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3 years ago

Here is a graph of a quadratic function f(x). What is the minimum value (y-value only) of f(x)?

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

4 0

Answer:

Zero.

Step-by-step explanation:

The minimum value is where the function touches the x axis , at y = 0.

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The dolphins at the Logan Aquarium are fed 3 7/8 buckets of fish each day. The sea otters are fed 2 9/10 times as much fish as t

Bond [772]

Answer:

Step-by-step explanation:

If the dolphins are fed half a bucket of fish then half of that would be a quarter, therefore the sea otters are fed 1/4 of a bucket.

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3 years ago

Explain whether the product of an even number x odd number x odd number is even or odd?

Dmitriy789 [7]

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3 years ago

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$14 meal; 20% tip please help me on this it is mathematics

Anastasy [175]

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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

What is the variable y in w= x y/z?

AleksAgata [21]

Multiply by z to get
wz = xy
divide by x
y = wz/x

8 0

3 years ago