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:
32 goldfish
Step-by-step explanation:
Given:
- Number of fish tanks = 8
- Volume of water per fish tank = 5,544 in³
- Water required by 1 goldfish = min 1,386 in³
Number of fish per tank = water per tank ÷ water per goldfish
= 5544 ÷ 1386
= 4
Therefore, each tank can hold a maximum of 4 goldfish.
Greatest number of goldfish = number of tanks × fish per tank
= 8 × 4
= 32
Step-by-step explanation:
17) 3x+5-12+4x+2x
3x+4x+2x +5-12
8x-7
if x =6
8*6-7 =48-7
= 41
18.) 9(3x-4y+8)
27x-36y+72
A constant is a number, or a letter that represents a number that
never changes. From the time the problem starts until as long
as it lasts, its value is constant.
A variable is a letter that stands for a number that can change.
A coefficient is each of the items in a group of them that are all
multiplied together.
Example: 17x + 4y
That's an expression with two terms.
The terms are '17x' and '4yz'.
In the first term:
'17' is the numerical coefficient.
'x' is the literal coefficient.
In the second term:
'4' is the numerical coefficient.
'y' and 'z' are both literal coefficients.
