Let d represent the distance of the destination from the starting point.
After 45 min, Henry has already driven d-68 miles. After 71 min., he has already driven d-51.5 miles.
So we have 2 points on a straight line:
(45,d-68) and (71,d-51.5). Let's find the slope of the line thru these 2 points:
d-51.5 - (d-68) 16.5 miles
slope of line = m = ----------------------- = ------------------
71 - 45 26 min
Thus, the slope, m, is m = 0.635 miles/min
The distance to his destination would be d - (0.635 miles/min)(79 min), or
d - 50.135 miles. We don't know how far his destination is from his starting point, so represent that by "d."
After 45 minutes: Henry has d - 68 miles to go;
After 71 minutes, he has d - 51.5 miles to go; and
After 79 minutes, he has d - x miles to go. We need to find x.
Actually, much of this is unnecessary. Assuming that Henry's speed is 0.635 miles/ min, and knowing that there are 8 minutes between 71 and 79 minutes, we can figure that the distance traveled during those 8 minutes is
(0.635 miles/min)(8 min) = 5.08 miles. Subtracting thix from 51.5 miles, we conclude that after 79 minutes, Henry has (51.5-5.08), or 46.42, miles left before he reaches his destination.
Answer:
9/4
Step-by-step explanation:
When you divide by a number, whole number or fraction, it's exactly like multiplying by its inverse.
Like if you divide 4 by 2, you can easily express that has 4 * 1/2.
In the same manner, when you divide 3/4 by 1/3, you can say that you're multiplying 3/4 by 3/1
The result of 3/4 * 3/1 = 9 / 4
Which you cannot simplify because 9 and 4 don't have any common factors (other than 1). The only other way to express it would be 3²/2² or (3/2)²
Answer:
we need a picture...
Step-by-step explanation:
Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk , I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere .
a. Let denote the hemispherical <u>c</u>ap , parameterized by
with and . Take the normal vector to to be
Then the upward flux of through is
b. Let be the disk that closes off the hemisphere , parameterized by
with and . Take the normal to to be
Then the downward flux of through is
c. The net flux is then .
d. By the divergence theorem, the flux of across the closed hemisphere with boundary is equal to the integral of over its interior:
We have
so the volume integral is
which is 2 times the volume of the hemisphere , so that the net flux is . Just to confirm, we could compute the integral in spherical coordinates:
You said 2x - 9 < 7
Add 9 to each side: 2x < 16
Divide each side by 2 : x < 8 .