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3 years ago

Find the sum of 997 + 992 + 987 +...+ 257 +252

Mathematics

1 answer:

Vikentia [17]3 years ago

7 0

Answer:

93,675

Step-by-step explanation:

We see that the given sequence is an arithmetic sequence with first term 997, common difference -5, and last term 252.

The number of terms in the sequence (n) can be found from the formula for the n-th term:

an = a1 +d(n -1)

(an -an)/d +1 = n

(252 -997)/(-5) +1 = n = 150

The sum of these terms is the average of the first and last terms, multiplied by the number of terms:

S150 = (997 +252)/2·150 = 93,675

The sequence sum is 93,675.

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Simplify using trigonometric identities<br> 2sinθ - sin2θ cosθ

Anit [1.1K]

Double angle identity for sine:

$\sin(2x) = 2 \sin(x) \cos(x)$

$\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)$

Factorize the left side.

$2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)$

Pythagorean identity:

$\cos^2(x) + \sin^2(x) = 1$

$\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)$

so that

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8 0

2 years ago

Which ordered pair (a, b) is a solution to the given system of linear equations? -2a+3b=14

Stels [109]

Answer:

The solution of the system is the ordered pair (-13,-4)

Step-by-step explanation:

we have

$-2a+3b=14$ -----> equation A

$a-4b=3$ ----> equation B

Solve the system by elimination

Multiply by 2 both sides equation B

$2(a-4b)=2(3)$

$2a-8b=6$ ----> equation C

Adds equation A and equation C

$-2a+3b=14\\2a-8b=6\\-------\\3b-8b=14+6\\-5b=20\\b=-4$

<em>Find the value of a</em>

substitute the value of b in any equation (i take equation B)

$a-4(-4)=3$

$a+16=3$

$a=-13$

therefore

The solution of the system is the ordered pair (-13,-4)

6 0

3 years ago

Read 2 more answers

I really appreciate all the help guys<3

Tems11 [23]

Answer:

2.4

Step-by-step explanation:

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3 years ago

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Andrews [41]

Answer:

Step-by-step explanation:

8 0

2 years ago

At the baseball stadium, the price for popcorn is $5.88 for 3 bags. If you want to buy 7 bags of popcorn, how much will it cost?

4vir4ik [10]

The answer will be $13.72 for 7 bags of popcorn.

to find this answer, you first take 5.88 and divide it by 3 to find out how much one bag costs.

the answer to 5.88/3 is 1.96, so you multiply 1.96 by 7 to get the answer of how much 7 bags of popcorn will cost.

hope this helps!

4 0

3 years ago

Read 2 more answers