Please help me thank you

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

salantis [7]

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!

3 0

3 years ago

5 divided into 290 show work

Archy [21]

How many times does 5 go into 29? It can go into it 5 times which equals 25. Now what's 29 - 25? 4 is the answer then you see how many times can 5 go into 4, well it can't so then you bring the number 0 to make it 40. Now how many times can 5 go into 40? It can go into 40 eight times since 8x5=40 so the answer is 58

8 0

3 years ago

Only answer if you know you are correct

Rama09 [41]

Answer:

The answer is red. I used process of elimination to solve this. I know that blue, yellow, and green aren't correct, so it's red.

Step-by-step explanation:

Please tell me if I'm correct.

7 0

3 years ago

Use the Venn diagram to calculate probabilities. Circles A and B overlap. Circle A contains 15, circle B contains 10, and the in

grin007 [14]

Answer:

$(B) P(B)=\dfrac{16}{31}$

Step-by-step explanation:

From the Venn diagram, n(AUB)=31

The given probabilities in the option are calculated below:

$P(A)=\dfrac{21}{31}\\\\P(B)=\dfrac{16}{31}\\\\P(A|B)=\dfrac{P(A\cap B)}{P(B)}= \dfrac{6/31}{16/31} =\dfrac{6}{16}=\dfrac{3}{8} \\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{6/31}{21/31} =\dfrac{6}{21}=\dfrac{3}{7}$

The only correct option is the probability of B which is $\frac{16}{31}$

8 0

4 years ago

A ; 1/2. B ; 1/3. C ; 2/3 D ; 4/9

hichkok12 [17]

Option B, 1/3

Since pepper topping can be in any size pizza, it remains as a 1/3 probability, since there are three toppings per size.

3 0

3 years ago