1. Find the product of 2.1 and 3.4.
2 answers:
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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
Answer:
5. None of the above
Step-by-step explanation:
We have this information:
A = 60 cm2
b = 2*h - 1
Let's find out b and h:
The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have
Let's find h with the quadratic formula:
h = 8 or h = -7.5
But h represents the height of the triangle, so it has to be a positive number, that's h = 8.
If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.
Now we can calculate the hypotenuse with the Pythagorean equation
<em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle).
</em>
The base and the height are our legs. We will use "H" for the hypotenuse
H = 17
If we decrease the base and the height by 2 centimeters, we have
b' = 15 - 2 = 13 and h' = 8 - 2 = 6
With this, let's calculate the new hypotenuse:
So, the hypotenuse decreases