A hose fills a hot tub at a rate of 2.99 gallons per minute. How many hours will it take to fill a 340 gallon hot tub?

Q: Show that [~q a (p → q)] →►p is tautology by constructing truth table.

A:   We know that A tautology is a compound statement in Maths which always results in Truth value. and...

Q: Q1: Sketch the region of the integral, label on each sketch Boundary curves with its equation, and g...

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

Q: Determine the value of x which satisfies the following linear system: [3 71 12 A. 2 В. 4 С.-2 D. -4

A: Given 3726xy = 24

Q: 2 ex | | sin x* dy dx by changing the When we rewrite the integral 0 1 order of integration, which o...

A: Here the area in yellow portion is to be calculated :

Q: Mike’s locker number has four digits and is not divisible by 3. The second digit is the square of th...

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Q: If x is equal to the square root of (-7+ 24i). Solve the principal root of x. C. 3 + 4i A. 3 + 3i B....

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Q: (b) If you have the symptoms, then you have to undergo a swab test. Find the converse of the stateme...

A: (b) Given statement : "If you have the symptoms, then you have to undergo a swab test." We have to f...

Q: c. The differential equation 1.25 u" + 20 u = 25 sin (t) +5 cos (t) describes a mass-on-a-spring sys...

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Q: (a) Find Z(H). (b) Prove that Z(H)=Q, Q is under addition.

A: This is a problem of Group Theory, Isomorphism.

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate th...

A: Given: ∫0πsintdtWe have to evaluate the integral using the Trapezoidal rule and Simpson's rule with ...

Q: In the complex number 3 + 4i, the absolute value is: А. 3 В. 4 С.5 D. 6

A: Solution

Q: Evaluate [csc^2 (-0.09-0.1i)]. Express your answer in rectangular form in 4 decimal places.

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Q: Find the selutim and define the interval at which Junc fion is depme

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Q: Find the general solution of the DE y" +2 y' +2 y= a cos (wt), where a and w are constants. Note: Wr...

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Q: If money is invested at 6% compounded semi annually, find the present value of P94 500 which is due ...

A: When the interest is compounded, then the formula used is A=P1+rnnt , where, A is the final amount, ...

Q: Find the quotient of z1 = -6+2i and z2 = 7+8i in polar form %3D %3D

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Q: How many ways can you choose 5 objects from 13 different objects? Select one: O 154440 1287 O 40320 ...

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Q: [2 -2 Determine the eigenvalues of the matrix 1 11 3 1 -1 А. —1,2, 3 В. 1, 2, — 3 3 С.- 1, 2, —3 D. ...

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Q: Eliminate all the constant in the equation and simplify your final answer. 1. Cx² + x + y = 0 2. y =...

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Q: II. Find the point (x, y) on the unit circle that corresponds to the real number t. Then evaluate th...

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Q: 2. Let V = Rª and let U be defined below: -x U = x, y E R x + y (a) Prove that U is a subspace of V....

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Q: Q1:Find an orthonormal basis for the Euclidean space Rª that contains the vectors -HH [0] u1 = ; Uz ...

A: Here we have to find an orthonormal basis for the Euclidean space R4 that contains the vector  U1=11...

Q: 2. The following are the results of a study on the number of defective oven toasters produced by a c...

A: From given data we want to find Mean, Variance and Standard deviation. As Mean = E(X) Variance = E(X...

Q: 2. For a given function f(x) – (x – 2)² + 6 a) Axis of symmetry : x= b) The vertex (h,k) is: ( c) Ma...

A: The  x co-ordinate of the vertex lies on the axis of symmetry which is situated at the midpoint of t...

Q: Evaluate log(1+i) (1+ v3i) A. 1.442 – 0.246i C. 0.151 + 0.341i - B. 1.198 – 0.215i D. 0.301 + 0.455i

A: Use following formula to find out result  log(z) = log(r) + i θ 

Q: A container has 5 red dice, 3 green dice and 4 black dice. If you randomly pick 2 marbles from the b...

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Q: Note: if f(x) is increase or decrease always.then f has an inverse Ex/ show that f(x) = x +7x + 4 x+...

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Q: If ax2 +2hxy+by2 =0 represents two straight lines such that the slope of one line is twice of the ot...

A: It is given that the slope of one line is twice the slope of the other line. Let m be the slope of t...

Q: Q3. By using mathematical induction, show that 52n – 1 is divisible by 24, for all positive | intege...

A: We can solve this using induction method

Q: (iii) List the order of the vertices of the given tree if it follows (A) inorder traversal. (B) preo...

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Q: Find the change-of-coordinates matrix from B to the standard basis in R". 4 B= 3 -2 3 -6 P3=

A: Solution:-

Q: A car dealer will sell you the $16,450 car of your dreams for $3,290 down and payments of $333.97 pe...

A: Introduction: APR is a term that is used in financial mathematics. It represents the annual percenta...

Q: Simplify 324-4x/2x+18

A: Let us consider the Rational function f(x)g(x) To simplified the function  Taking common factor fro...

Q: II. Find I =| 2 Im(z) dz where C is the semi-circle that is the left half of the unit circle from +i...

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Q: PROBLEM 1. Consider the sequence defined by a_ = n 3n + 3; n 2 1, find the following: 4. 1. Σα i=1 4...

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for...

Q: Prove that any positive integer greater than or equal to 8 can be written as a sum of 3's and 5's. (...

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Q: Let f : Nx N → N be a function defined by (n + 1)m(m + 1) f(n, m) = Answer the following questions. ...

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Q: Evaluate the following limits. 4 – 3y? – y y-2 6 - y – y? 3 - 712 + 14r – 8 5. lim 6. lim I-1 2r2 – ...

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Q: Find: Sdx. 6e* ex-1

A: Introduction: The process of determining the area of the region under the curve is known as integrat...

Q: Ços e cot & 12.) 1 = Csc e sin &

A:

Q: 9. Find all second order partial derivatives of the functions given below. (a) f(x,y) = In(x + y) (b...

A: We have to find all the second order partial derivatives of the functions fx, y=lnx+y and gx, y=tan-...

Q: Prove: “A graph G is a tree if and only if every two vertices of G are connected by a unique path." ...

A: Let G is the tree. If part: We have to prove, "if G is tree then every two vertices of G connected b...

Q: Solve the system -22 9. dx dt -54 23 with the initial value æ(0) = 5 -e^(-4t)-7e^(5t) æ(t) -2e^(-4t)...

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Q: Find the value of x that satisfies the following equation: (2x – 5yi) + (y + xi) = 8 - 7i В. 4 A. 2 ...

A: We have to find the value of x

Q: Is the following statement necessarily true? Provide a proof or a counterexample. If h : A → B, g : ...

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Q: Jenny borrows 3000 from her local bank at annual interest rate of 3.25% to be paid back in six month...

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Q: Determine whether the differential equation xy" - 12y - 32y = 0 s linear or nonlinear and find its n...

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Q: he vector v = ai + bj is parallel to the line bx – ay = c. Use this fact to find ector starting at t...

A: Introduction: The formula for the equation of the line passing through a point P(a,b) is given by, (...

Q: Solve 2x < 10. Explain how to find the solution set.

A: We have to solve the inequality: 2x&lt;10

Q: The differential equation a" + 2a - 5x = sint is equivalent to the system |a' = 5x – 2y a = y |y = 5...

A: To solve the system of the differential equation Differentiate  one of the equation  Now, simplify ...

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.