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4 years ago

Please help! Brainliest! How are the functions y = 2x2 and y = 2x2 + 7 related? How are their graphs related?

Mathematics

1 answer:

Leona [35]4 years ago

5 0

It’s should be B. The graphs will be identical in shape but the second one will be shifted up 7 units

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Hello, can somebody please help me with this word problem? Thanks.

erastovalidia [21]

We are given that this is an ideal gas, and that the volume and presumably the number of moles of gas are constant. We can use Gay-Lussac's Law, which describes volume and pressure. We have that pressure is directly proportional to volume. For a change in a gas, we can write the equation as
$\dfrac{P_i}{T_i} = \dfrac{P_f}{T_f}$ ,
where i denotes initial and f denotes final.

We have that $T_i=600 \ K$ , $T_f=800 \ K$ , and $P_f=30 \ atm$ . We need to find $P_i$ . To do so, let's first rearrange Gay-Lussac's equation to solve for $P_i$ .

$\dfrac{P_i}{T_i} = \dfrac{P_f}{T_f} \\\\P_iT_f=P_fT_i\\\\P_i= \dfrac{P_fT_i}{T_f}$

Now, we plug in our values to get $P_i$ .

$P_i= \dfrac{P_fT_i}{T_f}=\dfrac{30\ atm \ 600 \ K}{800 \ K} = 22.5 \ atm$ .

This seems like a reasonable value, because as temperature goes up, pressure goes up, and an increase in temperature corresponds to an increase in pressure.

Technically, you were given values with only one significant figure, so you can only report the value as $20 \ atm$ , but this depends on how your instructor usually does these problems!

4 0

3 years ago

A baker needs 4 3⁄4 cups of flour. If she uses a 1 1⁄2 cup measuring scoop, how many scoops of flour must the baker use to have

Juliette [100K]

Answer:

If you did it three times it would be 4 1/2. If you wanted to make it at least 4 3/4 then you would need to do 1 1/2 4 times.

Step-by-step explanation:

4 0

3 years ago

Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 80

Svetlanka [38]

Its an area equation. Area is length times width.

So to start, he needs 50x80 square feet in his front yard, BUT THAT IS ONLY HALF OF THE PROBLEM. For the front yard he needs 4000 sq. feet. For the back, it is different. He needs 10x40÷2. To first simplify, we do the multiplication. This comes to 400÷2. then it is simply 200.

Now for the easy part. Take the 4000 and add 200. Answer? 4,200.

7 0

3 years ago

1.7km = how many centimeters

Sedaia [141]

The equivalent of 1.7 km to centimeters is 170000 Because if 1 km is equal to 1 and 7 is equal to 700000 then the equivalent of 1.7 km is 170000 That's it

6 0

4 years ago

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago