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borishaifa [10]
3 years ago
12

Can u help me pls they are exponents with multiplication and division

Mathematics
1 answer:
Ronch [10]3 years ago
3 0
When there is a multiplication involving exponents, we need to evaluate the numbers and each variables separately. In this case, we have 5 and 4 as the numbers, and w and h for the variables.

When we multiply 5 and 4 we get:
5 \times 4 = 20

For w, we have {w}^{6}, {w}^{4}, w. While we are multiplying the w's, we need to add the exponents together to get the final answer: {w}^{6} \times {w}^{4} \times w = {w}^{11}

For h's, there are {h}^{2}, {h}^{5}, {h}^{4}. When we apply the same thing to h's, we get {h}^{2} \times {h}^{5} \times {h}^{4} = {h}^{11}

For the final step, we need to write all of these together: 20 \times {w}^{11} \times {h}^{11} \: \: or \: \: 20 {w}^{11} {h}^{11} \: \: or \: \: 20 {(wh)}^{11}
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g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur
sdas [7]

Answer:

The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

Step-by-step explanation:

A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

Recall that the volume for a cylinder is given by:

\displaystyle V = \pi r^2h

Substitute:

\displaystyle (300) = \pi r^2 h

Solve for <em>h: </em>

\displaystyle \frac{300}{\pi r^2} = h

Recall that the surface area of a cylinder is given by:

\displaystyle A = 2\pi r^2 + 2\pi rh

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

First, substitute for <em>h</em>.

\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r}  \end{aligned}

Find its derivative:

\displaystyle A' = 4\pi r - \frac{600}{r^2}

Solve for its zero(s):

\displaystyle \begin{aligned} (0) &= 4\pi r  - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

\displaystyle  \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2}  \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm}   \end{aligned}

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

7 0
3 years ago
What is the denominator of the fraction 2over3
Nataly [62]
<span>The number below the line in a common fraction

The answer is 3</span>
7 0
3 years ago
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Mama's Italian Restaurant has collected data about customer sauce orders. It calculated that P(marinara) = 0.82, P(alfredo) = 0.
Keith_Richards [23]
P ( m ) = 0.82
P ( a ) = 0.76
P ( m or a ) = 0.96
P ( m and a ) = ?
--------------------------
P ( m or a ) = P ( m ) + P ( a ) - P ( m and a )
P ( m and a ) = P ( m ) + P ( a ) - P ( m or a ) =
= 0.82 + 0.76 - 0.96 = 0.62
Answer: P ( marinara and alfredo ) = 0.62
7 0
3 years ago
A bag contains eight blue marbles six Green marbles 12 yellow marbles and 10 orange marbles a marble is drawn at random from the
Marta_Voda [28]
28/36=7/9
explanation












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3 0
3 years ago
Read 2 more answers
Joaquin is constructing the perpendicular bisector of AB. He opens his
vekshin1

Answer:

A

Step-by-step explanation:

The steps for constructing the perpendicular bisector is:

Step 1:

Open the compass more than half of the length of the segment AB and put it on point A and draw an arc across AB

Step 2:

Place the compass with the same width on point B and draw an arc across AB.

Step 3:

Place the ruler on the points above and below AB and draw a line.

Step 4:

The line is the perpendicualr bisector of the line segment AB ..

Hence, option A is the correct answer ..

9 0
3 years ago
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