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Mazyrski [523]
3 years ago
10

A safety regulation states that the maximum angle of elevation for a rescue ladder is 72º. A fire department's longest

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
6 0

Answer:

  110sin(72°) feet

Step-by-step explanation:

In the right triangle with the 110 ft ladder as the hypotenuse, the side opposite the 72° angle represents the maximum height the ladder will reach. The definition of the sine function tells you ...

  Sin = Opposite/Hypotenuse

so the Opposite side will be ...

  ladder height = (110 ft)sin(72°)

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Can someone help me in this plssss I really need it
kompoz [17]

Answer:

\boxed{-3xy^{2}\sqrt [3] {2x^{2}}}

Step-by-step explanation:

Your expression is

\sqrt [3] {-54x^{5}y^{6}}

Here's how I would simplify it.

\begin{array}{rcll}\sqrt [3] {-54x^{5}y^{6}} & = & \sqrt [3] {(-1)^{3}\times 2 \times 27 \times x^{2} \times x^{3} \times y^{6}} & \text{Factored the cubes}\\& = & \sqrt [3] {(-1)^{3} \times 3^{3}\times x^{3} \times y^{6}\times 2 \times x^{2}} & \text{Grouped the cubes}\\\end{array}

\begin{array}{rcll}& = & \sqrt [3] {(-1)^{3} \times {3^{3}\times x^{3} \times y^{6}}} \times\sqrt [3] { 2 \times x^{2}} & \text{Separated the cubes}\\&=& \mathbf{-3xy^{2}\sqrt [3] {2x^{2}}} & \text{Took cube roots}\\\end{array}

\text{The simplified expression is $\boxed{\mathbf{-3xy^{2}\sqrt [3] {2x^{2}}}}$}

6 0
3 years ago
Given three points A(-7, 1), B(m, 6) and P(-1, n). If the point P divides AB internally in the ratio of 3: 2, find the values of
vesna_86 [32]

Answer:

m = 3 , n = 4

Step-by-step explanation:

<u>Using Section Formula.</u>

<u />If \ the \ line \ segment \ AB \ where  \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \  the \ points \  of \  P  \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}<u />

   Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b  = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x =  -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3<u />

  y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4

<u />

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3 years ago
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See attached photo for answer.

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a) Draw the axis:x-axis is horizontal, y-axis is vertical
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That is it.

2)
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