A flagpole is located at the edge of a sheer y = 70-ft cliff at the bank of a river of width x = 40 ft. See the figure below. An observer on the opposite side of the river measures an angle of 9° between her line of sight to the top of the flagpole and her line of sight to the top of the cliff. Find the height of the flagpole.

Answers

Answer 1
I would solve this using tangents.  Let h be height of flagpole.
Set up 2 right triangles, each with a base of 40.
The larger triangle has height of "h+70"
Smaller triangle has height of 70.

Now write the tangent ratios:
[tex]tan A = \frac{h+70}{40} , tan B = \frac{70}{40} [/tex]

Note: A-B = 9
To solve for h we need to use the "Difference Angle" formula for Tangent
[tex]tan (A-B) = \frac{tanA - tanB}{1+tan A tan B}[/tex]
Plug in what we know:
[tex]tan(9) = \frac{ \frac{h+70}{40} - \frac{70}{40}}{1+ (\frac{h+70}{40})(\frac{7}{4})} [/tex]
[tex]tan (9) = \frac{ \frac{h}{40}}{ \frac{7h +650}{160}} = \frac{4h}{7h+650} [/tex]
[tex]h = \frac{650 tan(9)}{4-7 tan(9)}[/tex]
[tex]h = 35.6[/tex]

Related Questions

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7-x^2 .

What are the dimensions of such a rectangle with the greatest possible area?

Answers

if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2
the area of a rectangle = length * width
thus, area = x*(7-x^2)= 7x-x^3
in order to maximize the area, you would need to take the derivative of the area and set it equal to 0
Area = 7x-x^3Area' = 7 - 3x^2
7-3x^2 = 0thus, x = 1.5275
this x represents the x needed to create the largest possible area with the given parameters.
Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667
Final answer:

The rectangle with the maximum area that can be inscribed within the parabola y=7-x^2 has dimensions length 2√(7/3) and height 14/3.

Explanation:

The problem is asking to find the dimensions of a rectangle inscribed within a parabola with maximum area. This is an example of an optimization problem in calculus. Here, the parabola given by y=7-x^2 suggests that the rectangle's corners on the x-axis lie at (-x, 0) and (x, 0). The corners on the parabola would be located at (-x, 7-x^2) and (x, 7-x^2). The dimensions of the rectangle would be 2x for the length (base) and 7-x^2 for the height.

For the maximum area, we need to take the derivative of the area function A = length*width = (2x)*(7-x^2) and set it equal to zero, thus defining the critical points.

The derivative of A is given by A' = 14 - 6x^2. Setting A' equal to zero gives: x = √(14/6) which simplifies to x = √(7/3).

Finally, as we are looking for the dimensions of the rectangle, the length (base) is 2*x = 2√(7/3) and the height is given by y = 7 - x^2 = 7 - (7/3) = 14/3.

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In America, a person uses about 100 gallons of water each day, which is equal to 1,600 water-filled drinking glasses. How many water-filled drinking glasses would 281 Americans fill in a weeks time?
a. 449,600 water-filled glasses
b. 28,100 water-filled glasses
c. 3,147,200 water-filled glasses
d. 196,700 water-filled glasses

Answers

C. 3,147,200 water-filled glasses is the answer. sorry its late

Answer:

c. 3,147,200 water-filled glasses

Step-by-step explanation:

The amount of water consumed by an American per day= 100 gallons

So, the amount of water consumed by an American per week = 7×100 = 700 gallons

In 100 gallons of water 1,600 drinking glasses can be filled.

In 700 gallons of water 7×1,600= 11,200 drinking glasses can be filled.

The amount of water consumed by 281 American per week = 700×281 = 196,700 gallons

As in 700 gallons of water 11,200 glasses can be filled.

So, in 1 gallons of water [tex]\dfrac{11,200}{700}=16[/tex] glasses can be filled.

So, in 196,700 gallons of water [tex]16\times 196,700=3,147,200[/tex] glasses can be filled.

15 students ask to visit a college admissions counselor. Each visit includes one student. In how many ways can 10 time slots be assigned? ...?

Answers

There are ten time slots for these appointments. For the first time slot, there are 15 different students that can fill the slot. Next appointment, there are only 14 possible students since we already saw one. This goes on and on, 15 x 14 x 13... for 10 different time slots. 


15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 = 10,897,286,400 


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Only $1.87 to buy a present for Jim. Her Jim. Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling—something just a little bit near to being worthy of the honor of being owned by Jim.What inferences about Della can be made based on this excerpt Check all that apply

Della does not have much money to spend on Jim’s gift.
Della wants to buy Jim a watch chain for his watch.
Della loves her husband, Jim, very much
Della wants to buy Jim a really nice gift
Della will need to sell he

Answers

The inferences about Della can be made based on the excerpt are:

Della loves her husband, Jim, very much

Della wants to buy Jim a really nice gift

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!

Answer:

The following are correct inferences:

1. Della does not have much money to spend on Jim’s gift.

Della is financially poor and does not have enough to gift Jim. This can be understood from the line "Only $1.87 to buy a present for Jim."

2. Della loves her husband, Jim, very much.

Della has been saving for months to gift her husband something rare and unique that his husband is worth for.

"Something fine and rare and sterling—something just a little bit near to being worthy of the honor of being owned by Jim." these lines shows her love and affection for her husband.

3. Della wants to buy Jim a really nice gift.

"Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling—" These lines show that Della needs to buy something for Jim.

A popular video game claims that the average time needed to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours. James thinks that he and his four friends are more skilled than the average gamer because it took them an average of only 2.5 hours. Which of the following is the most restrictive level that would validate his claim?

a. 1%
b. 2.5%
c. 5%
d. 10%

Answers

Answer:

a

Step-by-step explanation:

1%

Final answer:

The z-score calculation for James and his friends' gaming performance indicates that their claim would be validated at even the most restrictive level of significance, which is 1%.

Explanation:

To determine which level of significance validates James and his friends' claim of being more skilled gamers, we use the concept of hypothesis testing in statistics. Given that the average time to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours, and James and his friends have an average of 2.5 hours, we can calculate the z-score to see how many standard deviations their average is from the population mean.

The formula for the z-score is: Z = (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size. Plugging in the values, we get:

Z = (2.5 - 3) / (0.4 / √5) = -6.25

This z-score is significantly below the mean. Looking at the z-table, a z-score of -6.25 falls well beyond the typical critical values for common levels of significance (1%, 2.5%, 5%, and 10%). Thus, James's claim would be validated at even the most restrictive level.

Therefore, the answer is:

a. 1%

There are 17 goats in the barn 8 goats goes outside how many goats are still in the barn

Answers

9 goats are still in the barn
17 (in the barn) -8 (not in the barn)= 9
17-8=9

Total number of goats still in Barn is 9 goats

Given that;

Total number of goats in Barn = 17

Number of goat go outside = 8

Find:

Total number of goats still in Barn

Computation:

Total number of goats still in Barn = Total number of goats in Barn - Number of goat go outside

Total number of goats still in Barn = 17 - 8

Total number of goats still in Barn = 9

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What is 2.5 in expanded and word form?

Answers

2+ 0.5 two and five fifths 

what is the square root of 8k=k

Answers

3.90506372e-23 m^2 kg s^-2 K^-1

Who is vladimir lenin?

Answers

Known by the alias Lenin, a Russian communist revolutionary, politician, and political theorist. 
Vladimir Lenin, also called Vladimir Ilich Lenin, original name Vladimir Ilich Ulyanov (born April 10 [April 22, New Style], 1870, Simbirsk, Russia—died January 21, 1924, Gorki [later Gorki Leninskiye], near Moscow), founder of the Russian Communist Party (Bolsheviks), inspirer and leader of the Bolshevik Revolution ( ...Sep 30, 2016

Calculate dy/dx
You need not expand your answer.

y=3x^2-9x+13/2x+4 ...?

Answers

The solution to the problem is as follows:

The quotient rule is ( f'(x)g(x)-f(x)g'(x) )/ (g(x))^2 {complex written on 1 line I know} 

let f(x)=9x +13 and g(x)=2x+4 

f'(x)=9 and g'(x)=2 

therefore just substitute the equations in. 

y'= 6x - ((9(2x+4)-2(9x+13))/((2x+4)^2)) 


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In a scatter plot or diagram, what is it called when all the points lie approximately along a straight line?

Answers

The answer to your question is Line Correlation .

(x-2)(x+2) Find The Product?

Answers

(x-2)*(x+2) = x*(x+2) - 2*(x+2)

(x-2)*(x+2) = x*x + x*2 - 2*x - 2*2

(x-2)*(x+2) = x^2 + 2x - 2x - 4

(x-2)*(x+2) = x^2 - 4

That's the long way to do it. You can use the difference of squares formula as a shortcut

(a-b)*(a+b) = a^2 - b^2

(x-2)(x+2) = x^2 - 2^2

(x-2)(x+2) = x^2 - 4

either way, the final answer is x^2 - 4
(X-2)(x+2)
So use "f.o.i.l" meaning you multiply each first term, the outside terms, the inside terms and last terms, and then add. You'd get x^2-4 in this example

Which of the following points does not lie on the line whose equation is x+ y = 7?
(-10, 17)
(13/3, 8/3)
(-1, -6)

Answers

The answer is (-1, -6)

Let's go through all choices:
1. (x, y) = (-10, 17)
x + y = 7
-10 + 17 = 7
17 - 10 = 7
7 = 7
So, these points lie on the line.

2. (x, y) = (13/3, 8/3)
x + y = 7
13/3 + 8/3 = 7
(13 + 8)/3 = 7
21/3 = 7
7 = 7
So, these points lie on the line, too.

3. (x, y) = (-1, -6)
x + y = 7
-1 + (-6) = 7
-1 - 6 = 7
-7 ≠ 7
So, these points DO NOT lie on the line.

What type of number is
- square root 81?
Select all that apply.

Whole number
Integer
Rational
Irrational

​​

Answers

Final answer:

The square root of 81 is 9. Hence, it falls under the categories of Whole number, Integer, and Rational number since it can be a positive whole number without any fractional part and can be written as a ratio.

Explanation:

The square root of 81 is 9. Now, considering the types of numbers, 9 is a Whole number, because it is not a fraction, and it does not have a decimal point. It is also an Integer, which are numbers that can be written without a fractional component, including both positive and negative whole numbers plus zero. Lastly, 9 is a Rational number, a number that can be written as a fraction. So, the square root of 81 is all three: Whole number, Integer, and Rational number. It is not an Irrational number, which is a number that cannot be expressed as a ratio of two integers.

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Final answer:

The square root of 81 is 9, which makes it a whole number, an integer, and a rational number. It is not an irrational number.

Explanation:

The type of number the square root of 81 is can be determined simply by calculating the square root. The square root of 81 is 9, since 9 multiplied by 9 equals 81. Now, let's classify this number:

Whole number: Yes, because whole numbers include all the non-negative numbers (0, 1, 2, 3...), and 9 falls into this category.

Integer: Yes, because integers are all whole numbers, both positive and negative, including zero (-3, -2, -1, 0, 1, 2, 3...), so 9 is also an integer.

Rational number: Yes, because rational numbers are ratios of integers (like 2/1 or -3/4), and 9 can be expressed as 9/1.

Irrational number: No, because irrational numbers cannot be expressed as ratios of integers. Examples of irrational numbers include √2 or π.

Therefore, the square root of 81 is a whole number, an integer, and a rational number, but it is not irrational.

Which equation could be used to solve this problem?

Kate weighs 3 times as much as Jen. Their total weight is 140 pounds. How much does each girl weigh?
A) 140 = 3x
B) 3x + x = 140
C) 3x - x = 140
D) x - 140 = 3x

Answers

B is the correct answer.

Kate is 3 times Jen. 3x
Their combined weight totals 140
3x + x = 140

Answer:

B

Step-by-step explanation:

Which of the following shows the correct value of 50
A. 4 < 50 < 5
B. 7 < 50< 8
C. 8 <50 < 9
D. 10 < 50 < 11

Answers

Answer:

None of the options is correct

Step-by-step explanation:

It is important to know that he expression a < x < b means that x is greater than a and less than b. So, for finding the correct value let's analyse each option.

A. 4 < 50 < 5

50 is greater than 4 but it is not less than 5, so, option A is incorrect.

B. 7 < 50 < 8

50 is greater than 7 but it is not less than 8, so, option B is incorrect.

C. 8 < 50 < 9

50 is greater than 8 but it is not less than 9, so, option C is incorrect.

D. 10 < 50 < 11

50 is greater than 10 but it is not less than 11, so, option D is incorrect.

Thus, none of the options is correct.

The correct inequality that should show the value of 50 is 49 < 50 < 51, but based on the provided options and context, all are incorrect. If choosing the closest correct answer, it would be 'C. 8 < 50 < 9', acknowledging that it is still incorrect because 50 is not less than 9. Hence, option C.

The student's question is about determining the correct inequality that shows the value of 50 within two consecutive integers. When comparing numbers, we need to find two consecutive integers between which the number 50 falls. The correct inequality that illustrates this is D. 10 < 50 < 11, as 50 is greater than 10 and less than 11. Considering context, this seems to be a typo, since 50 cannot be between 10 and 11. The correct answer should logically be none of the above, as 50 is actually between 49 and 51, making all the provided options incorrect. However, if the intention was to find which of the provided options is closest to being correct, then the answer would be C. 8 < 50 < 9, as 50 is greater than 8 but certainly not less than 9. It is important to note that this question involves an error in the provided options.

Segment BDSegment BD is a perpendicular bisector of segment ACsegment AC . AD=8x−15AD=8x−15 and DC=57DC=57 .

What is the value of x?

Answers

Since BD is a perpendicular bisector of AC, then ADC forms an isisceles triangle with AD = DC.
Thus 8x - 15 = 57
8x = 57 + 15 = 72
x = 72/8 = 9.

what is 100 x 100 ...............

Answers

The answer is 10,000

The product of the given multiplication is 10000.

What is multiplication?

Multiplication is when you take one number and add it together a number of times.

Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20.

Given that, multiply 100 x 100,

100 x 100 = 10000

Hence, the product of the given multiplication is 10000.

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explain why you can use subtraction to solve a division problem.

Answers

Subtraction is finding the difference between two numbers whereas division is putting numbers into equal pairs or undoing multiplication ( if that helps ) So... If they say divide 6 by 2 they mean put six into equal pairs of 2 which would equal 3 E.g.:- ( there are 3 pairs of six cars in twos ) You can't use subtraction because that will just find the number difference of 6 and 2 which is 4 Hope that wasn't complicated

Final answer:

Subtraction can be used to solve division problems as division can be thought of as repeated subtraction. In scientific notation, dividing numbers involves subtracting exponents, underscoring the relationship between subtraction and division, especially with exponent rules.

Explanation:

Subtraction can be used to solve a division problem because division essentially involves determining how many times a number (the divisor) can be subtracted from another number (the dividend) until nothing is left or a remainder is obtained. This concept is similar to repeated subtraction, and understanding this helps clarify why we subtract exponents when dividing numbers in scientific notation. For example, when dividing $10^6$ by $10^3$, you are essentially finding out how many times $10^3$ can be subtracted from $10^6$, which can be intuitively understood as reducing the exponent by 3 (hence $10^{(6-3)}$ or $10^3$).

When working with scientific notation, the operation of division is handled by dividing the coefficients (the numbers in front of the exponents), and then subtracting exponent of the divisor from the exponent of the dividend. This subtraction of exponents is based on the properties of powers where dividing two numbers with the same base results in a power with the base raised to the difference of the exponents. Division and subtraction are intimately related in mathematics, particularly in dealing with exponent rules which require a deep conceptual understanding, not just a mechanical execution of operations.

Find the ordered pairs for the x- and y-intercepts of the equation 3x − 2y = 18 and select the appropriate option below.

The x-intercept is (0, 6); the y-intercept is (–9, 0).
The x-intercept is (6, 0); the y-intercept is (0, –9).
The x-intercept is (3, 0); the y-intercept is (0, –2).
The x-intercept is (0, 3); the y-intercept is (–2, 0).

Answers

The x-intercept is (6, 0); the y-intercept is (0, -9)

Answer:

The x-intercept is (6, 0); the y-intercept is (0, –9).

Step-by-step explanation:

Suppose that the area of a square is eight times its perimeter. find the length of a side of the square.

Answers

Final answer:

To solve the problem, an equation is set where the area of the square (a²) is equal to eight times its perimeter (8(4a)). Solving for a, we find the side length of the square to be 32 inches.

Explanation:

The student is presented with a problem where the area of a square is stated to be eight times its perimeter. Let the side length of the square be a inches. The area of a square is given by a², and the perimeter of a square is given by 4a. According to the problem, we have a² = 8(4a).

Firstly, we set up the equation based on the given information:

a² = 8(4a)

Solving for a:

a² = 32a

a² - 32a = 0

a(a - 32) = 0

Therefore, the side length a can be 0 or 32. Since the side length cannot be 0, the length of a side of the square is 32 inches.

A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend. Which expression uses the distributive property to show equivalent expressions for this situation?

Answers

Answer:

D.) 54 + 42 = 6(9+7)

Step-by-step explanation:

This shows the distributive property as, when the 6 is distributed to the 9 you get 54 (pumpkins), and when distributed to the 7 you get 42 (pumpkins).

in the rectangle below, what is x?

Answers

a triangles sum is always 180 total.
so if one corner is 33 degrees. and the opposite corner is the same then you know that makes 66 degrees.
you take that minus 180. so 66 - 180 which leaves 114.
so X is 114
X is 90 degree because a horizontal line has its degree 180 and the half of it is 90 degree . In this case AD and BC are horizontal lines with their degree 180 and the half is 90 degree

Business: the charge on isongs is $4.50 per song. for his birthday, jason is allowed to spend at most $50 worth of music. write the inequality that describes how many songs he can buy; then solve the equation

Answers

Well... I'm not entirely sure how they want you to write the equation, however:
We know that $4.50 is for one song, since we don't know how many songs we can have 'x' represent the number of songs. Finally it ends up being $50 dollars, more than likely, so... from what I would draw it would be:

$4.50x = $50 ~ Divide $4.50 by both sides.
x = 11.1 (Estimated) ~ Roughly indicating that only 11 songs can be bought.

I hope that helps in someway, have a great rest of your day! ^ ^
{-Ghostgate-}

P.S. Considering that I'm not sure how they would want you to write it, this could be wrong. However it still gives you the proper answer.

y=3(1.2)x growth or decay

Answers

Thats growth because its two positive numbers

Calculate the average rate of change for the given graph from x = –2 to x = 0 and select the correct answer below.

A.) -2
B.) 2
C.) 3
D.) 6

Answers

We need to find f(x) on those 2 points and than divide y length (f(x2)-f(x1)) with x lenght (x2 - x1) to find average

f(x = -2) = 0

f(x = 0) = 6

Avg = 6 / 2 = 3

Answer is C

We have to use absolute valuee for x distance because distance between x1 and x2 cannot be negative it can only be positive.

Answer:

3

Step-by-step explanation:

plz helllppp.. Ill mark as brainliest to who hepls. :3 ThankU m8

A standard showerhead in Marty's house dispenses 7 gallons of water per minute. Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead.

y = 3x

How much water does Marty save each day with the change in showerheads if he uses the shower for 8 minutes each day?

4 gallons
12 gallons
32 gallons
53 gallons

Answers

First do ,60 divided by 7 =_____. Then do The product of that equation divided by 8. Then ur answer to that equation is a factor for the last equation u have to do witch is The product of ______ divided by 8, Then multiple that product by 3 like this (3❌_______=_______) then u have ur answer. Hope u understand more now that I've helped

Answer:

the answer would be 32

hope this helps :)

A department store is having a 30% off sale for all clothing items. what is the discount price of a pair of blue jeans that normally cost $39.99?

Answers

39.99x30%=11.99
39.99-11.99=$28
There are two ways you could answer this question, depending on whether or not you have a calculator:
1. (with a calculator) You do 39.99 × 0.3 = 11.997.
Then, 39.99 - 11.997 = $27.993, or $27.99.
2. (without a calculator). You have to figure out 30% of 39.99, so you divide it by 10 to get 10%, which is 3.999, and then multiply by 3 to get 30%, which is 11.997. Then, same as in the first way, you do 39.99 - 11.997 = $27.99.
Hope this helps!

Krystal bought a refrigerator from a rental center for $1,050. She makes 16 monthly payments of $112.75 with her credit card. The rental center charges $1.25 for every payment made with a credit card. What is the total cost of the refrigerator?

$1,050

$1,804

$1,824

$2,052

Description
SubmitToggle Dropdown

Answers

the total cost of the refrigerator was $1,824

Let

n--------> number of monthly payments

x-------> amount of monthly payments with Kristal's credit card

y-------> charges for every payment made with a credit card

T-------> total cost of the refrigerator

we know that

[tex] n=16\\x=\$112.75\\ y=\$1.25\\[/tex]

the total cost of the refrigerator is equal to

[tex] T=n(x+y) [/tex]

substitute the values in the formula

[tex] T=16*(112.75+1.25) [/tex]

[tex] T=16*114 [/tex]

[tex] T=\$1,824 [/tex]

therefore

the answer is

the total cost of the refrigerator is equal to [tex] \$1,824 [/tex]

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is -3/4?

Answers

you need to draw out the slope on a piece of graph paper and u can figure it out
in order for a line to be parallel it must have the same slope of -3/4
in order for a line to be perpendicular it must have the inverse of the slope which would be 4/3
if it is neither of the cases listed above it is neither parallel nor perpendicular
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