A vertical light pole on a hillside casts a
shadow of 55 m long down the hill. If the
angle of elevation of the sun is 48.3° and the
angle of inclination of the hill is 21.4. Find
the height of the pole.

Answers

Answer 1

Answer: [tex]37.4\ m[/tex]

Step-by-step explanation:

Given length of shadow [tex]l=55\ m[/tex]

Hill inclination [tex]21.4^{\circ}[/tex]

Angle of elevation for sun [tex]48.3^{\circ}[/tex]

Suppose the length of the pole is [tex]h[/tex]

from the figure, and using sine rule. It can written

[tex]\Rightarrow \dfrac{55}{\sin 41.7^{\circ}}=\dfrac{h}{\sin 26.9^{\circ}}\\\\\Rightarrow h=55\cdot\dfrac{\sin 26.9^{\circ}}{\sin 41.7^{\circ}}\\\\\Rightarrow h=55\cdot 0.68011\\\Rightarrow h=37.40\ m[/tex]

A Vertical Light Pole On A Hillside Casts Ashadow Of 55 M Long Down The Hill. If Theangle Of Elevation

Related Questions

HELPPP PLEASE!!!

Salvador reads 12 books from the library each month for n months in a row. Write an expression to show how many books Salvador read in all. Then, find the number of books Salvador read if he read for 7 months.

Answers

Answers:

The expression is 12n

He reads 84 books in 7 months

==================================================

Explanation:

For 1 month, he has read 12*1 = 12 books

For 2 months, he has read 12*2 = 24 books

For 3 months, he has read 12*3 = 36 books

and so on

If we let n represent the number of months, then 12*n or 12n represents the number of books read after n months. The variable n is some placeholder for a positive whole number.

If we replaced n with say n = 7, then 12*n = 12*7 = 84 books are read in 7 months.

Salvador reads 12 books each months so for n months he reads 12n books. In 7 months, n=7, so he reads 12*7 which is 84 books

Find the perimeter of the square. Be sure to write the correct unit in your answer.


21 yd

Answers

Perimeter is the distance around the outside.

A square has 4 equal sides:

Perimeter = 21 x 4 = 84 yards

Answer: Perimeter = 84 yd

Explanation:

Perimeter of square = 4 × side

Side = 21 yd

Perimeter = 4 × 21

= 84 yd

Must click thanks and mark brainliest

Use inductive reasoning to predict the next three numbers in the pattern.
9 ,3 ,1 ,1/3, 1/9
Predict the next three numbers in the pattern.

Answers

Answer:

the next 3 numbers in the pattern are 1/27 , 1/81. , and 1/243

Step-by-step explanation:

to go from 9 to 3 you either have to subtract 6 or divide by 3. if you subtract 6 it doesn't match with the numbers. if you divide by 3 it matches. you can multiply 1/9 by 1/3 or divide by 3. it end with the same answer

We have that The Next 3 patterns are

1/27,1/81,1/243

From the Question we are told that

Pattern. 9 ,3 ,1 ,1/3, 1/9

Generally

Using in inductive reasoning the pattern progresses as a function of  dividing by 3

Therefore

The next three number are

[tex]x_1=\frac{1/9}{3}\\\\x_1=1/27[/tex]

[tex]x_2=\frac{1/27}{3}\\\\x_2=1/81[/tex]

[tex]x_3=\frac{1/81}{3}\\\\x_3=1/243[/tex]

Therefore

The Next 3 Numbers are

1/27,1/81,1/243

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Find two numbers whose sum is sixty eight and whose difference is twenty two

Answers

Answer:

45 and 23

Step-by-step explanation:

Let x equal the first number and y equal the second number.

We can set the following equations up with our information:

[tex]x+y=68[/tex]

[tex]x-y=22[/tex]

Adding the two equations together, we get:

[tex]2x=90[/tex]

Dividing by two, we receive [tex]x=45[/tex]

We can plug this into our first equation to get [tex]45+y=68[/tex].

Subtracting 45 from both sides, we get [tex]y=23[/tex].

The two numbers are 45 and 23, solved using system of equations.

What is a system of equations?

A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.

How to solve the question?

In the question, we are asked to find the two numbers, whose sum is 68 and the difference is 22.

We assume the two numbers to be x and y.

The sum of the two numbers is given to be 68.

This can be shown as an equation, x + y = 68 ... (i).

The difference of the two numbers is given to be 22.

This can be shown as an equation, x - y = 22 ... (ii).

Equations (i) and (ii) together makes a system of equation in the variables x and y.

To solve for the system of equation, we add (i) and (ii), to get:

x + y = 68

x - y = 22

_________

2x  = 90,

or, x = 45.

Substituting x = 45 in (i), we get:

x + y = 68,

or, 45 + y = 68,

or, y = 23.

Thus, the two numbers are 45 and 23, solved using system of equations.

Learn more about system of equations at

https://brainly.com/question/13729904

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Find the circumference of this circle
using 3 for TT.
C ~ [?]
24
C = id

Answers

Answer:

72

Step-by-step explanation:

The diameter is 24

pi is approximated by 3

The circumference is given by

C = pi *d

   = 3 * 24

    = 72

Find f(x)+g(x)
f(x)=x^2+6x-5
g(x)=-x^2-3x-1

Answers

Answer:

2x²+3x-6

Step-by-step explanation:

f(x)+g(x)

= x²+6x-5+x²-3x-1

=2x²+3x-6

1) Let f be the function defined by the
graph shown at right, with y = f(x).
a) What is the value of f(-9)?
-14-13-12-)1-10-9
10 11 12
b) How many solutions are there to
the equation f(x) = -2? (Just
state how many there are.)
c) State any and all intervals on which fis decreasing
d State any and all values of x for which fax>0. Ilse intervals to do this

Answers

I think it’s C I hope this helps

who can help me out with this one?​

Answers

Answer:

(x + 1)² + (y - 2)² = 9

Step-by-step explanation:

Equation of the circle with center (h, k):

(x - h)² + (y -k)² = r²  where r is radius

Center(-1 , 2) ;  r =3

(x - [-1])² + (y - 2)² = 3²

(x + 1)² + (y - 2)² = 9

What is the image point of (5, 1) after a translation right 5 units and down 2 units?
Submit Answer
PLS HELP ASAP

Answers

Answer:

(10,-1)

Step-by-step explanation:

A translation to the right is (x+5)

A translation down 2 is (y-2)

(5+5, 1-2)

(10,-1)

Answer:

(10, - 1 )

Step-by-step explanation:

A translation right 5 units means add 5 to the x- coordinate

A translation down 2 units means subtract 2 from the y- coordinate

(5, 1 ) → (5 + 5, 1 - 2 ) → (10, - 1 )

Triangle ABC is translated right 8 units and down 15 units to triangle XYZ. Triangle ABC
has these angle measures:

m∠A=45∘
m∠B=53∘
m∠C=82∘

What is the measure of angle Y?

Answers

9514 1404 393

Answer:

  53°

Step-by-step explanation:

The names of the triangles indicate that angle B corresponds to angle Y. Translation does not affect side lengths or angle measures, so angle Y is the same measure as angle B.

  m∠Y = 53°

Answer: 53

Step-by-step explanation:


Need help ASAP plz

Answers

Answer:

C) postulate

An axiom or a postulate is an accepted statement of fact.

OAmalOHopeO

Answer:

Im pretty sure its definition

A company wants to determine the level of interest among its employees for an annual summer picnic. The company wants to survey
200 employees.
What is the best way to randomly choose these 200 employees?

Answers

Answer: Use employee identification numbers to randomly select 200 employees

Step-by-step explanation:

Random sampling refers to a sampling technique whereby each sample has an equal chance of being selected. It is an unbiased representation of the entire population and this is vital in drawing conclusion.

From the options given, the best way to randomly choose these 200 employees will be to use employee identification numbers to randomly select 200 employees.


The diameter of a cylinder is 4 m. If the height is triple the radius, which is the closest to the
?volume of the cylinder
75.40 m3 o
251.33 m3 o
100.53 m3 o
613.19 m3 o
WILL MARK BRAINLIEST OR WHATEVER NEEDED ASAP

Answers

Answer:

A. 75.40 m³

Step-by-step explanation:

Diameter of cylinder (d) = 4 m

Radius (r) = ½(d) = ½(4) = 2 m

Height (h) = 3 × r = 3 × 2 = 6 m

Volume of cylinder = πr²h

Substitute the values

Volume of cylinder = π*2²*6

Volume of cylinder = π*4*6

Volume = π*24

Volume = 75.40 m³

factorize: xy-3x - 5y + 15

Answers

Answer:

Step-by-step explanation:

xy-3x-5y+15

x(y-3)-5(y-3)

(y-3)(x-5)

Instructions: Find the missing side of the triangle.
25
20
х
X =

Answers

Answer:

x = 15

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 20² = 25²

x² + 400 = 625 ( subtract 400 from both sides )

x² = 225 ( take the square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

the expression below is a factorization of what trimonial (5x+6)(3x-2)

Answers

Answer:

[tex]15x^2 + 8x -12[/tex]

Step-by-step explanation:

(5x+6)(3x-2)

"foil" it out

F: 5x * 3x  = 15x^2

O: 5x * -2  = -10x

I: 6*3x = 18x

L: 6 * -2 = -12

Answer:

15x² + 8x - 12

Step-by-step explanation:

(5x + 6)(3x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

5x(3x - 2) + 6(3x - 2) ← distribute both parenthesis

= 15x² - 10x + 18x - 12 ← collect like terms

= 15x² + 8x - 12

Which polygon has an interior angle sum of 1080°?

Answers

Answer:

its octagon. first and last one it has total 8 sides

The polygon with an interior angle sum of 1080° is an octagon

find the third proportional of 3 5 7

Answers

Answer: Third proportion is 21/5.

Step-by-step explanation:

Let the proportion be x

so,

3:5:x:7

so

3:5 = x:7

or, 3/5 = x/7

or, 21 = 5x

or, x = 21/5

Choose the correct description of the graph of the compound inequality:

x-3<-9 or x+5>equal to 12

Answers

Answer:

C

Step-by-step explanation:

x - 3 < -9

simplifies to x < -6, which is to the left with an open circle

x + 5> 12

simplifies to x > 7, which is to the right a closed circle

Need help ASAP please

Answers

Answer:

10  

Step-by-step explanation:

1. AB

2 BC

3. CD

4. DE  

5. AC  

6. B D

7.CE

8.AD

9.BE

10. A E

write an inequality and show on a number line all numbers greater (-3) but less than equal to3

Answers

Answer:

-3<x<_3

You plot this on a number line by writing and open circle on -3 and drawing and arrow from that open circle all the way until 3 and them draw a closed circle on 3.

Step-by-step explanation:

I don't need a language ABC​

Answers

Answer:

yes

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

can i get some help please

Answers

Answer:

28.26

Step-by-step explanation:

We want to find the area of the circle shown.

We can calculate the area of a circle using the formula A = πr²

where r = radius

The circle shown has a given diameter of 6

We want the radius.

To convert diameter to radius simply divide the measure of the radius by 2

So radius = 6 / 2 = 3

Now to find the area we simply plug in the value of the radius into the area of a circle formula

Area of a circle: A = πr²

r = 3

( Note that the question says to use 3.14 for π )

So π = 3.14

* Substitute values *

A = (3.14)(3)²

3² = 9

(3.14)(9) = 28.26

A = 28.26

And we are done!

When 12% discount is given a calculator is sold for Rs 1760 find the marked price of the calculator.​

Answers

Answer:

- Hello Risap!

[tex] \large{ \red{\tt{❃ } \: \blue{ PROVIDED}}}[/tex] : Discount % = 12% & Selling price [ SP ] = Rs 1760

[tex] \large{ \tt{ \red{❀ \: \blue{TO \: FIND}}}}[/tex] : Marked price of the calculator [ MP ]

[tex] \large{ \tt{ \green❊ \pink { \: S \: O \: L \: U \: T \: I \: O \: N} \green { \: ❊}}}[/tex]

[tex] \large {\tt{✢ \: SP = MP - dis\% \: of \: MP}}[/tex]

[tex] \large{ \tt{⟶ \: 1760 = MP - 12\% \: of \: mp}}[/tex]

[tex] \large{ \tt{⟶ \: 1760 = MP - \frac{12}{100} \: mp }}[/tex]

[tex] \large{ \tt{⟶ \: 1760 = \frac{100 \: MP - 12 \: mp}{100} }}[/tex]

[tex] \large{ \tt{⟶ \: 88 \: MP = 176000}}[/tex]

[tex] \large{ \tt{⟶ \: MP= \frac{176000}{88} }}[/tex]

[tex] \large{ \tt{⟶ \: MP = Rs \: 2000}}[/tex]

[tex] \large{ \boxed{ \boxed{ \tt{⤳ \: OUR \: FINAL \: ANSWER : \boxed{ \red{ \tt{MP = Rs \: 2000}}}}}}}[/tex]

Hope this helps! Let me know if you have any other questions regarding my answer and also , notify me if you need any other help! :)

I don’t know what to write but ye I need help with this question. Thanks

Answers

Answer: the first table.

Step-by-step explanation:

The terms in the domain (x) should have only one range (y)

Answer:

A) x: -3, 0, -2, 8

    y: -1, 0, -1, 1

Step-by-step explanation:

Function has only one output for each input.

OAmalOHopeO

ef is the median of trapezoid abcd (please explain the answer im so confused lol)

Answers

Step-by-step explanation:

Okay, so...

The Median of a trapezoid is directly in the middle. For some weird mathimatical reason you won't ever need to know unless it's on an exam or you become a math major, its midsegment is the average of the top length and the bottom length.

In other words,

EF = ( BC + AD ) / 2

So for part 1, we can use that equation to find x.

[tex]EF = ( BC + AD ) / 2[/tex]

Insert known equations.

[tex]4x-18=[(x+12)+(3x-4)]/2[/tex]

Simplify within parentheses.

[tex]4x-18=[x+12+3x-4]/2[/tex]

[tex]4x-18=[x+3x+12-4]/2[/tex]

Add.

[tex]4x-18=[4x+8]/2[/tex]

Divide.

[tex]4x-18=2x+4[/tex]

Simplify.

[tex](4x-2x) +(-18+18)=(2x-2x)+(4+18)[/tex]

[tex]2x=22[/tex]

Divide both sides by 2.

[tex]x=11[/tex]

Part 2 is a lot easier now. All we have to do is plug in 11 for x.

[tex]BC =x+12[/tex]

[tex]BC = 11+12[/tex]

[tex]BC = 23[/tex]

-

[tex]AD = 4x-18[/tex]

[tex]AD = 4(11)-18[/tex]

[tex]AD = 44-18[/tex]

[tex]AD = 26[/tex]

-

[tex]EF = 3x-4[/tex]

[tex]EF = 3(11)-4[/tex]

[tex]EF = 33-4[/tex]

[tex]EF = 29[/tex]

Answer:

Part I: x = 11

Part II:

BC = 23AD = 26EF = 29

Complete the equation to represent finding x, the greater integer. x(x – ) = 143 What is the greater integer?

Answers

Answer:

[tex]x * (x - 2) = 143[/tex]

Where [tex]x = 13[/tex]

Step-by-step explanation:

Given

[tex]x (x - \_) = 143[/tex]

Required

Complete the blank

The complete question implies that the product include 2 consecutive odd numbers.

Two numbers whose products equal 143 are: 11 and 13

i.e. [tex]11 * 13 = 143[/tex]

So, we have:

[tex]x * (x - \_) = 13 * 11[/tex]

By comparison, we have:

[tex]x = 13[/tex]

[tex]x - \_ = 11[/tex]

Collect like terms

[tex]\_ = x - 11[/tex]

Substitute 13 for x

[tex]\_ = 13 - 11[/tex]

[tex]\_ = 2[/tex]

So, the complete equation is:

[tex]x * (x - 2) = 143[/tex]

Where [tex]x = 13[/tex]

Answer:

2

and

13

Step-by-step explanation:

Got it right on edge.

(PLEASE HELP you don't have to graph I just need the equations) Dr. Gilmore just got his PhD, and he wants to print copies of his thesis in hardcover book
format. He could use Belmont Printing, paying a setup fee of $40 and $4 for every book
printed. Alternately, he could go through Fairfax University, paying an up-front fee of $30
and $6 per book. It turns out that, given the number of books Dr. Gilmore wants to print, the
two options cost the same amount. How many books is that?
Write a system of equations, graph them, and type the solution.

Answers

the answer is B
yeah yeah that’s what she was saying she didn’t yyyyyyyyu

Given two consecutive integers whose sum is 45, find the smaller of the two integers.

Answers

Answer:

22 and 23

Step-by-step explanation:

let two consecutive number be

x and x+1

now,according to the question

x+x+1=45

or,2x=45-1

or,2x=44

or,x=44/2

:-x=22

Hence, the two consecutive numbers are

22 and 23

1)An average American human lives about 78.74 years. A survey gave an average time spent going to the bathroom to be 102 minutes per week. If there are 52 weeks in a year, 7 days in a week and 1 day is 24 hours, then how many minutes do Americans spend on the toilet in their life time?

2)How many minutes have you spent on going to the bathroom if you are at the age of 16?​

Answers

1) Americans spend 418,784.358 minutes on the toilet in their life time.

2) 85,096.56 minutes if you are at the age of 16.
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