Answer:
Area of PSTK = 50
Step-by-step explanation:
△SPK:
SK = 13, PK = 12
13^2 - 12^2 = SP^2
SP = 5
(8 + 12) /2 x 5 = 50
Right format of question:
Plot two points that are 7 units from Point D and also share the same x-coordinate as Point D.
Answer:
and 
Step-by-step explanation:
Given
Required
Determine a point 7 points from D and in the same x coordinate
Represent this point with D'.
From the requirement of the question, D' has two possible values and these values are:
----> 7 units down and
----> 7 units up
Substitute values for x and y in and
So, we have:
120 barrels x 12 quarts per barrel = 1440 total quarts
1440 quarts / 11 quarts per hour = 130.91 hours to fill all the barrels
1 day = 24 hours
130.91 hours / 24 hours = 5.45 days = 5.5 days
The answer is (1/2)xe^(2x) - (1/4)e^(2x) + C
Solution:
Since our given integrand is the product of the functions x and e^(2x), we can use the formula for integration by parts by choosing
u = x
dv/dx = e^(2x)
By differentiating u, we get
du/dx= 1
By integrating dv/dx= e^(2x), we have
v =∫e^(2x) dx = (1/2)e^(2x)
Then we substitute these values to the integration by parts formula:
∫ u(dv/dx) dx = uv −∫ v(du/dx) dx
∫ x e^(2x) dx = (x) (1/2)e^(2x) - ∫ ((1/2) e^(2x)) (1) dx
= (1/2)xe^(2x) - (1/2)∫[e^(2x)] dx
= (1/2)xe^(2x) - (1/2) (1/2)e^(2x) + C
where c is the constant of integration.
Therefore,
∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C
Answer:
406.72
Step-by-step explanation:
