Mathematics High School

What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

Answers

Answer 1
we know that
Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²

if 2π radians (full circumference) has an area of -----> 352.81 cm² 
3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²

the answer is 105.84 cm²

Related Questions

1. Is -7 + 9= -9 + 7 true, false, or open

A. True
B. False
C. Open

2. Is 4x - 3 = 19 true, false, or open

A. True
B. False
C. Open

3. Which of the following is a solution to the equation 16 = 4x - 4

A. -5
B. -4
C. 5
D. 16

4. An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student's model is 42 in. What should the width of the model be?

A. 17.5 in
B. 20.5 in
C. 83.6 in
D. 100.8 in

5. Use mental math to determine the solution to x - 3 = 10

A. X=7
B. X=13
C. X=30
D. X=0

Answers

1. -7 + 9= -9 + 7 is false 
2. Is 4x - 3 = 19 is open, because this could be a valid equation.
 3. 16 = 4x - 4 
  So, 16+4=4x; 4x=20; x=20/4; x=5..... option C is the correct one.
 4. length of the classroom is 2.4 times its width. 
  given length = 42 in, and since length = 2.4 times width, width = 42/2.4,
hence option A) 17.5 in is correct
 5. x - 3 = 10
  x = 10+3 =13
 Option B is the right one.

The answer of the following mathematical expressions are,

1. True

2. False

3. C. 5

4. A. 17.5 in

5. B. x = 13

Let's go through each of the expression ,

Is -7 + 9 = -9 + 7 true, false, or open?

It is option A. True

Both sides of the equation simplify to 2, so the equation is true.

Is 4x - 3 = 19 true, false, or open?

It is option B. False

When you solve for x, you get 4x = 22, and then x = 5.5. Therefore, the equation is false.

Which of the following is a solution to the equation 16 = 4x - 4?

The value of x is option C. 5

When you solve for x, you get 4x = 20, and then x = 5. So, x = 5 is a solution to the equation.

An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student's model is 42 inches. What should the width of the model be?

The width is equal to option A. 17.5 inches

If the length is 2.4 times the width, then the width should be 42 inches / 2.4 = 17.5 inches.

Use mental math to determine the solution to x - 3 = 10.

the value of x is option B. x = 13

Adding 3 to both sides of the equation gives x = 10 + 3, which is x = 13.

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Can you check my work please?

Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle.

Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.)

My Answer: Part one:
(360degrees/60minutes = 6 degrees per minute.)
1:25 to 1:50 is 25 minutes. 25 x 6 = 150.
150pi/180 = 5pi/6,

Answers

Your answer is correct. Indeed:

- In order to find the degrees per minute, you have to divide the full rotation angle (which is 360deg) by the number of minutes (which is 60):
360deg ÷ 60min = 6 deg/min

- In order to find how many minutes have passed, you subtract the times:
1h50m - 1h25m = 0h25m

- You then find how many degrees correspond to 25minutes:
6 deg/min × 25 min = 150deg

- Lastly, you transform degrees into radiants, through the proportion:
deg : 180 = rad : π
Therefore,
150 : 180 = rad : π
rad = (150×π)/180 = 5π/6

If the √4 is 2, what is 89²?

Answers

Your answer is 7,921.

Calculations: 

89x89 = 7,921
89x89=7,921 would be the answer

Please help !! I fan and medal!!

1.)rewrite the following expression using the distributive property.
5(2x-8)
A.)-30x
B.)10x-40
C.)10x+40
D.)10x-8

2.)simplify the following expression:
-16-18/2+25/5+1. ( the -16 and -18 are both on top of the 2 it's a fraction)
A.)-18
B.)6
C.)10
D.)-6

Answers

1. B. 10x-40
2 i think you wrote it wrong but I'm going to guess to the best of my abilities
D. -6

Find the image of P(–2, –1) after two reflections; first Ry=−5(P), and then Rx=1(P1).
(1, –5)
(–1, –6)
(4, –9)
(–2, –1)

Answers

Answer: third choice (4 - 9).

Explanation:

1) The first reflection, Ry = - 5, means a reflection is across the line y = - 5

2) Since the point P has y-coordinate  - 1, its discance to the line y = - 5 is 4 units (P is located 4 units upper the line y = - 5).

Then, the reflection of the y-coordinate will be 4 units below the line y = - 5, which is -5 - 4 = - 9,

Therefore, the y-coordinate of the image is - 9.

3) The second reflection, Rx = 1, means a reflection across the line x = 1.

4) Since the point P has x-coordinate - 2, its distance to the line x = 1 is 3 units (P is located 3 units to the left of the line x = 1).

Then, the reflection of P will be 3 units to the right of the line x = 1.

That is 1 + 3 = 4.

Therefore, the x-coordinate of the image is 4.

5) You have obtained the x and y - coordinates of the image, x = 4 and y = -9, that is (4, - 9) which is the third choice.

suppose you can factor x^2 +bx +c as (x+p)(x+q) . If c<0, what could be the possible values of p and q?

A: p= -3, q= 7

B: p= 11, q= 4

C: p= -2, q= -5

D: p= 1, q= 10

Answers

What you should know is that the value of c will be given by the following product:
 c = p * q
 So that c <0
 We have that the possible values are:
 p = -3
 q = 7
 Thus, the value of c is:
 c = p * q
 c = (- 3) * (7)
 c = -21 <0
 Answer:
 the possible values of p and q could be
 A: p = -3, q = 7
Ans: Option A

Explanation:
Let's solve it smartly!

Given expression: [tex] x^{2} + bx +c[/tex] --- (A)
Factors: (x+p)(x+q)

Condition: c<0

Now let us expand (x+p)(x+q):
=> [tex] x^{2} + (p+q)x + pq[/tex] --- (B)

By comparing (B) with (A), we can say that:

pq = c --- (C)

Now, as the condition says, c<0, it means either p or q is negative. Both cannot be positive or both cannot be negative.

1) If p>0, q>0, it means c>0 since (+p)(+q) = (+c)(according to equation (C)). Condition is not met.
Hence, option B and D are wrong.

2) If p<0, q<0 it means c>=0 since (-p)(-q) = (+c)(according to equation (C)). Condition is not met.
Hence option C is out as well.


We are left with Option A:
p<0, q>0 it means c<0 since (-p)(+q) = (-c)(according to equation (C)). Condition is MET!
Hence,
Ans: Option A: p= -3, q= 7

What is the definition of asymptote?
What is the facts or characteristics of asymptote?
What is some examples of asymptote?
What is some non-examples of asymptote?

Answers

A straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.
Final answer:

An asymptote is a line that approaches a curve indefinitely without intersecting it at any finite point. Examples include the line y = 0 for the function y = 1/x, whereas a non-example would be the intersecting line y = x with a parabola y = x^2.

Explanation:

An asymptote is a line that a curve approaches as it heads towards infinity, but never actually reaches.

There are several characteristics of an asymptote that are notable. First, the distance between the curve and the asymptote approaches zero as one moves along the curve towards infinity. However, the curve will never intersect the asymptote at any finite point. There are two main types of asymptotes: vertical and horizontal.

An example of an asymptote is the line y = 0, which is a horizontal asymptote for the function y = 1/x as x approaches infinity.

A common non-example of an asymptote is any line or curve that intersects a graph at a finite number of points, such as the line y = x when compared with a parabola y = x2.

Use a calculator to evaluate cot 3.14/5

Answers

You need to be a little careful here. cot(3.14/5) ≠ cot(π/5) to the accuracy shown. 3.14 is not a useful approximation for π if you want to use more than 3 significant digits in your result.

The 2nd selection is appropriate. (1.376)

What is the trigonometric ratio for sin C ?

Enter your answer, as a simplified fraction.

Answers

By definition we have to:
 Sin (x) = C.O / h
 Where,
 x = angle
 C.O = opposite leg
 h: hypotenuse.
 Substituting values we have:
 Sin (C) = AB / 82
 We should look for AB. For this, we use the following relationship:
 AB ^ 2 + 80 ^ 2 = 82 ^ 2
 Clearing AB:
 AB = root ((82 ^ 2) - (80 ^ 2))
 AB = 18
 Substituting we have:
 Sin (C) = 18/82
 Simplifying:
 Sin (C) = 9/41

 Answer:
 the trigonometric ratio for sin C is:
 Sin (C) = 9/41


What is the perimeter of rectangle EFGH?

+ units
+ units
22 units
39 units

Answers

Answer:

B. 2√10 + 2√29 units

1. Simplify the product.
7x (x+4)
A) 7x^2 + 4
B) 7x^2 + 28x
C) 8x + 4
D) 8x + 11,

Answers

Using the foil method the simplification of the product 7x (x+4) is the answer B) 7x^2 + 28x. The foil method is the standard method of multiplying two binomials. FOIL stands for First, Outer, Inner and Last. The order of the letters is not important and does not have to match the letters of the word FOIL

The simplified product is 7x² + 28x.

Option B is the correct answer.

We have,

To simplify the product 7 x (x + 4), we need to distribute the 7x to both terms inside the parentheses.

The distributive property states that for any numbers a, b, and c,

a x (b + c) = a x b + a x c.

Applying this property to the given expression, we have:

(7x) x (x) + (7x) x 4

Multiplying 7x by x gives us 7x², and multiplying 7x by 4 gives us 28x.

So the simplified expression becomes:

7x² + 28x

Therefore,

The simplified product is 7x² + 28x.

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NEED HELP WITH MY MATH

Answers

So for this problem we can recognize that it's a system of linear equations

recall the slope intercept form of a line
[tex]y = mx + b[/tex]
given the info we can write two linear equations one for John and one for Lyndon

take a look at johns part of the question. we can see that his bank starts with 100 dollars and every day after he saves 20 dollars. Now we can see that the 100 is the y intercept or b of our equation because it's our initial amount and the rate of change or m of the equation is 25. filling in this info we get this as johns equation:

[tex]y = 25x + 100[/tex]
now we can do the same for Lydon, she has 50 dollars to start and saves 30 dollars a day. So using the same steps as we did for John we get the equation
[tex]y = 30x + 50[/tex]
now we can do a little trick, to find out when their bank amounts will be equal we set both equations equal to each other (we're just substituting y into the equation) So we get
[tex]25x + 100 = 30x + 50[/tex]
now let's clean this up and solve for X with some algebra
[tex]100 = 30x - 25x + 50[/tex]
subtract 25x
[tex]100 = 5x + 20[/tex]
combine like terms
[tex]80 = 5x[/tex]
subtract 20
[tex]x = 16[/tex]
divide off 5 to get your x value

now we're almost done we just need to plug X back into any of our two equations we made at the beginning of the problem lets use johns equation and plug in 16 because as we found out x=16

[tex]y = 25(16) + 100[/tex]
multiply and add to get
[tex]y = 500[/tex]

now that we know
[tex]x = 16 \: \: and \: \: y = 500[/tex]
we can finalize our answer answer to the system as a coordinate (x,y) and we'll get

(16,500)

since the questions asks after how many weeks though we would say 16 or the x value because in a time related problem, time is always the x value so the final answer is

[tex]16 \: \: weeks[/tex]

What is the missing constant term in the perfect square that starts with x^2−4x

Answers

x² - 4x = x² - 4x + ([tex] \frac{4}{2} [/tex])² - ([tex] \frac{4}{2} [/tex])²
x² - 4x = x² - 4x + (2)² - (2)²

2² = 4

The constant term that is missing is 4

PLEASE HELP!!ABCD∼EFGH

AD=30 in. , EH=50 in. , and CD=15 in.

What is GH ?

Answers

Hello there user!

You're answer is going to be -

GH= 25 inches

Explain)

A-D= 30 inches

Half of AD = 15 inches, therefore all you need to do is split the next set in half as well.

50 divided by two is 25, therefore you're answer is 25 inches.

Hope this helps you! Have a great rest of you're day!

~Alexa

Answer: GH =25 in.

Step-by-step explanation:

Given: [tex]ABCD\sim EFGH[/tex]

We know that if two polygons are similar then their corresponding sides are proportional.

Thus, [tex]\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{AD}{EH}[/tex]

Since, AD=30 in. , EH=50 in. , and CD=15 in.

Then we have ,

[tex]\frac{CD}{GH}=\frac{AD}{EH}\\\\\Rightarrow\frac{15}{GH}=\frac{30}{50}\\\\\Rightarrow\ GH=\frac{50\times15}{30}\\\\\Rightarrow\ GH=25\ in.[/tex]

what is the simplified form of the following expression? sqrt 1/144

Answers

Rewrite using the quotient rule for radicals.√1/√144Any root of 1 is 1.1√144Simplify the denominator.The result can be shown in both exact and decimal forms.Exact Form:1/12Decimal Form:0.08333333333333

Plz help. ,,, ,,,,,,,,,,,,,,........





Answers

6. 3x - 3
7. -2b + 12
8. 2y-12

Hi there!

To simplify, we need to combine like terms.

6.
6x + 2 - 3x - 5
= 3x + 2 - 5
= 3x - 3

To simplify this, we need to distribute.

7.
-2 × b + 2 × 6
= -2b + 12

8.
4y - 12 + 2y
= 6y - 12

Hope this helps!

can someone check these questions?

Answers

4
4 is correct

5
The second one is also correct.

Can anyone help me on this problem, I have been stuck on it for a while now.

Answers

I think it should be 90 degrees since that angle seems to form a right angle.and right angles equal 90 degrees.
45 degrees
hope I helpeeeeeed

**** IS MY ANSWER CORRECT? ***Suppose you push your physics book against a wall hard enough to keep it from moving. Does the friction force on the book point (a) into the wall, (b) out of the wall, (c) up, (d) down, or (e) is there no friction force? Explain.

Answers

There is not friction force. Friction force refers to the an object moving and the friction not allowing it to move, however in this case the wall is what is keeping it from moving not friction.

Find an equivalent fraction for the decimal number. Be sure that your answer is in lowest terms. Enter the numerator into the first box and the denominator of the fraction into the box below. a0 0.6 = ________ a1

Answers

Well, it's asking for a fraction that is in it's lowest terms that is equivalent to 0.6, which is six-tenths or 6/10. so divide both the numerator and denominator by 2 and you get 3/5 or three-fifths. It's easy if you think about it! 

6/10 divided by 2= 3/5
6/10=0.6 
3/5=0.6
Hope this helps!

Answer:

The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Given : The decimal number is 0.6

To find : An equivalent fraction for the decimal number in the lowest terms.

Solution : The decimal number 0.6 is written in fraction by removing decimal.

Step 1 - Write the decimal number

[tex]0.6[/tex]

Step 2- Remove the decimal

[tex]0.6 = \frac{6}{10}[/tex]

Step 3 - Reduced the fraction by dividing Nr. and Dr. by 2

[tex]0.6 = \frac{6}{10}=\frac{3}{5}[/tex]

Therefore, The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]

Numerator is [tex]a_0=3[/tex] and Denominator is [tex]a_1=5[/tex]

Worker A earns $8.10 per widget produced, produces 10 widgets per day, and works 9 hours per day. Worker B earns $8.40 per widget produced, produces 8 widgets per day, and works 7 hours per day. Which of these statements is true?

A. Worker B earns more per day than worker A but less per hour than worker A.
B. Worker A earns more per day than worker B but less per hour than worker B.
C. Worker A earns more per day than worker B and more per hour than worker B.
D. Worker B earns more per day than worker A and more per hour than worker A.

Answers

Worker A:
Total earning per day = $8.10 x 10 = $81

He works 9 hours a day.  Find the rate for 1 hour.
81 ÷ 9 = 9
He earns $9 an hour

Worker B:
Total earning per day = $8.40 x 8 = $67.20

He worked 7 hours a day. Find the rate for 1 hour.
67.20 ÷ 7 = $9.60
He earns $9.60 per hour

Worker A earns more per day than worker B but less per hour than worker B. (Answer B)
Final answer:

By calculating the total earnings per day and earnings per hour for Worker A and Worker B, we deduce that Worker A earns more per day than Worker B but earns less per hour than Worker B.

Explanation:

To answer this question, we first need to calculate the total earnings per day and then the earnings per hour for both Worker A and Worker B.

For Worker A, the total earnings per day can be calculated as: 10 widgets/day * $8.10/widget = $81/day. For Worker B, the total earnings per day can be calculated as: 8 widgets/day * $8.40/widget = $67.20/day.

Therefore, we can see that Worker A earns more per day than Worker B.

Next, we calculate the earnings per hour. For Worker A, the earnings per hour amount to: $81/day ÷ 9 hours/day = $9/hour. For Worker B, the earnings per hour amount to: $67.20/day ÷ 7 hours/day = $9.60/hour.

Thus, Worker B earns more per hour than Worker A.

Given the calculations, the correct statement is B. Worker A earns more per day than Worker B but less per hour than Worker B.

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The beginning balance in the computers account was $2000.the company purchased an additional $1000 worth of computers.the balance in the account is a ?

A. Credit of $2000
B. Debit of $2000
C. Credit of $3000
D. Debit of $3000

I need the answer ASAP!!!!!!!

Answers

D. Debit of $3000
The balance of account a need to be as much as $3000

Explain what defines direct variation. Then, check which of the following tables include directly proportional quantities x and y x 1 2 3 4 y 7 14 21 28

Answers

Direct variation in mathematics is when two numbers are written in an equation where one of the numbers multiplied by a constant term to equal the other. 

In the table in the equation, we see direct variation.

X    Y
1     7
2     14
3     21
4     28

We can find the constant of the variation by dividing y by x. This constant should remain the same for all terms of x in the table with their corresponding y values.

y/x
7/1=7
14/2=7
21/3=7
28/4=7

As we can see, the values in the table all share a direct variation between x and y with the value 7.

This can be expressed in an equation: y = 7x.

Leslie says that 5 multiplied by an even number always results in an even product. Is Leslie's statement correct?

Answers

Yes, Leslie is correct. Two such examples are 5*100, which is 500 (even) and 5*18, which is 90 (also even).

Leslie's statement is correct. 5 multiplied by an even number always results in an even product

Number multiplication rules

From the question, we are to determine if Leslie's statement is correct.

From the given information,

Leslie says that 5 multiplied by an even number always results in an even product

An even number is a whole number that is able to be divided by two into two equal whole numbers

NOTE: The multiplication of any integer by an even number will always result in an even product.

An integer is a positive or negative whole number.

Since, 5 is an integer, then the multipliction of 5  by an even number will always results in an even product.

Hence, Leslie's statement is correct. 5 multiplied by an even number always results in an even product.

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How would you use a model to determine the approximate formula for the circumference of a circle with a diameter of 8 cm, and connect the model to the actual formula?

Answers

Sorry for the late response, but the formula would be:

Circumference = pi x diameter
Circumference = 3.14 x 8
Circumference = 25.12

Hope this helps!!

Answer with explanation:

Take a thread of length x cm.Convert it into circle of radius r cm.

If you divide the Length of circle by value equal to 2 π, you will obtain radius of the circle.The value 2π is a constant Quantity is an Irrational number.

[tex]\rightarrow \frac{\text{Length of thread}}{2 \pi}=r\\\\ \rightarrow \frac{x}{2 \pi}=r\\\\ \rightarrow x=2 \pi r[/tex]

Diameter of Circle =8 cm

Circumference of a circle with a diameter of 8 cm has radius equal to 4 cm because radius is half of diameter

           =2 × 3.14 × 4 cm

          = 25.12 cm

⇒So, Actual Length of thread =25.12 cm

Irrational Quantity=2 π=2×3.14=6.28 cm

So Radius

       [tex]=\frac{25.12}{6.28}\\\\=4 cm[/tex]

Diameter =Radius × 2

            =4 cm × 2

          = 8 cm

                                                                 

2/3 7/8 What is closer to 3/4

Answers

I’d say 7/8. Hope dis helps!!

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 2−x+1 intersect are the solutions of the equation 4−x = 2−x+1. (4 points) Part B: Make tables to find the solution to 4−x = 2−x+1. Take the integer values of x between −2 and 2. (4 points) Part C: How can you solve the equation 4−x = 2−x+1 graphically? (2 points)

Answers

You probably mean the equations are y = 4 - x and y = 2x -1. Else with given equations, the solution is not possible. The steps of the solution are listed below:

Part A) 
The solution to the equation 4 - x = 2x + 1 are the points where both the equations have same value for a given value of x. This means, if a points (x,y) lies on both the lines it will be the solution of the given equations. Since that point lies on both the lines, both lines will cross that point. Crossing that point can be seen as intersection of two lines at that point. 
Therefore, x-coordinates of the points where the graphs of equations y = 4 -  x and y = 2x + 1 intersect are the solutions of the equation 4 - x = 2x + 1

Part B)
The table is attached in the images below. As seen from the table, both lines have same value of y for x =1. So x=1 is the solution to the equation 4 - x = 2x + 1

Part C)
In order to solve the equation 4 - x = 2x + 1 , we plot the individual lines y = 4 - x and y = 2x + 1 on the graph. The point of intersection of two lines will be the solution to the equation. The graph of lines is attached below. 
A.  We have two lines:  y = 2-x   and   y = 4x+3 Given two simultaneous equations that are both required to be true.. the solution is the points where the lines cross...  Which is where the two equations are equal..  Thus the solution that works for both equations is when 2-x = 4x+3 because where that is true is where the two lines will cross and that is the common point that satisfies both equations.   B.  2-x = 4x+3   x     2-x      4x+3
______________

-3     5       -9
-2     4       -5
-1     3       -1
 0     2        3
 1     1        7
 2     0      11
 3    -1      15

The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3   To find the solution we need to rearrange the equation to the form x=n 2-x = 4x+3 2 -x + x = 4x + x +3 2 = 5x + 3 2-3 = 5x +3-3 5x = -1 x = -1/5   The only point that satisfies both equations is where x = -1/5 Find y:   y = 2-x  = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5 Verify we get the same in the other equation y = 4x + 3   =  4(-1/5) + 3 = -4/5 + 15/5 = 11/5   Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5)   C.  To solve graphically  2-x=4x+3 we would graph both lines...   y = 2-x  and   y = 4x+3 The point on the graph where the lines cross is the solution to the system of equations ... [It should be, as shown above, the point (-1/5, 11/5)]   To graph y = 2-x   make a table.... We have already done this in part B   x     2-x                x    4x+3 _______              ________ -1    3                   -1      -1  0    2                    0       3  1    1                    1       7   Just graph the points on a cartesian coordinate system and draw the two lines.  The solution is, as stated, the point where the two lines cross on the graph.  

Hope this helps.

two vertical cliffs are on opposite sides of a 90 foot wide river. From point A at the top of the shorter cliff, the angle of elevation of the top of the other cliff(b) is 28 degress and the angle of depression to the bottom is 38 degress.find the height of each cliff ,to the nearest foot

Answers

Answer: The tall cliff is 118.20 feet tall and the short cliff is 70.32 feet tall.

If you draw a picture with 2 cliffs and a river in the middle, you have find 2 right triangles. In each triangle the adjacent side to our known angle is the river of 90 feet. And the unknown side is the opposite leg.

Therefore, we can set up a tangent equation.

From the top of the short cliff to the top of the tall cliff, we can right and solve the following trig equation:

tan(28) = x /90
x = 47.88

From the top of the short cliff to the bottom, we can right and solve the following trip equation.

tan(38) = x/90
x = 70.32

The 70.32 is also the height of the short cliff. And adding the two answers together will give you the height of the tall cliff.

Final Answer:

The height of the shorter cliff is 70 feet and the height of the taller cliff is 118 feet.

Explanation:

To find the height of each cliff, we will use trigonometry. Specifically, we will use the tangent function, which is the ratio of the opposite side to the adjacent side of a right-angled triangle.

First, let's consider the shorter cliff (point A). We know the angle of depression from A to the bottom of the river is 38 degrees. If we imagine a horizontal line at the height of point A, we can create a right-angled triangle with one angle at the bottom of the river, the vertical side as the height of the cliff, the horizontal side as the width of the river, and the angle of depression at point A.

Using the tangent of the angle of depression, we can set up the following equation to find the height of the shorter cliff (which we will call hA):
tan(38 degrees) = height_shorter_cliff / width_river

Solving for the height of the shorter cliff, we get:
height_shorter_cliff = width_river * tan(38 degrees)

Using a calculator or trigonometry tables, we find that the height of the shorter cliff is approximately 70 feet.

Next, let's consider the taller cliff (point B). The angle of elevation from A to B is given as 28 degrees. Now we can imagine another right-angled triangle, this time with one angle at point A, the vertical side as the difference in height between cliffs A and B, the horizontal side as the width of the river, and the angle of elevation at point A.

Using the tangent of the angle of elevation, we can set up an equation to find the height difference between cliffs A and B (which we will call hB - hA):
tan(28 degrees) = (height_taller_cliff - height_shorter_cliff) / width_river

We can rearrange this to solve for the height of the taller cliff:
height_taller_cliff = width_river * tan(28 degrees) + height_shorter_cliff

Now, using our previous result for the height of the shorter cliff (70 feet), we plug it into our equation:
height_taller_cliff = 90 * tan(28 degrees) + 70

Using a calculator or trigonometry tables to evaluate tan(28 degrees), we find that the height of the taller cliff is approximately 118 feet.

Therefore, to the nearest foot, the height of the shorter cliff is 70 feet and the height of the taller cliff is 118 feet.

Please show work! Thank you

Answers

a) The greatest rectangular area will be the area of a square 10 m on each side, 100 m^2.

b) The new dimensions will be 11 m × 11 m.
.. The new area will be (11 m)^2 = 121 m^2.

c) The area was increased by 121 m^2 -100 m^2 = 21 m^2, or 21%.

d) Yes, and no.
.. If you increase the dimensions by 10%, the area will increase by 21%.
.. (40 m)^2 = 1600 m^2
.. (44 m)^2 = 1936 m^2 = 1.21*(1600 m^2), an increase of 21% over the original.

.. If you increase the dimensions by 1 unit, the area will increase by (2x+1) square units, where x is the side of the original. For x≠10, this is not 21 square units.
.. (41 m)^2 = 1681 m^2 = 1600 m^2 +(2*40 +1) m^2 = 1600 m^2 +81 m^2

how are three or more angles related

Answers

acute and obsute acute- mesures less than 90 and obsute- measures more than 90 degrees and no more than 180 degrees. tbh ion know what im saying XD :D
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