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andriy [413]
3 years ago
6

When solving a system of equations, how do you determine which method to use?

Mathematics
1 answer:
bazaltina [42]3 years ago
5 0
Substitution is best to use one one or both equations is already solved for one of the variables. Elimitation can be use if all variables have a coefficient other than 1.
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If f(x)=x^3−x, what is the average rate of change of f(x) over the interval [1, 5]? a)29.5 b)30 c)43 d)120
avanturin [10]
\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= x^3-x  \qquad 
\begin{cases}
x_1=1\\
x_2=5
\end{cases}\implies \cfrac{f(5)-f(1)}{5-1}
\\\\\\
\cfrac{[5^3-5]~-~[1^3-1]}{4}\implies \cfrac{125-5~~-~~0}{4}\implies \cfrac{120}{4}\implies 30
7 0
3 years ago
A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionl
KATRIN_1 [288]

Answer:

Rolling case achieves greater height than sliding case

Step-by-step explanation:

For sliding ball:

- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.

- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.

- The ball slides it only has translational kinetic energy as follows:

                                   ΔK.E = ΔP.E

                                   0.5*m*v^2 = m*g*h

                                    h = 0.5v^2 / g

For rolling ball:

- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:

                                  ΔK.E = ΔP.E

                                  0.5*m*v^2 + 0.5*I*w^2 = m*g*h

- Where I: moment of inertia of spherical ball = 2/5 *m*r^2

             w: Angular speed = v / r

                               0.5*m*v^2 + 0.2*m*v^2 = m*g*h

                               0.7v^2 = g*h

                               h = 0.7v^2 / g

- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.

4 0
3 years ago
(2p + 4) + 5 (p-1) - (p+7)
jonny [76]

<em>Your answer will be, </em><em>"6p - 8"</em>

Thanks,

<em>Deku ❤</em>

6 0
3 years ago
Kristen earns $13.50 for each hour she works. On Monday she worked 4 hours. She also worked Tuesday. If she earned a total of $1
insens350 [35]

Answer:8 hours on Tuesday

Step-by-step explanation:13.50 x 4=54

162-54=108

108÷13.50=8

8 0
3 years ago
The ______ average ignores compounding.
mars1129 [50]
The answer is:  [B]:  "arithmetic" .
______________________________________________________
         "The <u>  arithmetic  </u> average ignores compounding."
______________________________________________________
8 0
3 years ago
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