Is it true that ln x + ln y = ln (x + y) for all positive values of x and y?

Q: The radiation energy E emitted by a heated surface (per unit surface area) is directly proportional ...

A: a) Given, Radiation energy emitted per unit surface area is directly proportional to the fourth powe...

Q: please and thank you!

A: sides of right triangle is given

Q: Find the derivative of y = 3ln(4x – 7)

A:

Q: Use two methods to find volume for the solid of revolution generated by rotating the region bounded ...

A: a The volume for the solid of revolution generated by rotating the region using Disk/Washer method. ...

Q: Write the standard form and operation

A:

Q: Jse the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 2 + 9 %3D petween x...

A:

Q: Solve the differential equation (dy)/(dx) = 80 - 2y, such that y = 70 when x = 0.

A: The given differential equation is dydx=80-2y. Solve the above equation as follows. dydx=80-2ydy80-2...

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(r) = Vx²...

A:

Q: Find the minimum and maximum of A over a particular interval [0, 6]. A(x) = | S1) dt The graph of y ...

A:

Q: Need help!  I do not know what I did wrong!

A: Given: The speed of a runner increased steadily during the first three second of a race. Her speed a...

Q: Use the position function s(t) = -4.9t? + 650, which gives the height (in meters) of an object that ...

A: s(t)=-4.9t2+650Velocity at time t=a secondslimt->as(a)-s(t)a-t

Q: please and thank you!

A: sinsinθ = opposite (x)hypotenuse(8) detailed solution is given below

Q: 1+ x – e* lim x(e² – 1) а.

A: Since you have ask multiple  questions,so we will answering only first question.

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE...

A:

Q: Čóš (a+B) For all values of a and ß for which the expression is defined, = ? sin ß

A:

Q: I need your help with this

A: Given curve is r(t)=cost,sint,tx=cost, y=sint, z=tdxdt2+dydt2+dzdt2=(-sint)2+(cost)2+1=2

Q: Investigate the limit

A: The limit of the function is, limx,y→0,0x2x2+3xy+y2 As x,y→0,0 we see that the given limit is of the...

Q: A tank in the shape of an inverted right circular cone has height 5 meters and radius 4 meters. It i...

A:

Q: Sum of first 50 terms

A:

Q: Find the area to the nearest

A: Given,           We know that,          The area of the triangle with sides a,b and c is given by  ...

Q: What is the domain of g(x) = In(2x – 9)? Give your answer in interval notation using fractions or mi...

A:

Q: Which exponential function of the form y=a(b)x contains the points (2,44) and (3,88)?

A:

Q: A pyramid of height 15 ft is to be divided into three solids by passingplanes parallel to the base. ...

A:

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection ca...

Q: find sec (tan^-1(u+2/3). Assume u+2/3>0. Do not simplify

A:

Q: Calculus Question

A: We are solving the first question and for the next question post the question again and also mention...

Q: Complex numbers can be represented by points in the plane. Let the horizontal axis be the real axis ...

A:

Q: Need help for solving homework integrals with trig. Ty!

A:

Q: g(x) = x3 − 27x, domain [−6, 6]   Indicate any extrema.

A:

Q: /3 •arctan y Vrydrdy

A: Objective of the question is to solve the double integral ∫03∫0arctan yxydxdy The given problem can ...

Q: Let z be any complex number in polar form with 0≤θ <2π. Use z=re^iθ to define the logarithm of a ...

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of F(x) sin (t*)dt

A: ∫abf(x)dx=-∫baf(x)dxUsing fundamental law of calculusddx∫af(x)F(t)dt=f'(x)*F(f(x))

Q: For the stewart section 10.2 question 52 how do we solve this problem?

A:

Q: The circumference of a sphere was measured to be 8383 cm with a possible error of 0.50.5 cm. Use lin...

A: The circumference is,  C=83 cm Then, radius is, r=832π Consider the error is 0.5 cm. The surface are...

Q: Find the exact coordinates of the centroid for the region bounded by the curves y=sqrt(x) and y=x.

A:

Q: Calculate the volume of a water cylinder with total height of 10 meters and whosediameter is 400 cen...

A:

Q: Area between curves. Find the area bounded by the given curves. Trace the curve, shade the area re...

A: L

Q: Use the Product Rule to calculate the derivative for the function h(s) = (s¬1/2 + 4s) (3 – s-1) at s...

A:

Q: A rectangular tank that is 1372ft^3..... (check image)

A:

Q: The graph of f ( x ) is shown below. The domain of f ( x ) is [ 0 , E ].

A: To determine the local minimum and local maximum of the function F(x), find the values of x at which...

Q: The income from an oil change service chain can be considered as flowing continuously at an annual r...

A: Given , f(t) = 10,000e0.04t (dollars/year) We have to find the total income for this chain over the ...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.