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8 months ago

Mr. Haley is leaning a ladder against the side of his house to repair the roof.

Mathematics

1 answer:

natima [27]8 months ago

5 0

Answer:

15 ft

Explanation:

We can represent the situation with the following figure

Therefore, the length of the ladder is the hypotenuse of the right triangle formed, where the legs are 12 ft and 9 ft. Using the Pythagorean theorem, we can calculate the length of the ladder as

$\begin{gathered} Ladder=\sqrt{12^2+9^2} \\ Ladder=\sqrt{144+81} \\ Ladder=\sqrt{225} \\ Ladder=15 \end{gathered}$

Therefore, the length of the ladder is 15 ft

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The points (-4,r) and (2,-3) lie on a line with a slope-1. Find the missing coordinator r.?

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2 years ago

For questions 3 – 5, an airplane is heading south at an airspeed of 540 km/hr, but there is a wind blowing from the northeast at

GuDViN [60]

First, let's calculate the horizontal and vertical components of the wind speed (W) and the airplane speed (A), knowing that south is a bearing of 270° and northeast is a bearing of 45°:

$\begin{gathered} W_x=W\cos45°\\ \\ W_x=50\cdot0.707\\ \\ W_x=35.35\\ \\ \\ \\ W_y=W\sin45°\\ \\ W_y=50\cdot0.707\\ \\ W_y=35.35 \end{gathered}$ $\begin{gathered} A_x=A\cos270°\\ \\ A_x=540\cdot0\\ \\ A_x=0\\ \\ \\ \\ A_y=A\sin270°\\ \\ A_y=540\cdot(-1)\\ \\ A_y=-540 \end{gathered}$

Now, let's add the components of the same direction:

$\begin{gathered} V_x=W_x+A_x=35.35+0=35.35\\ \\ V_y=W_y+A_y=35.35-540=-504.65 \end{gathered}$

To find the resultant bearing (theta), we can use the formula below:

$\begin{gathered} \theta=\tan^{-1}(\frac{V_y}{V_x})\\ \\ \theta=\tan^{-1}(\frac{-504.65}{35.35})\\ \\ \theta=-86° \end{gathered}$

The angle -86° is equivalent to -86 + 360 = 274°.

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1 year ago

PLEASE HELP ME OUT..........

Vlad1618 [11]

Here is your answer

$\bold{x=12}$

REASON:

$Concept used$ : The opposite sides of a parallelogram are equal.

So, in above given figure

$3x+7=5x-17$ (measures of opposite sides)

$5x-3x= 17+7$

$2x= 24$

$x= 24/2$

$x= 12$

HOPE IT IS USEFUL

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3 years ago

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