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Vladimir79 [104]
3 years ago
15

√(4x-9) + 1 =2√x Find the value of X

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
7 0
There are no values for x that make the equation true
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Hi, am I supposed to find the stationary points of the f(x) and g(x) then use the distance formula to solve for the final answer
nikdorinn [45]

9514 1404 393

Answer:

  maximum difference is 38 at x = -3

Step-by-step explanation:

This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.

__

Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.

  h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2

Then the derivative is ...

  h'(x) = 3x² +4x -15 = (x +3)(3x -5)

This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.

The maximum difference between f(x) and g(x) is 38 at x = -3.

4 0
2 years ago
On a certain hot summer's day, 321 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for a
Paul [167]

Answer:

31 children and 290 adults

Step-by-step explanation:

Let a = number of adults and c = number of children.

a + c = 321

2a + 1.75c = 634.25

Multiply both sides of the the first equation by -2 and add it to the second equation.

         -2a -     2c = -642

(+)       2a + 1.75c = 634.25

--------------------------------------

                 -0.25c = -7.75

Divide both sides by -0.25

c = 31

Use the first equation to find a.

a + c = 321

Substitute 31 for c.

a + 31 = 321

Subtract 31 from both sides.

a = 290

Answer: 31 children and 290 adults

5 0
2 years ago
Read 2 more answers
1. Rewrite the sum of 24 and 40 by factoring out the greatest common factor.
elena-s [515]

Answer:

64

70

72

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
The area of a quarter circle is 38.465 square<br> inches. What is the quarter circle's radius?
LuckyWell [14K]

The formula for a circle's area is A=\pi r^2. We are given an area of 38.465 square inches for a quarter of it.

Multiply this value by 4 to compensate for the quarter circle.

4 \times 38.465=\pi r^2

153.86=\pi r^2

Divide both sides by pi (Note: I'm using the conventional value of 3.14)

49=r^2

Take the positive square root of both sides

7=r

The radius is 7 inches. Let me know if you have any questions, thanks!

3 0
2 years ago
Jake earned $62.50 in 5 hours. At the<br>same rate, how much will he earn in<br>8 hours?​
dem82 [27]

Answer:

one hundred which is 100

5 0
3 years ago
Read 2 more answers
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