The e half- lite of a ra to actine material 1S lle years. Sunppose we have a 10amg sa, How much of the ma fercal is lett after 30 years? 5ee l- n30 mg 10 10oe (na)10 mg 30 love (-)10 mg Soe(-), e mg. 110

Q: 25.) Find the radius of curvature of a parabola y? - 4x = 0 at (4,4).

A: Solution is given below:

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Q: The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his pioneeri...

A: Euler deduce that 12=1-1+1-1+1-1+......and-1=1+2+4+8+......by substituing x=-1 and x=2 in the formul...

Q: 2) To what number does E-L T Converges? (-3)" m=1 gn+T

A:

Q: 12) Find the exact length of the curve [4,16] on 3

A: We can find the exact length of the curve as below,  

Q: Sx (x +1) /3 dx

A:

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A:

Q: Find the general term of the sequence, starting withn 1. Determine whether the sequence converges, a...

A: The given sequence,19, 195, 1952, 1953,........

Q: Find A) The x values of all points where the function over the given interval has any relative extre...

A:

Q: Use the difference an+1 a, to show that the sequence {n - 3"+∞ Sn=1 is strictly increasing or strict...

A: Calculus  mathematics sequence 

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Q: Express the repeating decimal as a fraction. 5.262626...

A:

Q: Use the four-step process to find f'(x) and then find f'(3), f'(4), and f'(6). f(x) = 14 x+8 f'(x) =...

A: Given :f(x)=14x+8

Q: 2. H(x) = 4x2 + 4x - 4 %3D Circle the correct choice: Concave up or concave down? Vertical Stretch, ...

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A: a rational function f(x)=p(x)q(x)   is discontinuous at point wheher q(x)=0

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A:

Q: Consider the differential equation e' (3x-6x). Let y = f(x) be the particular solution to the differ...

A:

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

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A:

Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. cos'x sin x dy + (y cos>x – 1) dx = 0 2. xy' =2xex - ...

A: Given that: y.dx+x(lnx-lny-1)dy=0, when x=1, y=e

Q: Find cos(θ), if sec(θ)=−2.  Round your answer to four decimal places.

A:

Q: Calculate the integral. (Use symbolic notation and fractions where needed.) - sinh(15x) dx = +C

A:

Q: Find the general term of the sequence, starting withn = 1, determine whether the sequence converges,...

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Q: Evaluate the ff Sinx d /sinx+ casx

A:

Q: Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

A: As per our guideline we are supposed to answer 3 sub parts of a question please repost the other que...

Q: Evaluate the ff: 23 D S fda, given f 6)- and acx) F 1 3+3 X

A: Let's find. 

Q: Given the function: f(x, y, z) = æ²y*z³ + xy+ ² + 1. %3D Find a. f,(x, y, z) b. f:(x, y, z)

A: Topic:- partial derivatives

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A: he wave equation is closely related to the so-called advection equation, which in one dimension take...

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Q: If the limit of f(x) is 5 and the limit of g(x) is 2 as x approaches a constant k, what is the limit...

A: If the limit of f(x) is 5 and the limit of g(x) is 2 as x approaches a constant k, what is the limit...

Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate th...

A: Here, given that h-π4=12, hπ4=1 & ∫-11h(x)dx=2...(1)

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Q: Error Analysis. Below is the solution (possibly, with errors) for the derivative of the given functi...

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Q: The graph of f (x) is given by 3 Determine the following limits. Write your answer in the form lim f...

A: The graph of the function fx is given by Condition for the limit to exist:  limx→c-fx = limx→c+fx T...

Q: 28.lf a flash of lightning is observed in a cloud 2640 m away and the speed of sound in air is 330 m...

A: Given that: Distance between the observer and cloud=2640 mSpeed of sound=330 m/s

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A: Let's find. 

Q: Show that h, G) = (x+ n) converges %3D x4り? pointwise fo fa)=1, VXE [I, ) ノ

A:

Q: Find two positive numbers whose product is 36 and whose sum is a minimum. (If both values are the sa...

A: let the two numbers be x and y so  x×y=36sum=x+y since         xy=36⇒y=36x Substitute y value in sum...

Q: Find the point (x,y), at which the graph of y = 8x + 9x - 7 has a horizontal tangent. The function y...

A: Given that: y=8x2+9x-7

Q: d²f , df_ (a) +5- - + 6f =0, f(0)=1, f(0) =- 4 dt? dt

A:

Q: 1.which of the following is the inverse of f(x)=sqrt(x^2-4) a.f^-1(x)=sqrt(x^2-4);x≠4 b.f^-1(x)=x-...

A: Topic = Functions As per guidelines , At a time only one questions can be answered out of multiple q...

Q: Plot P(2, -4, 1) and Q(0, 3, 4) on the same set of coordinate axes

A: Give query is to plot P(2, -4, 1) and Q(0, 3, 4) .

Q: Evaluate the indefinite integral. | sec²(v#) dx

A:

Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

A:

Q: 21.) Give the slope of x'y=8 at the point (2,2).

A:

Q: Consider the differential equation 2 = Let y = f(x) be the particular solution to the given differen...

A: