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lidiya [134]
3 years ago
10

A painter has a 24 foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet

from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder sanely reach?
Mathematics
1 answer:
Lana71 [14]3 years ago
4 0

Answer:

The ladder can reach a height of 22.6 feet.  

Step-by-step explanation:

In order to find the height that the ladder can reach, you need to use the Pythagorean Theorem.  The Pythagorean Theorem assumes that the house to the ground will form a right triangle and the leaning ladder is the hypotenuse.  Using the formula:  a² + b² = c², we can plug in the values that we know and solve for the missing variable.  In this case we know the base of the triangle 'b' and the hypotenuse 'c':  a² + 8² = 24² or a² + 64 = 576.  To solve for a, we must first subtract 64 from both sides:  a² + 64 - 64 = 576 - 64 or a² = 512.  In order to find just the value of 'a', which represents the height, we need to take the square root of both sides:  √a² = √512 or a ≈ 22.6 feet.

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<h3>How to determie the equation of the cross-section?</h3>

The given parameters are:

Width = 6 feet

Depth = 1.5 feet

Express the width the sum of two equal numbers

Width = 3 + 3

The above means that, the equation of the cross section passes through the x-axis at:

x = -3 and 3

So, we have:

y = a(x - 3) * (x + 3)

Express as the difference of two squares

y = a(x^2 - 9)

The depth is 1.5.

This is represented as: (x,y) =(0,-1.5)

So, we have:

-1.5 = a(0^2 - 9)

Evaluate the exponent

-1.5 = -9a

Divide both sides by -9

a = 1/6

Substitute 1/6 for a in y = a(x^2 - 9)

y = 1/6(x^2 - 9)

Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)

Read more about quadratic functions at:

brainly.com/question/1497716

7 0
2 years ago
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storchak [24]
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Find the x- and y-intercepts of the graph of – 7x+ y = 19. State your answers as
mafiozo [28]

Answer:

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Mr. kelly uses an expression to represent the perimeter of a square, rewrite the expression to represent the length of a side of
sukhopar [10]

Answer:

therefore the side of the square is 2x + 5.

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