Step-by-step explanation:
In this case we have:
Δx = 3/n
b − a = 3
a = 1
b = 4
So the integral is:
∫₁⁴ √x dx
To evaluate the integral, we write the radical as an exponent.
∫₁⁴ x^½ dx
= ⅔ x^³/₂ + C |₁⁴
= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)
= ⅔ (8) + C − ⅔ − C
= 14/3
If ∫₁⁴ f(x) dx = e⁴ − e, then:
∫₁⁴ (2f(x) − 1) dx
= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx
= 2 (e⁴ − e) − (x + C) |₁⁴
= 2e⁴ − 2e − 3
∫ sec²(x/k) dx
k ∫ 1/k sec²(x/k) dx
k tan(x/k) + C
Evaluating between x=0 and x=π/2:
k tan(π/(2k)) + C − (k tan(0) + C)
k tan(π/(2k))
Setting this equal to k:
k tan(π/(2k)) = k
tan(π/(2k)) = 1
π/(2k) = π/4
1/(2k) = 1/4
2k = 4
k = 2
Answer: 4b^6
Remember if theres a bracket you multiply the power instead of adding
For example if it was 2b^3 x 2b^2 then the answer would be 4b^5 instead according to indices law, read up on it if you havent yet itll help a bunch! :)
Answer:
D.) 256
Step-by-step explanation:
The first week she made 4 hats, the next week she made 4 times as much which is 16( 4x4=16). The third week she made 64 (16x4=64). The fourth week she made 256 (64x4)
Answer:
y int= 12.50
slope= 2.00
equation= y=2x+12.5
Step-by-step explanation:
the y intercept in this case is the cost when you've watched 0 movies- its the initial price you pay, or the y value when the x value is equal to 0
the slope is the cost of each movie, or the increment by which the y values goes up when the x value goes up by 1 in this case. (for example the slope would be 5 if the movie price were 5 for each one movie)
y=mx+b is the equation for a linear equation, where m is the slope and b is the y intercept.
