4. In a Music club with 15 members, 7 people played piano, 6 people p 4 people did not play either of these instruments. a. How many people played both piano and guitar? b. How many people played piano only? c. How many people played guitar only? d. How many people did play piano or guitar? (Note: Include the notations.)

Q: 1. Given: f(x) = x + 1. Sketch the graph of the function using the information obtained from f' and…

A: Consider the given function, fx=x3+1 It can be observe from the the given graphs of f' and f'' that,…

Q: 10. A five-member committee is being formed from a group of 9 sophomores and 12 seniors. How many…

A: This is basic problem in counting. The detailed solution is presented below as the next step.

Q: The profit function for a company selling x units of a certain commodity is given by P(x) = -1500 +…

A: We have to solve given Questions

Q: O find othonormal bases: O x-2y-32 =0 W x+y+ 27=0

A:

Q: 13. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: We have 9 friends and 5 rooms.  So, basically, we need to find the number of ways to choose 5…

Q: Given the initial conditions y=1 at x-1, estimate y at x=1.2 using a stepsize h=0.1. Use…

A:

Q: A) dx = x² – 2x + 2 dy %3D

A: The given differential equation is in separation from.  To find the general solution of the given…

Q: 21. A group of 10 women and 6 men must select a four-person committee. How many committees are…

A: Given:Number of women =10 Number of men = 6 Part(a) Two men and two women            Number of…

Q: For the following system: Use the Lyapunov function V(x) =r+r2+ to show that the system is stable.

A: The given system is: x˙1(t)=-x1+x2.............(i)x˙2(t)=-x2..................(ii) Given Lyapunov…

Q: dt dy la) what is associated dineorijed System ar Hhe equilibrium lo,0) ? 10,.0) ! 11 ity of the…

A: This is a problem with the system of differential equations and their stability.

Q: O Calculate the integral y dydx

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: x"(t) – 4x'(t) + 4x(t) = 4e2t; x(0) = -1,x'(0) = -4

A:

Q: I Example 11.6. Solve the equation V?u = 10(x2 + y? + 10) over the square with sides x = 0 = y, x =…

A: To obtain the solution of the Poisson's equation ∂2u∂x2+∂2u∂y2=fx,y, use the following standard…

Q: Determine if the given function is continuous and differentiable at the indicated values of x. Show…

A:

Q: Let ~ CX *X be an equivalence relation on a set X. For x EX define x := := {x |x E X} is a partition…

A: This is a question from Relation.

Q: For the following functions Y(s), determine the inverse Laplace transforms. (a) Y(s) =…

A:

Q: Solve the two items using Integration by parts. 1. [x' v9-x? dx Se sin x dx 2.

A: To find the given integral by integration by parts :-

Q: Example 10.29. Find the value of y(1.1) and y(1.2) from y" + y"y' = x°; y(1) = 1, y(1) =1, using…

A: Here we need to use the Taylor series to solve the given problem.

Q: primitive root modulo

A: Given: Value of n=223 in  mod n. To find: Primitive root modulo 223.

Q: Find the area V2 centered a) Inside the cardioid r= 2 cos (0/3) and outside the circle of radius r =…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 3. f(x) = es* – x² – 1 (Xi-1= 8)(x; = 5) (х-1 3D 8)(%; — 5)

A: F12=EXP(2*E12/3)-E12^2-1 H12=EXP(2*G12/3)-G12^2-1 I12=G12-H12*(G12-E12)/(H12-F12) Error=ABS(J12)…

Q: dy 2y+x B) %3D dx

A:

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: The sum cost price of products P and V is P 15000. The selling price of the same two products is P…

A: The system of equations can be solved graphically or algebraically. The method of substitution and…

Q: Example 10.34. Solve the equation y" = x + y with the boundary conditions y(0) = y(1)

A:

Q: a a2 a a 12. Using cofactor method, prove that det N = +99 9 = ab?c'd* - %3D %3D 0 0 c c4 0 d 0 0

A:

Q: 9. : (y²dx + x²dy) = 0 (x – y)²

A:

Q: Establish that if a is an odd integer, then 2" aʻ = 1 (mod 2" *2) for any n 2 1.

A:

Q: FIGURE P1-8 80 a b FIGURE P1-9 Determine angles a, b, and c (Figure P1-9).

A: Vertically opposite angles are equal. Now, in the given figure 80° and angle a are vertically…

Q: Calculate x z dS, where S is the cylinder (including the top and bottom) x? + y = 16,0 < z < 5. (Use…

A:

Q: Let wi be a number associated with player i = 1, 2, 3. Suppose a coalition Sc{1,2,3} has value v(S)…

A: Given: Let wi be a number associated with player i=1,2,3 and a coalition S⊂1,2,3 has value…

Q: Maximize q(x) = 2x² + 72xy + 23y² , where x = subject to the condition ||x|| = 3. %3D Select one:

A: This is a problem of optimization.

Q: If A Supset of B then int(A)Supset of int(B)

A:

Q: Answer the following system of linear equations though: a) Inverse of a Matrix (using Determinants)…

A:

Q: Estimate the volume of the solid that lies below the surface z = xy and above the following…

A: Given function and region is z=fx,y=xyR=x,y/1≤x≤7,5≤y≤9

Q: -4 (b) If u find and expressing all derivatives in their simplest 3xy form. Hence, Show that

A: The solution is given as

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x² +1, y =…

A:

Q: |Example 10.37. The deflection of a beam is governed by the equation d'y + 8ly = (x), where o(x) is…

A: please find step by step answers below:

Q: Solve this Solutions of Linear Equations using Cramer's Rule x1 - x2 + 3x3 - 2x4 = 1 -2x1 +…

A:

Q: Determine the two square roots of the given complex numbers in cartesian form and show the results…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 12 6. 59° W X 5,5 Y

A:

Q: Calculate x-z lmage 24 ) 8х -2 2x + 1 z + 22 3z O 10 O 10

A: Solution

Q: Find the flux of F across S, F.N dS where N is the upward unit normal vector to S. F(x, y, z) = xi +…

A: The given integral is ∬SF·N ds , where S: z=a2-x2-y2  and F(x,y,z)=x i^ + y j^- 2z k^ .....1. To…

Q: Calculate a - b c in degrees. [Image 17 ] 30° O 120 O 180 O 210 O -120 O 60 O -60 oooo oo

A:

Q: frunction Vercaty the u Cmiy) = verity the eelen's thertem Lore

A:

Q: Q:Determine a solution for the pDE, and canjecture the form of the general Solution マン fnbtれてhiy h-

A: Given, homogenous Partial differential equation  uxx-4uyy+2ux+4uy=0 Substitute uxx=D2u, uyy=D'2u,…

Q: ydx + x(x*у — 1)dy %3D 0

A:

Q: spade. 4 A card is drawn from a standard deck of 52 cards. Find the probability that it is a red or…

A: We have to solve the 14th question. A card is drawn from a standard deck of 52 cards. We need to…

Q: 11) Find the rate of change of output with respect to time, if the production function is Q =…

A:

Q: #6 Find the volume of the solid bounded by the cylinders x2 + y? = 4r2, y? + z? = 4r

A: