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3 years ago

Explain how you can find 4 x 754 using two different methods

Mathematics

2 answers:

Citrus2011 [14]3 years ago

6 0

Solution: The value of $4\times 754$ is 3,016.

Explanation:

The first method of multiplication is given below:

Multiply the ones digit by the multiplier and write the ones digit of the result in the bottom line and add the tens digit to the next resultant, and same happens with the next number multiplied. This method show in given figure.

The second method of multiplication is given below:

Write the digits as the addition of their place values and then multiply those place value by multiplier individually after that add the results.

$4\times 754=4\times (700+50+4)\\4\times 754=4\times700+4\times50+4\times4\\4\times754=2800+200+16\\4\times754=3016$

Therefore, the value of $4\times 754$ is 3,016.

tresset_1 [31]3 years ago

5 0

The first method you can use is mental

754 * 4 = 3,016

The second method you can use is ...
21
754
4
*_____
3,016

4 * 4 = 16
5 * 4 = 20
7 * 4 = 28

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5 with some change left over.

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3 years ago

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A line passes through the two given points. Is it vertical, horizontal, or neither?

Leviafan [203]

Answer:

A line passes through the two given points (5,2), (5,-2). The line is vertical line

Solution:

Given, two points are (5, 2) and (5, -2)

We have to find that a line that passes through the given two points is vertical or horizontal or neither.

First let us find the slope of the line that passes through given two points.

So, slope of line m $=\frac{y_{2}-y_{1}}{x_{2}-x_{2}} \text { where, }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are two points on line. }$

So slope of our line $=\frac{-2-2}{5-5}=\frac{-4}{0}$ = undefined

Here slope of our line is undefined which means it is parallel to the y – axis.

Hence, line passing through given points is vertical line

6 0

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:

Solution 2:

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

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

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2 years ago

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hichkok12 [17]

Answer:

$x=+-10$

Step-by-step explanation:

$x^2=100\\\sqrt{x^2}=\sqrt{100}\\x=+-10$

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3 years ago

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grandymaker [24]

The total length of the dental floss in 150 packages will be 26250 meters.

Explanation

A package of dental floss has 175 m of floss.

Suppose, the number of meters of dental floss in 150 packages is $x$

So, the equation according to the ratio of "number of packages" to "dental floss" will be.....

$\frac{1}{175}=\frac{150}{x}\\ \\ x= 175*150=26250$

So, the total length of the dental floss in 150 packages will be 26250 meters.

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3 years ago