Ask question

Ask question

All categories

3 years ago

9

Find the exact length of the curve. Use a graph to determine the parameter interval.. r = (cos(θ/2))^2

1 answer:

harkovskaia [24]3 years ago

8 0

Cos(2θ) = 2cos^2θ - 1,

<span> cos^2(θ/2) </span>
<span>Solving </span>
<span>cos^2θ = [1 + cos(2θ)]/2. </span>

<span>replacing θ with θ/2 gives. </span>
<span>cos^2(θ/2) = (1 + cosθ)/2. </span>

<span>length of a polar curve of the form r = f(θ) on [a, b] is given by: </span>
<span>L = ∫ √[r^2 + (dr/dθ)^2] dθ (from θ=a to b).
hope this helps</span>

You might be interested in

You are running a fuel economy study. One of the cars you find is blue. It can travel 38 1/2 miles on 1 1/4 gallons of gasoline.

Alex Ar [27]

Answer:

Step-by-step explanation:

3 0

2 years ago

What is the slope of the line that passes through (-3,4) and (-3,-4)

suter [353]

Answer:

undefined

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

= ( -4-4)/( -3 - -3)

= ( -4-4)/( -3+3)

= -8/0

When we divide by zero, the answer is undefined so the slope is undefined

8 0

2 years ago

PLEASE HELP!! URGENT!!!! UNIT TEST!!!!

slavikrds [6]

ANSWER

$y=-\frac{4}{3}x+\frac{16}{3}$

Or

$3y+4x=16$

EXPLANATION

Let us find the gradient of the line:

$-3x+4y=4$ by rewriting it in the slope intercept form.

$\Rightarrow 4y=3x+4$

We divide through by 4 now;

$\Rightarrow y=\frac{3}{4}x+1$

This is now in the form;

$y=mx+c$

where

$m=\frac{3}{4}$ is he slope.

This implies that the slope of the line that is perpendicular to this line will be the negative reciprocal of $m=\frac{3}{4}$ .

Thus the perpendicular line has slope,

$m=\frac{-1}{\frac{3}{4}}= -\frac{4}{3}$ .

Let the perpendicular line have equation,

$y=mx+c$

When we substitute the slope we have;

$y=-\frac{4}{3}x+c$

We substitute the point. $(4,0)$ to find c.

$0=-\frac{4}{3}(4)+c$

$0=-\frac{16}{3}+c$

$\frac{16}{3}=c$

We substitute c to obtain;

$y=-\frac{4}{3}x+\frac{16}{3}$

Or

$3y+4x=16$

7 0

3 years ago

Read 2 more answers

Are these correct? If not please help me write the correct answer.

Keith_Richards [23]

Answer:

Mostly correct

For Q3, you are doing great, you remembered that negative numbers can happen if the exponent is an odd number.

For Q4, I think you were confused with the fractions,

4(i)

$(\frac{2}{3} )^{4} = (\frac{2^{4}}{3^{4}}) = (\frac{16}{81}) =0.198$

4(ii) is also wrong but I'll let you try to fix it yourself following what I given you for 4(i). You should get 1/64

Hope this helps!

4 0

3 years ago

Read 2 more answers

an English teacher would like to divide 15 boys and 6 girls into groups each with the same combination of boys and girls and nob

tamaranim1 [39]

Answer:

7groups

Step-by-step explanation:

15+6/3=7groups

6 0

3 years ago