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Ivanshal [37]
3 years ago
10

50+51+52+...+101=...Can you help me? I do not understand

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
5 0

Suppose

S=50+51+52+\cdots+100+101

At the same time, we can write

S^*=101+100+99+\cdots+51+50

Note that S=S^* (just reverse the sum). Let's pair the first terms of S and S^*, and the second, and the third, and so on:

S+S^*=(50+101)+(51+100)+(52+99)+\cdots+(100+51)+(101+50)

Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas

S+S^*=52\cdot151

But S=S^*, as we pointed out, so

2S=52\cdot151\implies S=\dfrac{52\cdot151}2=3926

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horrorfan [7]

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3 years ago
Zach wants to build a slanted skateboard ramp. He knows he wants the ramp to form a 15 degrees angle with the ground and be 4 fe
Fynjy0 [20]

Answer: The ramp would be 15.5 feet long.

Step-by-step explanation: Please refer to the attached diagram for details.

Angle C shows the angle to be formed by the ramp from the ground, which is 15 degrees. Also, from the ground, it’s going to be four feet tall, which is line AB. The top of the ramp is point A, which makes line AC the entire length of the ramp. Since we have a reference angle (angle C) and two sides, the opposite and the hypotenuse, we shall apply the trigonometric ratio.

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3 years ago
Bozena is an ecologist who studies the change in the tiger population of Siberia over time. The relationship between the elapsed
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2 years ago
Ok i have a few questions please give examples and descriptions as well
Arte-miy333 [17]

Answer:

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2)Where you multiply the two exponents together

3)The negative law is where for example, if it were in the numerator, then it would be placed at the denominator with a positive exponent whereas if it were in the denominator it would be on the numerator with the positive exponent. The zero law just states the anything to the power to zero is one.

Step-by-step explanation:

1) 3^3 x 3^4 = 3 ^3+4 = 3^7

3^9 ÷3² = 3^9-2 = 3^7

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3^-7 =1/3^7

2^0 = 1

8 0
3 years ago
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