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2 years ago

Find the variable (this is special right triangles unit)

Mathematics

1 answer:

scZoUnD [109]2 years ago

6 0

Answer:

a= 10sqrt(2) , b= 10

Step-by-step explanation:

In the picture above that you can see the explanation of solution.

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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

Which expression is equivalent to 12 × 3 × 5?

Nikolay [14]

What are the other expressions then I can help

5 0

3 years ago

Read 2 more answers

What is 6,570 rounded to the nearest thousand?

almond37 [142]

Answer:

7,000 is the answer

Step-by-step explanation:

5 0

3 years ago

Find the average value of f over region

yan [13]

The area of D is given by:

$\int\limits \int\limits {1} \, dA = \int\limits_0^7 \int\limits_0^{x^2} {1} \, dydx \\ \\ = \int\limits^7_0 {x^2} \, dx =\left. \frac{x^3}{3} \right|_0^7= \frac{343}{3}$

The average value of f over D is given by:

$\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49$

3 0

3 years ago

Find missing number sequence 1,2,5,10,13,__,__,58,61

lys-0071 [83]

The pattern is *2 +3 *2 +3 *2 +3 .... 1 *2 = 2 , 2+3 = 5 , 5 *2 = 10, 10 +3 = 13, 13*2 = ?...

7 0

3 years ago