February 2016

differential equation: Determine whether a member of the family can be found that satisfies the initial conditions

Submitted by Dutsky Kamdon on February 1, 2016 - 10:27pm

The given two-parameter family is a solution of the indicated differential equation on the
interval (−∞,∞). Determine whether a member of the family can be found that satisfies the
initial conditions.
y = c1e^x cos x + c2e^x sin x; y" − 2y' + 2y = 0,
i. y(0) = 1, y'(π) = 0
ii. y(0) = 1, y(π) = −1

differential equation: given $f(x)$, show that $f(x)$, $f'(x)$, and $f''(x)$ are continuous for all $x$

Submitted by Dutsky Kamdon on February 1, 2016 - 10:39pm

Let
f1(x) = 1 + x^3 for x ≤ 0 ,1 for x ≥ 0
f2(x)= 1 for x ≤ 0, 1 + x^3 for x ≥ 0
f3(x)= 3 + x^3 for all x.

show that
a) f, f' , f", are continous for all x for each f1, f2, f3.

differential equation: Show that if f and f' are continuous on a ≤ x ≤ b then f and f' are linearly independent on a ≤ x ≤ b

Submitted by Dutsky Kamdon on February 1, 2016 - 10:41pm

Show that if f and f' are continuous on a ≤ x ≤ b and f(x) is not zero for all x on a ≤ x ≤ b,
then f and xf are linearly independent on a ≤ x ≤ b.

Discussion on: Solution to Problem 225 Biaxial Deformation

Submitted by PHizzogs on February 3, 2016 - 12:28pm

Following is a discussion on the Reviewer item titled: Solution to Problem 225 Biaxial Deformation. Feel free to add your own comments!

proving: $\arccos x = \dfrac{\pi}{2} - \arcsin x$

Submitted by Jose Jesus Josh... on February 3, 2016 - 11:58pm

arc cos x = π/2 - arc sin x

maxima minima: cylinder of maximum lateral surface are inscribed in a sphere

Submitted by Jose Jesus Josh... on February 4, 2016 - 12:23am

find yhe dimension of right circular cylinder of maximum lateral surface area which can be inscribed in a sphere of radius 4 in.

find the interval: third order differential equation

Submitted by Dutsky Kamdon on February 4, 2016 - 4:01pm

(sin x)y''' − 3xy'' + 2y = tan x

Discussion on: Solution to Problem 593 | Spacing of Rivets or Bolts in Built-Up Beams

Submitted by ce-mac on February 4, 2016 - 8:25pm

Following is a discussion on the Reviewer item titled: Solution to Problem 593 | Spacing of Rivets or Bolts in Built-Up Beams. Feel free to add your own comments!

Engineering Student

Submitted by Jezreel Mikaela... on February 8, 2016 - 3:41pm

Thank you for this site. I can now understand the lessons :)

solid mensuration

Submitted by Renzyl Sarmient... on February 8, 2016 - 6:29pm

definite integral hirap po talaga hindi ko masagot

Submitted by Jeanvill Palada... on February 9, 2016 - 2:18pm

Engineering mechanics( plane friction)

Submitted by Ahniah on February 9, 2016 - 8:30pm

How do you solve this? I have tried but could not get the answers:( someone please help me.

This is the question

This is my working.

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differential operator please solve this problem

Submitted by Dutsky Kamdon on February 9, 2016 - 9:03pm

1. (2xD2 + 1)(3xD + 2)
2. (xD − x)(xD2 − 2)

Use the exponential shift to find the general solution.

Submitted by Dutsky Kamdon on February 9, 2016 - 9:07pm

1. (4D + 1)^4 y = 0.
2. (6D − 5)^3 y = 0.

Find the general solution.

Submitted by Dutsky Kamdon on February 9, 2016 - 9:10pm

1. (D^5 + D^4 − 7D^3 − 11D^2 − 8D − 12)y = 0.
2. (D^4 − 2D^3 + 2D^2 − 2D + 1)y = 0.

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Solids For Which V=Bh

Submitted by tacdol01 on February 10, 2016 - 8:28pm

Imagine a cube measuring 3 units on an edge, and having its total surface area painted blue. Without the aid of a figure, answer the following questions.
(A) How many times must you cut completely through the cube to make cubes which measure 1 unit on an edge?
(B) How many of the cubes of question (A) will have
(a) Three blue faces?
(b) Two blue faces?
(c) One blue face?
(d) No blue face?
(C) How many cubes are there in all?

Discussion on: Solution to Problem 311 Torsion

Submitted by Reil on February 15, 2016 - 1:54pm

Following is a discussion on the Reviewer item titled: Solution to Problem 311 Torsion. Feel free to add your own comments!

Flux

Submitted by Jack Waddell on February 16, 2016 - 8:22am

I need to understand FLUX through a closed surface, say a sphere.

Solid Mensuration (Paki sagot po)

Submitted by Angel Pabria Dayao on February 16, 2016 - 9:45am

1. The official distance bet. home plate and second base in a baseball diamond is 120ft. Find the area of the official ball diamond and the distance bet. the bases.

2. A metal washer 1inch in diameter is pierced by a 1/2 inch hole. What is the area of one face of the washer.

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river

Submitted by Lyneth Foman-eg on February 17, 2016 - 4:31am

A river flows 1.5 miles an hour.(a) In what direction must a man swim in order to go straight across if his rate of swimming in still water is 2.5 miles an hour?(b) How long will it take him to cross the river if it is 1/ mile wide?

plane and solid geometry

Submitted by sims on February 17, 2016 - 10:17am

hello po, patulog po ako

1. two tangent lines drawn from an external point to a circle makes an angle of 60 degrees with each other. The distance from the external point to the center of the circle is 10 cm. Find the radius of the circle and the length of the tangent segment.