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3 years ago

Highest common multiple of 8 and 14

Mathematics

1 answer:

Dovator [93]3 years ago

8 0

The highest common multiple is 14 because
8x2=14
14x1=14
Thus, 14 is the highest common multiple!
Hope this Helps :)

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Evaluate (−23)×(−23)3 by using the Laws of Exponents

Nikolay [14]

Given:

$\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3$

To find:

The value of given expression by using the Laws of Exponents.

Solution:

We have,

$\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3$

Using the Laws of Exponents, we get

$=\left(-\dfrac{2}{3}\right)^{1+3}$ $[\because a^ma^n=a^{m+n}]$

$=\left(\dfrac{-2}{3}\right)^{4}$

$=\dfrac{(-2)^4}{(3)^4}$ $[\because \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}]$

$=\dfrac{(-2)\times (-2)\times (-2)\times (-2)}{(3)\times (3)\times (3)\times (3)}$

$=\dfrac{16}{81}$

Therefore, the value of given expression is $\dfrac{16}{81}$ .

3 0

3 years ago

The city council plans to build a new water storage tank for the community. The tank is cylindrical with a base diameter of 25 f

Stella [2.4K]

Answer:

a. $14726.216ft^{3}$

b. $110446.62gal$

Step-by-step explanation:

I attach the diagram of the new water tank.

a. In order to find the volume of the tank in cubic feet, we will need to calculate the volume of a cylinder. We know that its base measures $25ft$ and its height is $30ft$ .

The volume ''V'' of a cylinder is :

$V=(\frac{\pi D^{2}}{4}).(H)$

Where '' $D$ '' is the diameter of the base and '' $H$ '' is the height of the cylinder.

If we replace all the data in the equation :

$V=\frac{\pi .(25ft)^{2}}{4}.(30ft)=14726.216ft^{3}$

We found out that the volume of the tank in cubic feet is $14726.216ft^{3}$

b. We know that 1 cubic foot of water is equal to 7.5 gallons. To find the amount of gallons that the new tank can hold, we need to do an unit conversion.

This equivalence is given to us :

$1ft^{3}=7.5gal$ ⇒ Using the equivalence ⇒