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Juliette [100K]
3 years ago
10

how far from the base of a building must the bottom of a 15 foot ladder sit for it to make a 52 angle with the ground

Mathematics
1 answer:
Morgarella [4.7K]3 years ago
4 0

Answer:

9.23 ft

Step-by-step explanation:

Right triangle = cos 52 degrees = adjacent side/hypotenuse

Cos (52 degrees) = 0.615661

0.615661 = x/15

(0.615661)*(15) = x

x = 9.23 ft

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What is the volume of a square prism that is 4 centimeters by 4 centimeters by 8 centimeters
My name is Ann [436]

Answer:

138 is the answer

Step-by-step explanation:

128 square

6 0
3 years ago
4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia
Ad libitum [116K]

The <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its <em>standard</em> form from the coordinates of the foci and a <em>general</em> equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the <em>general</em> equation of the circle into its <em>standard</em> form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0​

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (<em>semi-major</em> distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

#SPJ1

5 0
2 years ago
The perimeter of the picture frame is 38 inches. The width of the frame is 7 inches, what is the length?
o-na [289]

Answer:

12 inches

Step-by-step explanation:

So you know that the perimeter of a picture frame (a rectangle) is 2 widths plus 2 lengths.

Let x= lengths and w= widths

From the question we already know that w=7, so we can set up an equation that says:

2x + 2w = 38

2x + 2(7) = 38

2x+14 = 38

2x +14 -14 = 38-14

2x = 24

2x/2 = 24/2

x= 12

Since x= lengths =12

the length of the frame is 12 inches.

7 0
3 years ago
HELP WILL GIVE BRAIN!!!
postnew [5]

Answer:

8/5

Step-by-step explanation:

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The equation would be y=2/3x+300
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