d?y at this point. dx2 Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of x = 8 sin t, y = 2 cos t, t= 4

Q: Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

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Q: A particle travels along the x-axis such that its velocity is given by v(t) = t0.5 sin (2t − 3).…

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Q: Find the lengths of the curves x = 8 cos t + 8t sin ty = 8 sin t - 8t cos t,0 ≤ t ≤π/2

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Q: y = cos(6t) –- sin(6t) where y is measured in feet and t is the time in seconds. Determine the…

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Q: A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the…

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Q: Find the length of the curve. x= 5 sint- 5t cos t, y = 5 cos t + 5t sin t, 0sts The length is units.…

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Q: dy -10 cos(z) Find for the function y dx dy dx

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Q: find sin (x) Given tan(x) and x E 5 a) b) V41 4 d) 41 c) া Ln

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Q: f(x) = 7 sin a + 2 cos a, then cos T. f'(x) = %3D f'(3) =| Find the equation of the tangent line to…

A: Given  f(x) = 7sinx + 2cosx To find f'(x) and f'(3) Also to find the equation of the tangent on the…

Q: Q.5/ A) Find dx for the following equation y = In(x2 + 4) – x tan-() %3D

A: Given equation is y=lnx2+4−xtan−1x2 We have to find dydx. Used Formula:- ddxlnx=1x ddxtan−1x=11+x2…

Q: y=sin?t+ tant, x=- In(– cost) – e sinr, find the value of y' when t= 4 여 V2-e ? 6 2+ Vze V? 2-Vze 2…

A: We have to find dy/dx

Q: Determine whether the equation is exact. If it is, then solve it. (tan y – 2)dx + (xsec²y+ ÷)dy = 0.…

A: A differential equation Mx,ydx+Nx,ydy=0 is said to be exact differential equation, if ∂M∂y=∂N∂x. To…

Q: If y = sin?t+ tant, x= – In(-cost) –e sinr, find the value of y' when t=. 6 A 2/3 V2-e? 3/2 6 D 2+…

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Q: Sadako is crawling out of the television while a scared stationary 5-foot-tall man is watching while…

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Q: 2) Find and of the following equation then simplify whenever possible. dx x = 1+ Sin t y = Cos? t

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Q: Use the formula for the slope of the tangent line to find 2 of c(t) = (5t + 9, 3t – 8) at the point…

A: The curve is defined by the following parametric equation  c(t) = 5t+9,3t-8 Where, x = 5t+9 and y =…

Q: dy at the value of the parameter. dx Find X = 4 cos(2ns), y = 3 sin(2ns), s = - 1/4

A: Given query is to find the value of dy/dx at s =-1/4.

Q: Find the value of d'y/dx at the point defined by the given value of t. x = sin t, y = 9 sin t, t =…

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Q: The position of a particle is given by F(t) = t i+ In(t)? j+ sin nt k where t is measured in seconds…

A: Given position :

Q: y = cos? x and the line y = 1:

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Q: dy for the function e²* = /2 sin (x + y)at the point 0, dx 6. Find 4

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Q: The equation of motion of a particle is given by s = 4 sin(Ct2 + πt), where C is a constant. Find…

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Q: Match the equation with its graph. r(t) = cos(at)i + sin(xt)j + t?k, -1 <t< 1 %3D y 4 y 2.

A: The solution of the problem is given in the next step.

Q: V1+cos.x dx = ?

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Q: cos(zt),nt, sin(nt)) e point where t = 0 to the point point where E1

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Q: If the position of a moving object is s(t) = (sin t)< meters above zero at t seconds, then what is…

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Q: Q1: find dx of the following statement: a) y = cos? sec

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Q: If y= sin?t- 2+ + tant, x= – In(- cost) – e sinr, find the value of y when t= (=- 2/3 V2-e 2 6. 2le…

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Q: Given y= cos-(tanhx), determine dx A sechx sech?x B В 1-tanhx - sechx D none of the given choices…

A: The chain rule for differentiation is given by, ddxfgx=f'(gx).g'x.

Q: t/2 Find the value of sin(2x) sin(x) dx.

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Q: dy y cos x+sin y +y Solve the following 1. dx 0. %D sin x+x cos y+x differntail equation

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Q: dy c) Determine for the function sin? x – 5 sin x cos y + tan y = 0 dx

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Q: y=e sin x- cos

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Q: If y = sin?t+ tant, x= - In(- cost) – e sinr, find the value of y' when t= A 1 1 2+ V2e v7 2 D 2-Vze…

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Q: Determine if the following equation is exact and if so solve it: (3x? + 5y)dx + (5x + cos y) dy = 0.

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Q: (d) 2 sinu =|- Sin u (e)2 cos?t + 3 cost t1 =0 %3D (Đ cos 2x + 3 cos e + 2=0

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Q: dx (b) | sin x· cos? x

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Q: Determine whether the equation is exact. If it is, then solve it. (tan y - 2) dx + (x sec2 y + 1/y)…

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Q: "y= sin?t+ tant, x=- In(-cost) -e sinr, find the value of y' when = 2+ Vze V? 6 2-Vze ? 2/3

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Q: 11 Consider the function y = sin-' 2x. a Write down the range of the function. b Make x the subject…

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Q: If y=sin?t+ tant, x=- – In(- cost) – e sinr, find the value of y' whent=". 4 6 2 2- Vze ? 2/3 V2-e ?…

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Q: dy dr for the equation (0, 0) at the given point tan(12x + 2y) = 12x 5. Evaluate nswer to two…

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Q: The total energy in megawatt-hr (MWh) used by a town is given by the equation shown below, where t20…

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Q: If y = sin?r+ tant, x= - In(- cost) – e sinr, find the value of y' when t= 3/2 6. 2le 6. 2+ Vze v?…

A: If x=f(t) and y=g(t) , then dydx=dydtdxdt Note : In your question , options are incorrect.

Q: y' + y = cos(e*)

A: Let us consider the differential equation dydx+P(x)y=Q(x) The integrating factor is I.F.=e∫P(x)dx…

Q: If y= sin?r+ tant, x=- In(-cost) - e sinr, find the value of y' when t=-. 6 (A) -Vzle? 2/3 B Vz-e ?…

A: Given that: y=sin2t+tan tx=-ln (-cos t)-esin t We have to find the value of y' when t=π4

Q: dx b) sin x· cos? x

A: let's find integral

Q: Identify the order and degree of the following equations. Order dy = cos X 1. dx

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Q: If y = sin?t+ tant, x=- In(- cost) – e sinr, find the value of y' when t= . (A 2/3 (B - e 3/2 (D 2+…

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Q: The velocity of a plane is modeled by v(t) = -1+ cos ) + 3 sin ), measured in miles per minute, for…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.