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3 years ago

if f(x) and g(x) are a quadratic function but (f + g)(x) produce the graph below, which statement must be true

Mathematics

1 answer:

ArbitrLikvidat [17]3 years ago

7 0

The leading coefficients are opposites.

For instance
f(x) = 2x^2 + 5x + 6
g(x) = -2x^2 + 8x - 3
here the leading coefficients 2 and -2 are opposites

Adding function f(x) and g(x) gets us
f(x) + g(x) = (2x^2+5x+6) + (-2x^2+8x-3)
f(x) + g(x) = (2x^2-2x^2) + (5x+8x) + (6-3)
f(x) + g(x) = 0x^2 + 13x + 3
f(x) + g(x) = 13x + 3

The two quadratics add up to a linear equation

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You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

Hii i’ll give brainliest please help thanks :)

Juliette [100K]

Answer:

Step-by-step explanation:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest.

Hope this help

6 0

2 years ago

What is the equivalent ratio of 82:36?

Tom [10]

41:18

82 / 2 = 41

36 / 2 = 18

I hope this helps.

8 0

2 years ago

Read 2 more answers

Find the mean and range 26 19 23 39 31 34 23 25

Delicious77 [7]

I got 27.5 for the mean
mean: you add up all the #'s and divide them my their quantity( in other words by how many numbers there are)
In your case you have 8 numbers, you add them and divide them by 8!

Hope it helps ;)

4 0

2 years ago

PLEASE ANSWER QUICK

makvit [3.9K]

For the first equation, I put it in y=mx+b form, so y=-3x-9
the second one is x=4
hope i helped

3 0

3 years ago