1. For questions A and Given: Radium decomposed at a rate proportional to the qualit of radium present. Suppose that it is found that in 25 years approximately 1.10% of a certain quantity of radium has decomposed. Determine approximately how long it will take for the original amount of radium to decompose. A. The value of the constant of proportionality is B. The amount of unconverted substance at any time t is given by

Q: Question 1 A body cools from 60°C to 50°C in 5 minutes. How much more time (in minutes) will it take…

A:

Q: An equation of a hyperbola is given. (x+3)²-(y - 3)² - 1 9 16 (a) Find the center, vertices, foci,…

A:

Q: 9. What is the general solution for the differential equation y"" - 3y' - 2y = 3x? A. y C₁x +…

A:

Q: Lim X-0 √1+x-√1-x x

A: evaluate the limit limx→01+x-1-xx

Q: 은 J4-√x dx

A: This question can be solved using integration by substitution.

Q: The graph of y=5x*-x³ has a point of inflection at (A) (0, 0) and (4, 256) B (0, 0) and (3, 162) (3,…

A: Given graph,y=5x4-x5Aim : To find point of inflection.

Q: (a) Verify that tanh P-tanh Q 1-tanh P tanh ọ tanh( P – Q)

A:

Q: dx 2 X - 25

A:

Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

A:

Q: Evaluate: L{cos(3+2t)} s cos3+2sin3 A s² +4 S (B (s+3)² - 4 S (s+3)² +4 s cos32sin3 s² +4 (c) (D)

A:

Q: y = Arctan (2x)

A:

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3. A (e²-1)² e2 sq. units (e³ + 1)² e3 (e²+ 1)² e²…

A: Given:-the region bounded byf(x)=ex, g(x)=e-xand x=3

Q: Which of the following is the antiderivative of the integral function: * f(xex) dx - ex + C none of…

A:

Q: Numerical Integration: •2 S² 1. -dx X

A:

Q: xdx (x + 1)²

A:

Q: To evaluate the integral sin³0cos ede by trigonometric transformation, we use the identity; A sine…

A: On solving this we will get  To evaluate the given integral we use the the identity in given option…

Q: Estimate the value of 82^(1/4)

A:

Q: O O O O It is reflected over the x-axis and shifted right three units. It is reflected over the…

A:

Q: dy Reduce the linear DE (2xy + x²+x¹) dx = (1+x²) dy=0 to standard form dx (A) +y dy dx -2x 1+x² =x²…

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Let's find  initial population and after 10 year population.

Q: Evaluate each of the following line integrals. Jc [(3x² - 3yz + 2xz)dx + (3y² - 3xz + z²)dy+ (3z² −…

A: Solved below.

Q: Refer to the given function below to answer the following questions: dr 0 de 2 = COS-

A:

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A:

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A:

Q: The triple integral ¹²-x² √4x²-y x dzdydx is equal to 0.33 0.08 None of them O

A: Let's evaluate given triple integral.

Q: Using the method of undetermined coefficients, the modified form of a particular solution for the…

A:

Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=. cos x…

A:

Q: when the first nine terms of an arithmetic sequence is added. its sum is 72. what is the value of…

A: The fifth term will be ,a5=a+4d=8

Q: y=Arccos (x²)

A:

Q: 2. Use the disk method to determine the volume of the solid obtained by the revolving the region…

A:

Q: The function is x % = y? What is 8 2 dude Y æ2

A: We need to find derivative.

Q: Evaluate: lim (1cosec²x + 2cosec²x + 3cosec²x + ... + n° x-0 +ncosec²x)sin²x

A: Given problem:-

Q: f(x)=√x+1and g(x)=x²+1. 1. Find the area of the region bounded by the given curves.

A:

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

A:

Q: Question 7 In evaluating 4 2 dx X√√x²-4 s-¹(f(x)). Determine the value of f(x) if x=0.35 is same as…

A:

Q: Vector-valued function R(t) = 1. Reparametrize R using the directed arc length s from the reference…

A:

Q: S. S. (x + 2y)dydx = 10, Jo a

A:

Q: Suppose that f(x, y) = ²/" on the domain D = {(x, y) |0 ≤ y ≤ 1,0 ≤ x ≤y³}. D Then the double…

A: Given: fx,y=exy and D=x,y| 0≤y≤1, 0≤x≤y3   As we know the basic integration formula.…

Q: What is the differential equation corresponding to the general solution y² = Cx³. dy 2y = A dx 3x dy…

A: solution:-y2=Cx3where C is only one arbitrary constantdifferentiate both…

Q: efv. Evaluate dx Use rationalizing substitution. A B 8 √e² - 2 - 2√2 Arctan — √e² - 2 + C e³ − 2 −…

A: Let's evaluate given integral by using rationalizing substitution.

Q: Integrate the equation using the method in trigonometric substition

A:

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: Given:      fx=x-13       gx=x-1 Volume of solid generated by revolving around the region is…

Q: Question 4 If f is continuous on [a,b], then T) True F False [xf(x)dx= x₁ b a f(x) dx

A: Given query is to find the statement is true or false.

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

A:

Q: 6. Find a²z дгу of z = In(xy)

A:

Q: дz дz Givenz = xey +yex, Find дх’ду

A: in partial differentiation , other variable is considered as constant when function is…

Q: tan (3x) lim x→0 sin (2x)

A: Given query is to find the limit of the expression.

Q: So x² dx √4-x²

A: To find out the integration.

Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

A:

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A: