EXAMPLE 2 Finding Volume Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and the lines y = x and x = 1 and whose top lies in the plane z = f(x, y) = 3 - x - y.
Q: 9) ²-4r-91=7
A:
Q: Evaluate the following integral. 6 x (x² + 5)² dx Find the partial fraction decomposition of the…
A:
Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…
A:
Q: III. Find the differential equation by eliminating the arbitrary constant/s. 1. y-¹ = x(3e* + c)
A:
Q: Write a parameterization for the curve in the xy-plane that is a vertical line through the point…
A:
Q: 11. The table of values below shows the rate of oil consumption in gallons per minute at selected…
A: Solution: Approximate the integral ∫012f(x)dx with the left Riemann sum using the table below:…
Q: C) g'(x) = 3x²; g'(1) = 3 D) g'(x) = 3x2 + 5; g'(1) = 8 mits to find the derivative function f' for…
A:
Q: For which interval is the function f(x)=x√√4-x² continuous O (-∞, -4] and [4, ∞) O (-∞, -2] and [2,…
A:
Q: K False 3. True or False? An independent variable represents the range value or output of a…
A: To write down that the given statement is true or false.
Q: Determine the point(s) at which the given function f(x) is continuous. f(x) = 15x - 21+5 sin (2x)…
A: GIven function:- fx=5x-2+5sin2x
Q: Find the value of c such that the function is continuous on the entire real number line. f(x)=…
A: Topic = Functions
Q: Re-write the given equation in slope intercept form, give the slope and y-intercept, and graph the…
A:
Q: Given the values for sine and cos0, use the reciprocal and quotient identities to find the values of…
A:
Q: 3. Doubling time is the amount of time it takes to double an initial deposit. You deposit $20,000 in…
A:
Q: Find the limit. Enter the exact answer. If the limit does not exist, enter NA. t³ + 125 lim 1-5 t +…
A:
Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…
A: Given data:- Nonzero vectors are u→ & v→ Nonzero scalar α v→=αu→
Q: f(x) = √√√5x - 2, g(x) = x² - 25, and h(x) (fh)(x) = 1 x - 3
A:
Q: 6 5 4+- 3 2 1 1 +- I lim 1-8 lim lim → 4¹ 1 0 1 2 y = f(x) →4 T T I T 1 Enter each answer as a whole…
A:
Q: 2. Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x…
A: given goaph of f'(x)
Q: (a) If the point (1, 7) is on the graph of an even function, what other point must also be on the…
A: Topic- functions for even function if (x,y) is on the graph then (-x,y) is also on the graph for odd…
Q: Find the following limit. Answer as a fraction or integer (no decimals.) x² x +9x-22 x²-4 lim X-2 -
A:
Q: Assume that u v = 5, ||u|| = 5, and ||v|| = 8. Calculate the value of (4u + v) · (u – 5v). (Give…
A: Given u.v=5, u=5 and v=8
Q: 3. f(x)=-2[x]
A:
Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…
A:
Q: n=1 1 n√n
A:
Q: Hello, can you help with the below math exercises with the explanation please? Thanks a lot! 5/…
A:
Q: Your friends, Fernando and Amelia, each own a video game designer company. They both want you to…
A: Given: in part time job making $8.00 per hour. Femando offers to pay you $15 per hour for the first…
Q: Find lim x→-3 sin(−4 π x) lim x→-3 sin(−4 π x)
A:
Q: 1. Find the derivatives of the following function (a) y=4²+2
A: Given Equation: y=4x2x-3xx+2xx .....................(1)y=2x+3x2+x+1…
Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12…
A:
Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2
A: Disclaimer: “Since you have asked multiple question, we will solve the first question for you. If…
Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :
A: According to our guidelines, In case of multiple questions we are supposed to answer the first…
Q: Use an appropriate Pythagorean identity to find the indicated value. Write your answer as a…
A:
Q: if 8-x² -3x - 10 if In(x-1) + 3 if Select the graph of the function above: Let f(x) = - x= 6 5 4 9 2…
A:
Q: Write an equation of the plane with normal vector n (7,5, -4) passing through the point (1, −5, 1)…
A: Given; n=<7,-5,4> Point (1,-5,1).
Q: Find a vector n normal to the plane with the equation x+6y + 4z = -10. n= 00> (1₂)
A: Concept: The equation of the plane is written as: ax-x0+b(y-y0)+c(z-z0)=0 or ax+by+cz=d Here the…
Q: The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph…
A:
Q: Use the graph to find the average rate of change. 5) Monthly Cellular Phone Charge in Dollars 80+…
A: To find average rate of change of given function through its graph.
Q: Find the value of a, b, c, and d. Enter all answers in exact, reduced form. No decimals are allowed.…
A: Please refer to the image below
Q: Thank you!! How about if I want to know the angular speed in radians/sec?
A: Let's find angular speed in radians per seconds.
Q: A sports franchise revenue can be modeled by the function R(t) = 337 + 8t. Their operating costs are…
A: Given data:- Revenue function R(t) = 337+8t Cost function C(t) = 245+20t
Q: C. Find the standard form of the equation of a circle given the following conditions. 11. Radius is…
A:
Q: Find ||u₁y|| if u = (2,5), v = (8,2). # 5 -X (Express numbers in exact form. Use symbolic notation…
A:
Q: Given the graph of f(x) = x² as shown, graph the function - 5ƒ(x + 4). 10+ 9+ 8+ 7+ 6+ 5- 4+ 3+ 2+…
A: The function is fx = x2 The graph of the function is To evaluate: The graph of the function -5fx+4
Q: How are you getting a negative for a and where is the equation coming from for b?
A:
Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -
A:
Q: 2) Suppose that a fashion company determines that the cost, in dollars, of producing x cellphone…
A: NOTE: Refresh your page if you can't see any equations. . take x=400
Q: log₂log 1 (x − 6) < 0 2
A: Here we are asked to solve the inequality: log2log12x-6<0
Q: əz əs дz at 11 || z = e cos(8), r = st, 0 = √ s6 + 15
A: We can answer both the answer in the following steps.
Q: Prove that tan'z= leto 1/2 in (1+2) tan't z • tanw=Z Z = Sinw cosw
A:
Step by step
Solved in 2 steps with 2 images
- A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 5x+6y+z=1. What is the maximum volume of such a box? Volume=A rectangular box has three of its faces on the coordinate planes and onevertex in the first octant on the paraboloid z = 4 − x^2 − y^2. Determine themaximum volume of the box.The volume of a nose cone is generated by rotating the function y = x – 0.2x2 about the x-axis. What is the volume, in m3, of the cone. The volume of a nose cone is generated by rotating the function y = x – 0.2x2 about the x-axis. What is the volume, in m3, of the cone? What is the x coordinate of the centroid of the volume?
- The centroid of the plane region bounded by the graphs of y = f (x), y = 0, x = 0, and x = 3 is (1.2, 1.4). Without integrating, find the centroid of each of the regions bounded by the graphs of the following sets of equations. Explain your reasoning.(see the graph as attached here). y = f (x) + 2, y = 2, x = 0, and x = 3The centroid of the plane region bounded by the graphs of y = f(x), y = 0, x = 0, and x = 3 is (1.2, 1.4). Without integrating, find the centroid of each of the regions bounded by the graphs of the following sets of equations. Explain your reasoning. (a) y = f(x) + 2, y = 2, x = 0, and x = 3 (b) y = f(x − 2), y = 0, x = 2, and x = 5 (c) y = −f(x), y = 0, x = 0, and x = 32. Find positive values a, b and c such that the planex/a + y/b + z/c = 1 passes through the point (2, 1, 2) and cuts off the least volume from the first octant.
- Mass of a box A solid box D is bounded by the planes x = 0, x = 3,y = 0, y = 2, z = 0, and z = 1. The density of the box decreases linearly in the positive z-direction and is given by ƒ(x, y, z) = 2 - z. Find the mass of the box.A rectangular box is inscribed in the region in the first octant bounded above by the plane with x-intercept 6, y-intercept 6, and z-intercept 6. a. Find an equation for the plane. b. Find the dimensions of the box of maximum volume.Pigeonhole Principle: consider the 3D grid with integer coordinates (That is, a point (x, y, z) lies on the grid if and only if x, y and z are all integral). Prove that if we take nine points on the grid then there exist two of the points whoseaverage is also a point on the grid.
- Find the volumes of the regions. The region in the first octant bounded by the coordinate planes and the surface z = 4 - x2 - yR is the region bounded by y= sqrt x , and y= 6-x and the vertical y-axis. Q is the region bounded by y= sqrt x, and y=6-x, and the horizontal x- axis. (They Intersect at (4,2) ) Write an expression that gives the volume of the solid formed by rotating R around the horizontal line y=-2Volume of a paraboloid cap Find the volume of the solid bounded bythe paraboloid z = 9 - x2 - y2 and the xy-plane.