All categories

3 years ago

Use the Distributie Property to express 27 + 60

Mathematics

2 answers:

Lunna [17]3 years ago

5 0

Once you add 27+60, the answer is 87

Mrac [35]3 years ago

4 0

27+60=87 is the answer

You might be interested in

What is the distance between the florist’s shop (D) and the car wash (E)? Explain using coordinate subtraction.

VARVARA [1.3K]

Answer:

hi! once you link the picture I will answer the problem.

Step-by-step explanation:

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

why is it not usually realistic to measure the distance between two points on a map as a straight line? explain.

aksik [14]

The map is a flat schematic of some actual distance, on a map, the distance form point A to point B may well be 10 units say, however, in actuality, if you go and walk from point A to point B, you'd notice that, first off is not a straight line most of the time, and also it may have a slanted or sloped section, and the map is not including that slope or hill, whilst you do have to walk it.

so, adding all the twists and curves along the way and any bumps or slopes, is really not exactly 10 units from A to B.

3 0

4 years ago

Read 2 more answers

/Algebra/ please help, I'll help you if I can.

viva [34]

Answer:

the answer is b and you can help by being my girl friend

Step-by-step explanation:

6 0

3 years ago

What is the slope of the line that passes through the points (2, 3) <br> and (–2, 6)?

saw5 [17]