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1 year ago

HELP!! Select the values for the domain and range of the functions graphed below.

Mathematics

1 answer:

Goryan [66]1 year ago

3 0

Answer:

Graph 1

Domain = -8 =< x =< 10

Range = -9 =< f(x) =< 9

Graph 2

Domain = -1 =< x =< 5

Range = -1 =< f(x) =< 2

Explaination:

Domain means the inputed x values on the x-axis, so to make things simpler and to not write every individual x values. We write it with <, >, and =<. (you can see it as the 'width' of a graph).

Range means the output y values on the y-axis. It's like the 'height' of a graph. And also, to make things simpler and to not write every individual y values. We write it with <, >, and =< with f(x) too because f(x) = y.

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Find the value of y.

Phoenix [80]

$\boxed{y=6\sqrt{3}}$

<h2>Explanation:</h2>

For a better understanding of the problem I've built up two triangles from the given triangular shape. So these two triangles are similar. Therefore, we can solve this problem by using ratios and corresponding sides in this way:

$\frac{x}{3}=\frac{12}{x} \\ \\ x^2=36 \\ \\ x=\sqrt{36} \\ \\ x=6$

But our goal is to find y. Let's call w the height of the small triangle, then:

$w=\sqrt{6^2-3^2}=3\sqrt{3}$

Applying the concept of ratios again:

$\frac{y}{w}=\frac{x}{3} \\ \\ y=w \left(\frac{x}{3}\right) \\ \\ y=3\sqrt{3}\left(\frac{6}{3}\right) \\ \\ \boxed{y=6\sqrt{3}}$

<h2>Learn more:</h2>

Right triangle: brainly.com/question/10684799

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Hi, can someone help me pretty please?

Tju [1.3M]

It’s 174 square feet

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2 years ago

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From a point 50m from the base of the Skylon Tower in Niagara Falls, the angle of elevation to the top of

VladimirAG [237]

Answer:

The tower is about 235 m.

Step-by-step explanation:

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tan θ = opp / adj

tan 78 °= x / 50

x = 50 tan 78 °

x = 235

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Hope this answer helps you :)

Have a great day

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2 years ago

The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

$h(t)=-16t^2 + 96t$

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

$To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)$

$Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution$

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

$0 \leq t \leq 6$

The height will be positive in the above interval.

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2 years ago

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