The lines represented by the equations 4y + 4x = 8 and y - x = -2 are
1 answer:
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Let
F--------> represent the force
m--------> represent the mass
a-------> represent the acceleration
we know that
The formula that relates three quantities: Force (F), mass (m), and acceleration (a) is equal to
<u>Part a)</u> Solve this equation for a
Divide both sides by the mass
therefore
<u>the answer part a) is equal to</u>
<u>Part b) </u>Let the force be 25 units and the mass be m = 10 units. What is the acceleration, a?
we know that
the formula of acceleration is equal to
in this problem
we have
Substitute the values n the formula
therefore
<u>the answer part b( is equal to</u>
<u>Part c)</u> Let the force be F = 25 units and the acceleration be a = 5 units. What is the mass, m?
we know that
Solve for m
Divide both sides by the acceleration
in this problem
we have
Substitute the values n the formula
therefore
<u>the answer Part c) is </u>
Answer:
The value of n is 10
Step-by-step explanation:
The formula of the nth term of the arithmetic progression is a = a + (n - 1)d
- a is the first term
- d is the common difference between each 2 consecutive terms
- n is the position of the term
The formula of the sum of nth terms is S =
[2a + (n - 1)d]
∵ An AP has a common difference of 3
∴ d = 3
∵ The nth term is 32
∴ a = 32
→ Substitute them in the 1st rule above
∵ 32 = a + (n - 1)3
∴ 32 = a + 3(n) - 3(1)
∴ 32 = a + 3n - 3
→ Add 3 to both sides
∴ 35 = a + 3n
→ Switch the two sides
∴ a + 3n = 35
→ Subtract 3n from both sides
∴ a = 35 - 3n ⇒ (1)
∵ The sum of the first n terms is 185
∴ S = 185
→ Substitute the value of S and d in the 2nd rule above
∵ 185 = [ 2a + (n - 1)3]
∴ 185 = [2a + 3(n) - 3(1)]
∴ 185 = [2a + 3n - 3]
→ Multiply both sides by 2
∴ 370 = n(2a + 3n - 3)
∴ 370 = 2an + 3n² - 3n
→ Substitute a by equation (1)
∴ 370 = 2n(35 - 3n) + 3n² - 3n
∴ 370 = 70n - 6n²+ 3n² - 3n
→ Add the like terms in the right side
∵ 370 = -3n² + 67n
→ Add 3n² to both sides
∴ 3n² + 370 = 67n
→ Subtract 67 from both sides
∴ 3n² - 67n + 370 = 0
→ Use your calculator to find n
∴ n = 10 and n = 37/3
∵ n must be a positive integer ⇒ 37/3 neglecting
∴ n = 10
∴ The value of n is 10