What is the volume, in cubic meters, of a cube with an edge length of 5 meters?

When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a ra

Sergeu [11.5K]

Answer:

$r=\sqrt{10}\text{ m}$

Step-by-step explanation:

We have been given that when a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. We are asked to find the approximate radius of tank in meters.

We will use volume of cylinder formula to solve our given problem as:

$V=\pi r^2h$ , where,

r = Radius,

h = Height of cylinder.

Since the level of water in the tank rises at a rate of 0.7 meters per hour, so height of cylinder would be $h = 0.7$ meters at $V=22\text{ m}^3$ .

Upon substituting these values in above formula, we will get:

$22\text{ m}^3=\frac{22}{7}\cdot r^2(0.7\text{ m})$

$22\text{ m}^3=\frac{22}{10}\cdot r^2\text{ m}$

$\frac{10}{22}\cdot\frac{22\text{ m}^3}{\text{m}}=r^2$

$r^2=\frac{10}{22}\cdot\frac{22\text{ m}^3}{\text{m}}$

$r^2=10\text{ m}^2$

Now, we will take positive square root of both sides as radius cannot be negative.

$\sqrt{r^2}=\sqrt{10\text{ m}^2}$

$r=\sqrt{10}\text{ m}$

Therefore, radius of tank would be approximately square root of 10 m.

5 0

3 years ago

7 times the difference of x and 8

Thepotemich [5.8K]

Answer:

7(x - 8)

Step-by-step explanation:

times means multiplication

difference means subtraction

7 times the difference of x and 8 -> 7 * (x - 8) -> 7(x - 8)

Simplify if needed.

7(x - 8)

~Distribute

2x - 56

Best of Luck!

8 0

3 years ago

PLS help with the question in the picture!

slega [8]

Answers:

y = 50

angle AOB = 100

=========================================

Explanation:

Angle x is an inscribed angle that subtends or cuts off minor arc AB. This is the shortest distance from A to B along the circle's edge.

Angle y is also an inscribed angle that cuts off the same minor arc AB. Therefore, it is the same measure as angle x. We can drag point D anywhere you want, and angle y will still be an inscribed angle and still be the same measure as x.

-------------------

Point O is the center of the circle. This is because "circle O" is named by its center point.

Angle AOB is considered a central angle as its vertex point is the center of the circle.

Because AOB cuts off minor arc AB, and it's a central angle, it must be twice that of the inscribed angle that cuts off the same arc.

This is the inscribed angle theorem.

Using this theorem, we can say the following

central angle = 2*(inscribed angle)

angle AOB = 2*(angle x)

angle AOB = 2*50

angle AOB = 100 degrees

6 0

3 years ago

A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation form

frozen [14]

If you draw a diagram of this, your given values of the resulting triangle give you the sides opposite and adjacent of the angle. The formula that uses these sides is tangent.

The tangent of an angle is equal to the ratio of the opposite side over the other non-hypotenuse side (adjacent).

Therefore;

$tan(40)=70/x$
$0.83909963117=70/x$
$0.83909963117x=70$
$x=70/0.83909963117$
$x=83.4227514823$

Where x is the length of the string in feet.

3 0

3 years ago

Please find x and a

aev [14]

Answer:

x = 36

a = 25

Step-by-step Explanation

By Pythagoras Theorem:

$x = \sqrt{ {39}^{2} - {15}^{2} } \\ \\ x = \sqrt{1,521 - 225} \\ \\ x = \sqrt{1,296} \\ \\ x = 36 \\ \\ a = \sqrt{ {20}^{2} + {15}^{2} } \\ \\ a = \sqrt{400 + 225} \\ \\ a = 25 \sqrt{625} \\ \\ a = 25$

8 0

3 years ago