Which of these numbers are irrational?

The angle of elevation of the top of a tower from two points 121 m and 144 m away from the foot of the tower on th same side are

Dennis_Churaev [7]

Answer:

132 m

Step-by-step explanation:

Refer to attachment for figure.

In smaller triangle with angle theta , we have ,

⇒ tanθ = p/b

⇒ tanθ = h/121m

⇒ tanθ = h/121 m

In triangle with angle 90-∅

⇒ tan(90-θ) = p/b

⇒ cot θ = h/144 m

Multiplying these two ,

=> tanθ . cotθ = h/121 m × h/144m

=> 1 = h²/ (121 m × 144m )

=> h² = 121m × 144m

=> h= √ ( 121m × 144m)

=> h = 11m × 12m

=> h = 132 m

6 0

3 years ago

Find the x- and y-intercepts of the line that passes through ( 3, -8) and ( -4, 13).

Ivenika [448]

Answer:

x-intercept = 1/3, y-intercept = 1

Step-by-step explanation:

y = mx + b (general equation where m=gradient, b=constant)

-8 = 3m + b (from first pair of coordinates)

13 = -4m + b (from second pair of coordinates)

3m + b - (-4m + b) = -8 - 13

7m = -21

m = -3

Using one of the linear equations above:

-8 = 3(-3) + b

-8 = -9 + b

b = 1

Therefore, the linear equation is: y = -3x + 1

To find x-intercept:

Let y = 0

0 = -3x + 1

-1 = -3x

x = 1/3

To find y-intercept:

Let x = 0

y = -3(0) + 1

y = 1

Therefore the x-intercept = 1/3 and y-intercept = 1 for the line that passes through (3, -8) and (-4, 13)

5 0

3 years ago

What is the value of 'x' in the equation shown below? 2 (x + 8) - 4x = 10 x + 4

Nat2105 [25]

Answer:

x=1

Step-by-step explanation:

2x+16-4x=10x+4

-2x+16=10x+4

16-4=10x+2x

12=12x

1=x

5 0

3 years ago

Read 2 more answers

PLZ, help me with this question.

zhannawk [14.2K]

Answer:

catastrophic

Step-by-step explanation:

Cuz it means "destructive"

5 0

3 years ago

Read 2 more answers

#16 i

Vlad1618 [11]

The tuition is an illustration of a linear function.

The cost of tuition and fees in the academic year 2023-2024, is $12260

Let the number of academic years after 2014-2015 academic year be x.

So, we have:

$\mathbf{(x,y) \to (0,9200)(5,10900)}$

A linear function is represented as:

$\mathbf{y = mx + b}$

Where m represents the slope (i.e. constant rate), and b represents the y-intercept (i.e. the value of y when x = 0)

So, we have:

$\mathbf{10900 = 5m + 9200}$

Subtract 9200 from both sides

$\mathbf{1700 = 5m}$

Divide both sides by 5

$\mathbf{340 = m}$

So, we have:

$\mathbf{m =340 }$

The function becomes

$\mathbf{y = mx + b}$

$\mathbf{y = 340x + 9200}$

In the academic year 2023-2024, x = 9.

So, we have:

$\mathbf{y = 340x + 9200}$

$\mathbf{y = 340 \times 9 + 9200}$

$\mathbf{y = 3060 + 9200}$

$\mathbf{y = 12260}$

Hence, the cost of tuition and fees is $12260