Answer:
<h2>
(e³ - 1)/3e²</h2>
Step-by-step explanation:
Given the function y = e^x between the interval x = -2 and x =1, the average rate of change for the function will be the slope of the function expressed as m = Δy/Δx where;
Δy = f(b)-f(a) and Δx = b-a
m = f(b)-f(a)/b-a where a and b is the interval [-2, 1]
m = f(1)-f(-2)/1-(-2)
m = f(1)-f(-2)/3
Given the function f(x) = e^x,
at the end point x = b, f(1) = e^1; f(1) = e
at the end point x = a, f(-2) = e^-2; f(-2) = 1/e²
m = (e - 1/e²)/3
m = [(e³ - 1)/e²]/3
m = (e³ - 1)/e² * 1/3
m = (e³ - 1)/3e²
Hence, the average rate of change for the function at the interval [-2, 1] is (e³ - 1)/3e²
Answer:
S₁₀=620
Step-by-step explanation:
This is an arithmetic sequence with a common difference of d=12
The formula for an arithmetic series is Sₙ=(n/2)(a₁+aₙ) where aₙ is the nth term and a₁ is the first term.
We know that a₁=8 and d=12 where the 10th term would be a₁₀=8+(10-1)12=116.
Therefore, the sum of the first 10 terms of the arithmetic series is S₁₀=(10/2)(8+116)=(5)(124)=620
<span>
<span>first off your answer is 21.90 and the step by step i wrote it for you:) Finding the
square root of a number is the inverse
operation of squaring that number. Remember, the square of a number
is that number times itself. </span>
The perfect
squares are the squares of the whole numbers.
The square root
of a number, n, written below is the number that gives n when multiplied by
itself.
</span> <span>Many mathematical
operations have an inverse, or opposite, operation. Subtraction is the opposite
of addition, division is the inverse of multiplication, and so on. Squaring,
which we learned about in a previous lesson (exponents),
has an inverse too, called "finding the square root." Remember, the
square of a number is that number times itself. The perfect squares are the
squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … </span>
The square root
of a number, n, written
<span>
is the number that gives n when multiplied by itself. For example,</span>
<span>because
10 x 10 = 100</span>
Examples
Here are the
square roots of all the perfect squares from 1 to 100.
Finding square
roots of of numbers that aren't perfect squares without a calculator
1. Estimate
- first, get as close as you can by finding two perfect square roots your
number is between.
2. Divide -
divide your number by one of those square roots.
3. Average -
take the average of the result of step 2 and the root.
<span>4. Use the result
of step 3 to repeat steps 2 and 3 until you have a number that is accurate
enough for you.
</span>
Example:
Calculate the square root of 10 ()
to 2 decimal places.
<span>1. Find
the two perfect square numbers it lies between.
</span>
<span><span>Solution:
</span><span>32
= 9 and 42 = 16, so
lies between 3 and 4.</span></span>
<span>2. Divide
10 by 3. 10/3 = 3.33 (you can round off your answer)</span>
<span>3. Average
3.33 and 3. (3.33 + 3)/2 = 3.1667</span>
<span>Repeat step
2: 10/3.1667 = 3.1579</span><span>Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span>
Try the answer
--> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001
If this is accurate
enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.
<span>Note:
There are a number of ways to calculate square roots without a calculator.
This is only one of them.</span>
<span><span>
</span>
</span>
<span>
<span />Example:
Calculate the square root of 10 ()
to 2 decimal places.
<span>1.
Find the two perfect square numbers it lies between.
</span>
<span><span>Solution:
</span><span>32
= 9 and 42 = 16, so
lies between 3 and 4.</span></span>
<span>2.
Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)</span>
<span>3.
Average 3.33 and 3. (3.33 + 3)/2 = 3.1667</span>
<span>Repeat
step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span>
<span>Try
the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 =
10.0001</span>
If
this is accurate enough for you, you can stop! Otherwise, you can repeat steps
2 and 3.
</span>
<span>
<span><span>
<span> </span></span></span></span>
<span>3n - (2 + n)
Substitute 4 for variables
3(4) - (2+4)
Combine like terms
12 - 6
Subtract
Final Answer: 6
And so the correct answer would be B. 4.</span>
Answer:
$960
Step-by-step explanation:
30^2 is 900
30x2 is 60
900+60 is 960.
Hope this helps plz hit the crown :D