R).

e) (3x) (3(2-x)=5+8(1-x)). (R) - This statement is false. There is no value of x in the universe (R) that satisfies the equation 3(2-x)=5+8(1-x).

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R) - This statement is true. For any two elements x and y in the universe (R) where x<y, 3x is always less than 3y, so the implication (3x<3y) is true. Since this is true for all x and y, the universal quantifiers (Vx)(Vy) make the statement true.

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V = r²h where,

V is the volume of the cylinder

r is the radius of the cylinder

h is the height of the cylinder

in this case, h is the value we want to find, h, r is 3m and V is 155.43m³ !!

155.43 = × (3)² × h

17.27 = × h

h = 5.4972117...

= 5.50m (3.s.f) = height of cylinder

hope this helped, if you have any questions feel free to ask !! :D

The original length of each side of the square was 14 inches.

A square is a geometric form with two dimensions that has four equal sides and four angles that are each 90 degrees (also known as right angles). With all sides being the same length and all angles being right angles, it is a particular case of a rectangle and a parallelogram. A square's sides are all perpendicular to one another, and its diagonals are at right angles to one another. Squares exhibit rotational symmetry of order 4 because they are symmetrical in both their vertical and horizontal axes.

Let's assume that the original length of each side of the square was "x" inches.

When each side of the square is decreased by 2 inches, the new length of each side will be (x-2) inches.

The perimeter of the new square is given as 48 inches. Since a square has four equal sides, the perimeter of a square is given by the formula:

Perimeter = 4 * Side

So, for the new square, we have:

48 = 4 * (x-2)

Simplifying the above equation, we get:

12 = x-2

Adding 2 to both sides, we get:

x = 14

Therefore, the original length of each side of the square was 14 inches.

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3x - 8y = -19 would be -6x + 16y = 38. Option A is correct when we multiply the equation by factor -2

The systems of equation that would be equivalent to

3x - 8y = -19 can be gotten by using a common factor that can get us the solution

3x - 8y = -19 we would multiply this by 2

6x - 16y = -38 this is not in the solution

Then we have to multiply the first equation by -2

-2(3x - 8y = -19)

-6x + 16y = 38

Therefore the first option is equivalent to the first equation in the system

proof using 7 and 5

- 6 * 7 + 16 * 5 = 38

-42 + 80 = 38

Also 3x - 8y = -19

= 3 * 7 - 8 * 5 = -19

21 - 40 = -19

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Answer:

Step-by-step explanation:

The expression "X divided by 5 multiplied by 12" can be written as:

( X / 5 ) * 12

To simplify this expression, we can first multiply 12 by X/5, which gives:

( X / 5 ) * 12 = X * (12/5)

So the simplified expression is:

X * (12/5)

or

(12/5)X

which is equivalent to "12/5 times X".

The sequence of transformations that maps triangle ABC onto triangle A”B”C” is: First the triangle is rotated by 90 degrees thus following the transformation rule (x, y) → (y, -x) and then dilation.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the centre of dilatation. The dilation transformation is determined by the scale factor and the centre of dilation.

The image stretches when the scaling factor exceeds 1.

When the scale factor is between 0 and 1, the image gets smaller.

The resulting image and the original image are identical if the scale factor is 1.

The coordinates of the triangle ABC are:

A(0, -1)

B (0, 1)

C (0, 1.8)

First the triangle is rotated by 90 degrees thus following the transformation rule:

(x, y) → (y, -x)

The new coordinates are:

A(0, -1) → A (1, 0)

B (0, 1) → B (-1, 0)

C (0, 1.8) → C (1.8, 0)

Then, the rotated figure is dilated using a scale factor of:

SF = 6/2 = 3

Hence, the sequence of transformations that maps triangle ABC onto triangle A”B”C” is: First the triangle is rotated by 90 degrees thus following the transformation rule (x, y) → (y, -x) and then dilation.

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The question you have indicated appears incomplete. However, here is a very similar example that uses the same logic and principles of probability and proportion. In this case, the proof is given below.

a.

Given: f(x) = 2(x+2)/5 , 0 <x< 1

Calculating P(0 <X< 1)

P(0 <X< 1) = ∫ f(x) dx {0.1}

Substitute 2(x+2)/5 for f(x)

P(0 <X< 1) = ∫ 2(x+2)/5 dx {0.1}

P(0 <X< 1) = 2/5 ∫(x+2) dx {0.1}

Integrate with respect to x

P(0 <X< 1) = 2/5 (x²/2+2x) {0.1}

P(0 <X< 1) = 2/5 (1²/2+2(1))

P(0 <X< 1) = 2/5 (½+2)

P(0 <X< 1) = 2/5 * 5/2

P(0 <X< 1) = 1 ----- Proved

b.

Here we're to solve for P(¼<X< ½)

P(¼<X< ½) = ∫ f(x) dx {¼,½}

Substitute 2(x+2)/5 for f(x)

P(¼<X< ½) = ∫ 2(x+2)/5 dx {¼,½}

P(¼<X< ½) = 2/5 ∫(x+2) dx {¼,½}

P(¼<X< ½) = 2/5 (x²/2+2x) {¼,½}

P(¼<X< ½) = 2/5 [ (½²/2+2(½)) - (¼²/2+2(¼))]

P(¼<X< ½) = 2/5 [(⅛+1)-(1/32 + ½)]

P(¼<X< ½) = 0.2375

The probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation is 0.2375

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Full Question:

The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function f(x) = 2(x+2)/5 , 0 <x< 1, 0, elsewhere.

(a) Show that P(0 <X< 1) = 1.

(b) Find the probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation.

The distance across the lake VW is 185m.

Triangles that are similar but not necessarily the same size are called similar triangles. This indicates that their sides are proportional and that their angles are the same.

We can see there are two similar triangles with interior parallel line.

So, apply the Side Angle Side (SAS) rule for ΔUVW ≈ ΔUXY;

⇒   [tex]\frac{VW}{XY} = \frac{UV}{UX}[/tex]

⇒   [tex]\frac{VW}{120.25}=\frac{(130+70)}{130}[/tex]

Cross multiply both sides,

⇒   VW  =  [tex]\frac{200}{130}*120.25[/tex]

⇒    VW = 185 m

Therefore, the value of VW is 185m.

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Using the graph of the line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

What is meant by inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given that the boundary line of equality has points (4,5) and (1,-1) on it.

So we can write the equation of the line.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = -1-5 / 1-4 = 2

Equation of the line:

y - y1 = m (x-x1)

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3

y + 2x = -3

Point (−3, −5) makes the inequality false.

Substituting,

-5 + 2 * -3 = -5 - 6 = -11

y + 2x should not be -11

When graphing the line it should not include the point (−3, −5).

This point is present on the lower portion of the line.

So the upper portion of the line should be the inequality including the line itself.

Therefore using the graph of line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

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The Spirit Club makes $2.5 profit on each shirt at the end of the year.

What is profit?

Cost price and selling price are better ways to explain profit. Cost price is the actual cost of the good or service, whereas selling price is the price at which it is offered for sale. In this case, the business has made a profit if the selling price of the good is higher than the cost price. Consequently, the profit calculation formula is;

Selling price minus cost price equals profit or gain.

Given that the cost of a shirt for the Spirit Club is $8.

They mark up the shirts 75% to sell in the school store.

The amount that is up on each shirt is $8×75%

= $8×(75/100)

= $8×(3/4)

= $6.

The marked price of each shirt is  $8 + $6 = $14.

They sell the shirts for 25% off at the end of the year.

The discount amount is $14×25%

= $14×(25/100)

= $14×(1/4)

= $3.5

The selling price of each shirt at the end of the year is $14 - $3.5 = $10.5.

The profit is Selling price - cost price = $10.5 - $8 = $2.5

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The values and heights obtained using the trigonometric ratios are as follows;

4. The six trigonometric ratios are;

5. The two other ways to write cot(θ) are;

6. The six trigonometric function values are;

7. The function for the height of the tree is; H = 100·tan(θ)

The completed table is presented as follows;

θ   [tex]{}[/tex]               10°                 15°              20°                 25°

H[tex]{}[/tex]               17.63             26.79          36.4               46.63

Trigonometric ratios are functions that relate the ratio of two of the sides of a right triangle to an interior angle of the right triangle.

4. The length of the adjacent side to the angle θ according to the Pythagorean Theorem is; Adjacent = √(17² - 8²) = 15

The six trigonometric ratios are;

cos(θ) = 15/17, sec(θ) = 17/15 = 1 2/15

sin(θ) = 8/17, csc(θ) = 17/8 = 2 1/8

tan(θ) = 8/15, cot(θ) = 15/8 = 1 7/8

5. The 2 other ways to write cot(θ) are;

cot(θ) = 1/(tan(θ))

cot(θ) = cos(θ)/sin(θ)

6. The location of the point on the terminal side of the angle is; (-3, -4)

Length of the hypotenuse side = √((-3)² + (-4)²) = 5

Let x represent the angle, we get;

The six trig functions of the angle are;

7. The length of the shadow of the tree = 100 m

Angle of elevation of the Sun = θ

Let h represent the height of the tree, we get;

tan(θ) = h/100

Therefore, the height of the tree, h = 100·tan(θ)

The values of the height of the tree at the different angle of elevation in the table are;

θ = 10°, h = 100 feet × tan(10°) ≈ 17.63 feet

θ = 15°, h = 100 feet × tan(15°) ≈ 26.79 feet

θ = 20°, h = 100 feet × tan(20°) ≈ 36.4 feet

θ = 25°, h = 100 feet × tan(25°) ≈ 46.63 feet

Learn more on trigonometric ratios here: https://brainly.com/question/30646429

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Answer:

Step-by-step explanation:

up to beyond hald a milimeter in length

2mm