A student says that the graph of the equation y = 3(x + 8) is the same as the graph of y = 3x, only translated upwards by 8 units. Do you agree? Why or why not?
A.S.A.P. I HAVE TO TURN THIS IN AT 10:30 HURRY PLEASE :)

Answers

Answer 1

Given:

A student says that the graph of the equation [tex]y = 3(x + 8)[/tex] is the same as the graph of [tex]y = 3x[/tex], only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

[tex]y=3x[/tex]

[tex]f(x)=3x[/tex]

Equation of after transformation is

[tex]y=3(x+8)[/tex]

[tex]g(x)=3(x+8)[/tex]

Now,

[tex]g(x)=f(x+8)[/tex]      ...(i)

The translation is defined as

[tex]g(x)=f(x+a)+b[/tex]        ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

[tex]a=8\text{ and }b=0[/tex]

Therefore, the graph of [tex]y=3x[/tex] translated left by 8 units. Hence, the student is wrong.


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Step-by-step explanation:

Associative property is applied on three numbers which states that when two numbers are being added or multiplied the order of addition and multiplication doesn't matter i.e. the answer is same.

If a,b and c are three numbers then associative property for multiplication can be given as:

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[tex](14.\frac{1}{7})\frac{2}{5}[/tex]

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is 10 feet, and the height is 15 feet. The shape of the water in the tank is conical with radius r feet and height h feet. At noon, water is leaking from the bottom of the tank at a rate of 12 cubic feet per hour, and the volume of water in the tank is 27π cubic feet. At noon, what is the rate at which the height of the water in the tank is changing? (The volume V of a right circular cone with radius r and height h is V=13πr2h.)

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The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]

Step-by-step explanation:

Given information:

[tex]\text{\bold{The diameter of cone}}=10\;\rm{ ft.}[/tex]

[tex]\rm{The\; height\; of\; the\; cone}= 15\;\rm{ ft.}[/tex]

[tex]\text{The rate at which the water is leaking }= 12 \; \rm ft^3/hr.[/tex]

[tex]\text{Volume of water tank}=27 . \pi \; \rm ft^3[/tex]

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If ,we take a right circular cone with radius r and height h , its volume

[tex]\text{volume (V)} = (1/3) \times \pi \times \rm{r^3 \times h[/tex]

Now, the radius of cone when the volume of water tank is given

[tex]\frac{1}{3}\times \pi \rm\times{r^2 \times h = 27 \times \pi[/tex]

The ratio of height to radius of the cone :

[tex]\text {h/r} =3[/tex]

[tex]\text r = \text h/3[/tex]

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[tex]dV/dt= dV/dh \times dh/dt[/tex]

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[tex]12 = \frac{d(\text h^3/27 \pi)}{dh} \times \frac{d\text h}{dt} \\\\\frac{d\text h}{dt} = \frac{12}{\pi \text h^2/9}[/tex]

As ,

[tex]27=\frac{1}{27 \times h}[/tex]

[tex]\text h^3=27^2\\\text h= 9\\[/tex]

Now,

[tex]dh/dt=12/(\pi.\text h^2/9)\\dh/dt=4/3\pi\\dh/dt=0.4244\\[/tex]

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Answer: 64 fluid ounces

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For 8 hours, Toya would have drank:

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To calculate the amount of fluid ounces

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Answer:y = mx + b formaty = 1/4x + 2Hope this helps!!

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