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2 years ago

Which graph shape represents the polar curve r = 1 + 4sin(θ)?

Mathematics

2 answers:

umka2103 [35]2 years ago

7 0

Answer:

A cardioid

Step-by-step explanation:

A cardioid is a curve in the shape of a heart traced by a point on the circumference of a circle as it rolls around a fixed circle of the same radius.

The equation of vertical cardioid is $r=a$ ± $a\sin \theta$

Given the polar curve is $r=$ $1+$ 4 $\sin \theta$

This is an equation of vertical cardioid.

So, it represents a cardioid.

Tomtit [17]2 years ago

6 0

Answer:

C - a limaçon with an inner loop

Step-by-step explanation:

If you have a graphing calculator, use it to plug in the equation.

Based on what you have learned, you will recognize the graph is C

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<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%20%5Cinfty%20%20%5Cfrac%7B%20%5Csqrt%5B%20%20%5Cscriptsize%5Cphi%

Rasek [7]

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

$I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx$

Replace $x \to x^{\frac1\phi} = x^{\phi-1}$ :

$I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

Split the integral at x = 1. For the integral over [1, ∞), substitute $x \to \frac1x$ :

$\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

The integrals involving tan⁻¹ disappear, and we're left with

$I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}$

8 0

1 year ago

Mr seidel filled up his 14 gallon gas tank for $29.96 what was the price per gallon

Genrish500 [490]

2.14 is the price per gallon.

I figured this out by dividing 14 by 29.96 and I got 2.14 and to check my work I multiplied 2.14 by 14 and got 29.96 .

6 0

2 years ago

Need help pls help me

Kryger [21]

$y = \frac{3}{4} x + ( - 2)$

4 0

2 years ago

PLEASE HELP WILL NAME BRAINLEST

Schach [20]

Answer:

All of them are parallel

Step-by-step explanation:

This is due to the all of the 90 degree angle which would make the rest of the line a would be another 90 degree angle Which are found on every line. This would make all of the lines parallel because it is a total of 180 degrees.

7 0

2 years ago

A bowl contains 11 white stones and 3 black stones. One stone is chosen and not replaced, then another stone is chosen. What is

Nataly [62]

Answer:

11/ 14 chance that you will pick a white stone

3/14 chance to picka a black stone

Step-by-step explanation:

Hope that helps

7 0

2 years ago

Read 2 more answers