Given: JK tangent, KH=16, HE=12 Find: JK.

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

7 0

Answer: $JK=8$

Step-by-step explanation:

You can observe in the figure that JK is a tangent and KH is a secant and both intersect at the point K. Then, according to the Intersecting secant-tangent Theorem:

$JK^2=KE*KH$

You know that:

$KH=KE+HE$

Then KE is:

$KE=KH-HE$

$KE=16-12$

$KE=4$

Now you can substitute the value of KE and the value of KH into $JK^2=KE*KH$ and solve for JK. Then the result is:

$JK^2=4*16\\JK^2=64\\JK=\sqrt{64}\\JK=8$

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Sphinxa [80]

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x=2.125

y=0

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Step-by-step explanation:

To solve this problem we can use a graphical method, we start first noticing the restrictions $x\geq 0$ and $y\geq 0$ , which restricts the solution to be in the positive quadrant. Then we plot the first restriction $8x+10y\leq 17$ shown in purple, then we can plot the second one $11x+12y\leq 25$ shown in the second plot in green.

The intersection of all three restrictions is plotted in white on the third plot. The intersection points are also marked.

So restrictions intersect on (0,0), (0,1.7) and (2.215,0). Replacing these coordinates on the objective function we get C=0, C=11.9, and C=19.125 respectively. So The function is maximized at (2.215,0) with C=19.125.