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3 years ago

Round 6.512459 to the nearest ten thousandths?

1 answer:

4 0

$6.512459\\\\Since\ the\ fifth\ place\ (hundred\ thousandths)\ is\ 5\ or\ more\ (it's\ 5),\\the\ fourth\ place\ (ten\ thousandths)\ is\ increased\ by\ 1.\\\\Answer:6.512459\approx6.5125$

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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

Q + 5/9= 1/6 from big ideas mathbook

Alika [10]

9We have such eqation
Q $+ \frac{5}{9} = \frac{1}{6}$ /*9 (multiply both sides by 9)
9Q+5= $\frac{9}{6}$ /-5 both sides
9Q= $\frac{9}{6}- 5$
9Q= $\frac{9}{6}- \frac{5*6}{6}$
9Q= $\frac{9-30}{6}$
9Q=- $\frac{21}{6}$ /:9 divide both sides by 9
Q=- $\frac{21}{6}:9$
Q $\frac{21}{6*9} =- \frac{21}{54}=[tex] \frac{7}{18}$ - its the answer

6 0

3 years ago

Read 2 more answers

40 POINTS THERE IS MORE THAN 1 ANSWER BRAINLIEST IF CORRECT

mash [69]

Answer:

Whole numbers are also integers. There are other integers which are the opposites of the whole numbers (−1, −2, −3, ...). These negative numbers lie to the left of 0 on the number line. Integers are the whole numbers and their opposites.

4 0

3 years ago

The area of a circle is 39.62cm2.<br> Find the length of the radius rounded to 2 DP.

Shkiper50 [21]

Using the formula for area of a circle:

Area = pi x radius^2

Replace area with the given value:

39.62 = pi x radius^2

Divide both sides by pi

Radius^2 = 39.62/pi

Radius^2 = 12.62

Solve for radius by taking the square root of both sides

Radius = sqrt(12.62)

Radius = 3.55 cm

4 0

3 years ago

Solve the following equation for m:<br> -7+ m = -15

Solnce55 [7]

M = -8

-15 minus -7 equals -8

6 0

3 years ago