What the heck guys please help me

The following is a parallelogram solve for the variables

Andrews [41]

X = 66 degrees. (Co interior angles are supplementary, add up to 180)

2y + 4 = y + 7
2y - y = 7 - 4
Y = 3

6 0

3 years ago

At a baseball game, a vender sold a combined total of 104 sodas and hot dogs. the number of sodas sold was three times the numbe

Reil [10]

You have to set up a system of equations

x+y=104
3x-y=104

Sodas = 78
Hotdogs = 26

7 0

3 years ago

Anna needs 6 pints of milk to make yogurt. How many cups of milk does Anna need?

kupik [55]

Answer:

Anna needs 12 cups.

5 0

3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

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 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

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

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

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

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

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

$\displaystyle A''=2\pi+\frac{16}{r^3}$

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

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

Answer key says 50, but i have no idea how to get it. can anyone please help me?

Lady_Fox [76]

Answer:

x=50

Step-by-step explanation:

note that 40% is 2/5

Therefore, 30 tomatoes is 1- 2/5 = 3/5

3/5 of the tomatoes last year is 30

lets say tomatoes = x

3/5 x = 30

divide by 3 on both sides

1/5 x = 10

multiply by 5 on both sides

x=50

:D

hope it helped :D

6 0

3 years ago

Read 2 more answers