Two buildings are 12m apart on the same horizontal level. From the top of the taller building, the angle of depression of the bottom of the shorter building is 48degrees and from the bottom, the angle of of elevation of the top of the shorter building is 36 degrees. Calculate the difference in the heights of the buildings

Answers

Answer 1

Answer:

4.61 m

Step-by-step explanation:

The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building

Using trig ratios

tan48° = H/d where H = height of taller building and d = their distance apart = 12 m

H = dtan48° = 12tan48° = 13.33 m

Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°

Using trig ratios

tan36° = h/d where h = height of shorter building

h =dtan36° = 12tan36° = 8.72 m

Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m


Related Questions

Suppose you are facing west. First you turn 180 degrees to the left. Then turn 45 degrees to the right. Then turn 90 degrees to the left. Then swap left with right. Then turn 180 degrees to the right. What direction are you facing now, if we are marking the directions with letters (North - N, South - S, East - E, West - W).

Answers

Answer:

we would be facing the North West

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point) [tex]y=\frac{7}{x^{2} } +10[/tex]

Answers

Answer:

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Step-by-step explanation:

Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:

[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]

[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]

Thus,

[tex]f(x) = 7\cdot x + 10[/tex]

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Why Norway and Switzerland have high HDI value?

Answers

Step-by-step explanation:

because of the revenue it recieves from North sea oil and gas

1. Classify the following numbers as rational or irrational.
a) √45 b) √55 c) √196 d) √576 e) √27

Can u guys answer this question pls

Answers

Answer:

a) irrational

b) irrational

c) rational

d) rational

e) irrational

Note:

rational numbers are numbers that can be expressed in fractions.

irrational numbers are numbers that cannot be expressed in fractions i.e. they are never-ending-non-repeating decimals. examples √2, pi etc.

The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2

Answers

Answer:

[tex]4x^2-21x-2[/tex]

Step-by-step explanation:

Given that:

Difference of two trinomials is [tex]x^2 - 10x + 2[/tex]

One of the two trinomials is  [tex]3x^2 - 11x - 4[/tex]

To find:

The other trinomial = ?

Four options are:

[tex]2x2 - x - 2 \\2x2 + x + 6 \\4x2 + 21x + 6\\ 4x2 - 21x - 2[/tex]

Solution:

Let the two trinomials be A and B.

Given A - B = [tex]x^2 - 10x + 2[/tex]

B = [tex]3x^2 - 11x - 4[/tex]

We have to find the other trinomial A.

A - B = [tex]x^2 - 10x + 2[/tex]

A - ([tex]3x^2 - 11x - 4[/tex]) = [tex]x^2 - 10x + 2[/tex]

[tex]\Rightarrow[/tex] A = [tex]x^2 - 10x + 2[/tex] + ([tex]3x^2 - 11x - 4[/tex])

[tex]\Rightarrow[/tex] A = [tex]4x^2-21x-2[/tex]

So, the correct answer is [tex]4x^2-21x-2[/tex].

Please help! Change 3/8 to a decimal fraction.

Answers

Answer:

0.375

Step-by-step explanation:

0.125 x 3 = 0.375

Answer:

0.375

Step-by-step explanation:

3 x 125

8 x 125

=

375

1000

=

0.375

Other sample problem:

5 = 5×125 = 625 = 0.625

8         8×125         1000

Hope this helps, have a good day :)

Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline. Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline. Approximately how many gallons of gasoline are saved on a 300-mile trip if the car is driven at a rate of 45 miles per hour instead of at 70 miles per hour?
A) 2
B) 3
C) 12
D) 20

Answers

Answer:

B) 3

Step-by-step explanation:

Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline.

In 300 miles journey the gallon of gasoline consumed will be

300/26= 11.54 gallons

Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline.

In 300 miles journey the gallon of gasoline consumed will be

300/36= 8.33 gallons

The amount of gasoline saved= 11.54-8.33

The amount of gasoline saved= 3.21

approximately 3 gallons of gasoline

Find the value of z. A. 141 B. 110 C. 80 D. 100

Answers

Answer:

B. 110

Step-by-step explanation:

z is supplemental to 70°, so the add up to 180°

z+70°=180°

z=180°-70°

z=110°

Option B is correct. The required value of z is 110 degrees

Supplementary angles are angles summing up to 180 degrees. According to the circle geometry, we can see that z and 70 degrees lie on the same line, this shows that both angles are supplementary.

Since supplementary angles sum up to 180degrees, hence;

[tex]z + 70 = 180\\[/tex]

Subtract 70 from both sides

[tex]z+70-70=180-70\\z=110^0[/tex]

Hence the value of z is 70 degrees

Learn more here: https://brainly.com/question/22261921

Tatenda takes ttt seconds to mow a square meter of lawn and Ciara takes ccc seconds to mow a square meter of lawn. Tatenda mows 700700700 square meters of lawn per week and Ciara mows 750750750 square meters of lawn per week. Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 444 weeks? Choose 2 answers: Choose 2 answers: (Choice A) A 4(750c-700t)4(750c−700t)4, left parenthesis, 750, c, minus, 700, t, right parenthesis (Choice B) B 3000c+2800t3000c+2800t3000, c, plus, 2800, t (Choice C) C 2800t-3000c2800t−3000c2800, t, minus, 3000, c (Choice D) D 4(700t-750c)4(700t−750c)4, left parenthesis, 700, t, minus, 750, c, right parenthesis (Choice E) E 4(700t+750c)4(700t+750c)

Answers

Answer:

C.) 4(750c-700t) ; D.) 2800t - 3000c

Step-by-step explanation:

Time taken :

Tatenda = t sec/m^2

Ciara = c sec/m^2

Tatenda = 700m^2 per week

Ciara = 750m^2 per week

Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 4

Total Time taken over four weeks :

Tatenda = 4(t * 700) = 4(700c)

Ciara = 4(c * 750) = 4(750c )

Number of seconds Tatenda spends more than Ciara : meaning Tatenda spends more seconds than

Tatenda - Ciara

4(700t) - 4(750c) = 4(700t - 750c)

4(700t - 750c)

Or

4(700t - 750c) = 2800t - 3000c

2800t - 3000c

Top Hat Soda has 300,000 milliliters of cola to bottle. Each bottle holds 500 milliliters. How many bottles will the cola fill?

Answers

Answer:600

Step-by-step explanation:

300,000/ 500 =600

Can someone please explain the answers?

Answers

Answer:

3. Fifth degree polynomials are also known as quintic polynomials. Quintics have these characteristics: One to five roots. Zero to four extrema.

4. x = -5 or x = 0 or x = 5

Step-by-step explanation:

Solve for x:

6 x^5 - 150 x^3 = 0

The left hand side factors into a product with four terms:

6 x^3 (x - 5) (x + 5) = 0

Divide both sides by 6:

x^3 (x - 5) (x + 5) = 0

Split into three equations:

x - 5 = 0 or x^3 = 0 or x + 5 = 0

Add 5 to both sides:

x = 5 or x^3 = 0 or x + 5 = 0

Taking cube roots gives 0 times the third roots of unity:

x = 5 or x = 0 or x = 0 or x = 0 or x + 5 = 0

Subtract 5 from both sides:

x = 5 or x = 0 or x = 0 or x = 0 or x = -5

There are {2} duplicate solutions:

Answer: x = -5 or x = 0 or x = 5

Find combinations using a school cafeterias meal! (20 POINTS! PLEASE HELP) Fruits: Apples, Bananas, and Grapes. Vegetables: Cauliflower, Carrot, and Corn. Protein: Green beans, Salmon, and Almonds. List all possible combinations and count the total number of possibilities.

Answers

Answer:

1. Apples, Cauliflower, Green beans

2. Apples, Cauliflower, Salmon

...

27. Grapes, Corn, Almonds

Step-by-step explanation:

There are 3x3x3 = 27 combinations possible. You can enumerate them systematically.

Answer:

There are 27 combinations possible.

Hope this helps!

Answer ASAP, will give brainliest

Answers

Answer:

Step-by-step explanation:

1) Diagonal bisect the angles of Rhombus

∠CAB = ∠CAD

CAB = 71

2) ∠DAB = ∠CAB + ∠CAD

 ∠DAB = 71 + 71 = 142

In Rhombus, adjacent angles are supplementary

∠DAB + ∠ABC = 180

142 + ∠ABC = 180

           ∠ABC = 180 - 142

         ∠ABC = 38

3)  In rhombus, opposite angles are congruent

∠ADC = ∠ABC

∠ABC = 38

In rhombus, diagonal bisect angles

∠BDC = (1/2)*∠ADC

∠BDC= 38/2

BDC = 19

4) Diagonals bisect each other at 90

∠DEC = 90

5) Diagonals bisect each other

BE = DE

BE + DE = DB

7x -2 +7x -2 =24   {add like terms}

        14x - 4 =24

              14x = 24+4

              14x = 28

                 x = 28/14

                 x = 2 m

6) AB = 13m

BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m

In right angle ΔAEB,  {use Pythagorean theorem}

AE² + BE² = AB²

AE² + 12² = 13²

AE² + 144 = 169

         AE² = 169 - 144

         AE² = 25

         AE = √25

        AE = 5 m

Diagonals bisect each other

AE = EC

AC = 2*5

AC = 10 m

7)Side = 13 m

Perimeter = 4*side

                  = 4*13

 Perimeter = 52 m

8) d1 = AC = 10 m

   d2 = DB = 24 m

Area = [tex]\frac{d_{1}*d_{2}}{2}[/tex]

         [tex]=\frac{10*24}{2}\\[/tex]

          = 10 *12

          = 120 m²

need help please. Will give you 5-stars and a big thank you comrades

Answers

Answer:

first answer

Step-by-step explanation:

(8x³ - 22x² - 4) / (4x - 3)

when you do long division you get the first answer

Maggie drew lines of best fit for two scatter plots, as shown. Which statement best describes the placement of the lines Maggie drew?

Answers

Answer:

B. Only line B is a well-placed line of best fit.

Step-by-step explanation:

A good line of best fit is a line drawn to represent, as much as possible, all data points. As long as the data points are clustered along the line, and are not farther from each other, the line is a best fit for such data points.

Therefore, from the two lines drawn by Maggie, Line B seems to be the only well-placed line of best fit, as virtually all the data points are clustered along the line, compared to Line A. Line A only runs across 2 data points. The rest data points are scattered far apart from the line.

Therefore, the statement that best describes the placement of the line of best fit drawn by Maggie is: "B. Only line B is a well-placed line of best fit."

Answer:

Only line B

Step-by-step explanation:

Line A is too low on the graph to be best fit for the plot

Determine the standard deviation of the data below. (1, 2, 3, 4, 5)

Answers

Answer:

[tex]\sqrt{2}[/tex] or 1.414

Step-by-step explanation:

1) Find the mean. 1+2+3+4+5 = 15. 15/5= 3

2) For each data point, find the square of its distance to the mean. (4, 1, 0, 1, 4)

3) Sum the values from Step 2. 10

4) Divide by the number of data points. 10/5= 2

5) Take the square root. [tex]\sqrt{2}[/tex]

Answer:

the answer square root of 2! just did the test and got it right :)

Step-by-step explanation:

what is this expression in simplest form.(-11/2x+3)-2(-11/4x-5/2)​

Answers

Answer:

The simplest form of the given expression is 8.

Step-by-step explanation:

(-11/2x + 3) - 2(-11/4x - 5/2)

Distribute 2 to (-11/4x - 5/2)

(-11/2x + 3) - (-11/2x - 5)

Now, combine like terms. The terms with the x value will cancel each other out because a negative plus a positive of the same number will equal zero. For example, -2 + 2 = 0.

So, the expression in the simplest form is going to be 8. The x values have cancelled each other out so all there is left is the constant number which is 8.

pls help will give you good rating

Answers

Answer:

-1

Step-by-step explanation:

Question 1 of 18
The Waves and the Wolves are evenly matched baseball teams. When they
play, there is a 0.5 probability that the Waves will win. If they play 15 times,
what is the probability that the Waves will win 8 of the games? Round your
answer to the nearest tenth of a percent.
A. 9.2%
B. 4.2%
C. 15.3%
O D. 19.6%

Answers

I believe the answer is D 19.6 percent

Write each of the following in the simplest exponential form please help

Answers

Answer:

Step-by-step explanation:

[tex]a^{m}*a^{n} =a^{m+n}\\\\\\2^{3}*2^{5} = 2^{3+5} =2^{8}\\\\\\3^{2}*3^{4}=3^{2+4} = 3^{6}\\\\\\a^{2}*a^{5}=a^{2+5}=a^{7}[/tex]

I NEED HELP PLEASE !!!!

Answers

Answer:

No, all of her work is correct.

Step-by-step explanation:

Answer:

No, all of her work is correct.

Step-by-step explanation:

All of her work is correct.

The first step is showing factorization of √50

The second step is simplifying the factorization

The third step is simplifying the entire radical.

When you take a square root of a square, they cancel out, so:

√5² = 5

We multiply it with our leftover √2 and we get:

5√2

i need help please asap 10 points!

Answers

Answer:

1) Real Number

2)Whole Number

3)Irrational Number

4)Rational Number

5)Integers

6)Natural Numbers

find the value of tan(arcsin(1/2))

Answers

Answer:

0.577

Step-by-step explanation:

inv. sin (0.5) = 30

tan (30) = 0.577

The value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

What are trigonometric identities?

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Tan[tex](Sin^{-1}(1/2))[/tex]

[ Sin 30° = 1/2 ]

= Tan([tex]sin^{-1}sin30)[/tex])

= Tan 30°

= 0.58

Thus,

0.58 is the value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ2

find the product of the first 3 positive integers and then the first 5 negative integers.

Answers

Answer:

6 and -120

Step-by-step explanation:

The first 3 positive integers are 1, 2 and 3 and their product is 6, the first 5 negative integers are -1, -2, -3, -4 and -5 and their product is -120.

7 kids on the basketball team return sick from a weekend playing games at Lakenheath High school with a virus. The aggressive virus spreads at 130% each day. How long many days till 500 students are sick at school?

Answers

Answer:

It would take 6 days for 500 students to be affected.

Step-by-step explanation:

Given that:

1. Seven kids returned with the virus.

2. The aggressive virus spreads at 130% each day.

We want to find how many days until 500 students are infected by the virus.

First day:

7 students have the virus, 130% of 7 student will contract the virus again.

130% of 7 = (130/100) × 7

= 1.3 × 7 = 9.1 ≈ 9

9 new students are affected

New total affected = 7 + 9 = 16 students.

Day 2:

Affected = 1.3 × 16 = 20.8 ≈ 20

New total affected = 20 + 16 = 36

Day3

Affected = 1.3 × 36 = 46.8 ≈ 46

New total affected = 36 + 46 = 82

Day4

Affected = 1.3 × 82 = 106.6 ≈ 106

New total affected = 106 + 82 = 188

Day5

Affected = 1.3 × 188 = 244.4 ≈ 244

New total affected = 244 + 188 = 432

Day6

Affected = 1.3 × 432 = 561.6 ≈ 561

New total affected = 561 + 432 = 993

Therefore, it would take 6 days for 500 students to be affected.

Find the next three terms in the geometric sequence.

Answers

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

An isosceles triangle has two sides of equal length. The third side is five less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm what is the length of the third side?

Answers

Answer:

9

Step-by-step explanation:

We can set up a systems of equations to find the value of the third side.

Let's assume that [tex]x[/tex] is the length of both sides 1 and 2. Let's also assume that [tex]y[/tex] is the length of the third side.

We know that [tex]x + x + y = 23[/tex], and looking at the first clue we can make the equation [tex]y = 2x-5[/tex].

We can substitute y into the equation [tex]x + x + y = 23[/tex].

[tex]x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7[/tex]

So the length of the side that is the same as the second is 7.

Now we can plug this into the equation [tex]y = 2x-5[/tex] to find [tex]y[/tex].

[tex]y = 2(7) - 5\\\\y = 14-5\\\\y = 9[/tex]

Hope this helped!

Answer:

9 cm

Step-by-step explanation:

Let's say that the length of the 2 equal sides is x.

That means:

Side 1 = x

Side 2 = x

We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5

Side 3 = 2x-5

The perimeter is all sides together.

Side 1 + Side 2 + Side 3

We know the length of each side, so let's put that in instead.

x + x + 2x-5

Let's simplify this expression:

x + x + 2x - 5

2x + 2x - 5

4x - 5

We know the perimeter, 4x-5, is 23 cm.

4x - 5 = 23

4x = 28

x = 7

The third side is 2x-5. If x is 7...

2*7 - 5 = 14-5 = 9

Answer: 9 cm

1. Find the area of a triangle (PLEASE ONLY in CM²) 2. Seven squared equals seven times .........

Answers

Answer:

30 cm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 6 and h = 10 , thus

A = [tex]\frac{1}{2}[/tex] × 6 × 10 = 3 × 10 = 30 cm²

and 7² = 7 × 7 = 49

Answer:

1)        30 cm²

2) Seven squared equals seven times 7

Step-by-step explanation:

Base = 6 cm

Height = 10 cm

Area of triangle = [tex]\frac{1}{2}[/tex]*base * height

                          = [tex]\frac{1}{2} * 6 * 10[/tex]

                         = 3 * 10

                          = 30 cm²

2) 7² = 7 * 7

How to do this question plz answer me step by step plzz ​

Answers

Answer:

Hope it helps U can still ask me if u have confusions

Answer:

  60+16√30 cm² ≈ 147.64 cm²

Step-by-step explanation:

You can figure the height of the object from ...

  V = Bh

  120 cm^3 = (30 cm^2)h

  4 cm = h . . . . . divide by 30 cm^2

However, this is insufficient to tell you the surface area.

__

If you assume that the base is square, then its side length is

  A = s^2

  s = √A = √(30 cm^2) = (√30) cm

The lateral surface area can then be found from the perimeter of the base and the height

  LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2

The total surface area will be the sum of this lateral area and the area of the two bases:

 total area = 16√30 cm^2 +2·30 cm^2

 total area = (60 +16√30) cm^2 ≈ 147.64 cm^2

__

For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.

Write your answer in scientific notation.
(6.4 x 10^3 ) + (5.2 x 10^4 )

Answers

Answer:

5.84 x10.^4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

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