Given that f(x) = 4x2 and g(x) = 6 - x², calculate (a) f(g(0))- (b) g(f(0))-

Q: Give an equivalent rectangular equation for r = 3sin theta

A: given  r=2sin thetar=3sinθfor rectangular coordinates we know ⇒x=rcosθ⇒y=rsinθ⇒x2+y2=r2

Q: If a force of 24 N stretches a spring 0.2 m beyond its natural length, how much work does it take to…

A: The force required to stretch the spring 0.2m beyond its natural length is 24 N. To determine: The…

Q: Perform the indicated operation and write the answer in the form of a + bi. (6+5)) - 10i O O 6-5i O…

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Q: Exact Differentail Equation M (x,y) dx + N (x,y) dy = 0 is an Exact DE when ∂M/∂y = ∂N/∂x Solution…

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Q: 3. By changing the order of integration, evaluate •ffer² dydx

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Q: g(x) = 3()*+4 9 (x). - 8 is a transformation of the function f(x) = (-¹) ². Determine the range of

A: fx =12xgx =312x+4 -8

Q: ď²y. -2t dt²³ y = e¯²t sin 3t

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Q: Consider the function ƒ(x, y) = y√x – y² − 4x + 15y. Find and classify the critical point of the…

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Q: A disease spreads through a population. The number of cases t days after the start of the epidemic…

A: The general form of an exponential growth function is  N(x) = A0 e rt  Where  N0 - Initial value…

Q: Identify the center, vertices, co-vertices, and foci of the ellipse. (x-8)² 81 + (y-3)² 36 O Center:…

A: x-8281+y-3236=1

Q: A B C D 2/3 43 Let R be the region in the first quadrant bounded by the graphs of x = y² and x = 2y,…

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Q: esin x dx

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Q: The first derivative of f(x)= = 10x³ - 3 √(5x4 - 6x)³ C. (3-10x³)√(5x4 - 6x)³ A. Select one: Ο Α OB…

A: The Power Rule: ddxxn=nxn-1 The Chain Rule: fgx'=f'gx·g'x

Q: Find the absolute extrema of the function h(x) Absolute maximum value: at x = ± Absolute minimum…

A: Given: h(x)=ex2-4  We are required to find: Absolute maximum and Absolute minimum values of function…

Q: Charging the Capacitor Having stabilized the fuel, you look to your computer for next steps. You are…

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Q: a b 1 12. Use matrix multiplication to confirm that the inverse of the matrix A = where we assume…

A: By using matrix multiplication to confirm that the inverse of the matrix A=abcd  is A-1=1ad-bcd-b-ca…

Q: Find the length of the graph of y = f(x) where f(x) = - and a 2, correct to two decimal places.…

A: To find the arc length of the graph of y=fx where fx=x2+2323 between x=1 and x=2, correct to two…

Q: For this question, we are going to consider the global extrema of the function p(t)- 8t5 - 5ct where…

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Q: The function p(t)- 20 sin 2xt + 100 models a person's blood pressure while resting, where p(t)…

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Q: Consider the function f(x) = e³ and the general formula for Maclaurin series, 1. Find the Maclaurin…

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Q: A (В) (С D 15 29 44 D 58 v(t) A Over the time interval 0 ≤t≤ 10, a particle moves along the z-axis.…

A: Total displacement is difference of distance travelled is left and distance travelled in right…

Q: Find the unique anti-derivative F of 2e5x – 2e²x + 4e−3x e2x f(x) for which F(0) 1. F(x) 2. F(x) 3.…

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Q: Q26. Order and degree of the differential equation (3) (²2) is? < dx² ex = In (a) order= 4, degree=…

A: To find out the order and degree of the given differential equation.

Q: Your computer informs you that this gas follows the Ideal Gas Law (PV = nRT), and that the units for…

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Q: 3=e4x +1 a) .693 b).234 c) .1732 d) .205 e) 0.67

A: 3=e4x+1

Q: Find the indefinite integral. Check your work by differentiation. S5x 5x(3-x) dx 5x(3 - x) dx =

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Q: a. Use the product rule to find the derivative of the given function. b. Find the derivative by…

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Q: Prove that the linear function f(x) = ax+b is continuous.

A: To prove that the given linear function is continuous.

Q: Verify the expression. Show all your work

A: tan2x - cot2x = sec2x -csc2x

Q: Complete the table for the radioactive isotope. (Round your answer to two decimal places.) Half-life…

A: Isotope  Half-life (in years) Initial quantity   amount after 4000 years 239PU 24,100 ...g 2.6 g…

Q: 11) The price of a truck will depreciate exponentially from $45,000 in 2015 to $13,000 in 2021. a)…

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Q: Perform the indicated operation and write the answer in the form of a + bi. 5+ (6+2) 5+2i O 6+7i O…

A: We need to choose correct option.

Q: А b C с = a = 17 12,2° 24 - В

A: The figure of the triangle is given by To determine: The value of b Formula Used: b = a2+c2-2ac…

Q: A 90 ft 120 ft 134.2 ft

A: In a public park, a triangular region of grass is bounded by walkways. Sprinkler heads are placed…

Q: For each n the interval [2, 9] is divided into n subintervals [ri-1, il of equal length Ar, and a…

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Q: Write the following first-order differential equations in simplified standard form. x dy/dx =…

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Q: The velocity graph of a particle moving along a straight line is shown below. The velocity is given…

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Q: 3. A box container, in a shape of a rectangular prisin, has a square base. 64000 inch³. (a) Find the…

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Q: At the time a bowl of ramen is served, its temperature is 100 degrees Fahrenheit. The ramen's…

A: To find out the temperature after 3 minutes of the Ramen.

Q: Answer all of the questions below about the function f(x) graphed below when x = -5. -∞ DNE…

A: A graph of a function y=fx is given below. To find the following. (i) limx→-5- fx (ii) limx→-5+ fx…

Q: In Exercises 45-46, we demonstrate that, in general, you antiderivative of a product of functions by…

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Q: Find the value of f(-1) when ƒ"(t) = 6(2t − 1) and ƒ'(1) = 6, ƒ(1) = 1.

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Q: Consider the system of equation: and 2x+3y=z=8 2-4y+2z = -1 5x + 2y = 15 2x+3y-z = 8 The second…

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Q: Consider the surface z + 16 = xey cos z. Find an equation of the tangent plane to this surface at…

A: The given surface is:z+16=xey cos z

Q: f ‴(x) = cos(x),    f(0) = 4,    f ′(0) = 6,    f ″(0) = 7 Find f.

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Q: 5x+1 dx 2x²-x-1

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Q: 3) ƒ(x)=(e²x +1)5

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Q: Use the information provided to write the standard form equation of the hyperbola. Show your work…

A: We need to find equation of hyperbola.

Q: Multiply and write the answer in the form of a + bi. (-9) (2-√√-25) O 18+45 i O 6+15/ O 15+6i O -18…

A: (-1)1/2  = i  (25)1/2 = 5  (a.b)1/2 = (a)1/2(b)1/2

Q: Consider the equation y=x^3-16x^2+2x-4 a. Determine all intervals over which the graph is concave…

A: For a function y = f( x ) For concave up f''( x ) &gt; 0 For concave down f''( x ) &lt; 0  Given…