Simplify the expression.
24
The value of f(5) is 49.1
Step-by-step explanation:
To find f(x) from f'(x) use the integration
f(x) = ∫ f'(x)
1. Find The integration of f'(x) with the constant term
2. Substitute x by 1 and f(x) by π to find the constant term
3. Write the differential function f(x) and substitute x by 5 to find f(5)
∵ f'(x) =
+ 6
- Change the root to fraction power
∵
= 
∴ f'(x) =
+ 6
∴ f(x) = ∫
+ 6
- In integration add the power by 1 and divide the coefficient by the
new power and insert x with the constant term
∴ f(x) =
+ 6x + c
- c is the constant of integration
∵ 
∴ f(x) =
+ 6x + c
- To find c substitute x by 1 and f(x) by π
∴ π =
+ 6(1) + c
∴ π =
+ 6 + c
∴ π = 6.4 + c
- Subtract 6.4 from both sides
∴ c = - 3.2584
∴ f(x) =
+ 6x - 3.2584
To find f(5) Substitute x by 5
∵ x = 5
∴ f(5) =
+ 6(5) - 3.2584
∴ f(5) = 49.1
The value of f(5) is 49.1
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Answer: plan A lasts for 0.5 hour. Plan B lasts for 0.75 hour.
Step-by-step explanation:
Let x represent the duration of plan A.
Let y represent the duration of plan B.
On Friday there were 3 clients who did plan A and 2 who did Plan B.
Joe trained his Friday clients for a total of 3. It means that
3x + 2y = 3- - - - - - - - - -1
On Saturday there were 5 clients who did plan A and 6 who did plan B. Joe trained his Saturday clients for a total of 7 hours. It means that
5x + 6y = 7- - - - - - - - - 2
Multiplying equation 1 by 5 and equation 2 by 3, it becomes
15x + 10y = 15
15x + 18y = 21
Subtracting, it becomes
- 8y = - 6
y = - 6/-8
y = 0.75
Substituting y = 0.75 into equation 1, it becomes
3x + 2 × 0.75 = 3
3x + 1.5 = 3
3x = 3 - 1.5 = 1.5
x = 1.5/3
x = 0.5
Hi there!
When a segment is tangent to a circle, it is perpendicular to the radius. If you're given measurements, like the image below, you can use the pythagorean theorem to determine if the triangle is a right triangle. If the triangle is right, then the segment is tangent to the circle.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Answer: $17,000 invested in bonds and $13,000 in certificate of deposit
Step-by-step explanation: let x = amount invested in bonds
y = amount invested in certificate of deposits.
According to the question, amount invested in bonds is $4000 more than the amount invested in certificate of deposits.
x = y + $4000 — (1)
Also from the question, the total money for investment is $30,000
x + y = $30,000 — (2)
By substituting eqn (1) into eqn (2), we have
y + 4000 + y = 30, 000
2y + 4000 = 30,000
2y = 30,000 - 4000
2y = 26,000
y = $ 13,000
But x + y = 30,000 where y = 13,000
x + 13, 000 = 30,000
x = 30,000 - 13,000
x = $17,000
Hence $17, 000 is invested in Bonds and $13, 000 in certificate of deposit