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3 years ago

What does relationship mean in algebra/ math?

Mathematics

1 answer:

NikAS [45]3 years ago

7 0

Answer:

A relation is a relationship between sets of values. In math, the relation is between the x-values and y-values of ordered pairs. The set of all x-values is called the domain, and the set of all y-values is called the range. ... The range consists of the y-values from each ordered pair.

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A tank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measuremen

Darina [25.2K]

Answer:

$100\pi\int\limits^9_0 {(\sqrt y)^2(14-y)} \, dy$ ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving $y=x^2$ about y axis in the interval $0\leq x\leq 3$ .

Density of the fluid in the tank, $D=100\ lbs/ft^3$

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is, $y(0)=0^2=0$

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in $x=3$ in the parabolic equation . This gives,

$H=3^2=9\ ft$

So, the height of top of tank is, $y(3)=H=9\ ft$

Now, 5 ft above 'H' means $H+5=9+5=14$

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

$\Delta y=(14-y)$ ft

Now, area of cross section of the tank is given as:

$A(y)=\pi r^2\\r\to radius\ of\ the\ cross\ section$

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have, $y=x^2$

So, $x=\sqrt y$

Therefore, radius, $r=\sqrt y$

Now, area of cross section is, $A(y)=\pi (\sqrt y)^2$

Work done in pumping the contents to 5 feet above is given as:

$W=D\int\limits^{y(3)}_{y(0)} {A(y)(\Delta y)} \, dy$

Plug in all the values. This gives,

$W=100\int\limits^9_0 {\pi (\sqrt y)^2(14-y)} \, dy\\\\W=100\pi\int\limits^9_0 { (\sqrt y)^2(14-y)} \, dy\textrm{ ft-lbs}$

7 0

3 years ago

Which of the following is the function representing the graph below?

Mariana [72]

Easy, subsitute a point
we see it goes through (0,4)
so subsitte 0 for x and see if we get 4

4^0=1, nope
4^0-3=1-3=-2, nope
4^0+3=1+3=4, yep
4^(0+3)=4^3=64, noe

answer is 3rd option
f(x)=4^x+3

5 0

3 years ago

If h = 27, what is the value of h ÷ 9?

Tju [1.3M]

H = 27

subtitute the value of h to the expression h : 9

h : 9 = 27 : 9 = 3

7 0

3 years ago

Read 2 more answers

Which of the following is another way to express -13 - 7?

kaheart [24]

B is the answer because keep change change keep -13 change from subtraction to addition and change the 7 to -7

8 0