∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
----
∫(t = 2 to 3) t √(t - 2) dt
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}
= 26/15.
----
For the k-entry, use integration by parts with
u = t, dv = sin(πt) dt
du = 1 dt, v = (-1/π) cos(πt).
So, ∫(t = 2 to 3) t sin(πt) dt
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]
= 5/π + 0
= 5/π.
Therefore,
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.
Answer:
The Area of the square base is 114 In .2
The Area of each triangle face is 66 in .2
Gabriel will need 408 in .2 of paint
Answer:
SOLUTION #1
If the digits are allowed to repeat, the answer is 27. (There are three ways to fill digit 1, three ways to fill digit 2, and three ways to fill digit 3. Therefore, there are 3 x 3 x 3 = 27 possibilities.)
SOLUTION #2
If the digits are NOT allowed to repeat, the answer is 6. (There are three ways to fill digit 1, only two ways to fill digit 2, and only one way to fill digit 3. Therefore, there are 3 x 2 x 1 = 6 possibilities.)
Step-by-step explanation:
Hope this <em><u>Helped!</u></em> :D
Speed is the rate of change of distance.
the speed of the truck for the 100 miles within 2 hours is
speed = 100 miles travelled / 2 hours taken
speed = 50 miles/hour
assuming that the driver drives at 50 miles/hr
the time taken to drive 50 miles is - 1 hour
therefore to drive 300 miles - it takes - 300 miles / 50 miles/hr
the time taken is - 6 hours
it takes 6 hours to drive for 300 miles
A \greenD{4\,\text{cm} \times 6\,\text{cm}}4cm×6cmstart color greenD, 4, space, c, m, times, 6, space, c, m, end color greenD re
gayaneshka [121]
Answer:
356 cm².
Step-by-step explanation:
Step one: The first thing to do here is to Calculate the area of rectangle. The area of the rectangle can be calculated by using the formula below;
Area of rectangle = width × length = 6 × 4 = 24 cm².
Step two: the next step is to calculate the area of the circle. The area of the circle can be calculated by using the formula below;
Area of a circle = (radius)^2 × π.
Area of a circle = (11)^2 × π = 380.13 cm².
Step three: the next thing to do is to calculate the area of the shaded region which is the difference between the Area of a circle and the Area of rectangle.
That is; 380.13 cm² - 24 cm² = 356.13 cm².
