ots. S=C₁e-t + c₂e²t + c3e6t+₁е-5t O a. 2,-1,6, -5 O b. -2,-1,-5,6 O c. 5,-1, 2, 6 O d. 2,-1,2,6

Q: When an object is dropped on a certain earth-like planet, the distance it falls in t​ seconds,…

A: Motion: Recall that the velocity is the time derivative of the position, and the acceleration is the…

Q: The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of…

A: Given, Length of rectangle at rate 8 cm/s Therefore dldt=8 Width of rectangle is increases by 4cm/s…

Q: (b) fx d -2

A:

Q: Show that 3 is a factor of n3 + 2n for all natural numbers n. Let P denote the statement: 3 is a…

A:

Q: Finding Area by the Fundamental Theorem Find the area of the region. y = 5e-x/4 -4 -2 y 10r 8 6 4 2…

A:

Q: a Evaluate the indefinite integrals the method of substitution using dx d) S e) 3 -x ³ 3+xx 1) 40…

A:

Q: L₂ (x + 2)ex²+4x+3 dx -2 =

A: Given: I=∫-20x+2ex2+4x+3dx    ....1   As we know the common integral, ∫exdx=ex+C   Note: As per…

Q: 40. *3 dx o 5x + 1

A: We will use substitution method to solve the definite integral

Q: 10y=10sin(pi(x-5))+40 find amplitude

A: Solution : Given data, 10y=10sin(π(x-5))+40

Q: BOTTOM LINE What is the average velocity of a particle with velocity v(t)=4-t² ft/s from t = 1 to t…

A: NOTE: Refresh your page if you can't see any equations. . the velocity function is the given…

Q: To show that Pk+1 is true, add (2(k+ 1))3 to both sides of Pk. +(2k)³ +(2k +1 23 +43 +63 + ...…

A: According to question,Given equation,23+ 43 + 63 + ....... + 2k3 + 2k+13 = 2k2k+12+ 2k+13

Q: Consider the following. √²/²5 5 cos²(e) de State the half-angle identity that can be used to…

A: We have to write the half-angle identity for Cos2θ

Q: 6. Verify this identity: sec² (0)-1 sec² (0) = sin² (0) You must show all work! 7. Verify this…

A:

Q: Kosumi puts the base of a 9-foot ladder 6 feet from the wall of his house. How far up the wall does…

A:

Q: Let I be the length of a diagonal of a rectangle whose sides have lengths and y, and assume that and…

A: Here we have to use the concept of derivatives

Q: Use the substitution x = 5 sect to evaluate the integral f Note: Use C for an arbitrary constant. dr…

A:

Q: Evaluate the following integrals. 1 √(x + a)(x + b) (a) / dx.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use integration by parts to evaluate the definite integral S te-t dt.

A: We need to use the integration by parts to solve the definite integral.

Q: 5. The graph of a certain function f(x) with domain [-3,3] consist of a semicircle of center (-2,0)…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Evaluate the definite integral. -3 [₁₁2+. -3 (x+3) ex²+6x+8 dx =

A: ∫exdx=ex+c∫xndx=xn+1n+1+c

Q: Given f(x) = ²x + 2x, find the slope of the line tangent to the curve of f-¹(x) at (1,0) where (1,0)…

A:

Q: 6. / (314 3t+ + 2)t³ dt

A:

Q: Let P(t) be the population of bacteria in a glass dish, in millions after t hours. suppose we have…

A:

Q: 4. A straight river flows north at a speed of 3 mi/h. A boater attempting to cross the river heads…

A:

Q: Find the slope of the tangent line to the curve 2xy - 3y³ = -9 - -4x² - at the point (2, -1).

A: NOTE: Refresh your page if you can't see any equations. . the given curve is  and the given point…

Q: If a ball is thrown vertically upward with an initial velocity of 96 ft/s, then its height after t…

A:

Q: Find the distance between the points (-1.4,0.5) and (-3.1,1.7) Distance = Give the approximate…

A:

Q: A searchlight uses a parabolic mirror to cast a beam of light in parallel rays where the light bulb…

A:

Q: Eliminate the arbitrary constants lnx = Asin3y + Bcos3y + 9x2 - 5

A:

Q: 3. y = C₁ + C₂ e-4x

A:

Q: 3 What is the book's definition of a smooth curve? Write down a pair of parametric equations for a…

A: Solve the following

Q: Given the demand equation x = 120e-P/26, where p represents the price in dollars and a the number of…

A: elasticity of demand  E(p)=px*dxdp.......(1)

Q: of an object is given by The displacement = √ ¹ - 7t² + tdt t4 Eveluates for a = 3.85 and b = 9 Give…

A:

Q: Answer: 3 f²f If f is continuous and f(x) dx 50, find = б'я f(3x) dx.

A:

Q: ermine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A:

Q: A town has a population of 2000 people at year t=0, write an appropriate formula for the population,…

A: Given: Town population = 2000 at t=0 It is decreasing at the continuous rate of 6% per year . To…

Q: A runner is jogging at a constant speed of 3.1 miles per hour. a. Find the distance d that the…

A: We need to find the function for the distance traveled by the jogs as a function of the time.

Q: Answer: If f is continuous and [10 *f(t) dt = 12, find the integral [*²1² ƒ (1³) di dt.

A:

Q: 2. If A is 2x8, B is 8x3 and C is 3x4, which of the following exists? a. 2A+3C b. (AB)C c. BA-2C d.…

A: We have to solve above question

Q: dy/dx = 6x^5sqrt(y-1) equals to y = [(1/2)(x^6+c)]^2 + 1? Diff eqn.

A: ∫tndt=tn+1n+1+cgiven  dydx=6x5y-1          dyy-1=6x5dxintegrate both sides

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: We have to find the distance between 12:00pm and 2:30pm.

Q: Problem 5: Find the value of c that satisfies the conclusion of the Mean Value Theorem for f(x)= x³…

A: The given function is fx=x3-4x2+3 on 0, 4. We have to find the value of c that satisfies Mean value…

Q: The population of a herd of deer is represented by the function A (t) = 195(1.31)t, where t is given…

A:

Q: The gas law for an ideal gas at absolute temperature 7 (in kelvins), pressure P (in atmospheres),…

A: NOTE: Refresh your page if you can't see any equations. . P=pressure T=temeprature V=volume R, n=…

Q: A company's revenue from selling a units of an item is given as R = 1200x - x². If sales are…

A:

Q: ble : Fin if if · fax) = ² 2 then f'(x) = 3 5+9x²³+5 sin (t) dt

A:

Q: The given relations is a one-to-one function over its domain. True False YA 4 2 -2 व 2 4 X

A: Horizontal line test : if a horizontal line can intersect the graph of a function at a single point…

Q: Question 11 Calculate V. v and V x v. v(x, y) = 5yzi + 6 xzj + 4xyk

A:

Q: Identify where on the number line 1-1.8 is located. DA ◆◆◆ -14-13 -12 -11 -10 -9-8-7-6-5-4-3-2-1 0 1…

A: identify the point where |-1.8| is located ?

Q: 6. A woman launches a boat from one shore of a straight river and wants to land at the point…

A: