A man drops a penny from the top of a 500 m tall building. After t seconds, the penny has fallen a distance of s metres, where S(t) = 500 – 5t²,0 < t< 10. Determine the velocity at t = 5.

Q: Differentiate the function. H(x) = (x + x=1)3 %3D

A: Important formula ddxxn = x(n-1) (a+b)3 = a3 + 3a2b +3ab2 + b3

Q: dy +Zy =0 du

A: Given: dydx+2y=0   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where 'a' is the constant....

Q: 3-20 Find the limit. x² - 9 3. lim 4. lim + 2x - 3 x - 9 5. lim + 2x - 3 6. lim x² + 2x - 3 31-3 (- ...

A: Solution is given below:

Q: Using Laplace transform, find the solution of the initial value problem. 2y + y = 0, y (0) = –3 4.

A: Taking laplace on both side, and using y(0) =-3  

Q: Which represents the Period? (B) (C) (D) (A)- A D でビ

A: Topic = Functions

Q: The half-life of plutonium-239 is 24,360 years. If 10 g of plutonium is released into the atmosphere...

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Q: Find the derivative of the following function using logarithm laws. (2x2 + 3) y = (x – 1)2

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Q: Solve the differential equation. dy 10x 16 - y, -4<y<4 dx %3D - The solution is (Type an equation.)

A: Topic = Differential equation

Q: Find the corresponding angle measure in radians. O A. - 45° OA. 4 7T O B. 4 OC. 3 元 OD.

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Q: Let f(x)={x2+2x+1, if x≤3 ax+b,if x>3 Find a and b such that the function f(x) is differentiable e...

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Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. (1+ cos x)y = sin x(sin x + sin x cos x- y)

A: Find your answer below 

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D 8...

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Q: Evaluate the limit and justify each step by indicating the appropriate Limit Theorem(s). please sle...

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Q: Find the limit. Select the correct choice below and, if necessary, fill in the answer box within you...

A: Given that: limx→-9x3+729x+9

Q: 1. Determine the ORDER, DEGREE and LINEARITY (Yes or No) ORDER DE d² ds t2 - -t=1- sin(t) dt? dt x*y...

A: since we are given with the multiple number of question and our guideline is solve first question on...

Q: (c) y = e* sin 7x + In(cos(x)) (d) y= xarcsin x+ V1-x²

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Q: The vectors x and y are each of length 3 units (ie. |x| = |y| = 3)). If |x+y| = square root 17, then...

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Q: 4 y = (x +3) Lax-1)

A:   Since you have posted multiple question as per guidelines we can solve only one question at a time...

Q: Given the differential equation 3 r² y" - 2ty' - 2y = 1? Determine the value of u2. 10 A 70 H2 35 91...

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Q: D. Given the following polar equations, find the eccentricity and identify the type of conic; write ...

A: We know that the polar form of a conic with directrix x=±p and the focus at origin has form: r=ep1±e...

Q: g(x) = -13 – x| + 5 -6- -10 -9 3 10 -1- -2- -3-

A: The objective of the question is graph the given equation.

Q: SVEV4 + tVE dt

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Q: Use the definition of derivative to find the tangent and normal equations of f (x) = (x – 3)2 %3D

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Q: An insurance company has six branches in six states. Find the number of ways in which six branch man...

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Q: Graph the function fix) =x -1 over the interval (0, 21 Partkion the interval into four subintervals ...

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Q: Below is a value of cosh x. Use the definitions for hyperbolic functions and the identity coshx- sin...

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Q: sin x cos? x dx

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Q: Find an exponential function of the form P(t) = Pon that models the situation, and then find the equ...

A: Given Tripling time = 4 months Initial population P0=4000 Exponential functionPt=P0ntT

Q: 100 20.0 20.0 20,0 28,0 -20 100-20 100 -20 -20 m(x) п(2) Let h(x) = n(m(x)). Find a point x where h'...

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Q: Activity 6: You are testing an electrical device which can be modelled by the following equations: I...

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Q: Direction: Find the derivative of the function. y=- -z+ 2e Select one: O y' = 4x? – 1+ 2e" O y' = 4x...

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Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplic 2 at x = 2 and x...

A: roots : x=2,2,0,0, -5 Factors are given by:x-2,x-2,x-0.x-0,x+5hence P(x)=Product of factors P(x)=(x-...

Q: Given the polynomial P(z) = -9z - 9z² – 5z – 20 and divisor d(z) = -3z + 2, find the quotient Q(z) a...

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Q: The answer is: Find the exact value of a in the given interval that has the given circular value. Do...

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Q: Combination 1. A panel of judges is to consist of four women and three men. A list of potential judg...

A: This question can be solved using the concept of selecting r objects from n given objects when the o...

Q: 12. Find a polar equation for the hyperbola with focus at the origin, directrix x = -2, and eccentri...

A: Polar equation of hyperbola is      r=ed/(1+esinthetha) 

Q: Consider the following functions. f(x) g(x) = 3D Зх — 5 X + 5' Find (fo g)(x). Find the domain of (f...

A: Given that: f(x)=xx+5 and g(x)=3x-5

Q: Direction: Find the derivative of the function. I+5 w = 2x - 7 Select one: 17 (2г — 7)2 17 (2x – 7)2...

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Q: Solve the following DE by using separation of variables or method used in solving exact DE

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Q: A. B. ET D G. 2.

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Q: (x-G -0 +2) dx + 2(x+2y+2) dy:

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Q: Find the first derivative for the following function. Do not simplify. a) f(x) = (2x² + 4)(x* – 3x)

A: Given: (1)     f(x) = 2x3+4x4-3x (2)     f(x) = 1+cotx  2cosx

Q: Direction: Find the derivative of the function. y = -z² + 3 Select one: O y' = -2x O y' = 2x O y' = ...

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Q: ax+: xp:

A: In this question , we can solve given integral by using substitution method. ∫un du = un+1n+1+C

Q: Find the exact value of s in the given interval that has the given circular function value. V3 CoS s...

A: Topic = trigonometry

Q: 2. Given: f(х) - х* +4x? - 2х+9 g(x)=x² +2 h(n+2) = 2h(n+ 1)– 3[h(n)] h(1) =1 and h(3)= 5 f(-5) с. h...

A: Given, fx=x3+4x2-2x+9 hn+2=2hn+1-3hn2 ; h1=1and h3=5 We have to find f-5 and h6.  

Q: II. Write the equation of the circle in standard form and in general form given its center and radiu...

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Q: Evaluate the following indefinite integral. -x-2 (a) dx dx (b) cos 0 sin Od0

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Q: Find an equation of the tangent line to the curve at the given point. у - 9х - бух, (1, 3) y = Illus...

A: Find your answer below 

Q: 3. Find the domain or range of the following functions f(x)=x-|X|. Find the range. f. f(x)=. 2-x. Fi...

A: Given:    f. fx=x-x Range:    The set of values of the dependent variable for which a function is de...