water faucet can fill a sink in 8 minutes, whereas the drain can empty it in 7 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open? If both the faucet and drain are open, it will take __ minutes to empty the sink.

Q: О -10 -5 10 -10- y 10- 5 10 -10 10- 5 10 -50 50 -50 50 Д

A: r2θ=49 To sketch the curve, we can start by graphing r as a function of theta in Cartesian…

Q: 2. Use first principles to find the derivative of each. a) f(x) = √2x-1 b) y = ///

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x the derivative is…

Q: Answer: f(x) = What is the interval of convergence? Answer (in interval notation): + f(x) = x 1+ 3x…

A: As per guidelines we support only first question in one request.

Q: Let the vector v have an initial point at (-3,0) and a terminal point at (-4, –3). Determine the…

A: The initial point of the vector is x1, y1 = -3, 0 The terminal point of the vector is x2, y2 = -4,-3…

Q: 4. Suppose that the acceleration of a particle (in meters per second per second) is given by the…

A: Let a(t) ,v(t), s(t) are the acceleration, velocity and position of a particle respectively. vt=∫at…

Q: Find the centroid of the region bounded by the graphs of the functions y = 2x² x² +1 Y = The…

A: y=2x2, y=x2+1

Q: A vertical pole 32 feet tall stands on a hillside that makes an angle of 17° with the horizontal.…

A:

Q: [²*62²³e ²² Find the value of 2 Determine whether Σ(6n²e™²)

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in…

A:

Q: Calculate r' (t) and T(t), where r' (t) = 6 T(t) = ( 2 -4 r(t) = (7 + 6t, 5 — 4t, 2t - 5). " 2

A:

Q: / If f(x) = 2x (Sinx+cosx) find. f'(x) = ' (5) =

A: Given function  f( x ) = 2x( sinx + cosx )

Q: Let x) = (x+3)³ +2 The graph of the inverse function y = f¯¹(x) has a vertical tangent at: (Hint:…

A:

Q: A poster inches with J drea and poster x is song tall to have 1 inch margins 2 inch in write of the…

A:

Q: 2. Compute the following limits x²-x-2 x 2 x²+x-6 (a) lim (b) lim xxx² (c) lim x² - 2x + 1 x-3

A:

Q: Compute the sum of the given series. If the series diverges, enter DNE. Use exact values. (-7²)…

A: If the sum of the series is converges then also find sum of the series

Q: (d) J x5 + 1 +1 x³(x + 2) dx

A: To evaluate the following integral by using partial fractions. ∫x5+1x3x+2 dx Note: Since, the…

Q: Divide the complex numbers below and leave the result in trigonometric 7(cos 150° +i sin 150°) 9(cos…

A:

Q: point

A:

Q: Given a = 6, b = 10, and c = 5, use the Law of Cosines to solve the triangle for the value of B.…

A: The sides of a triangles are a=6, b=10 and c=5.To find : Use the Law of Cosines to solve…

Q: Write a polar equation of a conic with the focus at the origin and the given data. ellipse,…

A:

Q: A circular swimming pool has a diameter of 18 m, the sides are 3 m high, and the depth of the water…

A: Given: Diameter= 18 m Sides = 3 m  Dept = 3 m  Acceleration = 9.8 Density = 1000

Q: Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope…

A:

Q: Consider the following. C dt = Let t = 7 tan(0) and determine the t = 0-0 = = 7 t = 70 = 0 dt 49 +…

A:

Q: answer the following:

A:

Q: 5) The function g(x) is always negative and has an average value of -12 over the interval 0 ≤ x ≤ 5.…

A: To find the area between the curve y = g(x) and the x-axis over the interval [0, 5], we need to…

Q: Find the surface area of the paraboloid with parameterization r(u, v) = 6v cos (u)i + 6v sin (u)j +…

A:

Q: Determine the value of k so that ū = [-5, k, 3] and = [1,2,- 7] are orthogonal.

A:

Q: (b) So = x-4 r2 – 52 + 6 dx

A:

Q: Solve the trigonometric equation for all values 0 < x < 5. tan ㅠ -X- 3 - √3=0

A:

Q: 4 -2 -2 -4 h(x). 10 X

A:

Q: The rate of change of the projected total assets (in constant 2005 dollars) in a government trust…

A: Given. f(x) = -0.364x2 - 0.296x + 176.3

Q: 59 Choose the correct integration technique to evaluate the following integrals. J a. b. X x² +9…

A:

Q: If u and v are collinear and the magnitude of u is 7 times the magnitude of v, write an expression…

A: If u and v are collinear vectors and the magnitude of u is 7 times the magnitude of v, then to write…

Q: on oil producer the shape об is to have What the Surface Surface orea is a fixed Value for the H…

A:

Q: First find f' and then find f. f"(x) = x³ + 8x² – 3x - 9. f'(1) = 10. f(1) = -10. f'(x) = 0 f(x) =

A: The given derivative function is:f''(x)=x3+8x2-3x-9The given condtions are:f'(1)=10      and…

Q: 5. For a = 3i-j+2k, b=2i+j-k and c=i-2j+2k, find (a)(a^b)^c and (b) a^(b^c). Comment on the need for…

A:

Q: [₁ 7 tan(x) sec³(x) dx 7 sec³(x) + C 3

A: We have to solve the indefinite integral. We can solve by substitution method.

Q: First find ƒ' and then find ƒ. ƒ"(x) = 5 − (2x³ + 3x²), ƒ'(1) = −3, f(1) = 3. ƒ'(x) f(x) = = 0

A: f''(x)=5-(2x3+3x2),f'(1)=-3,f(1)=3

Q: Consider the following. r(t) = (7t)i + (4t − 3)j + 6tk, P(6, 1, 6) (a) Find the arc length function…

A: The arc length of the  vector curve r(t) is given by St=∫abr'tdt

Q: Let the vector v have an initial point at (4, 7) and a terminal point at (-2, 6). Plot the vector v…

A:

Q: Consider the following curve. r² = sin(20) Set up an integral that can be used to find the shaded…

A: Yes given answer correct

Q: For the series given, determine how large n must be so that using the nth partial sum to approximate…

A: ∑k=1∞1k4;En≤0.000015

Q: The graphs of f(x) = x²-3x - 4 and g(x) = -2x - 2 intersect at the point (-1,0). The (acute) angle…

A:

Q: 3) Find the area bounded by the parabola x = 9-(y-2)² and the y-axis.

A: We know that area formula int_a^b f(x) dx

Q: raw View Help 49) log7 √7 A) 7 Picture B IU 2 B) =-/- OneNote for Windows 10 C) 1 32 Meredith…

A:

Q: ✓ 5) a) lim X-1 Hopital's rule 2 x²-7x +6 x2 - 5x-6 - b) lim ex- e - 2x X-0 2 x² Find the limit. IF…

A:

Q: Find area of the region under the curve y = 4x³ - 2 and above the z-axis, for 3 < x < 8. area =

A: We know that the area of the function f(x) at x=a to b is  int_a^b f(x) dx

Q: Find the volume of the solid obtained by rotating the region x², y = 0, and x = 1, about the y-axis.…

A: NOTE: Refresh your page if you can't see any equations. . here we have ..............radius…

Q: rom a point A, level with the foot of a hill, the angle of elevation of the top of the hill is 20°.…

A:

Q: Find the centroid of the region bounded by the graphs of the ㅠ - 18 || functions y the origin. The…

A: