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3 years ago

Simplify the expression d + 11 - 8d.

Mathematics

2 answers:

7nadin3 [17]3 years ago

7 0

11-7d is the answer.

lutik1710 [3]3 years ago

6 0

The answer is -7d+11

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400 A whole number a integer a real number or rational number

bearhunter [10]

Answer:

All of the above

Step-by-step explanation:

A whole number and integers are numbers that don't have decimals.

A rational number is a number that can be written as a fraction

A real number is any number that is not complex, which means that it has an imaginary solution or imaginary number part of it.

7 0

3 years ago

PLEASE HELP

Rudik [331]

$y=75\ \ \ \ x=5\\\\
y=?\ \ \ \ \ x=3\\\\
proportion:\\
\frac{75}{y}=\frac{5}{3}\ \ \ | cross\ multiplication\\\\
75*3=5y\\\\
225=5y\ \ \ | divide\ by\ 5\\\\
y=45
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5 0

3 years ago

The taxi fare in monopolis city is $1.50 for the first mile and additional mileage charged at the rate of $0.25 for each additio

kifflom [539]

Answer:

Step-by-step explanation:

if you add $1.50 +50 cents its $2.00 count by 2's until you get

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4 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

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