What is the vertical shift of the function? f(x)= sin x

how high up a vertical wall will a 26-foot-long extension ladder reach if its base is placed 10 feet away from the wall

allsm [11]

Answer:

24ft high

Step-by-step explanation:

Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.

<h3><u>The Pythagorean Theorem</u></h3>

For any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies. The Pythagorean Theorem describes the relationship between side lengths as $a^2+b^2=c^2$ , where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle). Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".

Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.

<h3><u>Substituting known values, and solving the equation</u></h3><h3> $a^2+b^2=c^2$ </h3>

Substitute known values, and simplify...

$a^2+(10)^2=(26)^2$

$a^2+100=676$

Subtract 100 from both sides...

$(a^2+100)-100=(676)-100$

$a^2=576$

Apply the square root property...

$\sqrt{a^2}=\pm \sqrt{576}$

$a=\pm 24$

$a=24$ or $a=- 24$

Since the distance height the ladder will reach is not a negative number, we reject the negative solution. Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.

8 0

2 years ago

The graph of a function is shown:

exis [7]

Answer:

C, (-3, -2, 3)

Step-by-step explanation:

I literally just had this question and i got a 100. You just find what the points are, and choose the y-axis point because it's the output, like the x-axis point is the input. So for starters, we can look at the point in the upper right square corner on the grid. You would go to the left 3 times, along the x-axis, and it would be -3. Then you would go up 2 times, along the y-axis, and it would be positive 2. So the plot for that point is (-3, 2) but we want the output which is the y-axis so it would be 2. Do the same with all of the points. [you can already rule out the first 2 choices because that's giving all of the points, not just the outputs] That leaves you with the bottom 2 and only one of the choices has the positive 2 which we already found. Hence, the answer is C. Trust me, it's not hard, i didn't have to read anything, i just figured it out. And if i can, you can. You got this!

5 0

3 years ago

Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

Reil [10]

To solve for the surface area of the pyramid, we make use of the formula:

A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

Substituting the given values into the equation:

A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

Therefore the surface area of the pyramid is about 20,149 mm^2.

8 0

3 years ago

This might take forever but I’ll mark u as brainlist!! This is due tomorrow lol

AysviL [449]

The vertex is x and the y intercept is 2

4 0

3 years ago

20 + 23 - 34 + 2 x 4^2

olasank [31]

20 + 23 = 43
43 - 34 = 9
9 + 2 = 11
11 x (4 x 4) = 11 x 16
11 x 16 = 176

8 0

4 years ago

What is the vertical shift of the function? f(x)= sin x - 3/2