If 0 is in the quadrant IV and sin 0=1/2, then cos0__

At a school carnival, three students spend an average of $10. Six other students spend an average of $4. What is the average amo

user100 [1]

$54 (if 10 for each of the 3 students and 4 dollars each of the 6 students)
$14 if not

6 0

3 years ago

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 $60 \:{\frac{mi}{h^2}}$ .

4 0

3 years ago

A cabbage palmetto has a height of 80 feet. what is the approximate height of the tree in meters?

frutty [35]

1 foot is about 0,3 meters.
If the height of the cabbage palmetto is 80 feet, it should be about 80*0,3 = 24 meters.

So a cabbage palmetto with 80 feet of height is about 24 meters.

Hope this helps! :)

6 0

3 years ago

Hi what is the answer for b please

Ray Of Light [21]

E = 352.50 euro × 1 pound / 1.41 euro = 250.00 pounds

J = 39856 yen × 1 pound / 188 yen = 212.00 pounds

a) Japan is cheaper

b) 250 - 212 = 38 pounds cheaper

7 0

3 years ago

I need assistance if anyone would be so kind.

uysha [10]

He shoots 20 arrows

6 0

2 years ago

If 0 is in the quadrant IV and sin 0=1/2, then cos0___