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:
1. 32, 12
2. Enlargement
Step-by-step explanation:
Enlarged by a scale factor of 4
(Multiply all points by 4)
8 x 4 = 32
3 x 4 = 12
It is an enlargement because the points are larger than before.
Answer:
Probability that the person preferred milk as his or her primary drink = 0.3
Step-by-step explanation:
Given -
In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast .
Total no of people is = 18 + 29 + 13 = 60
If a person is selected at random ,
The probability of person preferred milk = 
The probability of person preferred coffee = 
The probability of person preferred juice = 
Probability that the person preferred milk as his or her primary drink =
P ( milk ) = 
= = 0.3
Answer:
D
Step-by-step explanation:
If its right let me know I think this is right
Answer:
Savings on electricity per year by brand B = 114.3 - 104.76 = $9.54
Step-by-step explanation:
Ms. Wang is shopping for a new refrigerator. Brand A costs $569 and uses 635 kilowatt-hours per year. Brand B costs $647 and uses 582 kilowatt-hours per year.
Let's assume he buys brand B, so he already has a loss over the price of the commodity that is , loss = 647 - 569 =$78
Cost of electricity = $0.18
Now in the case of electricity,
spending on Brand A = 635
0.18 = $114.3
spending on Brand B = 582 0.18 = $104.76
Savings on electricity per year by brand B = 114.3 - 104.76 = $9.54
