1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
slavikrds [6]
3 years ago
8

The sum of two nonnegative numbers is 50. What is the maximum value of the product of these two numbers ?

Mathematics
1 answer:
Umnica [9.8K]3 years ago
7 0

Answer:

625

Step-by-step explanation:

Let two number be x and (50-x).

The product of numbers be x(50-x).

P = 50x-x²

For maximizing the product,

\dfrac{dP}{dx}=0\\\\\dfrac{d}{dx}(50x-x^2)=0\\\\50-2x=0\\\\50=2x\\\\x=25

So, the maximum product, P = 50(25)-(25)²

P = 625

Hence, the maximum value of the product of these two numbers is 625.

You might be interested in
Solve the system using substitution. Show all work
kramer

Answer:

x = -2 , y = 3

Step-by-step explanation:

Solve the following system:

{4 x + 5 y = 7

y = 3 x + 9

Hint: | Perform a substitution.

Substitute y = 3 x + 9 into the first equation:

{4 x + 5 (3 x + 9) = 7

y = 3 x + 9

Hint: | Expand the left hand side of the equation 4 x + 5 (3 x + 9) = 7.

4 x + 5 (3 x + 9) = (15 x + 45) + 4 x = 19 x + 45:

{19 x + 45 = 7

y = 3 x + 9

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{19 x + 45 = 7

y = 3 x + 9

Hint: | Isolate terms with x to the left hand side.

Subtract 45 from both sides:

{19 x = -38

y = 3 x + 9

Hint: | Solve for x.

Divide both sides by 19:

{x = -2

y = 3 x + 9

Hint: | Perform a back substitution.

Substitute x = -2 into the second equation:

Answer:  {x = -2 , y = 3

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=4x%20%5E%7B2%7D%20%20-%2081%20%3D%200" id="TexFormula1" title="4x ^{2} - 81 = 0" alt="4x ^{2}
OverLord2011 [107]

Sum 81 to both sides to get


4x^2 = 81


Divide both sides by 4 to get


x^2 = \frac{81}{4} = \frac{9^2}{2^2}


Consider the square root of both sides. Note that this requires the \pm sign, since a^2=b^2 implies a=b, but also a=-b. So, the solutions are


x = \pm\sqrt{\frac{9^2}{2^2}} = \pm\frac{9}{2}

8 0
3 years ago
What are the zeros of the function f(x) = x4 − 4x2 − 5?
Gekata [30.6K]

Answer:

A graph shows zeros to be ±3. Factoring those out leaves the quadratic

 (x-2)² +1

which has complex roots 2±i.

The function has roots -3, 3, 2-i, 2+i.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Which of the following checks done during the exterior pre-trip inspection is impossible to complete by yourself?
Anna11 [10]

the correct answer is A brake lights

4 0
3 years ago
-7(6a - 3) - 2a = -27 + 4a
Klio2033 [76]
the letter a is 1
good luck!!!!!!!
5 0
3 years ago
Other questions:
  • A scalene triangle has symmetry with respect to a line containing an altitude of the triangle.. . true or false?
    7·2 answers
  • Solve for number eight please ! I really need help with this !!!
    11·2 answers
  • X2y − 7xy + xyz + x Classify the following expression by degree and term
    12·1 answer
  • How many seconds are in 3.14 hours, why?
    5·1 answer
  • What is the slope of the line through the points (-3 , -6) and (-6, 12)?
    9·2 answers
  • The zeros of a parabola are -5 and -3. The point (0, 60) is on the graph as represented by the equation.
    10·2 answers
  • According to this astronomer's depiction of Venus' orbit, Venus is an average of ______ million miles from the Sun. (Enter only
    5·1 answer
  • What multiplies to -26 and adds to -25
    13·1 answer
  • A parent volunteer group is raising money by making custom hats to sell at
    12·1 answer
  • Factor 60s - 20 and choose the correct option
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!