A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? (Round your answer to two decimal places.)

Answers

Answer 1

Answer:

Answer:

16.65 ft

Step-by-step explanation:

You want the length of the shortest ladder that will reach a building over an 8 ft high fence that is 4 ft from the building.

Similar triangles

As in the attached diagram, we can define the length of segment AX from the fence to the ladder base as 'x'. Then the length of the ladder to the top of the fence is found using the Pythagorean theorem to be ...

BX = √(x² +8²)

The remaining length of the ladder is the hypotenuse of a triangle similar to ∆BAX. The scale factor is DA/AX = 4/x, so the length of the remaining ladder is ...

CB = (4/x)BX = (4/x)√(x² +8²)

Ladder length

The total ladder length is the sum of its parts:

CX = CB +BX

CX = (4/x)√(x² +8²) +√(x² +8²)

CX = (1 +4/x)√(x² +8²)

Minimum length

The minimum length will be that associated with the value of x that makes the derivative of CX be zero. The second attachment shows the derivative of the total length function in terms of generic distances DA=d and BA=h. For this problem, where (d, h) = (4, 8), the derivative is ...

CX' = (1+4/x)x/√(x² +8²) -(4/x²)√(x² +8²)

Expressing this over a common denominator, we have ...

CX' = (x³ -4·8²)/(x²√(x²+8²))

This is zero when ...

x³ -4·8² = 0 ⇒ x = 4∛4 ≈ 6.3496

Total length

Using this value in the ladder length formula above, we find the length of the ladder to be ...

CX = (1 +4/6.3496)√(6.3496² +8²) ≈ 16.64775

The length of the shortest ladder is about 16.65 feet.

Related Questions

Put the following equation of a line into slope-intercept form, simplifying all fractions2x+4y=4
What is 9+1 O.o plssssss help its in my 7th grade math question
How was pre-image CDEF transformed to create image CꞌDꞌEꞌFꞌ?A. 180° clockwise rotation around point G B. 270° counterclockwise rotation around point G C. reflection over segment CF D. translation 2 units to the right
0.1m+8-12 when m=30 and n=1/4
Which statement is true? All constants are of degree 0. All monomials are of degree 1. All binomials are of degree 1. All trinomials are of degree 3.

Don't know how to do the math

Answers

You have to find the surface area of the shapes, then add them all together. Then divide the SA to the 0.5 m² can of grey paint.

My sister needs help !!!!!!!A coin is flipped 150 times. The results of the experiment are shown in the following table:
Heads 63
Tails 87

Which of the following statements best describes the experimental probability of getting heads?

It is equal to the theoretical probability.
It is 8% lower than the theoretical probability.
It is 8% higher than the theoretical probability.
The experimental probability cannot be concluded from the data in the table

Answers

A coin has one of two outcomes: heads or tails.
Each has an equal probability of occurring, meaning that they each have a 50% chance to occur. (They need to add up to 100% because they include all the outcomes, divide that into two equal parts and...)

This is what we call theoretical probability. It's a guess as to how probability should work. Like in the experiment, it's not always going to be 50-50.

What actually happens is called experimental probability. This may vary slightly from theoretical probability because you can't predict probability with complete certainty, you can only say what is most likely to happen.

We want to find the probability of getting heads in our experiment so we can compare it to the theoretical outcome. To do this, we need to compare the number of heads to the total number of outcomes.

We have 63 heads, and a total of 150 coin flips.
That makes the probability of getting a heads 63/150.
The hard part is getting this ratio into a percent.

You can try simply dividing, but you should be able to notice something here.
SInce the top and the bottom of our fraction are both divisible by 3, we can simiplify.
63 ÷ 3 = 21
150 ÷ 3 = 50
So we could say that 63/150 = 21/50.

A percent is basically a fraction out of 100.
Just like you can divide the parts of a ratio by the same number and it will stay the same, you can also multiply. To get the fraction out of 100, let's multiply by 2.
(since 50 × 2 = 100)

21 × 2 = 42
50 × 2 = 100
21/50 = 42/100 = 42%

Comparing our experimental probability to the theoretical one...it is 8% lower.

Answer: 8% lower

Step-by-step explanation:

Got it right on test.

A mason's assistant's rate of pay is $0.95 per cubic foot of earth moved. He digs a trench 1.5 ft. wide by 1 ft. deep by 150 ft. in length. What is his pay for this job?213.75
236.84
256.50
284.21

Answers

1.5 ft x 1ft x150ft =225 cubic feet

225ft x $0.95=$213.75

Have you ever worked with variables? Algebra is a branch of mathematics that specifically deals with the idea of using variables to solve problems. What kinds of problems have you already solved using variables? Do you know any real-life applications for variables?Think about the numbers you encounter in the world around you. Do you understand what they really mean? Interactions at grocery stores, gas stations, and online shopping commonly involve numbers. These interactions can be better understood using algebra. Is there anything you don’t know involving numbers that you wish you better understood?

Answers

Answer:

Well, I think we all worked with variables, but don't realise about it, because when people see these terms ''variable'', ''algebra'', they freak out.

The reality is that variables are everywhere, they are all those stuff that can variate: weigh, highness, money, population, interests, and so on.

A common problem I solved using variables is measuring time. For example, when I'm going to school I tend to calculate the time of my way.

Well, whenever you are playing a sport many things causes you to consider the variables. That is the first variable that popped in my head.

Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks. Write an equation that represents the relationship between the dollar amount (y) in her bank account and the number of weeks (x) of savings

Answers

Answer: y=mx+b is the proper equation

Step-by-step explanation:

Factorise 3a squared + 7a

Answers

GCF: 1 (3 cant go into 7 and the other way around in whole number terms.)
So, 1 is the factor you are distributing.
1 goes into 3 three times.
1 goes into 7 seven times.
Don't forget your variable!

So the answer is: a(3a+ 7).

to factorise this we have to first find the biggest common factor. 3 and 7 are both are prime numbers so we can't factorise it by a number. but both numbers have an 'a' so we have to factorise it by a. hence the answer is,
a(3a+7).
hope it helps.

Other Questions

how many different 10 letter words (real or imaginary) can be formed from the following letters?K,Y,T,G,W,C,Y,D,A,A

Please answer ASAP! I need the answer put very clearly- thanks :)

PLZ HELP URGENT!!!!!!!!!f(x) = -3x2 + 2x - 7f(-1) = A) -12 B) -8 C) -6 D) 0

Question 1 (1 point)Find the coordinates of point P that divides the directed line segment from A to B in the given ratio. A(1, 2), B(5, 4), 1 to 1