Cami and Enrique's ages add up to 46. Cami is two years older than three times Enrique's age. How old are Cami and Enrique?

walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts p

laila [671]

Answer:

5 trees should be planted to maximize the yield per acre,

The maximum yield would be 1250

Step-by-step explanation:

Given,

The original number of trees per acre = 20,

Average pounds of nuts by a tree = 60,

Let x be the times of increment in number of trees,

So, the new number of trees planted per acre = 20 + x

∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,

So, the new number of pounds of nut = (60 - 2x)

Thus, the total yield per acre,

$Y(x) = (20+x)(60-2x)$

Differentiating with respect to t ( time ),

$Y'(x) = (20+x)(-2) + 60 - 2x = -40 - 2x + 60 - 2x = 20 - 4x$

Again differentiating with respect to t,

$Y''(x) = -4$

For maxima or minima,

$Y'(x) = 0$

⇒ 20 - 4x = 0

⇒ 20 = 4x

⇒ x = 5,

For x = 5, Y''(x) = negative,

Hence, Y(x) is maximum for x = 5,

And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,

i.e. 5 trees should be planted to maximize the yield per acre,

and the maximum yield would be 1250 pounds

4 0

3 years ago

How do I "undo" multiplication

Law Incorporation [45]

A way of undoing any operation, is using the inverse of the operation. So if you want to ‘undo’ addition you subtract, and if you want to ‘undo’ multiplication you divide.

Hope this helps!!

8 0

3 years ago

Read 2 more answers

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b

Olegator [25]

Answer:

Number of ovens must be manufactured in a given week to generate a profit of $1610 is 70

Step-by-step explanation:

We are given

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula

$P=\frac{1}{10}x(300-x)$

provided that 0 ≤ x ≤ 200

We are given

profit is $1610

so, we can set P=1610

and then we can solve for x

$1610=\frac{1}{10}x(300-x)$

Multiply both sides by 10

$1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10$

$16100=x\left(300-x\right)$

$16100=300x-x^2$

$-x^2+300x-16100=0$

now, we can factor it

$(x-70)(x-230)=0$

we can solve for x

and we get

$x=70,x=230$

Since, x=230 does not lie on 0 ≤ x ≤ 200

So, we will consider only x=70

So,

Number of ovens must be manufactured in a given week to generate a profit of $1610 is 70

7 0

3 years ago

What is 93 divided by 7

igomit [66]

7 goes into 9, that's 1.
Remaining 2.

Move the 2 close to 3, you have 23.

7 into the 23, that's 3 times. 3 times 7 is 21.
So you are left with 2.

The answer is 13 remainder 2.

13\2\7

5 0

3 years ago

Read 2 more answers

Determine the next 3 terms after : 1 , -2 , 3 , -4 , 5

baherus [9]

<h3>Answer: -6, 7, -8</h3>

Start with the sequence {1, 2, 3, 4, 5, 6, 7, 8, ...}

Then change the sign of every other term so you'll have the first term positive, the second term negative, and so on.

That updates to {1, -2, 3, -4, 5, -6, 7, -8, ...}

Every odd term (1,3,5,..) is positive while every even term (-2,-4,-6) is negative.

4 0

3 years ago