In order to find out whether something is a function or not, you can choose to graph the equation or find out using other methods. If the equation passes the vertical line test, such that each x value has only one corresponding y value, then the equation is a function. In other words, something is a function only if each of its inputs has only one output. You can find out whether the equation is a function through substituting values into the equation or finding the table of the graph of the equation. The simplest method available if you have a graphing calculator is to just draw a straight line above any x-value. If there's only one point on the graph that has that x-value, then the equation you're talking about is a function. If not, then it's not a function.
Answer:
The answer would be 19
Step-by-step explanation:
You plug in the x and y values, and it looks like this
2(4)^2/8+5(3)
Simplify
2(16)/8+15
32/8+15
4+15
--->19<---
To find the average, add both up and then divide by 2:
Answer:
x= 8
Step-by-step explanation:
(17x + 14)+(4x - 2) = 180
21x + 12 = 180 : add like terms
21x = 168 : subtract 12 from both sides
x = 8 : divide by 21 to get x alone
Let P be Brandon's starting point and Q be the point directly across the river from P.
<span>Now let R be the point where Brandon swims to on the opposite shore, and let </span>
<span>QR = x. Then he will swim a distance of sqrt(50^2 + x^2) meters and then run </span>
<span>a distance of (300 - x) meters. Since time = distance/speed, the time of travel T is </span>
<span>T = (1/2)*sqrt(2500 + x^2) + (1/6)*(300 - x). Now differentiate with respect to x: </span>
<span>dT/dx = (1/4)*(2500 + x^2)^(-1/2) *(2x) - (1/6). Now to find the critical points set </span>
<span>dT/dx = 0, which will be the case when </span>
<span>(x/2) / sqrt(2500 + x^2) = 1/6 ----> </span>
<span>3x = sqrt(2500 + x^2) ----> </span>
<span>9x^2 = 2500 + x^2 ----> 8x^2 = 2500 ---> x^2 = 625/2 ---> x = (25/2)*sqrt(2) m, </span>
<span>which is about 17.7 m downstream from Q. </span>
<span>Now d/dx(dT/dx) = 1250/(2500 + x^2) > 0 for x = 17.7, so by the second derivative </span>
<span>test the time of travel, T, is minimized at x = (25/2)*sqrt(2) m. So to find the </span>
<span>minimum travel time just plug this value of x into to equation for T: </span>
<span>T(x) = (1/2)*sqrt(2500 + x^2) + (1/6)*(300 - x) ----> </span>
<span>T((25/2)*sqrt(2)) = (1/2)*(sqrt(2500 + (625/2)) + (1/6)*(300 - (25/2)*sqrt(2)) = 73.57 s.</span><span>
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</span><span>mind blown</span>