In 100 yrs, 132mg of radium decomposes to 96mg. How many mg will be left after 200 yrs?

Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

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Q: F = (x²yz, - xy²z, -2xyz²)

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Q: Find a differential operator that annihilates the given function. -2x+3x³+x²e5x

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Q: You have decided to start saving for college and open up a 529 account. You invest $5,000 into the…

A: Given :Invest Amount=P=$5000Rate =r=2%=0.02Time =t=5 year

Q: 4 (A): If A = 2 -2 Find AB and AC. 2 01 1 -1 0; 1 2 B = 2 -1 3 1 -2 -2 and 2 1 3 C = 0 1-31 6 1 2 -1…

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Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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Q: Q5: Find d for the following functions: dx (1) In(x - y) = xy + y³ ; (2) y =

A: As per Bartleby guidelines rule I am answering only first question as other questions are not the…

Q: 67. Suppose sin x = - 120 (A) 169 120 (D) - 169 5 13' where * terminates in Quadrant III. Find…

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Q: Q4: Answer two only: 2 1 -1 (A): I A=2 -2 Find AB and AC : - 1²/2 3 11 -2 -2 and 2 -- }

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Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform thickness. If the…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k ;

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Q: The half-life of Strontium-90 is 28.79 years. If a sample contains 490 mg, how many mg will remain…

A: Given half life is 28.79 years Initial mass =490mg To calculate mass after 180 years.

Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: (A): solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

A: Calculation of determinant is the key requirement of this problem.

Q: 7√2 2 0 x² 49-x² dxl

A: The given integral,        ∫0722x249-x2dx

Q: 1 2 Identify the true statements. Incorrect 3 4 56 f(1) is a local maximum. f(5) is a local maximum.…

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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: (1) In(x - y) = xy + y³ ;

A: According to rules, I need to solve first question.. Please repost remaining questions

Q: 2. What is the radius of the circle defined by x + y² - 6x + 4y - 1 = 0

A: x2 +y2 -6x +4y -1 = 0 here we have to find radius standrad form of circle is (x-a)2 + (y-b)2 = r2…

Q: Find a differential equation whose general solution is 8t y = c₁est + c₂e-2t. = 0

A: We can find the differential equation as below.

Q: Write a polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial with…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x =

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Q: f'(x) = (x+3)(12 - 1)(x - 14) Then the first relative extremum (from the left) for f(z) occurs at z…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Discuss the continuity of the function. 41 √x² + y² + z² f(x, y, z) == continuous except where x² +…

A: The given function,   fx,y,z=41x2+y2+z2

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Use substitution to evaluate the definite integral given below. 1² (Enter an exact answer.) Provide…

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Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: Given :lnx-y=xy+y3y=tan3cot7x

Q: 31-4 A piecewise function f(x) is defined by f(x)=x²+3x+4 x² -7x+12 Part A: Graph the piecewise…

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Q: Let g=yf(xy). Show that: - მყ У ӘУ дд - X- = g дх

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Q: Q3: Evaluate the following integrate: (chose three only) 1. dx 1+x4 2. ex-edx ex+e-x 3. fxsec² x dx…

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Q: Find the gradient field F = Vo for the potential function = 2x³y-4y³x.

A: We have to find out gradient

Q: Find f if f"(x) = 2 + cos(x), f(0) = -1, f(π/2) = 2. f(x) =

A: Find f if f"(x)= 2+cos(x), f(0)= -1 , f(π/2)= 2

Q: x-1/2c (4) y = x sinh 2x – cosh 2x

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Q: The Doyle Log Rule is one of several methods used to determine the lumber yield of a log (in…

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Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] y O 2 1 -1 -2 y 3 2 - -1 -2 2 4 4 Find its length…

A: This question is related to vectors and parametric equations, we will solve it using given…

Q: 12. x² sin(x + y) = 1, -

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Q: The pH can be calculated using the equation pH = -log(H"), where H" is the hydronium ion…

A: We can find the hydronium ion concentration as below.

Q: y"+y=t y'(0) = -2 y(0) = 1

A: The differential equation is given by      y'' + y = tThe auxiliary equation of the corresponding…

Q: Given: f(x) = 0.2 + 25x-200x^2 +675 x^3-900 x^4 + 400 x^5 from a = 0 to b = 0.8 and segment equal to…

A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

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Q: Given the following vector field and oriented curve C, evaluate F = (x,y) on the parabola r(t) =…

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Q: 28. For each of the following equations, find the most general function N(x, y) so that the equation…

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Q: Consider the position function below. r(t) = (1-1²,3-5t4) for t≥ 0 a. Find the velocity and the…

A: Given;  r(t)=<1-t2,3-5t4).

Q: al speed seball, hit 3 feet above the ground, leaves the bat at an angle of 45° and is caught by an…

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Q: If f(x) = 1/√x, use the definition of the derivative to find f'.   You must show ALL of your work…

A: The given problem is solved below in detail.

Q: Consider the following situation, which involves two options. Determine which option is less…

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Q: y = sin(x), y = 0, x = 0, x = Exercise (a) the volume of the solid formed by revolving the region…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

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Q: At what rate is the angle between a clock's minute and hour hands changing at 7 o'clock in the…

A: To find: Rate of change of angle between a clock's minute and hour hand at 7 AM. In other words, the…

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…