Answer:
(-2,4) , (0,5) , (2,6) , (4,7)
Step-by-step explanation:
you just substitute every value of x in the equation and you get y
∫(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:
940
Step-by-step explanation:
The scatter plot below shows the sales (in multiples of $1000) for the company over time (in months).
Also the sales can be modeled by the help of a linear function as:
y = 0.94x + 12.5.
Now we know that the company's sales increase per month is the slope of the linear function by which this situation is modeled.
We know that for any linear function of the type:
y=mx+c
'm' represents the slope and 'c' represents the y-intercept of the line.
Hence, by looking at the equation we get:
m=0.94
but as the sales are multiplied by 1000.
Hence,
0.94×1000=$ 940.
Hence, the company's sales increase per month is:
$ 940
