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Margarita [4]
3 years ago
6

The rate at which sand is poured into a bag is modeled by the function r given by r(t)=15t−2t2, where r(t) is measured in millil

iters per second and t is measured in seconds after the sand begins pouring. How many milliliters of sand accumulate in the bag from time t=0 to time t=2 ?
Mathematics
1 answer:
balu736 [363]3 years ago
6 0

Answer:

35 mililiters

Step-by-step explanation:

Given

r(t) = 15t - 2t^2

Required

Accumulated amount from t = 0 to 2

This implies that, we substitute the values of t from 0 to 2 in the function

r(0) = 15*0 - 2*0^2= 0

r(1) = 15*1 - 2*1^2= 13

r(2) = 15*2 - 2*2^2= 22

The accumulated sand (r) is:

t = r(0) + r(1) + r(2)

r = 0 + 13 + 22

r = 35

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Answer:

Step-by-step explanation:

As you can see, this is a quadratic equation and if you were to graph this you would see that it is a parabola that opens down because of the negative leading coefficient (-34). The maximum profit would be at the vertex, of the graph. Therefore, we need to find the value of "y" when "x" is the line of symmetry. We find this by  x=-b/(2a) where a = -34 and b = 1542:

x=-1542/(2)(-34)

x=-152/-68

x=152/68  

We put this value of "x" into the original formula to find out the value of "y":

y=-34x^2+1542x-10037

y=(-34)(1542/68)^2+1542(1542/68)-10037

y= -17483.5588235 + 34967.1176471 -10037

y=7446.5588236

Therefore, the maximum profit would be $7446.56.

Hope this helps!

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3 years ago
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3 years ago
Determine weather randomly picking a blue card from a bag containing all blue cards is impossible, unlikely, as likely as not, l
Anuta_ua [19.1K]

Answer:

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Step-by-step explanation:

Probability is a mathematical framework which helps us to analyze chance of the outcome in a particular experiment. The value of probability is given by the ratio of the possible outcomes favorable to a certain experiment to the total outcomes.

We say an event is certain when the probability is 1 and the probability is zero when the event is uncertain.

Here the experiment is picking a blue card from a bag containing all blue cards.

Possible outcomes are all the cards colored blue in the bag.

Total outcomes are also all the blue cards in the bag.

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