2. A closed rectangular box with a volume of 16 ft3 is made from two kinds of materials. The top and bottom are made of material costing 10 pesos per square foot and the sides from material costing 5 pesos per square foot. Find the dimensions of the box so that the cost of materials is minimized.

Q: What is the gradient of a line that has an angle of inclination of 55°? Enter your answer, rounded…

A:

Q: Ily approximate the differential dy when x changes from 64 to 64,07 Y

A: Since the student has posted multiple questions and mention to solve question numbers 1 and 2. But…

Q: Prove the identity. COS X 1-sin x 1+ sin x COS X Note that each Statement must be based on a Rule…

A: Solution )  cos x / ( 1 - sin x ) Multiply cos x in numerator and denominator =cos x × cos x /  […

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

A:

Q: y is independent of A. Given y e sin x. Evaluate at the point x = 0. answer. y = -x (cos(xx+b) d'y…

A:

Q: ||r' (t) × r"(t)|| ||r' (t)||³ Use the formula k(t) = r(t) = e³ti + e-tj k(t) 12 (9 e¹ t + e−¹ t) ·…

A:

Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

A:

Q: Question 11 > Suppose f(x)=√√. Give the function for each of the following transformations. The…

A:

Q: Applying the First Derivative Test In Exercises 29-36, (a) find the critical numbers of the function…

A:

Q: If f(x) = 6 + 6x - 2x², find f'(-3).

A:

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: Q1:-Solve the following equations (choose three only):- 3- x²y + 3xy' + y = 0 4- 2-4x+ 5y = sin3x dx…

A: Given

Q: Find the values of x for which the series converges. (If the answer is an interval, enter your…

A:

Q: 12. Prove that the intersection of any family of normal subgroups of a group (G, *) is again normal…

A:

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² − c² and y = c² – x² is…

A:

Q: Find the indefinite integral. (Use c for the constant of integration.) [ (41³1 (4t³i + 14tj - 6√tk)…

A:

Q: (D² – D − 2)y - COS X

A:

Q: Find the value(s) of c such that n=0 enc = 10

A:

Q: 1. Find f(x) if f'(x)=12x¹+3√x+7-2e -4 and f(1) = 4

A: Given f'x=12x3+3x+7x-2ex-4  and f1=4 To find f(x):

Q: Consider the following function. f(x) = (8 - x)(x + 1)² (a) Find the critical numbers of f. (Enter…

A:

Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). ● r(t) = 2t²i - 2tj + 53³k (a) r'(t) (b) r"(t)…

A:

Q: 1. Use operator / elimination method to solve the given system dx dy + 2x + 2y+ 1 dt dt dx dy +2: dt…

A: Elimination method : In the elimination method, by using fundamental arithmetic procedures, we can…

Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Value of x for which series is convergent is given.

Q: The angle of elevation of the sun is 63°. Find the length of a shadow cast by a person who is 5 feet…

A: Here we have to use the concept of the trigonometric ratios

Q: = [₁²2² I = x² dx I = fa da x

A:

Q: d [r₁(t) · r2(t)] = [r₁(t) × r₂(t)] : = d

A: Given: r1t=costi+sintj+8tkr2t=7i+tk

Q: r = 12 sin 18ti + 12 cos 18tj

A: Given :

Q: Differentiate using delta method y=6x2-24

A:

Q: Express the integral as a limit of right endpoint Riemann sums. Do not evaluate the limit. 4 Sª √5 +…

A:

Q: nd the area between y = 8 sin x and y = = = 10 cos x over the interval

A: Topic:- application of integration

Q: 3. Write down the name of the conic given by the polar curve r = 6/(2-sine). Determine the vertices…

A: Given problem:- 3Write down the name of the conic given by the polar curve r = 6/(2-sin(θ))…

Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

A: Here we have given a linear programming problem with equations as given below:  x + 3y ≥ 20 7x + y ≥…

Q: (D² − 4)y : 4)y = 8e²x - 12 Your answer

A:

Q: 8 765 4 3 2 1 -7-6-5-4-3-2 4 -2- -3 Clear All Draw: 4 -3 -6- 1 2 3 4 5 6 7 8

A:

Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: Given

Q: Jc = − xj; P(−2, −4), Q(-2,-2)

A:

Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

Q: Find the area of the shaded region below. УА x=y² - 4y (-3, 3) Area = = x = 2y-y² FI

A:

Q: 8. SHOW ALL WORK =I Determine the values of the other five trigonometric functions of 8, given that…

A:

Q: Find f. f(x) = f''(x) - 10 + 6x + 24x², f(0) = 5, f(1) = 16

A:

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

A:

Q: Consider the curve C of equation: (x² + 2y + y²)² = 4(x² + y²). From the following options choose…

A:

Q: and the magnitude of the given vector. (-4, 4, 7)

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: Finding the Area of a Region In Exercises 5-14, sketch the region bounded by the graphs of the…

A:

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A:

Q: ³ _ x + 2y x-2y find first derivative X = to

A:

Q: 5. f(x) a=-2,2 2 √4-x2 -2 x 2

A:

Q: Use logarithmic differentiation to find dy/dx. y = (4 + x)5/x dy dx II

A: