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3 years ago

Determine if the following series converges or diverges. Show steps!

Mathematics

1 answer:

MAXImum [283]3 years ago

3 0

Converges by p series test
top section is almost constant, can never be larger than 3
so, compare degrees of their exponents, in this case it’s at a maximum of 3/1000n^2. the same as saying (3/1000)*summation of p series.
converges absolutely.

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A chocolate bar contains 50 calories and s of protein and makes a

Alla [95]

Answer:

He should serve 2 chocolate bars and 2 granola bars

Step-by-step explanation:

Let's define

x: amount of chocolate bar

y: amount of granola bar

We are asked to solve the following optimization problem:

maximize 7*x + 2*y

subject to

50*x + 25*y ≤ 150

5*x + 15*y ≥ 40

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In the figure attached, the feasible region is shown. The solution is one of the vertex

vertex objective function

(0, 2.667) 7*0 + 2*2.667 = 5.334

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3 years ago

A card is drawn from a well shuffled deck of 52 cards. find the probability of drawing a 7 of hearts

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3 years ago

Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the qua

goblinko [34]

<h2>Hello!</h2>

The answer is: There is a total of 5.797 gallons pumped during the given period.

To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)

The given function is:

$D(t)=\frac{5t}{1+3t}$

So, the integral will be:

$\int\limits^4_0 {\frac{5t}{1+3t}} \ dx$

So, integrating we have:

$\int\limits^4_0 {\frac{5t}{1+3t}} \ dt=5\int\limits^4_0 {\frac{t}{1+3t}} \ dx$

Performing a change of variable, we have:

$1+t=u\\du=1+3t=3dt\\x=\frac{u-1}{3}$

Then, substituting, we have:

$\frac{5}{3}*\frac{1}{3}\int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du\\\\\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u}{u} -\frac{1}{u } \ du$