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iris [78.8K]
3 years ago
7

during the first round of game show, jackson scored 300 points. After the second round,after the second round, his total score w

as -300. how many points did jackson score in the second round? (it is not 300)
Mathematics
1 answer:
mrs_skeptik [129]3 years ago
4 0

Answer:

-600

Step-by-step explanation:

Jackson's initial score was 300, then his later score became -300, so you know that he had to lose points.

-300=300+x

** x represents the point change

Then just solve the equation by getting x by itself. You do this by subtracting 300 from both sides:

-300=300+x

-300 -300 = -300-300+x

-600 = x

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Find the equation of a line tangent to the circle x2+(y−3)2=34 at the point (5, 0).
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Answer:

Step-by-step explanation:

In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line.  Let's begin by expanding through the parenthesis to get the standard form of the circle:

x^2+y^2-6y+9=34

Moving the 9 to the other side since the derivative of a constant is 0 gives us

x^2+y^2-6y=25

By implicit differentation, the derivative of that function is

2x+2y\frac{dy}{dx}-6\frac{dy}{dx}=0

To find the derivative, we have to solve for dy/dx:

2y\frac{dy}{dx}-6\frac{dy}{dx}=-2x

Factor out the dy/dx to get:

\frac{dy}{dx}(2y-6)=-2x

Now divide to get your slope formula (first derivative):

\frac{dy}{dx}=\frac{-2x}{2y-6}

Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:

\frac{dy}{dx}=\frac{-2(5)}{2(0)-6}=\frac{-10}{-6}=\frac{5}{3}

So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line.  The point-slop form of a line is:

y-y₁ = m(x-x₁)

Filling in we get:

y - 0 = 5/3(x - 5) so the equation of the tangent line is:

y=\frac{5}{3}x-\frac{25}{3}

Good luck in your calculus class!

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