Write the function for the following chart,

Mathematics

1 answer:

timurjin [86]3 years ago

7 0

Dy/dx=1/2, 1/2, 1/2 etc

So this is a linear equation of the form y=mx+b where m=dy/dx=1/2 so

y=x/2 +b, now we can use any point to solve for the y-intercept, "b", I'll use (7,0)

0=7/2 +b

b=-7/2 so

y=x/2-7/2

y=(x-7)/2

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I am Lyosha [343]

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3 years ago

A farmer finds that if she plants 85 trees per acre, each tree will yield 80 bushels of fruit. She estimates that for each addit

vova2212 [387]

Answer:

52 Trees

Step-by-step explanation:

If she plants 85 trees per acre, each tree will yield 80 bushels of fruit.

Yield = 85 X 80

Let x be the additional tree planted per acre.

For each additional tree planted per acre, the yield of each tree will decrease by 4 bushels.

Therefore, the yield:

$F(x)=(85+x)(80-4x)\\F(x)=6800-260x-4x^2$

Next, we maximize F(x) by taking its derivatives and solving for its critical point.

$F'(x)=-260-8x\\$Setting $F'(x)=0,$ we have:$\\-260-8x=0\\8x=-260\\$Divide both sides by 8$\\x=-32.5$

$F''(x)=-8, $therefore we have a maximum$

It is apparent that she currently has too many trees per acre. To get a maximum harvest, she needs to reduce the number of trees by approximately 32.5 trees.

Therefore, number of trees per acre she should plant:

85+(-32.5)

=85-32.5

=52.5 Trees

Since the number of trees can only be an integer and it cannot be greater than 52.5, the number of trees to be planted per acre to maximize her harvest is 52.

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gregori [183]

A.1
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Read 2 more answers

Seema deposited $800 in a saving account earning 2.88% compounded annually. To the nearest cent, how much will she have in 16 ye

ehidna [41]

Answer:

1260.04

Step-by-step explanation:

The formula for compound interest is:

A = P(1+ $\frac{r}{n}$ $)^{nt}$ where A is the final amount, P is the initial principal balance, r is the interest rate, n is the number of times interest applied per time period and t is the number of time periods elapsed. Since the deposit was compounded annually, just like the interest, we can omit the n in the equation.