A ball is thrown at an angle of 45 degrees to the ground, and lands 55 meters away. The initial speed of the ball was m/sec.

Q: : Solve the following first-order differential equation 2x³y' = y(y² + 3x²).

A:

Q: Find values of m so that the function y = xm  is a solution of the given differential equation.…

A:

Q: Q2: A: Find the volume of the region enclosed by the cylinder x² + y²4 and the planes z 0 and y+z=4.…

A:

Q: V The size of a balloon is changing with respect to time, such that the volume is given by V(t),…

A:

Q: 8) f(x)= x³ + x²; Find f(-6) 3120 - x; Find w(-4) 10) w(x)=-3x²- (2--2-2; Find 12) h(x) = 4x + 3;…

A: We can evaluate each of the function in the below steps.

Q: lim _e¯x (x³ – x² +9) X18

A: We have to use the concept of limits

Q: For the function graphed in the accompanying figure, find the following limits. (a) lim p(x) 8118 =…

A:

Q: Let X= the time between two successive arrivals at the drive-up distribution with a = 1), compute…

A:

Q: 2. What equal payments at the end of 2 years and 5 years will equitably replace these obligations,…

A: Explanation: P = A(1 + i/n)^nt P = 4000(1+.09/2)^(2*7)P = 4000(1.045)^14P = 4000(2.369)P = 9476.00…

Q: y=Get+Cocos x + C3 sinx

A: Since in this equation there are three arbitrary constant so differential equations is of order 3.

Q: Q4. Evaluate the following partial integrals: [₁21 -1 (a) (b) 2x - y dx r3x Love -x S dy xy dy

A:

Q: y = q cos2x+c₂ sin 2x

A: To eliminate the arbitrary constants for the following equation.y=c1 cos 2x+c2 sin 2x

Q: how do I develop a model for the depth of a swimming pool as a function of the distance from the…

A: We need to develop a model for the depth of a swimming pool as a function of the distance from the…

Q: Q2 is The sequence A) strictly increasing C) eventually strictly increasing B) strictly decreasing…

A: We have to check whether the sequence is increasing or decreasing.  For this we will calculate an+1…

Q: 4-3/x lim X→+* 2+5/x

A:

Q: The curve y²-x²= -5x is a solution to the differential equation y'= (2x - 5)/2y A) FALSE B) TRUE

A: The answer is given below

Q: Using the equations below, what is the value of Y, C, T? -0.2 Y + T = 20 -0.6 Y+ C = 70 Y C = 30

A:

Q: rob 2 Evaluate lim (√92² +2² - 32) 846

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: Find the following limits. Type NA in case the limit is undefined. (a) limg(t) = 1-0 (b) limg(t) =…

A: To find the limits for the given function.

Q: Q5. Evaluate the following iterated integrals: 5 (2) L. f xy dx dy 3 π/2 3 (b) √²/² [²³: 3x sin xy…

A:

Q: What happened to 4/3? (exponent in numerator).

A: Let's solve given integration.

Q: Q/If you have the two matrices S M below, then the determinant of S*M is 22 17 S= 75 85 --[] 12 17…

A: Given S=221775851217 and M=954310605648

Q: Q16 Find of y-In(In(e)) A))))

A: 16)y=ln(ln(ex)).

Q: Find the area bounded by the curve y = In x and the lines x = e, x = 2e and x-axis

A: formula used ∫lnx dx=xlnx-x+C

Q: x(x+1) 2x-1 4. y = 5. f(x) 6. y = = J at x = 0.6 1-3x+x3³ x2 1 2 at x = : 0.77 J at x 1 (1+√1-x)²¹…

A:

Q: 5. Compute the area bounded by the curve x = 1/y, the line x = 6, 2x - y = 0 and y = 0.

A:

Q: Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function…

A: A sinosoidal curve can be view as y=Asin(kx)+C, where A is the Amplitude, k is the period, and C is…

Q: 0=8-1号-25号+ex (2)

A:

Q: What is the auxiliary equation associated with the differential equation y'"-3y" +4y=0? (A) There is…

A: solution is given below..option(d) is correct

Q: Find the next term of the sequence: 2, 4, 8, 16, 32,

A:

Q: 3. If x³y-xy³ = 2 find y' and y" at x=1.

A: Given data:- The given value of x is 1. x3y-xy3=2    ----(1)

Q: Question 6 Determine the value of k such that x²y=1+x\ is a solution to (x²y + k) dx + x³dy=0

A: To verify that y is a solution of differential equation we find derivative of that substitute on the…

Q: 19. y = tanh(e*)

A: Given; y=tanh(ex).

Q: 02 01 Q3 Q4 05 Q6 07 Q8 09 Q10 Q13 Q14 Q15 The trigonometric substination to evaluate the integral…

A:

Q: A college professor never finishes his lecture before the end of the hour and always finishes his…

A: This is a problem related to probability. Please follow the procedure given below.

Q: Let f be the function given by f (x) = = x¹ + x³-5x² + tan (). Of the following values of a, at…

A: We have to find the point that gives greatest slope.

Q: ]: Show that the following functions are linearly dependent f₁(x) = tanx, f₂(x) = -tanx, f(x) =…

A:

Q: √√9-² A) sin ¹(3x) + c. B) sin-¹x+c. C) sin-¹ x + c. 22. dx = c sin(In x) D) sin-¹+c. E) sin-¹+c.

A:

Q: Suppose that the function g is defined, for all real numbers, as follows. g(x) = -(x + 1)²+1 if-2…

A: find the function g(x) value at indicated x value.

Q: Find the volume formed by rotating about the y-axis the region enclosed by: x= 3y and y x with y> 0…

A: Given: The region is enclosed by the curves x=3y and y3=x To find: we have to find the volume of the…

Q: Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have…

A:

Q: C. Determine the differential equation on which the general solution is given or describe below by…

A: Since you have asked to answer question no. 4, we will solve that question.Question 4.We need to…

Q: 53. So 0 ex sin x dx

A:

Q: (x+3)dx 1-x2

A: The answer is given below

Q: Determine the domain and range for the graph below. 5+ 4 3 -5 -3 -2 -1 a. Domain: C 1 b. Range: +…

A:

Q: V The size of a balloon is changing with respect to time, such that the volume is given by V(t),…

A:

Q: In Problems 11-14, y = ciet + c₂e" is a two-parameter family of solutions of the second-order DE y"…

A:

Q: b/ For the following function the range is y = √4-x

A: We have to determine range

Q: 91. f (3x − 1) dx 9−2x+3x2

A: The given problem is solved below in detail

Q: Find the general solution of the differential equation y (iv) + 2y''' y '' — 2y'=0.

A: