7. Given A(3,1,0), B(1,0,2) and C(5,2,−2) determine the following: a. AB b. AC- c. Are points A, B, C are collinear (on the same line)? Justify your answer.

Q: in winding up the cable when there is a 400-pound load attached to the end of the cable. ft-lb

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Q: 10. Find the 87th derivative of y = cos(2x) at IT

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Q: 3. The Laplace transform of the f(t) = t²e-2t cos(3t) is (a) 2(+2)(8²+45-23) (s²+45+13)³…

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Q: xp (x+)ɔ zx f

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Q: D Operator: Solve the DE y" - 7y" +14y - 8y = 0 y = c₁e¹ + c₂e²x + c3e4x Oy=c₁e²x + c₂e4x + c3e6x y…

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Q: A region bounded by f(x) = x², y = 0, and x = 4 is shown below. 2 Find the volume of the solid…

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Q: 5. Iny+ea²²x+y = 10 -

A: Given :According to given , only 5 solvedlny+ex2y2-x+y=10

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Q: Use the matrices below to perform matrix multiplication. B = If the operation is undefined, enter…

A: We have to find products

Q: Evaluate the antiderivatives. 2x dx 5 S

A: ∫2xdx/5 ∫axdx = ax/lna here a =2

Q: 1) Which of the points (x, y) does NOT lie on the unit circle? a) O P(0, -1) b) (-3/3, 3/3) R…

A: Given :Equation of unir circle : x2+y2=1

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Q: [(x+1)e(x²+2x dx

A: The given integral,         ∫x+1ex2+2xdx

Q: Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2.

A: Area enclosed by curve r=f(θ), α≤θ≤β is given by  Area = 12∫αβr2dθ

Q: ا 1 x2(x – 1) dx

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Q: 1 3x (2x + = + ₁). x+1 Find k'(x) if k(x) = 3x (2x + Provide your answer below: k'(x) =

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Q: Let k(x)=f(x)g(x)h(x). If f(−2)=−5,f′(−2)=9,g(−2)=−7,g′(−2)=8,h(−2)=3, and h′(−2)=−10 what is…

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Q: 2 1 Lotes So I+ y² xyer² 0 1+ 0 Evaluate Select one: ○ In 2 O ln 2 O 1/4 ○ In 2 O 1/2 O 1 -dydx.…

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Q: The base of a three-dimensional figure is bound by the line X = √y on the interval [0, 4]. Vertical…

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Q: Evaluate f 10x(x² the following antiderivatives + 5) 7dx

A: The given integral is;  10x(x2+5)7.

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: 15. y = (In x) Inz

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Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is…

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Q: The vector v= (6,-4, 0) starts at the point P = (-2,5, -1). At what point does the vector end?…

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Q: A population of a small city had 3000 people in the year 2000 and has grown at a rate proportional…

A: In this question, we will use growth topic of differential equations.

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A: Given that  a spherical planet with a radius of 3 units and let its origin is centered at (0 , 0, 0…

Q: Use the formula for the area of a trapezoid to evaluate √₂² (2x- 2 (2x + 3) dx.

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Q: : Find area of triangle whose vectors P1(4,2,0), P2(-1,1,1), P3(0,4,3)

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Q: Let R be the region bounded by a = y² and x = y + 2. Find the volume of the solid generated when R…

A: The given curves are: x=y2and x=y+2 Now find the point of intersection between the given curves.…

Q: 8. Solve the ff DE y" -9y = 0 y = c₁e³x + c₂e-3x y = c₁ cos 3x + c₂ sin 3x y = ³x (c₁ cos 3x + c₂…

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Q: why do you think is important to calculate those 8 basic ratios  shown in picture

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Q: 2. Evaluate the definite integral|z- 3| dr. (a) (b) (c) (d) 25 2 25 2 29 29

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Q: Question 10 of 17 > dh\ dt =2 5 The variable h is the height of the ladder's top at time t, and x is…

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Q: Find the indicated limits, noting L'Hôpital's Rule wherever it is used. lim (1-ª)* (constant a)

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Q: How much money should David invest today into a fund that earns interest at 3.50% compounded…

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Q: R is the region bounded above by the function f(x) = −2x+1 and below by the function g(x) = 2x/3 − 8…

A: Area bounded by two functions f(x) and g(x) over the interval [a, b] can be determined as…

Q: Compute TOT/ cos(y³) dydx. [Hint: Change the order of the integration.] Show your solution. Select…

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Q: Find dy at the given point. dx 17) 5xe9y= 12; (1,0) 18) x2 + 3y2 = 13; (1, 2)

A: Given :17)  5xe9y=1218) x2+3y2=13

Q: 13. Integral √x dx

A: Here we have to find the integral.

Q: Solve the given differential equation. 16x2y" + 16xy' - y = 0 C₁ cos(In(x)). + C₂sin (In(x)) 4 4…

A: here we have to solve differential equation.

Q: Find the area enclosed by the curves f(x) = 33 - x² and g(x)=x². The area (rounded to two decimal…

A: The region bounded by the curves fx=33-x2 and gx=x2

Q: Using the Limit Laws, find limt→0 t2+9−3t2. Do not use L'Hospital's Rule.

A: By using the Limit Laws, to find limt→0 t2+9-3t2.

Q: 1-p p#1 u(c) = In c Show that limp-11-p C¹-p Given this result, is u continuous at p=1 ? p=1 = In c

A: Given that,uc=c1-ρ1-ρρ≠1ln cρ=1

Q: 20. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the…

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Q: Determine if the series. HE 10 n² 4n+3 74 converges or diverges. If the series converges, give its…

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Q: I. Integration by Parts. Evaluate the following integrals. 3. sin (In x)dr

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Q: Q2) A: By using partial method solve [2x² cos x dx

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Q: B: Draw the function y = √√x-8

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Q: Evaluate the given integral by changing to polar coordinates. sin(x² + y²) da, where R is the region…

A: Given :∫∫Rsinx2+y2dAR :Radius of unit circle is 3 and 4