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Q: has a half-life of 1,599 years. Given an initial amount of 13 grams of the isotope, how many grams 2...

A: half life formula : No=initial value =13t12=half life=1599 put the values :

Q: Q.1 In the study offrost penetration in highway engineering the temperature T at time t hours and th...

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Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 АЗ The are...

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Q: Let A(x) = | f(t)dt where f is the function given by the graph below. 4 -1 -2 -3 A(5) = A(9) -

A: Given graph with values with x and y axies

Q: 3. 1

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Q: Producers' Surplus  The demand function for a certain brand of CD is given by p = −0.01x2 − 0.2x + ...

A: given  p = −0.01x2 − 0.2x + 16=D(x) p = 0.01x2 + 0.8x + 4=S(x)   to find equilibrium price D(x)=S(x...

Q: The average cost per item for a product is given by: AC(x)= x^3/3-7x^2/2+12x+10 Where x is the numbe...

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Q: Calculus question

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Q: Show that the vector field F = i + sin(z) j + y cos(z) k is conservative and then find the correspon...

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Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos² x.cos"...

A: Given: In=∫0π2x cosnx dx

Q: Please provide the answer clearly

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Q: 14.

A: Recall that the directional derivative of f at x0,y0 in the direction if the unit vector v=(xv,yv)  ...

Q: Find the rational function if the vertical asymptotes are x=−98x=−98 and x=82x=82 and the horizontal...

A: Given query is to find the missing function.

Q: Please show work

A: Given: ∫14 f(x) dx=8∫49 f(x) dx=-5∫79 f(x) dx=2∫49 g(x) dx=1

Q: 5. Find the solution of the differential equation that satisfies the given initial condition. dy =y²...

A: Topic- differential equations

Q: 305. Compute F· NdS, where F(x, y, z) = xyzi + xyzj + xyzk and N is an outward normal vector S, wher...

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Q: Find the measure of arc HG. 5х-4, G 9x+3 O 128° 136° 770 102°

A: To find: The measure of arc HG. Formula used: The angle subtend by the arc on the centre is double t...

Q: Evaluate the improper integral. 6 dx V36 - x? O A. 12 O B. 1 12 О с. O C. O D. 1 KIN

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Q: Determine whether the series is convergent or divergent. 1. 3. 1 8. 1 3. ... 4 16 32 64 O convergent...

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Q: Find the moments M2, My and the mas: The density function is p(x, y) = (xy) significant digits.

A: Given, Vertices are :(0, 0) (0, 8), and (7, 8)          density of functionρ(x, y)=xy12

Q: Find the slope of the curve: y= x^2/x^2 -1 at x=2

A: Slope of curve is the derivative of curve at the point .  Slope = m = ( dy/dx ) | x = a 

Q: 21.

A: We need to find dy/dx at the point (-1,-1)    

Q: Find the entire Maclaurin Series for f(x).

A: This question is taken from the calculus in which we have to find the Maclaurin Series given functio...

Q: 2. The region enclosed by the given curves is rotated about the specified line. Find the volume of t...

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Q: Find a power series representation for the function. (Give your power series representation centered...

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Q: Solve for x. 140° 6x-8

A: Solve for x  

Q: Carmen has leaned an algorithm tor subtraction. She uses it to find 54 – 18 as tollows. so 54 + 10 =...

A: Closure property                       : Whole number + whole number = whole numberAdditive inverse ...

Q: Given the force field F, find the work required to move an object on the given oriented curve r(t). ...

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Q: Factor the trinomial 40x2−75x+3540x2−75x+35:

A: Given equation is 40x2-75x+3450x2-75x+353490x2-150x+35=0

Q: The number of bacteria in a culture was initially 8000 and it was 12,400 after 2 hours. find a funct...

A: number of bacteria initially=8000 number of bacteria after 2 hours=12,400

Q: nd the distance between G and H on the number line below. G ++ -12 -11 -10 -9 -8 -7 -6 + 5 6 7 8 9 1...

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Q: 27

A: Given,    F=(-6x+8y-4z)i+(-8x-5y+3z)j+(x+5y+2z)k

Q: 386. Use the divergence theorem to calculate surface integral F-dS, where F(x, Y, z) = xªi – a³z²j+ ...

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Q: Find the consumers' surplus at a price level of p= $130 for the price-demand equation below. p= D(x)...

A: Topic- price demand and surplus

Q: Integration do

A: Given 6∫(t-3)23+(2t-3)tdtwe need to integrate the given equation

Q: In order for a function to be continuous at X=a, which of the following conditions must be satisfied...

A: 1st condition For a function f(x) to be continuous, left hand limit and right hand limit should exis...

Q: Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the ...

A: Ans.  1. The graph of this equation will be option c) circle with center at (0,6) 2. The graph will ...

Q: Find an equation for each ellipse.Graph the equation

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Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 АЗ The are...

A: SOLUTION-

Q: Could you show all the steps in handwriting?

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Q: Find a power series representation for the function. (Give your power series representation centered...

A: fx=x2x2+1 ffx=x1--2x2 Power series representation:- fx=x∑n=0∞-2x2n            ; -2x2<1 fx=∑n=0∞-1...

Q: A geometric progression has 6 terms. The first term is 192 and the common ratio is 1.5. An arithmeti...

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Q: 16 f(x) - f(z) = | f(x) where a= and b=

A: Given integration is : ∫216fxdx-∫27fxdx=∫abfxdx To find the value of a and b.

Q: Pls draw this vector. Pls draw neatly.

A: It states that if we curl the fingers of right hand, keeping the thumb erect, in such a way that the...

Q: Compute the limit. Type in the number, round to the nearest whole number if necessary.lim ?→4+(3?^2−...

A: to find:- limit.

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.  ...

A: Given data is : dxdt=5et-3 , x0=4 To find the antiderivative 

Q: 3) The average cost per item for a product is given by:  AC(x)=x^3/3-7x^2/2+12x+10 Where x is the nu...

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Q: Is this statement TRUE or FALSE?

A:

Q: 18

A: The figure of the  cone is  To evaluate : The volume of the cone.

Q: In the given equation as folows , use the Root Test to determine the convergence or divergence of th...

A: The given series is ∑n=1∞1n-1n2n To find: Determine whether the series is convergent or divergent