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3 years ago

What is the domain of the square root function graphed below?

Mathematics

1 answer:

Xelga [282]3 years ago

5 0

Answer:

Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.

Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.

Step 3: Write the answer using interval notation.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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A ball is thrown from a height of 38 meters with an initial downward velocity of 3 m/s

ANTONII [103]

<h2>Hello!</h2>

The answer is:

The ball will hit the ground after $t=2.47s$

Since we are given a quadratic function, we can calculate the roots (zeroes) using the quadratic formula. We must take into consideration that we are talking about time, it means that we should only consider positive values.

So,

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}$

We are given the function:

$h=-5t^{2}-3t+38$

Where,

$a=-5\\b=-3\\c=38$

Then, substituting it into the quadratic equation, we have:

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}=\frac{-(-3)+-\sqrt{(-3)^{2} -4*-5*38} }{2*-5}\\\\\frac{-(-3)+-\sqrt{(-3)^{2} -4*-5*38} }{2*-5}=\frac{3+-\sqrt{9+760} }{-10}\\\\\frac{3+-\sqrt{9+760} }{-10}=\frac{3+-\sqrt{769} }{-10}=\frac{3+-27.731}{-10}\\\\t1=\frac{3+27.731}{-10}=-3.073s\\\\t2=\frac{3-27.731}{-10}=2.473s$

Since negative time does not exists, the ball will hit the ground after:

$t=2.473s=2.47s$

Have a nice day!

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