Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
= 3·4ⁿ + 51
= 3·4ⁿ⁺¹ + 51
- = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
- = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ - is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since - is divisible by 9, we have;
- 
= 
- is divisible by 9
Therefore is divisible by 9 and is divisible by 9 for all positive integers n
Step-by-step explanation:
Answer:
19°
Step-by-step explanation:
I have attached an image showing this elevation.
From the image, let's first find the angle A by using cosine rule.
Thus;
8.1² = 5.5² + 13.1² - 2(5.5 × 13.1)cos A
65.61 = 30.25 + 171.61 - 144.1cos A
144.1cos A = 171.61 + 30.25 - 65.61
144.1cosA = 136.25
cosA = 136.25/144.1
cosA = 0.9455
A = cos^(-1) 0.9455
A = 19°
Answer would be <span>6.
i've done this one before.</span>
A percentage is a way to describe a part of a whole. The money that is raised by Nina in the second month is $960.
<h3>What are Percentages?</h3>
A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the money raised by Nina in the first month is $800, while the money raised by Nina in the second month is 20% more.
Therefore, the money raised by Nina in the second month is,
Money raised = $800 + 20% of $800
= $800 + 0.20($800)
= $800 + $160
= $960
Hence, the money that is raised by Nina in the second month is $960.
Learn more about Percentages here:
brainly.com/question/6972121
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Answer:
.fnm k.v tkr vijt 3ogubt4er giutbgo6jgn43o4goujgnogno'itng'
Step-by-step explanation:
