10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and the altitude is 4 ft if the altitude is increasing at 6 inches per min and the radius is constant?

Q: 1. Evaluate the integral: (a-1/3 - 2/3) da X

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answer of other,…

Q: Sequences and Series 17. Determine if the following sequence is Arithmetic or Geometric. Then…

A:

Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: Let K/L be ideal of quotient ring R/L. If K is prime ideal and contains L, then K/L is prime ideal.…

A:

Q: Used Cramer's Rule to find the value of the variables (X,Y,Z) in the following equations x + 2y + 3z…

A: The objective is to find the value of the variable x, y, z by using crammer's rule.

Q: Written Respons 1) A school's debate team consists of 9 students and must consist of at most 3 boys.…

A: team consist 9 student  maximum 3 boys it means 0 , 1,2,3 consider  total boy 12 total girl 9 so…

Q: Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

A:

Q: Using Cramer's Rule to solve (if possible) the system of linear equations 1 A -10 1 B 11 N SSSUSU…

A:

Q: 2. Find the area of the region bounded by x = y² - 4 and x = 3y.

A: Given query is to find the area of the region.

Q: 9. y = 3 Arcsec 3x

A: On solving this we will get

Q: 11. y = tan e³x + etan3x

A: We can find y' as below.

Q: Evaluate the integral. Do not use hyperbolic functions as the final answer. 1 -dx 2 √√3x²-4

A:

Q: 14 Find the slope of the function ƒ(x) = -x - 1, by the definition of a limit. Slope =

A:

Q: (a) Find the parametric equations for the line segment that joins P(1, 0, 1) to Q(2, 3, 1).

A: Given, P(1,01), Q(2,3,1)

Q: soon as posible

A: We will use substitution.

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: We need to choose correct option.

Q: Find the center and radius of the circle whose diameter has an endpoint at (3, -4) and the origin. 5…

A: Given that the endpoints of the diameter are 3,-4 and 0,0.

Q: 15. Find the inverse of matrix A. A = 38 26

A:

Q: A spherical ball of radius 3 cm was dropped into a conical vessel of depth 8cm and radius of base 6…

A:

Q: What is the amount of work done on a spring when it is compressed from its natural length of 1 meter…

A: Topic = Algebra

Q: A bacteria culture starts with 500 bacteria and doubles in size every half hour. (c) How many…

A: Topic:- exponential growth function

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise…

A: Basic identities of integration are used

Q: Solve: y(x) dy dx = = (8x² - 7x + 6) (y-7), where y(0) = 11.

A: We will solve the given differetial equation by variable separation method.

Q: (d) Let an = 6n²+ n-1 ntn and bn √n n+1' (i) Determine whether {an} is convergent or divergent.…

A: Given;  an=(6n2+n-1) /(n2+n)  bn=sqrt(n)/(n+1)

Q: A conical water tank has its top at ground level (consider this to be the x-axis) and its base 12 ft…

A: Let's find total work(W).

Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations…

A:

Q: y = 2 sin 3x 1+3 cos2x

A:

Q: (a) Find the slope of the tangent line to the given polar curve at the point specified by the value…

A: We have to find the slope of the given polar curve at the point specified.

Q: For the function f(x) = 2x², find the difference quotient ƒ(a + h) − ƒ(a) h 4a + 2h h 4 a² + h 4 a +…

A:

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A:

Q: 3 2. x1 + x² dx

A: Definate integration

Q: Find a function y(x) such that 6yy' = x and x and y(6) = 9. y =

A: Topic = Differential equation

Q: Given: c= 8, a = 5, C = 67°

A:

Q: Identify the focus and directrix of the parabola: y = -4(x - 2)² - 3. f: (1, -4), d: y = 2 f: (2,…

A: If the equation of parabola is of the form x-h2=4py-k(i)  if p>0  then focus is h,k+p  and…

Q: test if (AB)¹ = B¹A¹ A = 4 1 0 2 L3 5. B = 14 0 2 - -3 1

A: To test if ABt=BtAt.A=410235, B=14-3021

Q: (d) The set of points in space equidistant from the origin and the point (0,2,0). (e) The set of…

A: Question d and e has been solved as per the request of the student.

Q: 12) Consider the following exponential function f, Given that f(x) = -616, what is the value of x?…

A: exponential function

Q: egion in the first quadrant is bounded by the curve y=1+ sin²x, the coordinate axes and the line x==…

A: Topic:- application of integration

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATION:

A:

Q: The value of arcsin KIJ 4 O K|6 O KIM R 3 KIN 2 (9) is___

A: SOLUTION-

Q: What integration technique can be used to integrate: (A) Integration Formulas (B) Integration By…

A: Option (d)

Q: Q. Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6e-t at y(0)=1 and y (0)=2

A:

Q: === =+ = ²x² 6 2x Find the arc length given: y = - on the interval [1,2]

A:

Q: Choose an item below and explain your selection. The direction of proj, u + vis 1. The same as u.…

A: When we write  projv→ u+v→    It means the components of vector u+v→ along the direction of v→…

Q: Problem 2: Use the definition of the Laplace transform to find the transform of the piecewise fu…

A:

Q: Solve for So So Szyzdzdydz. 0522 108

A: To solve for ∫03∫02∫15 xyz dz dy dx.

Q: (D² - 2D + 2)y=e²x (cosx - 3sinx)

A:

Q: Assume that y is a differentiable function of r such that y² = x² + 4x sec y. Find y' by implicit…

A: implicit differentiation

Q: Find the determinant of the matrix, O2²-12-13 O22-12+13 O²+12+13 Oλ-13 2-11 4 6 2-1

A: Determinant , λ-11λ-1-24 λ2-11λ-λ+11-24 λ2-12λ-13

Q: Find the lower sum for f(x) = +4 on the interval [-4, 0] using 2 rectangles. 10 "F Submit your…

A: Here we have to find the left sum of given function.