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Dmitrij [34]
3 years ago
10

Find two positive numbers satisfying the given requirements. the product is 192 and the sum of the first plus three times the se

cond is a minimum. (first number) (second number)
Mathematics
1 answer:
Zepler [3.9K]3 years ago
6 0
<h3>Given</h3>

Two positive numbers x and y such that xy = 192

<h3>Find</h3>

The values that minimize x + 3y

<h3>Solution</h3>

y = 192/x . . . . . solve for y

f(x) = x + 3y

f(x) = x + 3(192/x) . . . . . the function we want to minimize

We can find the x that minimizes of f(x) by setting the derivative of f(x) to zero.

... f'(x) = 1 - 576/x² = 0

... 576 = x² . . . . . . . . . . . . multiply by x², add 576

... √576 = x = 24 . . . . . . . take the square root

... y = 192/24 = 8 . . . . . . . find the value of y using the above equation for y

The first number is 24.

The second number is 8.

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Passes through<br> (-8, 3) and (8, -1).
lawyer [7]

Answer:

Slope = Y2 -Y1 / X2 - X1

Slope = -1 -3 / 8 --8

Slope = -4 / 16

Slope = -1 / 4

To calculate the equation we fill in this equation:

(y - y1) = slope • (x -x1)

We only need to choose 1 point so we'll choose (-8, 3)

(y - 3) = -1 / 4 * (x --8)

So the Equation equals

y = -1 / 4 x -2 + 3

y = -1 / 4x +1

Source:

http://www.1728.org/distance.htm

Step-by-step explanation:

5 0
3 years ago
PlEASE HELP ME PEOPLE HUMPTH OK ILL SAY IT PEOPLE WANT MONEY TO ANSWER PROBLEMS HERE If the mean of six nu m b e rs is 48, does
SpyIntel [72]

Answer:

No, none of the number need to be 48 for the mean to be 48. To get a mean, you add up all the number and divide it by the amount of numbers.

Example:

the mean of 10, 79, 42, 88, 19, and 50 is 48, but the actual number 48 was not part of the set.

10 + 79 + 42 + 88 + 19 + 50 = 288

288 ÷ 6 = 48

6 0
3 years ago
If f(x)=3x-2,find f(8)-f(-5)
Alexandra [31]

To find both f(8) and f(-5), we will need to plug in their values for x and solve for each. Then, we can subtract them to find the final answer.

Finding f(8):

f(8) = 3(8) - 2

f(8) = 24 - 2

f(8) = 22

Finding f(-5):

f(-5) = 3(-5) - 2

f(-5) = -15 - 2

f(-5) = -17

Subtracting f(8) and f(-5):

f(8) - f(-5)

22 - - 17

22 + 17

39

Hope this helps!! :)

6 0
3 years ago
Two friends are biking. Greta starts at mile marker S on a bike trail and is biking at a speed of 12 miles per hour The table sh
Alinara [238K]

The distance covered by Greta after biking at a speed of 12 miles per hour for x hours is 12x miles.

<h3>What is speed?</h3>

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Greta starts at mile marker S on a bike trail and is biking at a speed of 12 miles per hour. If she biked for x hours:

Distance covered = 12 mph * x = 12x miles

The distance covered by Greta after biking at a speed of 12 miles per hour for x hours is 12x miles.

Find out more on speed at: brainly.com/question/4931057

7 0
2 years ago
A major baseball diamond is a square with side lengths of 90 feet.
iren2701 [21]

Answer: \bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}

<u>Step-by-step explanation:</u>

Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square.  Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

90^2+90^2=c^2\\8100+8100=c^2\\16200=c^2\\\sqrt{16200}=c\\\boxed{90\sqrt2}=c\qquad \qquad \text{which is approximately 127.28}\\\\\\\\\text{Halfway between home plate and 2nd base means divide that length by 2:}\\\\\dfrac{90\sqrt2}{2}=\boxed{45\sqrt2}

7 0
3 years ago
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