The half-life of a certain substance is 3.6 days. How long will it take for 20 g of the substance to decay to 7 g?

Q: Flight of a Rocket The altitude in feet attained by a model rocket t seconds into flight is given by…

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Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 22 - 2y? - 35 - -4…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question.

Q: Find the equation of the tangent line to the curve at the given point using implicit…

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Evaluate the integral using the following values. 8 [³x x³ dx = 1,020, 2 [²x dx '8 8 L³x dx - 30,…

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Q: Needing

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Q: 3x lim x→∞ √x²+1

A: We can evaluate the limit as below.

Q: Use Euler's formula to write the expression e²+8i in the form a + ib. Round a and b to four decimal…

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Q: You are making a rectangular box with a square base. Its volume must be 8 ft^3 . Find the dimensions…

A: A rectangular box with a square base. Its volume must be 8 ft3

Q: Find the exact sum of the following series 0 In ( ) 3 5 OH(-) - 12 (²³) In 3 (²/²) - ²3/ In 23 ○ In…

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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: 7. Given f(x)=√x² + 3, determine p(x), q(x), and r(x) such that f(x) = p(q(r(x))). ✓✓

A: We need to find p(x),q(x),r(x)

Q: (1) Which is the correct formula for finding the derivative of the product of two functions? (fg)' =…

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Q: first order partial derivatives, i.e. dz/dx, dz/dy: xy³. z = In√√xy Z

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Q: Find the dimensions (in inches) of the open-top cylindrical tin can with volume 125 cubic inches…

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Q: Calculate the Taylor series for 1/x about 1. O 1+ (x + 1)(x-1) ²+ (x+1) ³-... ○1-(x-1) + (x − 1) ²—…

A: We know Taylor series expansion of 1/(1+x) is given by, 1/(1+x)= (1+x)-1= 1-x+x²-x³+x⁴-....

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface x² – 2y² − 3 ² = −4…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

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Q: Choose 1. Determine the radius of convergence and interval of convergence. (x+1) 2n 00 n=1 n! (x-2)"…

A: a) The summation of (x+1)2n/n!,  n from 1 to infinity.  b)  The summation of (x-2) n/[(n+1)3n], n…

Q: 11. Determine the divergence or convergence of the following improper integrals and evaluate if it…

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Q: y = x y 2 1 2 X

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Q: etermine the Laplace Transfor f(t) = 3te-5t cos(2t) stands ca

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Q: In y=e³ sinx

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Q: Find the function f(x) such that f'(x)=e^(3x)-6x+2 and f(0)=1. Thank you.

A: We need find the function f(x) such that f'(x)=e3x-6x+2 and f(0)=1

Q: it is the empirical formula for C10H20O5 O C₂H5O

A: Empirical formula  An empirical formula is the simplest whole number ratio of elements in a…

Q: Let f(x) be defined by f(x) = et² Find f'(1). Note: Your answer (if it's not an integer) should be…

A: On solving this we will get

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: The cost function for a particular product is given by C(x)=0.001x^3 −0.24x^2 +27.9x +110 dollars,…

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Q: (1 + 2.6) ² an = (1 +

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Q: Find the points on the graph of the function that are closest to the given point. F(x)=x², (0, 9)…

A: f(x)=x^2, (0,9)

Q: Graph the function showing all relative extreme points and inflection points. f(x)=√√√x6 + 4 ++ 2 3…

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Q: Find the centroid of the region bounded by y=x+3 and y=x²-3. O (1.098,1.68) O (0,1.68) O (1.68,…

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Q: Consider the following equation. =(21+√51) f(x, y) = y^/x, P(1, 3), u = (a) Find the gradient of f.…

A: Given :fx,y=y4x

Q: Choose the value of the area of the region enclosed by the curves y = 6x³, and y = 6x. O 3 O mla 316…

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Q: Find a particular solution to Ур || y" + 7y + 10y = 15te¹.

A: Given differential equation is y''+7y'+10y=15te4t We have to find a particular solution for it.

Q: A car depreciates by 17% each year. The value of a $30 000 over time is modelled by the function v =…

A: The given data is: The value of a $30,000 over time is modeled by the function v=300000.83t To find:…

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: So (2+7x) et ¹ dx

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Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

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Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared)…

A: To determine the drug usages, doctors estimate a person's body surface area BSA in meters squared…

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: y = ³/2, y = 8, x = 0

A: answer is in next step. please give a like .

Q: 4. Coffee at temperature 180°F is cooling in a room with constant temperature 75°F. If it takes for…

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Q: i) Find the general term (an) of the sequence 3e-²,4e¯4,5e¯6,6e-8, 7e-10, 8e-¹2,... ii) Calculate…

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Q: Take the derivative of  (x+y)3=3x-4y+5 with respect to the variable t . Do not rearrange and move…

A: NOTE: Refresh your page if you can't see any equations. . take derivative on both sides with…

Q: What is the area of the region between the curves 3 y = x³ and y = x², from x = -3 to x = -1? Select…

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Q: The integrating factor of the given DE are already given below. What is the value of “n” ?…

A: We need to find n.

Q: ies =gent. one: 2 Σ n: 4 7

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Q: Find the absolute extreme values of the function on the given interval. f(x) = 9x³ - 108x on [0, 5]

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