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3 years ago

In base, rate, and percent problems, the word “of” points to this

Mathematics

1 answer:

Marysya12 [62]3 years ago

5 0

Answer:

The word "of" refers to multiplication.

Step-by-step explanation:

Multiplication is what to do in all word problems when we see the word "of"

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IN NEED OF MORE HELP AND THANK YOU IF YOU ANSWER

Lorico [155]

Answer:

512

Step-by-step explanation:

5.12 converted to a fraction is 512/100

3 0

2 years ago

Stefanie spends entire allowance one month she spends 1/2 of a on new clothes 1/4 on food 1/6 on movies and 1/12 on Music how mu

Komok [63]

Answer:

Option D: 1/3

Step-by-step explanation:

Let

x ------> the entire Stefanie's allowance

we know that

She spends on clothes (1/2)x

She spends on movies (1/6)x

To find out how much more does she spend on clothes that he does on movies, subtract the amount she spends on movies from the amount she spend on clothes

$\frac{1}{2}x-\frac{1}{6}x=\frac{2}{6}x$

Simplify

$\frac{1}{3}x$

therefore

She spends 1/3 more on clothes that he does on movies

4 0

2 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

2 years ago

Austin opened a bank account. He deposited $100 on Monday and $70 on Tuesday.

shutvik [7]

Answer:

22 weeks

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Can a linear function be continuous but not have a domain and range of all real numbers

ivolga24 [154]

"Mathematically yes - but from an engineering point no. And micro black holes are very unstable. They will evaporate extremely violently" hope this helps

4 0

3 years ago