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3 years ago

8

Two candidates ran for class president. The candidate that won received 70% of the 350 total votes. How many votes did the winni

ng candidate receive?

1 answer:

labwork [276]3 years ago

3 0

Answer:

49 votes

Step-by-step explanation:

Because 70% of the 350 is 49

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The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

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3 years ago

Can someone explain the steps for how do solve this?! I can’t get it right

Ulleksa [173]

Answer:

x = 50

m∠D = 150°

m∠F = 30°

Step-by-step explanation:

supplementary angles are two angles whose sum is 180°

∠D + ∠F = 180°

3x + x - 20 = 180

3x + x = 180 + 20

4x = 200

x = 200/4

x = 50

D = 3*50 = 150

∠D = 150°

F = 50 - 20 = 30

∠F = 30°

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valentinak56 [21]

Step-by-step explanation:

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I NEED HELP ill mark brainilist to best answer

Arturiano [62]

All you have to do is add up the side lengths we already know then subtract by the perimeter.
60.3 is the side lengths all together that we know
82-60.3=21.7
Hope this helped!!

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