A building is 1 ft from an 8-ft fence that
surrounds the property. A worker wants
to wash a window in the building 11 ft
from the ground. He plans to place a
ladder over the fence so it rests against
the building. (See the figure.) He
decides he should place the ladder 8 ft
from the fence for stability. To the
nearest tenth of a foot, how long a
ladder will he need?

Answers

Answer 1

Answer:

This question is mainly about pythagorean theorm as if we just analyse this question we see the information given to us are

The height of the building = 11 ft The distance in between the fence and the building = 1 ftThe distance of ladder from the fence = 8 ft

Now it is said to find out the length of ladder as because the ladder is resting against the buiding so it will generally form an acute angle with the ground and as we can take the ladder to be as the hypotenuse of a right angled triangle in which the length of the perpendicular building forms one of the leg and the distance of the building from the point where the ladder is kept is said to be another leg

Now we get the measure of the vertical leg = height of the buiding = 11 ft

and another leg = distance in between the fence and the point on which the ladder is kept + the distance in between the fence and building

= (8+1)ft =9ft

Now we know hypotenuse = √base^2+√height^2

= √9^2+√11^2

= √81+√121

= √ 202

= 14.21 ft

Therefore the length of the ladder = 14.21 ft

Hope it helps you

Answer 2

The length of the ladder should be 11.1 feet long.

Let's denote the length of the ladder as L.

According to the given information:

The distance from the building to the fence = 1 ft.

The height of the window = 11 ft.

The distance from the ladder to the fence = 8 ft.

Using the Pythagorean theorem, we can set up the equation:

[tex]L^2 = (1^2) + (11^2)[/tex]

Simplifying:

[tex]L^2 = 1 + 121[/tex]

[tex]L^2 = 122[/tex]

Taking the square root of both sides:

[tex]L = \sqrt{122}[/tex]

[tex]L = 11.05 ft[/tex]

Therefore, the worker will need a ladder approximately 11.1 feet long.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ4


Related Questions

Can you please help me

Answers

Answer:

you will type your answers and send

Answer:

Step-by-step explanation:

⅔-2/5 = 4/15

Do 8 plz find OS thanks​

Answers

Answer:

OS = 10

Step-by-step explanation:

We can use a ratio to solve

QP     PR

-----  = ------

QO     OS

14          7

-----   = -------

14+6      OS

14          7

-----   = -------

20        OS

Using cross products

14 * OS = 7*20

14 OS = 140

Divide by 14

OS = 140/14

OS = 10

The answer above should be Cortes you

A camera with a price of d dollars is discounted 25%. write two expressions to represent the price of the camera with the discount.

Answers

Answer:

17d/20

Step-by-step explanation:

100-25=85

85/100×d

=17/20×d

=17d/20

Xdiveded by 20 x100=x\100

Gfxgbv


Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27

Answers

Answer:

3 e^t/2 + 4 = 27

e^t/2 = 23 / 3

Taking natural log of both sides

t/2 = ln 23/3 = ln 7.667 = 2.037

t = 4.074

Check:

3 e^4.074/2 + 4 = 27

27 = 27

X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b?

Answers

a perfect square trinomial, (x + y)² = x² + 2xy + y²

so, if we have the x of the bx, what is left is the b

the expression would have to be (x + 7)², since we have the 49 and the x²

so, what's left: x² + 14x + 49,

b = 14

hope it helps :)



A student writes
2
pages of a report in
2
an hour. What is her unit
rate in pages per hour?

Answers

Answer:

1 page of a report per hour

Step-by-step explanation:

2/2= 1 page per hour

A student rights 2 pages of report in 2 an half hour

Lets find unit rate

[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]

[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]

I’m so confused. Need the help

Answers

1.621 kN

Step-by-step explanation:

Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:

[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]

[tex]= 1.621\:\text{kN}[/tex]

Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:

Answers

Answer:

6 samples

Step-by-step explanation:

Given :

Sample size, = n

Standard deviation, = 6000

Margin of Error = 2000

Confidence interval, α = 95%

Zcritical at 95% = 1.96

n = (Zcritical * σ) / margin of error

n = (1.96 * 6000) /2000

n = 11760 / 2000

n = 5.88

n = 6 samples

!!!!!!!!PLEASE HELP NOW !!!!!!!!!!!!!!!!!!
What is the following product?
45 47 47.45
4(977)
O AN
74
7

Answers

Answer:

7

Step-by-step explanation:

You can convert the fourth square roots to [tex]7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}}[/tex]. Using the product of powers rule, we can add the four terms' exponents, resulting in [tex]7^1[/tex], which is 7.

please answer all the questions and get 15 pts

Answers

Answer:

Here you go

Ans is in pictures.

A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.​

Answers

Try the answer vertex

In the figure, L1 || L2. 2x=174º. Find Za+Zb.

Answers

9514 1404 393

Answer:

  12°

Step-by-step explanation:

We assume you mean ...

  ∠x = 174°

Angle a is supplementary to angle x, so is ...

  ∠a = 180° -174° = 6°

Angle b is a vertical angle with respect to angle 'a', so is the same measure.

  ∠a +∠b = 6° +6° = 12°

If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?

Answers

measure horizontally

measure vertically

measure depth..

What is the maximum amount of a loan you can get if you pay $700 each month at a yearly rate of 0.89% for 10 years?

Answers

Answer:

$785.17

Step-by-step explanation:

Given data

PV is the loan amount

PMT is the monthly payment

i is the interest rate per month in decimal form (interest rate percentage divided by 12)

n is the number of months (term of the loan in months)

PMT =$700

n = 10 years

i = 0.89%

The formula for the loan amount is

2) Consider the quadratic sequence 72, 100, 120, 132

2.1.1) Determine Tn the nth term of the quadratic.​

Answers

Answer:

Tn = -4n²+40n+36

Step-by-step explanation:

A general quadratic sequence, Tn = an²+bn+c, where n is the term of the sequence.

So, when n = 1, Tn = 72, which means T1 = a+b+c=72.

when n = 2, Tn = 100, which means T2= 4a+2b+c = 100

when n = 3, Tn = 132, which means T3 = 9a+3b+c = 132.

Now, use a calcaulatot to solve the 3 variable simultaneous equation. According to my calculator, a = -4, b = 40, c = 36.

Hence, you a, b, and c in the Tn equation given above.

Therefore, Tn = -4n²+40n+36

Find two numbers that have 2, 5, and 7 as factors.​

Answers

Step-by-step explanation:

One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.

To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140

The jury pool for the upcoming murder trial of a celebrity actor contains the names of 100,000 individuals in the population who may be called for jury duty. The proportion of the available jurors on the population list who are Hispanic is .40. A jury of size 12 is selected at random from the population list of available jurors. Let X = the number of Hispanics selected to be jurors for this jury.

a. What is the expected number of hispanic jurors being on the jury?
b. What is the expected value (or theoretical mean) of a great earthquake off the coast of Oregon in two years?
c. Use the poisson distribution to appropriate the probability that there will be at least one major earthquake in the next two years.

Answers

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Have a Spanish Jury possibility[tex]= 0.40[/tex]

Jury member No. to be chosen[tex]= n= 12[/tex]

Hispanic Juror Expected [tex]= np = 12\times 0.40 = 4.8[/tex]

The jury group will be constituted by Hispanic Jurors [tex]4.8[/tex]

OR

The binomial distribution defines the behavior of a count variable X, provided:

There are a set number of data points n.

Set [tex]n=12[/tex]

Each perception is independent. This will not affect others if your first juror is selected

One of two results is that each observation ("success" or "failure"). English or not

Each result has the same chance of "success" p. for every [tex]p=0.40[/tex]

Well by the binomial distribution. Mean[tex]=E(x)=np=4.8[/tex]

Help please, thanks

Answers

Answer: B. X It passes the vertical line test :)

Step-by-step explanation:

I’m pretty sure it’s x

Find the value of x in each case:

Answers

9514 1404 393

Answer:

  x = 36

Step-by-step explanation:

The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...

  (180 -2x) +x +(180 -4x) = 180

  180 = 5x . . . . . . add 5x-180 to both sides

  36 = x . . . . . . . divide by 5

__

Additional comment

This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.

I don't get this question i need some help please!!!

Answers

Answer:

2 sqrt(2) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/4

4 sin 45 = x

4 ( sqrt(2)/2) =x

2 sqrt(2) = x

Answer: D

Use sine to find the x-value:

[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]  

Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?

Answers

Step-by-step explanation:

100% = $70.99

there is a discount of 25%.

that means 75% (100 - 25) of the original price remains.

the equation to get any x% amount of a 100% total is simply

x% amount = 100% total amount × x/100

25% = 70.99 × 25/100 = $17.75

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
1
–1
i
–i

Answers

Answer:

B. -1 should be the answer

Step-by-step explanation:

Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).

1. g(x) = f(x + 1)
2. g(x) = f(x) - 2

Please help i also need to graph

Answers

9514 1404 393

Answer:

left 1 unitdown 2 units

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

__

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?

Answers

Answer:

The team can assign field positions to 9 of the 19 players in 181,440 different ways.

Step-by-step explanation:

Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:

3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X

21 x 30 x 12 x 24 = X

630 x 12 x 24 = X

181,440 = X

Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.

a family has two children. what is the probability that both are girls, given that at least one is a boy

Answers

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

44 and 45 are alternate interior
angles. Find the measure of 44.
t
115/65°
43/44
44 = [?]
t
45/46
47/48
274
Fnter

Answers

Answer:

115

Step-by-step explanation:

The opposite angles (115degree angle and angle 4) are equal.

Angle 3=65

Angle 4=115

Angle 5=115

Angle 6=65

Angle 7=65

Angle 8=115

Brainliest please~

How many solutions will each system of linear equation have?

Answers

Answer:

The top system of equations has one solution, the middle system has infinitely many, and the bottom system has no solution.

Step-by-step explanation:

We can immediately see the top system has one solution because the two equations have different slopes.

For the middle system, we can rearrange terms and multiply by 3 to get that the equations are the same line, so there are infinitely many solutions.

Finally, we can move the -2x to the other side in the first equation of the bottom system to get 2x+y=5. But it also equals -7 from the second equation! This is impossible, so there are no solutions to the bottom system.

Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.

Answers

Part 1: You can simplify [tex]a_n[/tex] to

[tex]\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}[/tex]

Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

[tex]|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}[/tex]

(b) And because both fractions in [tex]a_n[/tex] converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,

[tex]|a_n| \ge \boxed{0}[/tex]

(c) Finally, [tex]a_n[/tex] is bounded above and below, so it is a bounded sequence.

Part 2: Yes, [tex]a_n[/tex] is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since [tex]a_n[/tex] is decreasing and bounded below by 0, its limit as n goes to infinity is 0.

Part 4:

(a) We have

[tex]\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10[/tex]

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

[tex]\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty[/tex]

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.

Answers

Answer:

The answer is "[tex]\frac{5\pi}{6}[/tex]"

Step-by-step explanation:

Please find the graph file.

[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]

10(2x-3)=10


find the value of x​

Answers

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

10(2x-3)=10

20x-30=10

20x=10+30

20x=40

x=40/20

X=2

It is given that,

→ 10(2x-3) = 10

Then find required value of x,

→ 10(2x-3) = 10

→ 20x-30 = 10

→ 20x = 10+30

→ 20x = 40

→ x = 40/20

→ [x = 2]

Hence, the value of x is 2.

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