Let a = < 1, 2,4>. Find a unit vector in the direction of a

Q: The population of a city t years from now is predicted to be P(t) = 0.50t³ - 3t² + 3t + 200 thousand…

A: The given data is: Pt=0.50t3-3t2+3t+200 ..........(1)

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A:

Q: Evaluate the improper integral or show that it diverges. 6 S dx 0 √36-x² Select the correct choice…

A: Explanation of the answer is as follows

Q: 3 5 3-x - dx

A:

Q: 1. For the below ordinary differential equation, state the order and determine if the equation is…

A:

Q: DE 1. xy(5) y(4) + x²y"" = 2yy' TYPE ORDER DEGREE LINEARITY

A:

Q: In the find and prove of lim”→0 (x³), how and what should be defined in terms of ? A. 8 = min {1, §}…

A: This question is related to Limits, we will solve it using given information.

Q: x²-1 da X

A: We have to evaluate ∫x2-1x dx.

Q: Find the derivative of the logarithmic functions: y = ln(12x-4)

A: Solution of given question is written in below steps.

Q: On his first three quizzes, Patrick earned a 15, 18, and 16. (A perfect score would have been 20…

A: On his first three quizzes, Patrick earned a 15, 18, and 16. (A perfect score would have been 20…

Q: Find the derivative of the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)

A: Application of derivatives

Q: True or False: The definite integral is equal to Select one: O True False 1² (x² + 3e*)dx [²x²dx + 3…

A:

Q: Determine the area of the shaded region. 70. 15 4+ 3+ 2- 1 이 12x - x2 2 becodelating onesyde, −12 +…

A:

Q: The intervals on which f(x) = x² lnx is increasing and decreasing, and the intervals of concavity…

A:

Q: Write the partial fraction decomposition of the following rational expression. 3x² - 8x + 20 X(X +…

A:

Q: Write the given expression as an algebraic expression in x. cos(2 cos-¹(x))

A:

Q: OS: Find the solution of the following D.Est 5y-x7 at x- 2

A: Note:as per guidelines we support only one question in one request.kindly repost next question in…

Q: H.W: show that the equations are homogeneous and solve: 1. (x + y)dy + (x−y)dx=0

A:

Q: Evaluate the following definite integral. 1 18 18 -9 Find the partial fraction decomposition of the…

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: Find the sum of the series or show that it diverge 4 (a) Σn=1(3+2 + 8n-2

A:

Q: f(z) The residues of 4z (z − 1)(z + 2)² 4/9,-4/9 O 4/9.4/9 O -4/9, 4/9 O -4/9,-4/9 O 4/7,-4/7 O

A:

Q: 36. Determine the exact simple interest on P 2,000 for the period from January 10 to October 28,…

A: The solution is given in the next step.

Q: 9. Rotate the region bounded by y=y=9, x = -2, x = 1 1 3 about the y-axis.

A:

Q: Evaluate limx→∞ 3x^2 - x - 2/ 5x^2+4x+1

A:

Q: Juan Dela Cruz wants to deposit ₱5,000 every quarter at 16% compounded quarterly for 5 years. How…

A: We have to find out solution

Q: Q3: Let L be the line of intersection of the planes 3x + y -z = 4 and 5x + y + 2z = 1 Find the plane…

A:

Q: = / y ²³. (X²+1) (3x+4) 5/ (2x-3)(x²-4) Find dy da

A: To find dydx:

Q: 14. Given are two concentric circles with the outer circle having a radius of 10 cm. If the area of…

A: Let's find border between two circles.

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: A tank contains 240 litres of fluid in which 50 grams of salt is dissolved.pure water is then pumped…

Q: Prove the statement using the €, & definition of lim(x² + 2x - 7) = 1. →2

A:

Q: 5. r² = 1 2

A: According to the question, we can answer only first question and rest can be reposted.

Q: y = f(x)

A: We can answer all the three questions as below.

Q: the Tonowing Tun f₁(x) = x, f₂(x) = x², f3(x) = 4x - 7x² g(x) = C₁f₁(x) + C₂f₂(x) + C3f3(x) Solve…

A: To check whether f1,f2 and f3 is linearly independent or not , find solution of trivial linear…

Q: Determine the Inverse Laplace transform for 5s + 2 C-¹{² +65 +13) 1- f(t)= 5e³ sin 3t+ 13 e³ cos 3t…

A: Given problem:-

Q: Sketch a graph of the function f(x) = - 2 sin(a)-1

A: Given: fx=-2sinπ2x-1

Q: Consider the point P(-2, 1, 4) and the vectors Question 2 a = and b =. (a) Find the unit vector u…

A:

Q: ① use First_principle to solve 강종 If y=45-35

A: According to the company rule we can answer only first question and rest can be reposted.

Q: 3X Se ³x cos (2x) dx

A:

Q: Solve the following initial value problem. (-1/2) dr de = sin(-60), r The solution is r(0) = (Type…

A:

Q: Q1/ A- Represent the following data in a graph using the bar graph method. temperature [ today] 27…

A:

Q: 17. Use the method of disks/rings to determine the volume of the solid obtained by rotating the reg…

A:

Q: : Evaluate the integral: √2 3y 8-x²-y² 1. JIJ 00x²+3y² dzdxdy

A:

Q: y=x² from (0,0) to (1,1). | Compute the line integral of f(x)=2x over the curve 2009

A:

Q: Find the limit. (HINT: Treat the expression as a fraction whose denominator is 1 and rationalize the…

A:

Q: Write an equation for the transformed logarithm shown below, that passes through (2,0) and (1,3) N 4…

A:

Q: Q5: Find the area shared by the cardioid r = 1 + cos 0 and the circle r = 3 cos 0. Graph the two…

A:

Q: Q5: Find the area shared by the cardioid r = 1 + cos 0 and the circle r = 3 cos 0. Graph the two…

A: let"s find point of intersection  1+ cos θ = 3 cos θ  3 cos θ  - cos θ  = 1  2 cos θ = 1 cos θ = 1/2…

Q: Solve: y'' - 4y' + 4y = xsinx

A:

Q: Use the matrices below to perform matrix multiplication. B If the operation is undefined, enter NA.…

A: Using Matrix operation