Let x represent length of the slide.
We have been given that Ron is designing a new slide for the amusement park in town. The slide makes an angle of 39 with the ground. The top of the slide is to be 9 feet off the ground. We are asked to find the length of the slide.
The slide will make a right triangle with respect to ground, where length of the slide will be hypotenuse, and height of the slide will be perpendicular with ground.
We know that sine relates opposite side of right triangle with hypotenuse.
Upon rounding to nearest foot, we will get:
Therefore, the length of slide should be approximately 14 feet and option B is the correct choice.
Answer:
113.1 (113.0973355...)
Step-by-step explanation:
1. Use the sphere volume formula of π.
2. Divide 6 by 2 in order to get a radius of 3.
3. Substitute 3 in for r.
4. Cube the 3, you'll get 27.
5. Multiply 27 by Pi and 4/3.
6. You get 113.1 as a rough estimate, or 113.0973355... for a more exact number. If you leave it in Pi terms, it's 36π.
Using the vertex of a quadratic equation, it is found that the company should charge each customer $15 per day to maximize revenue.
<h3>What is the vertex of a quadratic equation?</h3>
A quadratic equation is modeled by:
The vertex is given by:
In which:
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, the number of bikes rented per day is given by:
n(p) = 300 - 10p.
Hence, the revenue function is given by:
R(n) = p x n(p)
R(n) = 300p - 10p².
Which is a quadratic function with coefficients a = -10, b = 300. Hence, the price in dollars that will maximize the revenue is given by:
More can be learned about the vertex of a quadratic equation at brainly.com/question/24737967
Answer:
see below
Step-by-step explanation:
length of arc = radius x angle (measured in radians)
minor arc = 3 x =
major arc = 3 x =
Remember that you can always multiply or divide BOTH the numerator and denominator
of the fraction by anything you want to. You just have to do exactly the same to both of
them.
The way to simplify a fraction is to divide both the numerator and denominator by their
greatest common factor.
Do you see all of those 'x's on the top and bottom ? The top and bottom can
both be divided by x-cubed.
<u>Numerator:</u>
Divide (-4³) by x³, and you have (-4) left.
<u>Denominator:</u>
Divide (x³ - 2x⁴) by x³, and you have (1 - 2x) left.
So, the simplified fraction is [ -4 / (1 - 2x) ].
That's a perfectly good answer, but you could make it look a little prettier
if you multiply the top and bottom both by -1 . Then it would be
4 / (2x - 1) .
Either one is fine.