Answer:
In Exercises 1-15 use mathematical induction to establish the formula for n ≥ 1.
1. 1
2 + 22 + 32 + · · · + n
2 =
n(n + 1)(2n + 1)
6
Proof:
For n = 1, the statement reduces to 12 =
1 · 2 · 3
6
and is obviously true.
Assuming the statement is true for n = k:
1
2 + 22 + 32 + · · · + k
2 =
k(k + 1)(2k + 1)
6
, (1)
we will prove that the statement must be true for n = k + 1:
1
2 + 22 + 32 + · · · + (k + 1)2 =
(k + 1)(k + 2)(2k + 3)
6
. (2)
The left-hand side of (2) can be written as
1
2 + 22 + 32 + · · · + k
2 + (k + 1)2
.
In view of (1), this simplifies to:
Answer: 180
Step-by-step explanation: 9.9 squared by 1.79 is 180
<span>Hey there, Lets solve this together.
</span>
<span>The variable (R) will be representing the rate as a decimal.
When you solve for (R) multiply by 100 to get the percentage. A percentage is </span><span>a rate, number, or amount in each hundred.
</span><span>"0.97" will be replaced by "(97/100)"
</span>
<span>Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the given equation
</span>
Rewrite the whole as a fraction using 10 <span> as the denominator :
</span>
The equation now takes the shape :
t • (10f-291)<span> = 0
</span>
<span><span> f = 291/10 = 29.100
</span> t = 0</span>
<span>Positive = Growth
Negative = Decay
</span><span>
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Answer:
8 : 2.5
Step-by-step explanation:
3√512: Convert the decimal into an equivalent fraction You can also use a calculate to divide 1 by the fraction.
<em><u>Please mark as brainliest if answer is right </u></em>
Have a great day, be safe and healthy
Thank u
XD
Answer: 1.1x
Step-by-step explanation:
Muhammad is getting paid x dollars and receives a raise of 10% of those x dollars.
New hourly wage is therefore:
= x + (10% * x)
= x + 10%x
= x + 0.1x
= 1.1x