Find an integrating factor to the linear D. E. In(9 x+16)y+ y =20 9x +16 p(x)= (6 x+ 14) In(18 x +18) 1 Hx)= 9 x +16 p(x)= In(9 x +16) None p(X)= In(6 x +14)

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Q: x2-3x+1 i) S xln²xdx and ii) S7 dx. (x+2)(x2+1)

A: Given: ∫x ln2 (x) dxFormula: (ln (x))'=1x∫ x dx=x22+C

Q: Question 3 Integrate: 1₂ 2x + 11 x² +8x+17 dx + C

A: Here we have to calculate the given integral. We have ∫2x+11x2+8x+17dx

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Q: t dt + ds = 3s²t² ds S

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Q: The integrating factor of y= 2x' is dx

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Q: 7. fox)=x-x-2 fix) = R²+2x3 %3D

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Q: Hand written plz 2. Standardize the following LP model. - max z = −3x₁ + 8x₂ − x3 + 12x, - 3x₁ +8x₂…

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Q: Consider T(r1,12, Ia) = (371 – 212 + 4ra, I1 + 273, 12). Find T!. %3D

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Q: Show that Q(V3, V3) = Q(v3+ V3) %3D

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Q: If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are…

A: Solution

Q: Differentiate. y=/3x² – 4 -3x y' = 3x - 4 3x y' = (3x2 - 4)-1/2 3 (3x² – 4) /2 3x V3x2 – 4

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Q: X 1 2 3 4 f(x) 2,6 3,5 3,2 2,4

A: From the given table, The general formula is,

Q: EXAMPLE 12 Solving Radical Equations /2r + 7 – x = 2 а.

A: a.2x+7-x=2 adding x on both sides, 2x+7=x+2 squaring on both sides,…

Q: ntegrate: 16x³ + 64x² 7x +41 16x² +9

A: ∫-16x3+64x2-7x+4116x2+9dx Lets first divide using long division.

Q: Find d da [e³²2²] dx 6xe ³x² e ³x² 6x e ³x² 6x (eª) (e³²²) (3x²) (6x)

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Q: 2. Show that for simple linear regression (SLR) we have that cov(B, B,) = - xoʻ/S

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Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

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Q: What is the significance of R and R2 in gression model?

A: Linear regression model consist of one dependent variable and one independent variable.

Q: 3. Suppose X~ Bin(4,2/3). Let Y = 2X+1. Find py (y), and fill out the table below. You may not need…

A: Ans#- Given, X ~ Bin4, 23. Let Y = 2X + 1            Find PY(y)        We know, In the binomial…

Q: Differentiate: y = (3x 교-5z) (4n3 +2) O y' = 60a + 80a- 12a 10 - O y' = 60x + 80a + 12x O y' = 60x4…

A: Let's find.

Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

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Q: Consider a logistic regression system with two features x1 and x2. Suppose 00 = 5, 01 = 0, 02= 0,…

A: In logistic regression, the hypothesis function hθx is a sigmoid function which returns the values…

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: A scientist has measured quantities y, x1,and x,. She believes that y is related to x, and x2…

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Q: If gcd( m,91) = gcd(n, 91) = 1 %3D %3D

A: Given, if gcd(m, 91)=gcd(n, 91)=1,  To prove that                     91|m37-n37

Q: Q3//A/By using co- factor 1 -2- if AD find A1 =? %3D 3. 2-

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Q: (xdx ydy + zdz)2z {(z²x²y²) (xdx + ydy + zdz) dz + %3D

A: Differential equation

Q: EVALUATE THE FOLLOWING: 1. S(5x5-6x + 2x +55)dx (5x-4x*+7x)dx 3. SV5X+7 dx

A: (1).                                ∫5x6 -6x4 + 2x+ 6dx…

Q: For the given data (0, 1), (1, 1), (2, 3), (3, 5) find the line y = ao + a1x that best fits the data…

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Q: Question 3 Integrate: 8x +5 x² + 2x + 2 -da + C

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Q: 3X ジ+ 5y+4 -2X -3e+キe मै -29 +8 ジ x ーズ %3D 12)

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Q: Question 7 Evaluate | (6x² – 3x2 + 5) dx (A x3+ 3x-1+ 5x+ C B 2x3+3x-1+5x+C 2x3+ 3x -1+x+C…

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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.