Select the equation of the line that passes through the point (5.7) and is perpendicular to the line x = 4.

Mathematics

2 answers:

Tema [17]2 years ago

5 0

Answer:

y=7

Step-by-step explanation:

Hunter-Best [27]2 years ago

4 0

C) y=7.

If it passes through the point (5,7) and is perpendicular to x=4, the line must be y=7.

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At 2:00 PM a car's speedometer reads 30 mi/h. At 2:20 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:20 the acce

Bad White [126]

Answer:

Let v(t) be the velocity of the car t hours after 2:00 PM. Then $\frac{v(1/3)-v(0)}{1/3-0}=\frac{50 \:{\frac{mi}{h} }-30\:{\frac{mi}{h} }}{1/3\:h-0\:h} = 60 \:{\frac{mi}{h^2} }$ . By the Mean Value Theorem, there is a number c such that $0 < c$ with $v'(c)=60 \:{\frac{mi}{h^2}}$ . Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly $60 \:{\frac{mi}{h^2}}$ .

Step-by-step explanation:

The Mean Value Theorem says,

Let be a function that satisfies the following hypotheses:

f is continuous on the closed interval [a, b].
f is differentiable on the open interval (a, b).

Then there is a number c in (a, b) such that

$f'(c)=\frac{f(b)-f(a)}{b-a}$

Note that the Mean Value Theorem doesn’t tell us what c is. It only tells us that there is at least one number c that will satisfy the conclusion of the theorem.

By assumption, the car’s speed is continuous and differentiable everywhere. This means we can apply the Mean Value Theorem.

Let v(t) be the velocity of the car t hours after 2:00 PM. Then $v(0 \:h) = 30 \:{\frac{mi}{h} }$ and $v( \frac{1}{3} \:h) = 50 \:{\frac{mi}{h} }$ (note that 20 minutes is $20/60=1/3$ of an hour), so the average rate of change of v on the interval $[0 \:h, \frac{1}{3} \:h]$ is

$\frac{v(1/3)-v(0)}{1/3-0}=\frac{50 \:{\frac{mi}{h} }-30\:{\frac{mi}{h} }}{1/3\:h-0\:h} = 60 \:{\frac{mi}{h^2} }$

We know that acceleration is the derivative of speed. So, by the Mean Value Theorem, there is a time c in $(0 \:h, \frac{1}{3} \:h)$ at which $v'(c)=60 \:{\frac{mi}{h^2}}$ .

c is a time time between 2:00 and 2:20 at which the acceleration is $60 \:{\frac{mi}{h^2}}$ .

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3 years ago

What name is given to the type of data that is descriptive rather than numerical?

dexar [7]

In statistics, thre are basically two types of data: qualitative and quantitative data

Qualitative data is information about qualities; information that can't actually be measured. While quantitative data are data that can be measured.

Therefore, the name is given to the type of data that is descriptive rather than numerical is qualitativre data.

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3 years ago

Find a solution to the system. Make sure to write as a coordinate.

RUDIKE [14]

Answer:

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Step-by-step explanation:

This is a system of equations.

To solve a system of equations, we use the substitution method.

We can plug in the first equation, $x=2y-4$ , into the value for x in the second equation. Now, the second equation looks like this: