Answer:
Diverges
General Formulas and Concepts:
<u>Algebra I</u>
- Exponential Rule [Dividing]:
<u>Calculus</u>
Limits
- Limit Rule [Variable Direct Substitution]:
Series Convergence Tests
- P-Series:
- Direct Comparison Test (DCT)
- Limit Comparison Test (LCT):
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Apply DCT</u>
- Define Comparison:
- [Comparison Sum] Simplify:
- [Comparison Sum] Determine convergence:
- Set up inequality comparison:
- [Inequality Comparison] Rewrite:
- [Inequality Comparison] Simplify:
∴ the sum is divergent by DCT.
<u>Step 3: Apply LCT</u>
- Define:
- Substitute in variables [LCT]:
- Simplify:
- [Limit] Evaluate [Coefficient Power Rule]:
∴ Because and the sum diverges by DCT, also diverges by LCT.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
Answer:
Step-by-step explanation:
y = -4x + 6.....switch x and y and solve for y
x = -4y + 6 ....subtract 6 from both sides
x - 6 = -4y....divide by -4 on both sides
(x - 6) / -4 = y or y = -1/4x + 3/2 <====
James is (B) 20 meters far from the finish line 9 seconds after the race has started.
<h3>
What is the distance?</h3>
- Distance is a numerical measurement of the distance between two objects or places.
- The distance can refer to a physical length or an estimate based on other criteria in physics or common usage.
- The distance between two points A and B is commonly expressed as |AB|.
To find the distance:
- James covers 8 meters in the opening second of the 100-meter race.
- Then he sprints at a 9-meter-per-second pace.
- We need to figure out how far James is from the finish line 9 seconds after the race begins.
- James travels 8 meters in the first second.
- After running 8 meters, the time remaining in 9 seconds is 9 - 1 = 8 seconds.
- James completes the distance = speed time = 9 8 = 72 meters in another 8 seconds.
- The total distance traveled in 9 seconds is equal to 8 + 72 = 80 meters.
- After 9 seconds, the distance remaining in a 100-meter race is 100 - 80 = 20 meters.
- 9 seconds into the race, James is 20 meters from the finish line.
Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.
Know more about distance here:
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The complete question is given below:
James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?
a. 11
b. 20
c. 28
d. 80
Answer:
500
Step-by-step explanation:
Hello!
Let the smallest number be x. The next number would be x + 1, then the next would be x + 2, then x + 3.
The sum of these four is 1998.
Solve for x:
- x + (x + 1) + (x + 2) + (x + 3) = 1998
- 4x + 6 = 1998
- 4x = 1992
- x = 498
The third number is (x + 2), so simply add 2 to 498 = 500
The third number is 500.
All 4 numbers are 498, 499, 500, and 501.
Answer:
878
Step-by-step explanation: