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3 years ago

The area of a rectangular dance floor is 8 1/4

Mathematics

1 answer:

kkurt [141]3 years ago

3 0

Answer:

2 5/14 yards

Step-by-step explanation:

Area of the rectangular floor = Length * Width

Given

Area = 8 1/4 square yards

width = 3

1/2 yards

Required

Length

Length = Area/width

Length = (8 1/4)/(3 1/2)

Length = 33/4 ÷ 7/2

Length = 33/4 * 2/7

Length = 33/14

length = 2 5/14 yards

This gives the required length

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3 years ago

Read 2 more answers

How to find unknown side

Elan Coil [88]

Answer:

C = 10

Step-by-step explanation:

Find the last side of the triangle using the Pythagorean theorem.

$a^{2} +b^{2} =c^{2}$

You have a and b already, a = 6, b = 8

$6^{2} +8^{2} =c^{2} \\\\$

solve this to get

$64 + 36 = \sqrt{100}$

C = 10

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3 years ago

Line k has a slope of 2/3. If line m is parallel to line k, then it has a slope of

puteri [66]

Answer:

Line M would also have a slope of 2/3.

Step-by-step explanation:

When two line are parallel that means that they will never intersect.

In order for two lines to avoid intersection they would have to be at the same slope.

Since lines K and line M are parallel to each other they have to have the same slope.

6 0

3 years ago

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 product? Enter your answer as a fraction, in simplified form, in the box. −1/4⋅(−6/11)

ivann1987 [24]

Answer:

3/22

Step-by-step explanation:

-1/4 . (-6/11)

You have to multiply the signs: As both are negative, the result will be positive.
You have to multiply the numbers in the top part (numerators) and the numbers in the bottom part (denominators)

1 . 6 / 4 . 11 = 6/44

Finally, you must simplify the answer by dividing both numbers among the same divisor, in this case the number is 2

6÷2 / 44÷2 = 3/22

4 0

3 years ago