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3 years ago

Find the two numbers whose sum is 24 and whose product is as large as possible.

1 answer:

4 0

Let, the numbers are: x, (24-x)
Let, P(x) denote their products. Then, we have:
P(x) = x(24-x) = 24x - x²
P'(x) = 24-2x
P''(x) = -2

Now, P'(x) = 0 ⇒ x = 12
Also,
P''(12) = -2 < 0

So, By second derivative test, x = 12 is the point of local maxima of p. Hence the product of the numbers is the maximum when the numbers are 12 and (24-12) = 12

So, In short that numbers would be 12,12

Hope this helps!

You might be interested in

Driving is difficult if the weather is stormy. Driving is difficult

amm1812

Answer:

answer: yes driving is difficult

Step-by-step explanation:

A. Driving is not difficult (not true because weather effects driving conditions)

B. Not possible (not true)

C. Driving is difficult (very true because weather makes driving harder)

D. If driving is difficult, then the weather is stormy  (this is true but not grammarly correct )

BEST OPTION IS DRIVING IS DIFFICULT !

4 0

4 years ago

Is y=X/2 or y=2/x proprtinal or non proportinoal

Irina-Kira [14]

Y = X/2 is directly proportional
Y = 2/X is not directly proportional

Hope this helps! :)

8 0

3 years ago

suppose you deposit $2,475 in a savings account that earns 6.25% simple interest per year. How much simple interest would be ear

Nikolay [14]

$116.02 interest will be earned in 9 months

Step-by-step explanation:

The formula for simple interest is given by:

$I = Prt$

Here

P is the initial amount

r is the interest

t is the time measured in years

Given

P = $2475

r = 6.25% = $\frac{6.25}{100} = 0.0625$

t = 9 months

Converting time into year by dividing by 12

$t = \frac{9}{12}\ years = 0.75\ year$

Putting the values in the formula

$I = 2475 * 0.0625 * 0.75\\I = 116.0156$

Rounding off to nearest hundredth

I = $116.02

Hence,

$116.02 interest will be earned in 9 months

Keywords: Interest, simple interest

Learn more about simple interest at:

#LearnwithBrainly

6 0

3 years ago

How many 1/4 servings are in a 12 cup container

aliya0001 [1]

Answer: The required number of $\dfrac{1}{4}$ servings in a 12 cup container is 48.

Step-by-step explanation: We are given to find the number of $\dfrac{1}{4}$ servings in a 12 cup container.

We will be using the UNITARY method to solve the given problem.

We have

Number of 1 serving in a 12 cup container = 12.

Therefore, the number of $\dfrac{1}{4}$ servings in a 2 cup container is given by

$\dfrac{12}{\dfrac{1}{4}}=12\times4=48$

Thus, the required number of $\dfrac{1}{4}$ servings in a 12 cup container is 48.

3 0

4 years ago

Read 2 more answers

What is the equation of the line that passes through the points (-4,3) and (2,-6)

Nonamiya [84]

Answer: y = -1.5x - 3

Step-by-step explanation:

We'll assume this is a straight line, with the form y=mx+b. m is the slope (the rate that y changes with a change in x) and b is the y-intercept (the value of y when x=0).

Once we can determine both m and b, we'll have an equation that answers this question. First, m.

m, the slope, is known as the Rise/Run. We can use the two given points to calculate this value. Take the two points, (-4,3) and (2,-6), and calculate the change in x (the Run), by subtrating the initial point (I'll choose (-4,3)) from the final point ((2,-6)). For x that is: 2-(-4) = 6. For y: -6-3 = -9. When x moved +6 units, y went down by 9, or -9. The slope is the Rise (-9) over the Run (6), or (-9/6). The slope of this line is - 1.5.

We now have y = -1.5x + b. To find b, use wither of the two points. I'll use (2,-6) because I like even numbers, but fell free to use the other. Both will give the same answer for b. [Try it].

Using (2,-6), we get:

y = -1.5x + b

-6 = -1.5*(2) + b

-6 = -3 + b

b = -3

The equation is y = -1.5x - 3

=====

For fun, try the other point, (-4,3) to find the value of b:

y = -1.5x + b

3 = -1.5*(-4) + b

3 = 6 + b

b = -3 The Same!

4 0

3 years ago