The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its area if its radius increases from 20 mm to 29 mm. [Recall that the area circle is A = r².]

Q: 5) You drop a basketball from a height of 8 feet, and let it fall and bounce. Every bounce, the ball…

A: We have to find the distance travelled.

Q: x³ + 8x² Consider the function f(x) = may be helpful to factor by grouping. 81x648 x + 8 O Answer…

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Q: (a) Find the volume of the solids generated by revolving the region bounded by the curves y = 4-x²,…

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Q: 3) Find the Taylor series for the function g(x) = x²e³x+¹ centered at a = 1.

A: To find the Taylor series for the function gx=x2e3x+1 centered at a=1.

Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: Find a linear equation that expresses the relationship between the temperature in degrees Celsius C…

A: The water freezes at 0°C  is (32°F) and boils at 100°C (212°F)

Q: The slope of the tangent line to the curve y = 4 X at the point 5, is: The equation of this tangent…

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Q: TL 3. sin²4ycos²2ydy T

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Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

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Q: The half-life of a certain substance is 3.6 days. How long will it take for 20 g of the substance to…

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Q: X (2-x) 6(E-x) Htx

A: The solution is given below

Q: S x²-x +2 -X X³ + 4x -dx

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Q: T 2 T . 3 -2x²+2x-2 (x² +1) sin x 1-2 cos x dx dx

A: We know that integration power rule is  Integration of xn is xn+1/n+1.     Here i attached the…

Q: 6 5 4 3 2 I | y = f(x) 1 1 01 2 ? | 3 4 | 1 + 5 6 7 1 X 89

A: Topic- limits

Q: An employee has two options for positions in a large corporation. One position pays $14.25 per hour…

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Q: Use the Product Rule or Quotient Rule to find the derivative. f(z) = (3x-²+5) (-4x−³+4). ○ f'(z) =…

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Q: A cable hangs between two poles that are 70-ft apart. The two poles are both 40 foot high. Sag is…

A: Let's solve length of cable.

Q: (d) Find the volume of the solids generated by revolving the region bounded by the curves y = 2x -…

A: Solved below

Q: Write the equation for the plane. The plane through the point P(-2,-5,3) and normal to n = (2,7,8 O…

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Q: Find the surface area of the torus generated by revolving the circle given by r = 5a about the line…

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Q: An $82,000 business can be purchased by making a down payment of $17,000 and financing the balance…

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Q: If f(x) = 4x + 14, find the slope of the secant line between the values of *₁ = 9 and ₂ = 2.

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Q: If f is an even function and fº, f(x) dx = 2 and f f(x) dx = 9, find ſº ƒ(x) dx. (Use symbolic…

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Q: Approximate the integral with the approximation. (Round your answers to one decimal place.) x²y dy…

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Q: First four terms of the sequence are: O O O ○ ○ O 6 {ff, 5 14 9 n²+5 n 1+4 n 61 36 26' 14 { 14/1/2,…

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Q: Select the graph that best matches the function. = -4 cos(x + ose y = O a) TL (-1/2, 4) (3x/2, 4)

A: Given equation:- y=-4cos(x+π/6)  To find:- Sketch the graph of given equation

Q: In a display, there are 20 toys in the first row, 23 toys in the second row, and so on in an…

A: topic- arithmetic sequence

Q: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=5i-j and…

A: We have to find the dot product of vectors and magnitude of vectors

Q: an = n 2.6 (1+2:0) "

A: Please see the below picture for detailed solution.

Q: A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 114 ft/sec Not…

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Q: Find the absolute minimum value of f(x) = 9x² - 5 x + 14 on the interval [0, ∞). Note: You need to…

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Q: Identify the vertical and horizontal asymptotes of f(x) = 2x+1 X-4 vertical: x = horizontal: y…

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Q: 5. Find the specific solution of the differential equation Oy=ex² O y=-1- ²³/2 O y=-ex None of these…

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Q: Consider the points P(0,0,6) and Q(-42,6,0). a. Find PQ and state your answer in two forms: (a,b,c)…

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Q: Find the third degree Taylor polynomial T3 (x)centered at a O T3 (x) = 3 - 6x + 9x² - 12x³ O T3…

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

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Q: Find the marginal profit function if cost and revenue are given by C(x)= 185 +0.3x and R(x) = 3x…

A: Recall: Profit, P(x)=Revenue-Cost Marginal profit=P'(x) We have, R(x)=3x-0.02x2, C(x)=185+0.3x

Q: Use the Product Rule or Quotient Rule to find the derivative of f(x) = O None of these. f'(x) =…

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Q: Find v-u. v=4i-7j and u= -9i+2j OA. -5i-5j OB. -50 O C. -36i-14j OD. -22

A: Given: v= 4i - 7j u= -9i+2j

Q: Determine whether each of the following vector fields is path independent (conservative) or not. If…

A: Solution is given below:

Q: L3Q6. If f(x) = 2x – 1 and g(x) = log x, compute (f – g) (x). A.2x – 1 + log x B.2x – 1 – log x

A: Given; f(x) = 2x – 1 and g(x) = log x

Q: L3Q11.The number of bacteria in a certain food is a function of the food’s temperature. The number…

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Q: Find the interval of convergence of the power series .x" /n². 0-1<x<1 0-1<x< 1 0-1≤x≤1 O-1<x< 1

A: The given power series is xn/n2.

Q: 5. Find the divergence and curl of the vector field F(x, y, z) = (xy - 2², 2x+cos(yz), 2y² - sinz)…

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Q: Two bacteria cultures are being studied in a lab. At the start, bacteria A had a population of 60…

A: Topic:- exponential growth function

Q: Plz

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Q: - Evaluate sin x dx using 3 i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

A: We have to evaluate ∫0π2sin x dx. Here a=0 and b=π2=1.570796 Given n=6 ∴ h = b-an = 1.570796-06 =…

Q: Consider the region B under the graph of y = 3x² + 1, x [1,3], and above the x-axis. Find the area A…

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Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

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Q: consider the hyperbola represented by the equation - (x+5)^2/9^2+ (y-7)^2/13^2= 1

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