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ANTONII [103]
4 years ago
6

Y=x(sin(x)), 0 ≤ x ≤ 2π?

Mathematics
1 answer:
Lemur [1.5K]4 years ago
4 0
Careful; (dy/dx)^2 = x^2 cos^2(x) + 2x sin x cos x + sin^2(x).

<span>So, the arc length equals </span>
<span>∫(x = 0 to 2π) √[1 + (x^2 cos^2(x) + 2x sin x cos x + sin^2(x))] dx </span>
<span>= ∫(x = 0 to 2π) √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)] dx, via double angle identity. </span>

<span>Let Δx = (2π - 0)/10 = π/5. </span>
<span>Using Simpson's Rule with n = 10, this integral approximately equals </span>
<span>((π/5)/3) * [f(0) + 4 f(π/5) + 2 f(2π/5) + 4 f(3π/5) + 2 f(4π/5) + 4 f(π) + 2 f(6π/5) + 4 f(7π/5) + 2 f(8π/5) + 4 f(9π/5) + f(2π)], </span>

<span>where f(x) = √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)]. </span>
<span>------- </span>
<span>I hope this helps!</span>
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explain how to use estimation to help find the product of two decimals. give an example with both estimated and actual answer
Marrrta [24]

To find the product of a reasonable estimate of two decimal numbers, round each decimals to the nearest whole number and then perform the multiplication.

For example:

3.2 x 5.7

Estimated answer

3.2 will be rounded down to 3 and 5.7 will be rounded up to 6

⇒ 3 x 6 = 18

Actual Answer

3.2 x 5.7

=18.24

7 0
1 year ago
Given the equation 3x - 4y = 8, which equation below would cause a consistent-dependent system?
Len [333]
3x - 4y = 8

y = mx + b ; m is the slope ; b is the y-intercept

-4y = -3x + 8
y = -3x/-4 + 8/-4
<u>y = 3/4 x - 2</u>

Need to check if the given choices have the same slope.

3x + 4y = -8
4y = -3x - 8
y = -3/4 x - 8/4 = -3/4 x - 2

6x - 8y = 12
-8y = -6x  + 12
y = -6/-8 x + 12/-8
y = 3/4 x - 1 1/2

9x - 12y = 24   This equation would cause a consistent-dependent system
-12y = -9x + 24
y = -9/-12 x + 24/-12
<u>y = 3/4 x - 2</u>  

16x + 12y = -10
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4 0
3 years ago
Read 2 more answers
Show all work please will give brainliest answer❕❗️❕❗️❕❗️❕❗️❕David drops a ball from a bridge at an initial height of 100 meters
Inessa [10]
First, 9.8 (Gravity) times 3 (time) equals 29.4, which is the velocity after 3 seconds. The kinematic equation for change in position that uses the variables we have is:
delta x= (v)(t) -0.5(acceleration)(time)^2
delta x= 29.4 times (3) - 0.5 (9.8) times 9
delta x= 44.1
100 minus 44.1 equals 55.9, which is the answer for part a.

Tell me if you need any clarification

PART B:
The kinematic equation for this is:
delta x= (initial velocity) times time plus 0.5 (a)(time)^2
100=(0)times(x) plus 0.5 (a)(time)^2
100=0.5(9.8)(x)^2
100=4.9x^2
100/4.9 is approxamitely 20.4.
The squareroot of this is approxamitely 4.5.
4.5 seconds

Tell me if you need any clarification
3 0
3 years ago
What is the approximate value of 200,000 x 200
Nesterboy [21]

it would be 40000000 because there there are 7 zeroes and then you and then you multiply the two twos together and then put it in the front.

3 0
3 years ago
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Which choice gives the solution of this inequality?<br> 3t + 7 &lt; 28
Butoxors [25]

Answer:7

Step-by-step explanation:

5 0
3 years ago
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