Solve the differential equation. g'(x) = 18x², g(0) g(0) = -4 g(x) =

Q: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it…

A: Topic-Linear function

Q: Find k if 2x + 1 is a factor of kæ³ +7x² + kx − 3. a) k = -2 b) k = 2 Ock= 11 d) none of the above

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Q: 4) The graph below represents the relationship between velocity and time during a motion. graph to…

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Q: Solve the following equations 1) 2 (y + 1)e* dx + 2(ex - 2y)dy = 0 dy — 2) 2xy dx + y² - 2x = 0

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Q: 2 TL (21) 3.The vertex is at (4,-4) and the directrix is y + 5 = 0.

A: Topic = Parabola As per guidelines, At a time only one question can be answered.

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A: Given data:- Equation of curve, x+12=4x-1 Line, y=4

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A: To solve the given differential equation.

Q: Variables Separable Solve. Show complete solution. sin x cos²y dx + cos²x dy = 0

A: Given differential eequationsinxcos2ydx+cos2xdy=0

Q: The angle between 0 and 27 in radians that is coterminal with the angle 41п 5 radians is

A: We can find the answer in the following steps.

Q: Find the Maclaurin series of the function. f(x) = ln (1 – 5x) Choose the Maclaurin series. In (1 –…

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Q: f(x) = 2 Lim f(x+x) - fox) AX f'(x)= 4x40 Lim AXO Lim (x+4x)² - + (x+AX)^2-x²² AX AX x= x + 2x (0x)"…

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Q: f(x) = -x² +9 d the x-values at which f is not continuous. Which of the discontinuities are…

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Q: An arc of length 19 meters subtends a central angle of 294 in a circle. a) Find the circumference of…

A: Topic:- geometry

Q: Compute the surface area of revolution about the x-axis of f(x) = (4- x²/3)³/2 in [0, 8].

A: A detailed solution is given below

Q: 7л Determine the exact value of cot 6 Oa) -2 b) √3 Oc) -√3 O d) 1 √3

A: Find the value of cot(7 pi)/6.

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Q: Find the exact value of the following expression for the given value of 0. Do not use a calculator.…

A: The given expression is tanθ4 if θ=2π3 use the trigonometric ratio and values,…

Q: -6 -5 -4 -3 256 224 192 160 128 96 64 32 -32 -64+ -96- -128 -160- -192 -224 -256- -288 -320- -352…

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Q: Convert the angle 420° to radians:

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Q: - What is the equation of the horizontal asymptote of y = 2* — 2? a) y = 0 b) y = -2 O c) y = -1 d)…

A: Given equation y=x2-2

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A: Topic:- trigonometry

Q: Let f(x) = 2x = 2x − 3 and g(x) = x² + 3x + 4. Evaluate the following. a. f(3) = 3 b. f(-4)=-11 c.…

A: As parts a,b,c and d are already correctly marked, the solutions for remaining questions are given…

Q: 5. What is the horizontal phase shift of the function f(x) a. b. TT 4 C. d. π = 3sin(x + 1)?

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Q: Find the general solution and the particular solution to the given initial condition of the…

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Q: 1. Give an example to show that vectors are not commutative under the cross product operation.…

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Q: Find the standard equation of the circle which satisfies the given conditions. 4. center at the…

A: The objective of the question is determine the standard equation of circles.

Q: 6 5 4 3 2 1 01 2 3 lim 2-17 lim z→4+ y = f(x) lim Enter each answer as a whole number (like -4, 0,…

A: To determine the following.f9=?limx→1- fx=?limx→4+ fx=?limx→1 fx=?

Q: The foci are on the x-axis, the x-intercepts are ±2 and they intercepts are ±1.

A: find the equation of ellipse

Q: 10. What is the amplitude of the function f(x) a. 12 b. 5 c. 4√10 = 3(sinx) + (4cosx)? d. 3√10

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Q: x - 39 X-39 VX + 10 -7 Find lim X-39 lim X-39 √x+10-7 (Type an integer or a simplified fraction.)

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Q: X y -3 4 -1 5 7. -4 6 -3 7 X y -3 5 -1 4 8. -4 0 5 7

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Q: 9. What is the period of the function f(x) a. 4π 5 b. 2 C. 2₁ = 2 (sin x)? d. 5π 2

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Q: Suppose an object is fired vertically upward from the ground with an initial velocity of 96ft/sec.…

A: Given: The height of the object above the ground after t second is given bys(t)=96t-6t2To Find:…

Q: 2x if a 1 Calculate the following limits. Enter "DNE" if the limit does not exist. f(x) = Let f(x)…

A: Please see the below picture for detailed solution.

Q: x³ - 3x²y = C

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Q: Question 1 1) Suppose that the function f is defined piece-wise as follows: f(x) = 4x² 3 whenever a…

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Q: State the derivative. Do not simplify. f(x) = log(x) + log₂ (x)

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Q: If lim f(x) = 2, and lim g(x) = 7 find: C→C I-C a) lim 4f(z) A C b) lim ln(g(x))

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Q: A committee of six people is chosen from seven senators and ten representatives. How many committees…

A: Given,          Number of senators = 7          Number of representative = 10

Q: Which expression DOES NOT represent a law of exponents? a) am xan = b) =am-n am an c) (am)n = amn d)…

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Q: Lim 60x2+X-1 ×→(-1/2)+6x²-3x-3

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Q: Consider the following. f(x) = = 8 - 2x, 3, x ≤ 2 2 < x < 4 x 24

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Q: EX: Find the F.T. of the triangular pulses g(t)=AA(+) Sols Apply differentiation property of F-T…

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Q: To graph the function f, we plot the points (x, f(x) ✔ (x₁ To graph f(x)=x2-4, we plot the following…

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Q: The angle between 0 and 360° that is coterminal with the angle 1124° is

A: Coterminal angles are angles in standard position that share the same terminal arm. Coterminal…

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Q: Given the following graph of a rational function and its equation 5(x+1)(x-3) (x+4)(x-5) , identify…

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Q: Consider the function f(x) = = √x and the point P(4, 2) on the graph f. (a) Graph f and the secant…

A: Note: The student has made a typing error in the phrase "Use the results of part (b)", it should be…