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3 years ago

Using complete sentences, explain how to find the quotient of 4 5/8 ÷ 2 3/4 . Make sure to include the quotient in your answer.

Mathematics

1 answer:

xeze [42]3 years ago

5 0

Answer:

$4\frac{5}{8}\div \:\:2\frac{3}{4}=\frac{37}{22}$

Step-by-step explanation:

Given

$4\frac{5}{8}\div \:2\frac{3}{4}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{5}{8}=\frac{37}{8}$

$=\frac{37}{8}\div \:2\frac{3}{4}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{3}{4}=\frac{11}{4}$

$=\frac{37}{8}\div \frac{11}{4}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{37}{8}\times \frac{4}{11}$

$\mathrm{Cross-cancel\:common\:factor:}\:4$

$=\frac{37}{2}\times \frac{1}{11}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{37\times \:1}{2\times \:11}$

$\mathrm{Multiply\:the\:numbers:}\:37\times \:1=37$

$=\frac{37}{2\times \:11}$

$\mathrm{Multiply\:the\:numbers:}\:2\times \:11=22$

$=\frac{37}{22}$

Therefore,

$4\frac{5}{8}\div \:\:2\frac{3}{4}=\frac{37}{22}$

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A letter in the word COURAGE is chosen at random, then a coin is tossed three times. How many outcomes are possible?

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I think about 10

Step-by-step explanation:

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3 years ago

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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

2 years ago

If you bent length 44 cm is bent into a circle find the radius of the circle?If the same wire is bent into the shape of a square

Tju [1.3M]

Answer:

r = 7 cm; l = 11cm

The circle encloses more area than the square

Step-by-step explanation:

(a) Radius of circle

The formula for the circumference of a circle is

A = 2πr

r = A/(2π)

Data:

C = 44 in

Calculation:

r = 44/(2 × 22/7)

= 44/2 × 7/22

= 2/2 × 7

= 7 in

(b) Side of square

P = 4l

l = P/4

= 44/4

= 11 in

(c) Areas

(i) Circle

A = πr²

= 22/7 × 7²

= 22/7 × 49

= 22 × 7

= 154 cm²

(ii) Square

A = l²

= 11²

= 121 cm²

The circle encloses more area than the square.

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3 years ago

What is the square root of 864

skelet666 [1.2K]

There are two ways to evaluate the square root of 864: using a calculator, and simplifying the root.

The first method is simplifying the root. While this doesn't give you an exact value, it reduces the number inside the root.

Find the prime factorization of 864:

$\sqrt{864} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3}$

Take any number that is repeated twice in the square root, and move it outside of the root:

$\sqrt{864} = \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3}$

$\sqrt{2 \cdot 2} = \sqrt{4} = 2$

$\sqrt{3 \cdot 3} = \sqrt{9} = 3$

$\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3} = \sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3}$

$\sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3} = (2 \cdot 2 \cdot 3) \sqrt{2 \cdot 3} = \boxed{12 \sqrt{6}}$

The simplified form of √864 will be 12√6.

The second method is evaluating the root. Using a calculator, we can find the exact value of √864.

Plugged into a calculator and rounded to the nearest hundredths value, √864 is equal to 29.39. Because square roots can be negative or positive when evaluated, this means that √864 is equal to ±29.39.

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3 years ago

Can someone please help me i will give free 50 points

Grace [21]

Would it be 11 and 12?

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2 years ago

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