<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
Answer:
(a) ΔARS ≅ ΔAQT
Step-by-step explanation:
The theorem being used to show congruence is ASA. In one of the triangles, the angles are 1 and R, and the side between them is AR. The triangle containing those angles and that side is ΔARS.
In the other triangle, the angles are 3 and Q, and the side between them is AQ. The triangles containing those angles and that side is ΔAQT.
The desired congruence statement in Step 3 is ...
ΔARS ≅ ΔAQT
Answer:
The reason for the columns adding up to 1 is that each individual consumes a proportion or a fraction of the total quantity produced under each product category and every product is consumed. There is no leftover.
When the proportions of all the individuals are added up, the sum is always 1 under each product category because each individual can only consume a part of the whole.
Step-by-step explanation:
a) Data and Calculations:
Food Clothes Housing Energy High Quality 100
Proof Moonshine
Farmer 0.25 0.15 0.25 0.18 0.20
Tailor 0.15 0.28 0.18 0.17 0.05
Carpenter 0.22 0.19 0.22 0.22 0.10
Coal Miner 0.20 0.15 0.20 0.28 0.15
Slacker Bob 0.18 0.23 0.15 0.15 0.50
Total 1.00 1.00 1.00 1.00 1.00
When multiplying variables with exponents, all you have to do is to add the exponents and that’s the ‘product.’
So;
(3y^10)(2y^2) is equal to (3)(2)(y^10+2).
6y^12/8y^5
When dividing exponents, you do the opposite and subtract the exponents. And you divide the whole number by half.
6y^12/8y^5 = 3y^7/4
