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3 years ago

Find the points of intersection of the graphs involving the following pair of functions.

Mathematics

1 answer:

jeka57 [31]3 years ago

4 0

Answer:

The point of intersection is $( \frac{-1\pm\sqrt{5}}{2}, 0)$

Step-by-step explanation:

f(x) = 2x^2 + 3x - 3 and g(x) = - x^2

By equating them

2x^2 + 3x - 3 = -x^2

3x^2 + 3 x - 3 = 0

x^2 + x - 1 = 0

$x^2 +x - 1 = 0 \\\\x = \frac{-1\pm\sqrt{5}}{2}$

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Complete parts a through c for the given function.

victus00 [196]

Answer:

a. The critcal points are at

$x=0,-5,3$

b. Then, $x = -5$ is a maximum and $x=3$ is a minimum

c. The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

Step-by-step explanation:

(a)

Remember that you need to find the points where

$f'(x)=0$

Therefore you have to solve this equation.

$20x^4 + 40x^3 - 300x^2 = 0$

From that equation you can factor out $20x^2$ and you would get

$20x^2 ( x^2 +2x - 15) = 0$

And from that you would have $20x^2 = 0$ , so $x = 0$ .

And you would also have $x^2 +2x-15 = 0$ .

You can factor that equation as $x^2 +2x -15 = (x+5)(x-3) = 0$

Therefore $x=-5 , x=3$ .

So the critcal points are at

$x=0,-5,3$

Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since

$f''(x) = 80x^3 + 120x^2 -600x\\f''(-5) = 80(-5)^3 + 120(-5)^2 -600(-5) = -4000 < 0\\\\f''(3) = 80(3)^3 + 120(3)^2 -600(3) = 1440 > 0 \\$

Then, $x = -5$ is a maximum and $x=3$ is a minimum

The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

6 0

3 years ago

Read 2 more answers

Stella wants to buy colored pencils that cost $3.50. She has 1 dollar, 5 quarters, 4 dimes, and 7 pennies. Does she have enough

Andrews [41]

Answer:

Step-by-step explanation:

Lets she how much money she has

1.00 dollars

5 * .25 = 1.25 quarters

4 * .10 = .40 dimes

7 * .01 = .07 pennies

Add it all together

1 + 1.25+ .40 +.07 =2.72

3.50 - 2.72 =.78

She is 78 cents short

6 0

3 years ago

Test scores: Scores on a statistics exam had a mean of 75 with a standard deviation of 5. Scores on a calculus exam had a mean o

beks73 [17]

Answer:

CV for statistics exam = 15%

CV for calculus exam = 19%

Since the CV for calculus exam is higher, it has a greater spread relative to the mean than the statistics exam.

Step-by-step explanation:

To find coefficient variation we use the formula:

CV = (SD/mean) * 100

CV for the statistics exam:

where; SD= 5

mean= 75

CV = ( 5/75) *100

= 0.15 or 15%

CV for calculus exam

SD = 11

Mean= 58

CV= (11 /58) * 100

= 0.19 or 19%

8 0

3 years ago

8 workers complete the construction of wall 6 days. How many workers are needed to complete the construction in 4 days?

ElenaW [278]

Answer:

I came up with -12

Step-by-step explanation:

8 workers = 6 days to complete

x workers = 4 days faster to complete

6/4=1.5 days faster

1.5 x 8 = 12 workers needed to complete the wall in fours days

8 0

2 years ago

What is one way that authors can come up with ideas for providing context for their readers?(1 point)

nataly862011 [7]

Answer:

Brainstorming i think

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers