Evaluate zdV where E is the region under the plane 4x + 2y + z = 4 in the first octant ( E х, у, z > 0)

Q: Solve the initial value problem (a differential equation) y" + 3y' +2y = 8 (t – 1), y (0) = 0, y'…

A:

Q: Consider the circle 2x² + 2y² - 12x+8y-24 = 0. (a) Find the center (h, k) and radius r of the…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Let P be the plane that is tangent to the equation xyz + 260 = z' + 30x + 26y at the point (7,7,4)…

A: The tangent plane to the surface is a plane that only touch the surface at the point.

Q: State form usg an appiopuate suusutuuo. Example 7 Example 8 Find the integral Find the integral Vī –…

A:

Q: Let C be the curve defined by T(t) = (2 + 2 sin(t), 3 – 2 cos(t)) for 0 < t < 4x=²) dx + (2xyev" +…

A: Given the integral is ∫Cy2exy2+4x-2dx+2xyexy2+2dy. Rewrite the integral as ∫CF·→dr→:…

Q: Let C be the curve connecting (0,0,0) to (1,3,1) to (3,4,4) to (2,1,3) to (0,0,0) Evaluate + y)dx +…

A: Given,     and

Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Consider the vector field F = |y² + xz, x² + yz, z² + xy| Find each of the following values (or…

A: The answer is given as follows

Q: 2. Modeling: A Drone's Shadow. Suppose a drone takes off with an angle of incline of radians, in a…

A:

Q: Let S be the surface of z = 6 –- x² – 4y² with z > 2 Find the flux of F = [1 – 4y, 1 + x, 2z]on S

A:

Q: Let E be the region between z = V12 – x² – y² and z = x² + y?

A: Given, E be the region between z=12-x2-y2 and z=x2+y2 F→=x2+y2-cosz,x2-y2+sinz,x2y2+4z

Q: please provide a complete solution for the problem below. thanks

A: Ok

Q: 14. Let f(x)=x²-2x. (a) Find the average rate of change from x=1 to x=4. (b) Find the equation of…

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Q: Use the divergence theorem to find the flux of F = [x²yz, –xy² z, 3 + z²] on the hemisphere S = {(x,…

A: Find the flux of the vector field F→=x2yz, -xy2z, 3+z2 on the hemisphere S=x, y, z : x2+y2+z2=4, z≥0…

Q: Consider the function (t) which is defined implicitly by the equation t+c= 1.) 1 √4+2 cos u @' (t) =…

A: The given function is defined implicitly as follows: t+c=∫0θt14+2cosudu Where c∈ℝ is constant. (a)…

Q: Evaluate // V9 + 3z² dS for the surface S defined by S r(u, v) = [6 cos(u) sin(v), 6 sin(u) sin(v),…

A: Given that, ru,v=6 cosusinv, 6sinusinv, 3cosv, 0≤u≤π2,0≤v≤π2. To evaluate the integral ∬S9+3Z2dS

Q: The annual amounts of rainfall in a certain region are modeled using the normal distribution shown…

A: here given mean = 41.8 cm and standard deviation = 5.3 cm

Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: a. Show that n(t) = -gʻ(t)i +f'(t)j and - n(t) = g'(t)i – f'(t)j are both normal to the curve r(t) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.