Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: Find of the curve the curve lenght from t=o to t=2M given C: P(t) = (cos 3t) î + (sin 3t) Î + ? tVt…

A: Here I am attaching image so that you understand each and every step.

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: 1. Consider the curve C: r(t) = (t - sin t)i + (1– cos t)j, 0StS 2. %3| | (a) Find an equation of…

A: Since solve the first question for you. If you wanting any specific question to be solved then…

Q: For what value of t will the slope of a line tangent to x = 6 sin t, y = t² + t be 0?

A: We have to find t

Q: Find the exact length of the curve. 1x2 - In(x), 1< x s 8 у3

A: Hello! Thank you for the question. We will answer the first question since the exact one wasn’t…

Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

A:

Q: Find the exact length of the curve (b) x = e' cos t, y= e' sint, 0<t<T

A: Length of the curve for parametric equation is given by:

Q: Find the length of the following curve: y = ln(cos(x)) from x=0 to x=pi/4

A:

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

A:

Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

A:

Q: Suppose the position function of a particle is given by r(t)=(√3 sin(t), t-2, √3 cos(t)). If the…

A:

Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

A:

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

A:

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: r = -1 + cos 0 0=t/2

A: In the question we have to find the slope of function -…

Q: Find the lengths of the curves x = ln (sec t + tan t) - sin t , y = cos t, 0 … t … pi/3

A: x=lnsect+tant-sint,  y=cost,  0≤t≤π3 Differentiating with respect to t, we get ⇒dxdt=1sect+tantsect…

Q: Find the lengths of the curves x = ln (sec t + tan t) - sin ty = cos t, 0 ≤ t ≤ π/3

A:

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

A:

Q: Find the lengths of the curves x = 8 cos t + 8t sin t, y = 8 sin t - 8t cos t, 0 … t … pi/2

A: The length of the curve of any given function by the formula L=∫t1t2dxdt2+dxdt2dt. Here t1 and t2…

Q: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: - X e + e Find the length of the arc Curve 2.

A:

Q: Find the exact length of the following curve y = Vx – x² + sin-'(/T).

A:

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

A:

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: 5. R = (sin 2t , cos 2t , 2t3/2), 0 <t<1.

A:

Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

A:

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

A:

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0≤ t ≤ π

A:

Q: Find the length of the curve y = ln (sin x),  pai/6&lt;=x&lt;=pai/2.

A: The given curve is,

Q: Find the length of the curve 7(t) = (ei cos(), ei sin(÷), e) n(4),e¿): for 0 <t < 5. CoS

A:

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

A: Since, we have to find the length of the curve over the given intervalr=2a cosθ over the interval…

Q: Find the exact length of the curve. y = 2 In(cos (÷)) Tt/3 < x <T/2

A: Here given Differentiate the given function with respect to x using the chain rule of derivative

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

A:

Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

Q: Use the formula below to find the length of the curve defined by the equation x= cos^2 t , y = sin^2…

A:

Q: Find the length of the curve. r(t) = cos(5t) i+ sin(5t)j + 5ln(cos(t)) k, 0<t< n/4

A: r(t)=cos(5t)i+sin(5t)j+5ln(cos(t))kWhere, 0≤t≤π/4

Q: Find, correct to two decimal places, the coordinates of the point on the curve y =sin x that is…

A: Given that y=sinx So coordinate point is x, sinx.

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

A:

Q: Find the length of the curve. x- 5 sin t+ 5t, y= 5 cos t, 0 st< O A. 5T O B. 20 O C. 10 O D. 30

A:

Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

A:

Q: Find the length of the curve r(t) = (cos(3t), sin(3t), 4t) for -6 ≤ t ≤ 5 Give your answer to two…

A:

Q: Find the exact length of the curve. y = In(cos(x)), 0 s xs- TO 6. Need Help? Read It

A: Given problem:- Find the exact length of the curve.   y = In(cos(x)),   [0, π/6]

Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.