(9) Find all prime numbers p for which both equations X²-2 0 mod p and have solutions. X²-3 0 mod p

Q: 4. A plane travels on a bearing of 15° at an air speed of 655 km/h. It encounters a wind blowing at…

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

Q: 2. (3x² - 2x + 1)dx Step 1: Find F(x) by integrating the function Step 2: Apply FTOC Step 3:…

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Q: 2|6x + 4 ≥ 1 OX- 7/12 O-7/12 - 12/7 choose the right ans оо

A: solution:-26x+4≥16x+4≥12using properties of modulus6x+4≥12  or  -6x+4≥12 6x≥12-4  or  -6x≥12+46x≥-72…

Q: Solve for y at x=2: (4x^3-6yx^2 + 2xy^2)dx + (2yx^2 - 2x^3)dy = 0; y(1)=4

A: This question can be solved using the concept of differential equation.

Q: Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

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Q: Solve the differential equation. 10. ( cos 2y – 3x^2y^2) dx + (cos 2y – 2x sin 2y – 2x^3y) dy = 0

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Q: A species of bacteria has a population of 250 at 6 a.m. It doubles every 8 h. a) Determine the…

A: Given: Population at 6 a.m =250

Q: A full tank consists of a hemisphere of radius 4 m surmounted by a circular cylinder of the same…

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Q: x2 X tet tx et + 1 A. lim x 2 B. lim - 3-1 2 - C. lim x⇒1 x² + x 2 x² - 1 Remember that if you…

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Q: Given the matrices A: = [1-4] 0 21. B=( )-C-1) ₁ [1 -5 5 and C= the matrix X in the equation AX + 5B…

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Q: Solve linear diff eq dy/dx = e^(-x) -4y ; y(0)=-10

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Q: V. A hemispherical basin of radius 4 ft contains liquid to a depth of 3 ft. If the liquid weighs 48…

A: This is a problem related to pumping volume of the spherical basin to the 3 ft above the container.…

Q: d. y""-6y" + 12y' - 8y = 0

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Q: 3. A 5-pound monkey is attached to a 20 ft hanging rope that weighs 0.3 lb/ft. the monkey climbs the…

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Q: x. e²ydy + (*²*¹) dx = ( 0 (Variable separable)

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Q: Given that lim f(x) = 9 lim g(x) = -2 lim_h(x) = 0, X→3 X→3 X-3 find the limits, if they exist. (If…

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Q: 1. Write a formula for f g h 2. Find the value of x [2x 31[¹3] = .f(x)=√x+1, g(x)=(x) -

A: 1) The given functions are: f(x)=x+1, g(x)=1x+4, h(x)=1x

Q: 4) y(2xy +1) dx - xdy = 0

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Q: mi I Τ 1+ d) √¤√ï√™

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Q: Determine whether the series converges. O The series diverges. O The series converges. Σ k In(k + 4)

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Q: sin () cot ()+cos ( cos (1) sec (7)

A: We use  sin(π+x)=-sin(x) cot(π-x)=-cot(x)  sec(π+x)=-sec(x)

Q: The loudness of sound is measured in decibels so that the decibel measurement is db = 10 log L where…

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Q: Express the number as a ratio of integers. 3.898 3.898898898...

A: 3.898898898..... this can be written as  3.898898898..=3+ 0.898 + 0.000898 + 0.000000898 + .. ...  .…

Q: For a battery of voltage V and internal resistance r, the total power delivered to a load with…

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Q: A group of 4 journalists is to be chosen to cover a murder trial. There are 4 television…

A: Let's find number of groups can be formed.

Q: Evaluate 17 5

A: To evaluate: 175  We know that nr = n!r!n-r!

Q: Higher Partial Derivative d'u ôxôxôy 4. _x³y² u 2 yz

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Q: H Suppose that f(5)= 1, f'(5) = 3, g(5) = -5, and g'(5) = 2. Find the following values. (a) (fg)'(5)…

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Q: tially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds of salt…

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Q: Use synthetic division to find the quotient and remainder when 2x3 -8x2 -1 is divided by x

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Q: A rectangular box is to contain 125 in3. Find the dimensions of the box for which the surface area…

A: Given problem:- A rectangular box is to contain 125 in3 Find the dimensions of the box for which the…

Q: An inverted conical tank is being filled with water at the rate of 2ft3 per minute. If the tank has…

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Q: ту 3) 2xydy = (x3 +y=) ax

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Q: 4. find the derivative 4v².4+ [7v¹.5-3v-2 Enter your answer

A: Given  Let y= (4v^2).4+(7v)^1.5 - 3v -2 y= 16v^2 + (7v)^1.5 -3v -2 Formula: (d(x^n)/dx) = n(x^(n-1))…

Q: Find the general solution for the following Deferential Equations: x.e²ydy + (2²¹) dx = 0 (Variable…

A: Given :xe2ydy+x2+1xdx=0

Q: d- dx3 ax d² y dx² +6- 15 dy dx Q.2-Solve the differential equation 100y = 0

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Q: Below is the graph of y=3√x. Translate it to make it the graph of y=3√x-2+4. of x 5

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Q: > Question 6 Let u and v be functions of and let u' and v' denote the derivatives of u ar (a) Dz…

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Q: Given f(x, y, z) = zey 02 √√3 O 2e² 01-1 √3 O none of the choices 0 0 √3 x sin (3), what is fzz…

A: Differentiate and put the appropriate values.

Q: Graph the function. g(x)=3x²-1 Plot five points on the graph of the function: one point with x = 0,…

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Q: Which of the following phrases describes an empty set? Common factors of 5 and 9. O Multiples of 2…

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Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: Use the Limit Definition of the Derivative to find f'(x) for the following function. You may NOT use…

A: Use limit definition to solve

Q: 2|6x + 4 ≥ 1 OX-7/12 - 7/12 - 12/7 choose the right answer

A: we have 26x+4≥1

Q: If 1 x+y True False = 1+ y, then dy || 1

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Q: A depositor currently has $6000 and plans to invest it in an account that accrues interest…

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Q: The logarithmic equation 2 log c = b, where a > 1, expressed in exponential form could be Oa² = bc…

A: Given

Q: Q3: Find the general solution for the following Deferential Equations using Variation of Parameters…

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Q: 3. g(x) = (2x - 1)³

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Q: 50 own. Draw the graph of y=g(2x).

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