Answer:
4/5
Step-by-step explanation:
Sin = Opposite / Hypotenuse
Note that hypotenuse = longest side
We want to find sinФ
The opposite side length of angle "Ф" has a length of 8 and the longest side or hypotenuse has a length of 10
So sinФ would equal 8/10 which can be simplified to 4/5
Answer:
128 servings
Step-by-step explanation:
5/4 cups of milk for 10 servings is equal to 1/8 cup per 1 serving
there are 16 cups in a gallon
let 'n' = # servings in a gallon
so 1/8 : 1 is 16 : n
1/8n = 16
n = 16(8)
n = 128
Answer:
x=1 is the correct answer
Answer:



Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
The procedure to optimize a function (find its maximum or minimum) consists in
:
- Produce a function which depends on only one variable
- Compute the first derivative and set it equal to 0
- Find the values for the variable, called critical points
- Compute the second derivative
- Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum
We know a cylinder has a volume of 4
. The volume of a cylinder is given by

Equating it to 4

Let's solve for h

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

Replacing the formula of h

Simplifying

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

Rearranging

Solving for r

![\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%7D%7B%5Cpi%20%7D%7D%5Capprox%201.084%5C%20feet)
Computing h

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.
The minimum area is


A rectangular garden is 45 ft wide and 70 ft long. On a blueprint, the width is 9 in. Identify the length on the blueprint.
<h2><u>
14in </u></h2>