1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AveGali [126]
3 years ago
9

How much greater is the sum of the first 100 triangular numbers than the sum of the first 99 triangular numbers? Answer: It is b

igger.
Mathematics
2 answers:
sergiy2304 [10]3 years ago
5 0

Answer:

First, a triangular number can be written as:

Tₙ = (n^2 + n)/2

where n is the number of our triangular number, n = 1 represents the first one, n = 2 represents the second one, etc.

The sum of the first 100 triangular numbers is:

S1 = (T₁ + T₂ + ... + T₉₉ + T₁₀₀)

The sum of the first 99 triangular numbers is:

S2 = (T₁ + T₂ + ... + T₉₉)

Then the difference will be:

D = S1 - S2 = (T₁ + T₂ + ... + T₉₉ + T₁₀₀) - (T₁ + T₂ + ... + T₉₉) = T₁₀₀

And we can find the value of T₁₀₀ if we use the equation for triangular numbers:

T₁₀₀ = (100^2 + 100)/2 = 5,050

frutty [35]3 years ago
5 0

Answer:

First of all I don't understand either, and I got it wrong.

Step-by-step explanation:

You might be interested in
Consider the functions f and g defined by \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt
tino4ka555 [31]

Answer:

The given functions are not same because the domain of both functions are different.

Step-by-step explanation:

The given functions are

f(x)= \sqrt{\dfrac{x+1}{x-1}}

g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}

First find the domain of both functions. Radicand can not be negative.

Domain of f(x):

\dfrac{x+1}{x-1}>0

This is possible if both numerator or denominator are either positive or negative.

Case 1: Both numerator or denominator are positive.

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

Case 2: Both numerator or denominator are negative.

x+1\leq 0\Rightarrow x\leq -1

x-1\leq 0\Rightarrow x\leq 1

So, the function is defined for x≤-1.

From case 1 and 2 the domain of the function f(x) is (-∞,-1]∪[1,∞).

Domain of g(x):

x+1\geq 0\Rightarrow x\geq -1

x-1\geq 0\Rightarrow x\geq 1

So, the function is defined for x≥1.

So, domain of g(x) is [1,∞).

Therefore, the given functions are not same because the domain of both functions are different.

4 0
3 years ago
How to name a ray 3 different ways?
MAVERICK [17]
<span>1)A ray has one endpoint and extends indefinitely in one direction.
2)A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions.
<span>3)Rays are always named with two points and the first point in the name must be the endpoint.</span></span>
5 0
3 years ago
What is the percent / degree of X ?
tia_tia [17]

Answer: 65

Step-by-step explanation:

All those angles added up have to equal 360 degrees.

The little square on the angle to the left of x means that it's a right angle, or 90 degrees.

360

- 180

= 180 <--- this is the bottom half,

180

- 90 <--- the right angle on the left

= 90

90

-25

= 65 <--- that's x

8 0
2 years ago
Need help pls pls!!!!!!
Artyom0805 [142]

Answer:

2916 ft³

Step-by-step explanation:

•the diameter of the sphere is 18 ft , to find the radius(r) you have to divide it by 2 ,

•which gives 9ft .

•And they also told you to take the value of pie as 3.

•So, substitute the values into the formula given for V and you will have your answer.

Hope I was able to help:))

4 0
3 years ago
Which multiplication problem is represented by the model
Ivenika [448]

Answer:

It's the second one. Press 'Ask For Help' if you need more help on problems

3 0
3 years ago
Other questions:
  • There were 11 friends playing a video game online when 5 friends quit.If each player left had 5 lives,how many lives did they ha
    6·2 answers
  • Solve for x and y. What is m
    12·1 answer
  • Hector waters his lawn if it does not get least 1 1/2 inches of rain each week. it has rained 3/8 inch already this week. which
    15·2 answers
  • penny reads 10 pages in one fourth 1/4 hour. What is the unit rate for pages per​ hour? For hours per​ page?
    10·2 answers
  • Which of the following values best approximates the length of C in triangle ABC where C=
    15·1 answer
  • The volume of a rectangular prism is 240 cubic feet. The length is 8 feet and the height is 5 feet. What is the width?
    5·1 answer
  • For which of the following displays of data is it not possible to find the mean?
    6·2 answers
  • Is 8(a+b) and (6a+3b)+2b equivalent
    13·1 answer
  • Hurry Plsssss answer!
    5·2 answers
  • A self-serve car wash charges $5.22 to use its facilities, plus an additional $0.84 for each minute the customer is at the self-
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!