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3 years ago

Simplify x/4+x/3 / x/2

Mathematics

1 answer:

marissa [1.9K]3 years ago

6 0

Answer:

$\frac{7}{6}$

Step-by-step explanation:

$\frac{\frac{x}{4}+\frac{x}{3}}{\frac{x}{2}}$

$\frac{\left(\frac{x}{4}+\frac{x}{3}\right)\cdot \:2}{x}$

$\frac{2\cdot \frac{7x}{12}}{x}$

$\frac{\frac{7x}{6}}{x}$

$\frac{7x}{6x}$

$\frac{7}{6}$

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A tank in the form of a right-circular cylinder of radius 2 feet and height 10 feet is standing on end. If the tank is initially

k0ka [10]

Answer:

$\frac{dh}{dt} = -3.48 \times 10^{-3}\sqrt{h}$ feet per second is the differential equation

Step-by-step explanation:

Given:

The radius of the cylindrical tank= 2 feet

The height of the cylindrical tank = 10 feet

The radius of the circular hole = 3/4 inches

To Find:

The differential equation for the height h of the water at time t.

Solution:

<u>Finding the surface area(A) of the tank</u>

Surface area = $\pi R^2$

On substituting the values

Surface area = $\pi(2)^2$

= $4\pi$ square feet

<u>Finding the surface area(a) of the hole</u>

The radius is given in inches, so converting into feet we have

1 inch = 0.083 foot

similarly

$\frac{3}{4} = 0.75 inches = 0.75 \times 0.083$ = 0.0625 feet.

Now the surface area,

= $\pi \times 0.0625$

= $0.0625 \pi$ square feet

Now let the velocity of water through the hole is v

According law of conservation of energy, the penitential energy due to the height h of the water gets converted into kinetic energy.

$\frac{1}{2}mv^2 =mgh$

$v^2 = \frac{2mgh}{m}$

$v^2 = 2gh$

$v= \sqrt{2gh}$

The rate of water flowing through the hole is = $a\times v$

= > $a \times \sqrt{2gh}$

At any time t

$V(t) = A \times h(t)$

$\frac{dV}{dt} = -a\sqrt{2gh}$

$\frac{d(Ah(t))}{dt} = -a\sqrt{2gh}$

$A \frac{d(h(t))}{d(t)} = -a\sqrt{2gh}$

$\frac{dh}{dt} = -\frac{a}{A} \sqrt{2gh}$

On substituting the values, we get

$\frac{dh}{dt} = -\frac{0.0625\pi}{4\pi}\sqrt{2\times 32 \times 10$

$\frac{dh}{dt} = -3.48 \times 10^{-3}\sqrt{h}$ feet per second

3 0

3 years ago

9x=5x+20 Please Help!!!!!!!

Natasha2012 [34]

Answer:

x=5

Step-by-step explanation:

subtract 5x from both sides

9x-5x=5x+20-5x

simplify

4x=20

divide both sides by 4

4/20=5

6 0

3 years ago

Read 2 more answers

A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation 3. 00 0. 50 m = 9. 5

Sliva [168]

The statement, which shows the meaning of the taxi driver’s equation for the mileage and fee formula are statement B and E.

<h3>What is linear equation or formula?</h3>

Linear equation or formula is the equation in which the highest power of the unknown variable is one.

Given information-

The formula equation for the mileage is,

$3.00+0.50m=9.50$

In the above formula the term <em>m </em>represents the number of miles traveled.

This formula written by the taxi driver shows the relation between the mileage and fee for his last customer. Using this expression the number of miles can be calculated as,

$3.00+0.50m=9.50$

Subtract with 3 both the sides,

$0.50m=9.50-3.00\\0.50m=6.50$

Divide by number 0.5 both the sides,

$m=\dfrac{6.5}{0.5}\\m=13$

Thus, his last costumer traveled 13 miles.

The 13 times 0.5 plus $3 is equal to the $9.50 which means nine dollars and fifty cents. Thus the option B is the correct option.

The number of miles traveled by customer is 13 miles. 13 miles of 50 cent is equal to $6.5. If we add three dollars in it the result will be equal to the nine dollars and fifty cents. Thus the option E is correct.

Hence, the statement, which shows the meaning of the driver’s equation, are,