Find the volume of an obround tank that is 14 in. wide, 15 ft. between centres and 38 in. high. (Round the answer to the nearest cubic foot.)

Q: Topic: Maxima-minima/optimization problems: Inverse trigonometric Functions For example, suppose we…

A: Minimum value= -pi/2  Maximum value = pi/2  For detail...go through the solution

Q: Find the length of the curve x = t³, 312 y = ²2² ²²₁ 0 ≤ t ≤ √3 t²,

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Q: The inverse Laplace transform of A. e³t (3 cos(5 t) + 5 sin(5 t)) C. e-3t (3 cos(5 t) + 25 sin(3 t))…

A: we want to find L-1 [ 3s + 34s2 + 6s + 34 ]

Q: 2- Say whether each given sequence is an arithmetic sequence. Find the common difference and the…

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Q: 31. dy If x³ - 2xy + 2y³ = 4 then, in terms of x and y, dx

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Q: Find the derivative of the function g(x) = g'(x)= = e² 4 - 2x

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Q: y = 12 - x², y = x² - 6

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Q: 6. f(x) 10. f(x) 12. j(x) f(x) 14. 16: Function 3. 7. 9. 11. f(x) 13. f(x) 15. f(x) 17: f(x) 15.…

A: Match the function with the graph of its derivatives.

Q: a²u əxəy ди dx = pt when x = 0, u = siny+ 3y² + 1 =e*cosy + 2xy when y = 0,

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Q: Express the following limit as a definite integral. n 1 lim Σ -Ax where P is a partition of [2,4]…

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Q: Find the points on the curve where the tangent is horizontal or vertical. 3 x = t³ - 3t, y = t² - 4…

A: The given curve x=t3-3t, y=t2-4. We have to find the points on the curve where the tangent is…

Q: Given f(x) = 19x - 3| +2 25. f'(²-) = If f(x)=(√3x-2)5 then f'(9) = Given f(x) = sin(3x)² 26. f'() =

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Q: er the equation of the parabola graphed below, using the vertex form y = a (x-h)²+k. y = (-1,0)…

A: To solve the following problem using graph

Q: Differentiate the function. F(t) = (3t - 5)² F'(t) =

A: Let's differentiate given function.

Q: If h(2) = 5 and h'(2) = -2, find d (h(x) dx X x = 2

A: given  h(2)=5  and  h'(2)=-2find   d dx(h(x)x)  at x=2we know   d dx(ab)=bdadx-adbdxb2

Q: enclosed

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Q: The average cost per item to produce q items is given by a(g) 0.01g²-0.6q+17, for q>0. What is the…

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Q: 14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

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Q: Determine the solution of the following differential equations. c) (D¹ + 2D6 + 7D5 + 14D4 + 8D³ +…

A: To determine the solution of the following differential equation.D7+2D6+7D5+14D4+8D3+16D3-16D-32y=0…

Q: Find the length and width of a rectangle that has an area of 392 square feet and whose perimeter is…

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Q: Find the area of the following region. The region inside the inner loop of the limaçon r=5+10 cos 0…

A: Please see the below picture for detailed solution.

Q: Find the derivative of the function. y' = y = 3 tan-¹(x - √₁+ 1 x² +

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Q: Is the function T(s) = (6s-4) (es-5) a power function? If so, identify k and p such that T(s) = ks².…

A: The given function is:T(s)=6s-4es-5

Q: It's wrong

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Q: Use mathematical induction to prove that the statement is true for every positive integer n. n(n +…

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Q: Find the first and second derivative for the following functions. 1. y =tan(x) 2. Y = 3(x²-4)5 no…

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Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 6x + 6 between x =…

A: The function is given as f(x) = 6x+6

Q: Solve the integral by substitution S- dx. -2x √25-x² Use the math type button tool ( √ ) under the…

A: We need to find out the integration by the use of substitution method.

Q: 1 x 69. g(x) = ₁ ₁³ + 14 dt 3

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Q: 9. Use the comparison theorem to show that So L'√T- 10. Find √1 + x² dx ≤ Also show that ²√1 + x dx…

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Q: dx + 7) Evaluate Sexy² vertices (0, 0), (2, 2) and (2,0) 2x²ydy where C is the triangle with

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Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: A population is modeled by the differential equation dP P d = 1.2P(1 - 2200) dt (a) For what values…

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Q: 11 . (870), they y equals; c) 3 mx 7) + y = x² lux, (X>0), they q) 3+hX D) 3+3nX B) 3+2nX E) 2+X+X

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Q: 10- You want to invest €1000. What interest rate is required to make this investment grow to €2000…

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Q: For a given commodity and pure competition, the number of units produced and the price per unit are…

A: Let's find consumer surplus and producer surplus.

Q: 5 5. Given that sin x== 13 (a) cos(x-y); 2√5 5 x is in Quadrant I, and cos y =—- y is in the…

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Q: If a principle of $4000 is invested at an interest rate of 6%, how many years will it be until the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: 8). If y is a differentiable function of X, then the slope of the curve of; 3 = 6 at point where y=1…

A: Note: Since the student has mentioned to solve question no. (8), so we are solving according to…

Q: Use integration by substitution to solve the integral below. Use Cfor the constant of integration.…

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Q: 15. If g(x)=√t² - 5t dt, find g"(x).

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Q: 18 Find the Equation for the Graph of a Logarithmic Function 10 (-20,-5) Previous 101

A: I have solved step by step in detail...go through the solution

Q: Find the volume of the solid generated by revolving the region bounded by the curves y = y=0, x= 0…

A: To find:- Volume of solid genrated by curves y=43x+3,x=0,y=0,x=3 about x axis

Q: Differentiate the function. g'(x) = g(x) 에너 1 VX +x

A: Given:g(x)=1x+x5

Q: What type of roots does 3x² - Imaginary Real, Rational, and Unequal Real, Rational, and Equal Real,…

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Q: Suppose that a is the area of a disc with radius r which is expanding in time t measured in seconds.…

A: Given a is the area of a disc with radius r which is expanding in time t measured in seconds.   We…

Q: Use Calculus to find the behavior of g. g(x) = x³ - 3x²is restricted to the interval.x € [-1,4] 19.…

A: Note: Since, the student has mentioned to solve question no. (21), so we are solving according to…

Q: Write the following limit as a definite integral on the interval [3, 8], where c, is any point in…

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