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3 years ago

ravis gas tank is 1/2 full .after he buys 2 gallons of gas it is 2/3 full how many gallons can ravis tank hold?

1 answer:

8 0

So
1/2x+2=2/3x
convert to common fraction
1/2=3/6
2/3=4/6
3/6x+2=4/6x
subtract 3/6x from both sides
2=1/6x
multiply boh tisdes by 6
12=x
the tank can hold 12 gallon

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Jenny uses a roller to paint a wall. The roller has a radius of 1.75 inches and a height of 10 inches. In two rolls, what is the

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Answer:

The area of the wall that she will paint in two rolls is <u>219.8 inches²</u>.

Step-by-step explanation:

Given:

Jenny uses a roller to paint a wall. The roller has a radius of 1.75 inches and a height of 10 inches.

Now, to find the area of the wall that she will paint in two rolls.

So, we find the lateral surface area of roller.

Radius (r) = 1.75 inches.

Height (h) = 10 inches.

So, to get the lateral surface area we put formula:

$A_{L} =2\pi rh$

$A_L=2\times 3.14\times 1.75\times 10$

$A_L=109.9\ inches^2.$

Thus, the lateral surface area of the roller = 109.9 inches².

Now, to get the area of wall that she will paint in two rolls we multiply 2 by the lateral surface area of the roller:

$109.9\times 2\\\\=219.8\ inches^2.$

Therefore, the area of the wall that she will paint in two rolls is 219.8 inches².

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3 years ago

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Determine if the following infinite series converges or diverges

Mandarinka [93]

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

<h3>How do we verify if a sequence converges of diverges?</h3>

Suppose an infinity sequence defined by:

$\sum_{k = 0}^{\infty} f(k)$

Then we have to calculate the following limit:

$\lim_{k \rightarrow \infty} f(k)$

If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

$f(k) = \frac{k^3}{k^4 + 10}$

Hence the limit is:

$\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0$

Hence, the infinite sequence converges, as the limit does not go to infinity.

More can be learned about convergent sequences at brainly.com/question/6635869

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2 years ago

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bezimeni [28]

Compound interest can be defined as the interest <em>on a deposited amount, an investment</em> that is <em>compounded based on its principal and interest rate.</em>

It will take about 3.239 years for the principal amount of $13,000 to double its initial value.

From the above question, we can deduce that we are to find the time "t"

The formula to find the time "t" in compound interest is given as:

t = ln(A/P) / r

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R = Interest rate = 21.4%

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From the question, the Amount "A" is said to be the double of the principla.

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