Answer:
slope of M'N' = 1
Explanation:
First, we will need to get the coordinates of points M' and N':
We are given that the dilation factor (k) is 0.8
Therefore:
For point M':
x coordinate of M' = k * x coordinate of M
x coordinate of M' = 0.8 * 2 = 1.6
y coordinate of M' = k * y coordinate of M
y coordinate of M' = 0.8 * 4 = 3.2
Therefore, coordinates of M' are (1.6 , 3.2)
For point N':
x coordinate of N' = k * x coordinate of N
x coordinate of N' = 0.8 * 3 = 2.4
y coordinate of N' = k * y coordinate of N
y coordinate of N' = 0.8 * 5 = 4
Therefore, coordinates of M' are (2.4 , 4)
Then, we can get the slope of M'N':
slope = (y2-y1) / (x2-x1)
For M'N':
slope = (3.2-4) / (1.6-2.4)
slope = 1
Hope this helps :)
Given:
Principal value = $240,000
Rate of interest = 6% compounded continuously.
Time = 30 years
To find:
The amount after interest.
Solution:
The formula for amount after continuous compounding the interest is:
Where, P is principal, r is rate of interest and t is the number of years.
Putting , we get
Therefore, Martins will pay $1451,915.39 for the house, including interest.
Answer:
- <u><em>The lamp burns 6 ounces of oil per min.</em></u>
Explanation:
That the oil of a lamp burns at a <em>linear rate</em> means that the rate of burn is constant.
Hence, you can calcualte the rate with which the lamp burns the oil using any two ordered pairs.
- Rate of burn = [ change in oil ] / [change in time]
- Rate of burn = [Oil at time 2- Oil at time 1 ] / [time 2 - time 1]
Your two ordered pairs are (13 ounces, 10 min) and (7 ounces, 38 min).
Substituting those pairs in the equation for the rate, you get:
- Rate = [ 7 ounces - 13 ounces ] / [38 min - 10 min]
- Rate = ( - 6 ounces) / (18 min) = - 1/3 oz / min ≈ - 0.33 oz / min
The negative sign just shows that the amount of oil is decreasing (the oil is being burned).
Hence, the lamp burns 6 ounces of oil per min.
Magnitude of momentum = mass*velocity = 480*40 = 19200 kg/km/hr