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Crazy boy [7]
3 years ago
15

Select the rational expression that is equivalent to the given expression below. 4 over x - 3

Mathematics
1 answer:
Ad libitum [116K]3 years ago
4 0
When you say 1 over 3, you are basically saying 1 divided by 3, or expressed as a rational number: \frac{1}{3}. in our rational number the denominator is 1, and the numerator is 3

Now, a rational expression is an algebraic expression in a rational for. If we apply the same to your problem. 4 over x-3 means 4 divided by x-3, or in mathematical notation: \frac{4}{x-3}. In this case, the numerator is 4, and the denominator is x-3.

We can conclude that the equivalent rational expression of <span>4 over x - 3 is </span>\frac{4}{x-3}.

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Answer:

Step-by-step explanation:

I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.

The position equation is

s(t)=-1.86t^2+15t  That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.

The first derivative of position is velocity:

v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):

0 = -3.72t + 15 and solve for t:\

-15 = -3.72t so

t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:

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s(4.03) = 30.2 meters.

Calculus is amazing. Much easier than most methods to solve problems like this.

7 0
2 years ago
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e-lub [12.9K]

Answer:

95% of monthly food expenditures are between $110 and $190.

Step-by-step explanation:

Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.

To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Solution :

At 95% of the data is between two standard deviation to left and right of the mean is given by,

To the left side, \bar{x}-2\sigma

To the right side, \bar{x}+2\sigma

We have given,

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The standard deviation \sigma=\$20

Substitute in the formula,

\bar{x}-2\sigma

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\bar{x}+2\sigma

=150+2(20)

=150+40

=190

Therefore, 95% of monthly food expenditures are between $110 and $190.

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