In Problems 35–38, find the volume of the solid under the graph of each function over the given rectangle.
35.
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
- 4. A right circular cylinder of height h = 2x is inscribed in a sphere of fixed radius R. (a) Show the volume of the cylinder is given by the formula V = 2Tx(R2-x²). (b) Determine the height h of the cylinder of largest volume that can be in- scribed in the sphere.arrow_forward6. Determine the absolute maximum and minimum values of f(x, y) = 2x² + 3y² on the rectangular region where -1 ≤ x ≤ 1 and -1 ≤ y ≤ 1.arrow_forward3. The following table shows the depth in feet at some cross-section checkpoint of the Allegheny River (Pennsylvania) measured at 100 foot intervals from one side of the river. distance (feet) || 0| 100 | 200 depth (feet) 300 | 400 | 500 | 600 | 700 | 800 |0 11.5 17 18.5 20 19 15 13 If the current (water flow) was 3 feet per second, use the trapezoidal rule to estimate the volume of water flowing through this cross-section in 2 seconds.arrow_forward
- 4. A rectangular box has sides of length x cm, y cm and z cm. Sides x and z are expanding at rates of 3 mm/s and 5 mm/s respectively and side y is contracting at a rate of 2 mm/s. Determine the rate of change of volume when x is 3 cm, y is 1.5 cm and z is 6 cm. [1.35 cm³/s]arrow_forwardREFER TO IMAGEarrow_forwardDetermine the length of x = 3 + (y – 2)² , 4 < x< 19 %3Darrow_forward
- 7. Please show the solution and give the correct answer.arrow_forward2 Jlgull If F=(x^2+y^2+z^2)^n (xi+yj+zk) then V.F is (2n +3)(r 2n) I O (2n +3)(r 2n-1). .II O (2n- 3)(r 2n).11 .III Oarrow_forward2. In this problem, you will find the dimensions of the right circular cone of minimal volume which circumscribes a sphere of radius 3". Refer to the diagram below when answering the questions which follow. C | AB | |ED| |EC| h X reflect ACDE about CE and rotate Ar ΦΕ B work to express V as a function of the variable x alone. - Simplify your expression for V as much as possible. C (a) Explain why |AC| (b) Rewrite the equality from (a) in terms of the variables x and r. (c) Solve your equation from (b) for the variable r. (d) Use the fact that the volume V of the cone is: V = r²h and your previous E 3D X (e) Use the properties of the derivative to minimize the volume of the cone. Then indicate the dimensions of r and h for the minimal cone.arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education