Mathematical oncologists sometimes approximate tumors with the bumpy sphere model given by the family of curves: p = a + b[cos(m*theta)*sin(n*phi)] which gives different shapes and sizes of spheres with bumpy surfaces for different values of real scalars a, b, m, and n are real numbers. An example of a bumpy spere is shown in the image below. For further research into injecting nanoparticles to kill cancerous cells, a biopsy was conducted on an extracted tumor from a patient’s brain. The research team has tasked you to advise on the mathematical specifications of the biopsied specimen. TASKS Show that the bumpy sphere given by the equation above is itself contained inside a smooth sphere of radius a+b. Find the values of theta and phi where the two spheres intersect.

Q: An object that moves with constant velocity so that its position at time t is (x. y) = (1,5) +1 (1L…

A:

Q: Find the area of the region bounded by the closed parametric curve = 5 sin t-2 cos t, y = 6 sin t+6…

A:

Q: 3. Provide the graph of the sinusoidal function over the interval [0, 24). f(x) = 6 cos + 2 %3D…

A: If           y = A sin(B(x + C)) + D then amplitude is A period is 2π/B phase shift is C (positive…

Q: A) Use Green's theorem to compute the area inside the = 1. 2² y² ellipse + 19² 14² Use the fact that…

A: (A). Given,                            x2192+y2142=1,      use the fact that the area can be written…

Q: A disk rotates about an axis through its center. Point A is located on its rim and point B is…

A:

Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

Q: 1 Evaluate f - dz over the unit circle in counter-clockwise direction using the parametriza- tions

A: To evaluate, ∮1zdz over the unit circle counter-clockwise

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

A:

Q: Find an equation in cylindrical coordinates for the rectangular equation y² = 10 - 2²

A: Let y=rsinθ, z=rcosθ ∴r2sin2θ+r2cos2θ=10⇒r2=10⇒r=±10∴y=10sinθz=10cosθtanθ=yz⇒θ=tan-1yzx=x Therefore…

Q: (b) Compute the marginal distributions of R and O. (c) What is the distribution of O? Are R and O…

A:

Q: Let 0 € [0, 27). Let A = cos 0 - sin sin 0 cos 0 ve R². (1) What is the length of Av, in terms of…

A: We use the given information.

Q: A typical dish antenna is built as a surface of revolution obtained by revolving a parabola about an…

A: We to find the surface area of the surface in terms of R and K

Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: Find the curvature κ(t)κ(t) of the curve r(t)=(−2sint)i+(−2sint)j+(2cost)k

A:

Q: Parametrize the intersection of the surfaces y² - z² = x - 1, y² + z² = 36 using trigonometric…

A:

Q: If C is a circle of radius 7 centered at the point ( -5, -1 ), then evaluate $ (34 (3y - esin(x)) dx…

A:

Q: The parametrization r(0,0) = ((3+2 cos 0) cos , (3+2 cos 0) sind, 2 sin 0) describes a urface that…

A:

Q: Find an equation in cylindrical coordinates for the rectangular equation x² + y² = 10x

A:

Q: Convert the following parametric curve into Cartesian form: z = 4 sin t, y = 5 sint O None of these.…

A: To convert the parametric equation into Cartesian equation.

Q: (f) Show that the cartesian equation of this curve is x3 + y³ = 3xy. (g) Show that the polar…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.