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3 years ago

Why does dividing 5 by a decimal less than 1 give a quotient greater than 5

1 answer:

5 0

If you divide by a decimal, you are breaking apart 1 into multiple pieces and so you are trying to find how many of that size piece will fit into 5. For example if you divide by .5 (point five), there are 2 point fives in 1 so there are 10 point fives in 5. The quotient is larger.

I hope you got that...

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The quotient of the division 2223÷57 is

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Jose tosses a fair coin 2 times. What is the probability it will land on heads two times in a row?

Umnica [9.8K]

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Write the ratio as a percent.

natali 33 [55]

Answer:

62%

Step-by-step explanation:

This one's easy to solve as a percentage because the total number was 100 to begin with. Simply divide the number of employed students by the total amount of students, 62/100, which gets 0.62, or 62%.

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3 years ago

Q2.What is the ratio of volumes of the two cylinders formed by rolling a sheet of dimensions lxb in two different ways? Q3.What

Kobotan [32]

Answer:

2. b : l

3. 20cm

4. 49 $cm^{2}$

5. $(2\pi+1):2\pi$

Step-by-step explanation:

<u>Solution 2:</u>

Let cylinder is rolled along 'l':

Height of cylinder , h = length of rectangle = l

Perimeter of base = b

Let 'r' be the radius of cylinder's base:

$2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}$

Volume of a cylinder is given as:

$V = \pi r^{2} h$

Putting the values:

$V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 = (\dfrac{b^2}{4\pi}) l$

Let cylinder is rolled along 'b':

Height of cylinder , h = length of rectangle = b

Perimeter of base = l

Let 'r' be the radius of cylinder's base:

$2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}$

Volume of a cylinder is given as:

$V = \pi r^{2} h$

Putting the values:

$V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 = (\dfrac{l^2}{4\pi}) b$

Taking ratio:

$V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l$

Solution 3:

Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.

$\therefore$ height of cylinder = 20 cm

Solution 4:

Side of square = 7 cm

Height of cylinder =Side of square = 7 cm

7 cm will be the circumference of the circle.

i.e. $2\pi r$ = 7 cm

Curved surface area of a cylinder:

$CSA = 2\pi rh$

Putting the above values:

CSA = 7 $\times$ 7 = 49 $cm^{2}$

Solution 5:

As calculated in above step:

CSA = $2\pi rh =$ 7 $\times$ 7 = 49 $cm^{2}$

Total surface area = $2\pi r^{2} + 2\pi r h$

Calculating value of r:

$2\pi r$ = 7 cm

$\Rightarrow 2 \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}$

Total surface area =

$2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2$

Ratio of TSA: CSA is

$49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi$

5 0

3 years ago

X^2+1/2x+____=2 + ____

natali 33 [55]

Answer: $x^2+\frac{1}{2}x+\frac{1}{16}=2 +\frac{1}{16}$

Step-by-step explanation:

Given the following Quadratic equation:

$x^2+\frac{1}{2}x=2 +$

You can change its formed by Completing the square.

In order to do Complete the square, you can follow these steps:

1. You can identify that:

$b=\frac{1}{2}$

2. Then, you can find $(\frac{b}{2})^2$ . This is:

$(\frac{\frac{1}{2}}{2})^2=(\frac{1}{4})^2=\frac{1}{16}$

3. Now you must add $\frac{1}{16}$ to both sides of the Quadratic equation in order to keep the balance. Then:

$x^2+\frac{1}{2}x+\frac{1}{16}=2 +\frac{1}{16}$

4. Finally, simplifying by actoring and adding the like terms, you get:

$(x+\frac{1}{4})^2=\frac{9}{4}$

3 0

3 years ago