35.5 ft is the width of the room
The coordinates of the focus of the parabola are (4 , 0)
Step-by-step explanation:
The standard form of the equation of the parabola is
(x - h)² = 4p(y - k), where
- The vertex of the parabola is (h , k)
- The focus is (h , k + p)
- The directrix is at y = k - p
∵ The equation of the parabola is 12(y + 3) = (x - 4)²
- The form of the equation is (x - h)² = 4p(y - k), compare
between them to find h, k and p
∴ h = 4
∵ - k = 3
- Multiply both sides by -1
∴ k = -3
∵ 4p = 12
- Divide both sides by 4
∴ p = 3
∵ The coordinates of the focus are (h , k + p)
∵ h = 4 , k = -3 , p = 3
∴ k + p = -3 + 3
∴ k + p = 0
∴ The focus is (4 , 0)
The coordinates of the focus of the parabola are (4 , 0)
Learn more:
You can learn more about the equation of the parabola in brainly.com/question/9390381
#LearnwithBrainly
The ball will bounce 72 cm high if dropped from a height of 120 cm
<u>Solution:</u>
Given, The height that a ball bounces varies directly with the height from which it is dropped.
A certain ball bounces 30 cm when dropped from a height of 50 cm.
We have to find how high will the ball bounce if dropped from a height of 120 cm?
Now, according to given information,
When dropped from 50 cm ⇒ bounces 30 cm
Then, when dropped from 120 cm ⇒ bounces "n" cm
Now by Chris cross method, we get,

Hence, the ball bounces 72 cm high.
A would be your answer.
(I am going to assume that the set of numbers are multiplied by exponents.)
To solve you just need to calculate each one. Note that for positive exponents you move the decimal point to the right and negative exponents you move the decimal point to the left.

The first scientific notation would be equal to 2700 because you move the decimal point 3 places to the right, since the exponent is positive.

The second scientific notation would be equal to 0.00424 because you move the decimal point 3 places to the left, since the exponent is negative.

The third scientific notation would equal 470 because you move the decimal point 2 places to the right, since the exponent is positive.

The last scientific notation would equal 0.043 because you move the decimal point 2 places to the left, since the exponent is negative.
