13. Find the distance from the point (2, 2, 3) to the plane 2x+y + 2z = 4.

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A:

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A: To find the distance between the two cars.

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: We need to find area.

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Q: Sketch the graph off and use your sketch to find the absolute and local maximum and minimum values…

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Q: ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated…

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Q: Question 8 Find the partial derivative of z with respect to x None of the choices dz (2r−y) да…

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Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

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Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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A:

Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 2. 2h(3)+g[f(-2)]…

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Q: Penny can see the clock on the top of her town’s courthouse from her front yard. The clock is at a…

A: Given:  horizontal distance from her front yard= 140 m            if the angle of elevation from…

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A: Given that,  tanx=sinxcosx to prove that ddxtanx=sec2x

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Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: Draw the graph:-    y=0 ( x-axis)  and y=√(x-x2)

Q: Find f'(0) if f(x) = = ad-bc d² ad+bc d² bc-ad d² ad-bc (c+d)² ax+b ca+d; a, b, c, d constant

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Q: Solve the equation 2x-1= 3x+1 algebraically.

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Q: Asymptotic to x= 0, x=5 and y=0

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Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i-3j-k, find vector normal to A and In plane of A and, B.

A: See the details solution in below

Q: Using the Inverse Function Theorem, what is (-1) (8) given that (x) = √6x-2? Note that (11) = 8. (Do…

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Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

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A: we need to convert polar coordinate into cartesian.

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A: given

Q: If 3x² + 2xy + y² = 2, what is? dx

A: Follow the procedure given below.

Q: Find , given y sec dy dx = final answer. √2x²+1, x > 0. Simplify your

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Q: let a=2+7i b=4-2i Choose the correct result of a*b* O 24+22i O22+22i O22+241 O 22-24i

A: Given that a = 2 + 7i and b = 4 - 2i. We have to find a*b. Clearly as  a = 2 + 7i and b = 4 - 2i so…

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A: Given p=400-0.02x

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A: Given

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Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: B)Solve the differential equation da x+4y

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Q: Use the Inverse Function Theorem to find (p-¹) (2) given that p(x) = √√x - 7. Note that p(−11) = 2.…

A: The solution is given below

Q: Consider the following. de Use the substitution u = sin(0) to rewrite the given integral. SCC du The…

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Q: Use the Inverse Function Theorem to find (h-¹)' (7) given that h(x)=√10x + 9. Note that h(4) = 7.…

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Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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Q: -4 -3 -2 -1 0 3 4 1 2 Write an interval to describe the set of values shown above.

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Q: Bonus ( Show that given R: x € [0,1] Ay € [0,2] [[3x²yexydy dx = 6

A: See this solution in below

Q: B)Evaluate the integrals: i) f/2 inzerdrde " 0 ii) f/25/2 sinx 2² siny dz dy dx. π/2

A: B.1. According to question,Given Integral,Let I = ∫0π2∫0sin 2θr dr dθ

Q: Let one week's supply and demand functions for gasoline be given by p= D(q) = 288-39 and p = S(q) =…

A: Here, the demand and supply functions are: D(q)=288-43q & S(q)=23q which are the linear…

Q: f(x-1) e-2x+x² dx = O 1 -2x+x² e 2 2e-2+2x+C 2e-²x+x² + C e-2x+x² + C + C

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Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

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Q: Find area bounded by y = 0, y = √x - x² using double integration.

A: Graph: Now, we need to find the area of the above figure.

Q: Find the derivative: g(x) = 6x² e- X O g'(x) = 6xe (2-x) Og'(x) = -12xe** O g'(x) = 6xe (2-x) O…

A: We have to find derivative of given function.

Q: Find , given y = 5² 6n² a dy dx

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Q: x - ln x + 1| + C

A:

Q: Differentiate implicitly to find the first partial derivatives of z. 2x2 + 11y2 + 3z2 = 36

A: