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3 years ago

How to convert 655.575 to word form?

Mathematics

1 answer:

Leni [432]3 years ago

6 0

Six hundred fifty five thousand five hundred seventy five

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Find the percent of the number 36% of 50

Hitman42 [59]

The 36% of 50

The answer is 18

3 0

3 years ago

5x – 12y – 17 = 0 1*9(x + 2) - (y + 1) + 3 = 0

valentina_108 [34]

Answer: $x=\frac{12y+17}{5}$

$y=\frac{-5x+17}{-12}$

$x=\frac{y-20}{9}$

y=9x+20

Step-by-step explanation:

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (plus 12y from both sides)

5x=12y+17 (divide 5 from everything)

$x=\frac{12y+17}{5}$

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (minus 5x from both sides)

-12y=-5x+17 (divide everything by -12)

$y=\frac{-5x+17}{-12}$

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (plus y to both sides)

9x=y-20 (divide 9 from both sides)

$x=\frac{y-20}{9}$

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (minus 9x from both sides)

-y=-9x-20 (divide -1 from everything)

y=9x+20

3 0

3 years ago

Find the average rate of change for f(x) = x2 − 3x − 10 from x = 4 to x = 6. A) 5 Reactivate B) 7 C) 9 Reactivate D) 11

White raven [17]

Answer:Rate of change is 7

Option B is correct.

Step-by-step explanation:

We need to find the average rate of change for $f(x)=x^2-3x-10$ from x = 4 to x = 6

The formula used to find average rate of change is:

$Rate\,\,of\,\,change=\frac{f(b)-f(a)}{b-a}$

Where b = 6 and x = 4

Finding f(6):

$f(x)=x^2-3x-10\\f(6)=(6)^2-3(6)-10\\f(6)=36-18-10\\f(6)=36-28\\f(6)=8$

Finding f(4):

$f(x)=x^2-3x-10\\f(4)=(4)^2-3(4)-10\\f(4)=16-12-10\\f(4)=16-22\\f(4)=-6$

Now Putting values:

$Rate\,\,of\,\,change=\frac{f(b)-f(a)}{b-a}$

$Rate\,\,of\,\,change=\frac{8-(-6)}{6-4}\\Rate\,\,of\,\,change=\frac{8+6}{2}\\Rate\,\,of\,\,change=\frac{14}{2}\\Rate\,\,of\,\,change=7$

So, Rate of change is 7

Option B is correct.

Keywords: Rate of Change

Learn more about Rate of Change at:

#learnwithBrainly

8 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:

Optimizing With Derivatives

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

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