All categories

3 years ago

What is the polar graph of r = 2cos3(theta) and a characteristic?

1 answer:

4 0

we are given the function r=2cos(3θ)
from the pythagorean theorem, r2=x2+y2
from the polar definition, x=rcos3θ x/r = cos3θ y=rsin3θ r=2x/r r2=2x x2+y2−2x=0.

This equation represents a parabola

You might be interested in

Write an equation in slope-intercept form for a line that passes through the given pair of points. (-6,5), (-9,0)

11111nata11111 [884]

Slope intercept form is y=mx+b because m=slope and b=y-intercept hence "slope intercept form"...

m=deltay/deltax=(0-5)/(-9--6)=-5/-3=5/3 so far we have now:

y=5x/3 +b, using any point, I'll use (-9,0) we can now solve for b or the y-intercept...

0=-9(5)/3 +b

0=-15+b, so b=15 and our line is:

y=5x/3 + 15 or more neatly

y=(5x+45)/3

4 0

3 years ago

What is 5 and 3 quarters

liraira [26]

Answer:

In general, 5 and 3 quarters would be 5.75 :)

Remember, there are 4 quarters in $1.00

7 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

Will give brainliest for answer

sleet_krkn [62]

Answer:

y > -x -3

Step-by-step explanation:

The graph is shaded above the dashed line, indicating y-values in the solution are greater than those on the line, so your inequality will start with ...

y >

The y-intercept of the line is (0, -3), so the "b" value in ...

y > mx +b

will be -3.

The line has a rise of -3 for a run of 3 (between the marked points), so the slope is ...

m = rise/run = -3/3 = -1

Then the inequality you want is ...

y > -x -3

7 0

3 years ago

What's $10,100 Afghanistan converted into US$ Please answer with how you got your answer

Wewaii [24]

Hi :)

10, 100 Afghani Afghani (currency name) is $1212 USD with the conversion you provided. Today it's like $117.41.

7 0

3 years ago