If x and y are two quantities, then y is directly proportionalto x if there is a nonzero number k such that ____________ .

Q: (b) Watermelon x is related to watermelon y if the measured weight of water- melon x is at least the…

A: b)Given, The watermelon x is related to watermelon y if the measured weight of watermelon x is at…

Q: 4. Given the reciprocal function, y = 1/x, if the values of x increase, then the values of y . . .…

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Q: 2. If e and b represent two non-zero numbers, find the ratio e : b if 2e + eb - 3b = 0. Solve for…

A: The factoring of a quadratic equation, ax2+bx+c=0, is used to factor the equation. The first step of…

Q: 5) Solve the Non-linear second ODE: d²y + 3 x² y dx? y? = x² ) (dy %3D

A: Given: Non-linear second order differential equation is 3 x2 y d2ydx2+y2=x2(dydx)2

Q: 1+x 10. y = e2x+1 11. y = (x+1)³ – 2 12. y = exp(x?) on [0, o0) 13. y = exp(x²) on (-0, 00, 0] 14. y…

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Q: If 19 x e 12 x dx = (Ax – B) e 12 x + constant, then %3D

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Q: dh + 2h = 0 dr

A: Given:rdhdr+2h=0

Q: Express the statement as a formula that involves the given variables and a constant of…

A: It is given that, y is directly proportional to x and inversely proportional to the square of z.…

Q: 19. What are all values of x for which [ P dt is equal to 0 ? (A) -2 only (B) 0 only (C) 2 only (D)…

A: We have to find the value of x.

Q: P(X) X*P(X) X-u (X-u)^2 [X-))^2]*P(X) 0.48 3 0.36 4 0.11 0.05 LO

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Q: 4. y = e-3*(Acos 5x – Bsin 5x) + Cx; A, B and C are arbitrary constants

A: Consider the equation

Q: 2 15 32. [(x + V1+ x? 5 32. f(*+ dx is equal to V1+x? 2.

A: Introduction :

Q: Which of the following assumptions do we take when solving mixing problems? O the liquid volume is…

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Q: The amount of radium present at any time t obeys the law Q(t) = Qoe¬kt (0 Find k if Qo= 200 and…

A: We have to find the value of k for the equation Qt=Q0e-kt, where Q0=200 and Q1600=100. We have to…

Q: 0, x<0, F(x) = { 공x?, O<x<2, 1, x22 a) Find E[X]. b) Find P(X 21|X)

A: From the distribution function we get:f(x)=ddxF(x)=ddx14x2=x2 for 0≤x&lt;2f(x)=0 otherwise. So,…

Q: An open-top box is to be constructed from a sheet of tin that measures 34 inches by 20 inches by…

A: Here given W=20 inches and L=34 inches. In the upper figure, we observe that X is decreasing from…

Q: 0 1 2 P(X=x) 0.15 | 0.20 0.15 0.50

A: We want to find the mean  Mean=E(X)

Q: 2 100 Given A = |4 3 6 x = and b = | 350 L0 -1 200 Solve the maxtrix equation Ax = b for x

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Q: y Iny Ae^+ Bex

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Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: Let p and q be integers with q>0. If y= x^p/q, differentiate the equivalent equation y^p=x^p…

A: Condsider p and q are the integres. We have to check the formula ddxxpq=pq·xpq-1 is true or not if…

Q: Oz If z = y f(x² – y²) then y +x ôx xy а. XZ b. zy с. d. None of these

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Q: Consider 250g of iodine which decomposes at a rate proportional to the amount present. Around 150g…

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Q: 2. Find Solution using Newton's Divided Difference Interpolation formula (x = 2.7)? X. f(x) 0.69315…

A: Newton's divided difference formula for 3 points can be defined as:…

Q: 17. In a chemistry laboratory there are three containers. One cone-shaped, one spherical and one…

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Q: 2. y = Vg(h(x)) (g) cha))た. A'(x)'a 1,

A: To find the derivative y=√(g(h(x))

Q: 15wr If C(w,r) = find the constant k such that wC (w,r) + rC(w,r) = kC(w,r). 7(w+r) Enter the answer…

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Q: Express the statement as a formula that involves the given variables and a constant of…

A: It is given that, w varies directly as z and inversely as the square root of u. So, w proportional…

Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

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Q: 4 The area under the curve y = 3x* and above the x-axis between I = 5 and x = 10 is: area The area…

A: Area under curve

Q: 1. What theorem states that the square of the hypoteuse of a right triangle is equal to the sum of…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3 2 1 (h) {x € R' : x = +s +i for some s, t E R}

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Q: (5)If 3, g(x)dx=5, then 2f(x)+3g(x)dx =. S 25(x) + 3g(x)dx =

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Q: 10) If y is inversely proportional to x, and the constant of proportionality is positive, then which…

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Q: Express the statement as a formula that involves the given variables and a constant of…

A: Given: y is directly proportional to x and inversely proportional to the sum of r and s.

Q: X SC Y= SC XiVi X? 10° 0.14 0.2 0.028 0.0196 200 0.45 0.8 0.36 0.2025 30° 1.2 1.7 2.04 1.44 40° 2.1…

A: Linear regression is the modelling of the relationship between two variables by a linear function or…

Q: 22-23. Which of the following is the area. enclosed by y=x²-4 and y = x -4? A) √²(x-x²) dx ²(x² -…

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Q: dy If = xy and f (0) = 3, then f (2) = e +3 3e 3e? O 3 (e +1)

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Q: 1. Find Solution using Newton's Divided Difference Interpolation (x = 301)? f(x) 300 2.4771 304…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 2 x+ xeʻx + ve?x y' = ,where x 0 %3| 25 2xe´x

A: To find : general solution for the ODE                 y'=x+xe2yx+ye2yx2xe2yx ,            where x≠0

Q: y'(x) = P(x) + Q(x) * y(x) + R(x) * y (x) P(x) = -e2** ricatti dif. Q(x) = 2 R(x) = e-2*x

A: The given Ricatti's differential equation is                    y'(x)=-e2x+2y(x)+e-2xy^2 ⋯⋯⋯⋯ (1)…

Q: 1. (x+ a)y' = bx – ny; a, b, and n are constants with n+ 0,n ± 1

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Q: Let a and b are positive constants. If P(2 3) = 0.2. Then a and b equal to: %3D

A: We have to find a and b with the help of given distribution function and probabilities.

Q: If cov (x,y) is positive, then variable --- as variable y increase. Select one: a. None of these b.…

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Q: A. Express the following ratio to its lowest terms 1. 30:100= 2. 14/24= 3. 24:48= 4. 18:72= 5.…

A: A. Express these ratios in their lowest terms: 1. 30 : 100=30100=3103:10 2.  1424=14÷224÷2=712 3.…

Q: 1/2 b) What is ||x|| = (E\x|* )" if x = (x1, X2, X3, ….) where xn 2-n/2 and xn = =? %3D n

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Q: van [ f(x)dx = 5, [_o(x)dx=7, and [_n(x) dx = - -5 Which of the following can be determined given…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Humber of nalfunctions: 0 1 2 3 4 5 6 f(x) | 0.17 0.29 0.27 0.16 0.07 0.03 0.01

A: Solution

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.