7x-32=3
7x=3+32
7x=35
x=35/7
x=5
HOPE IT HELPS U!!
have a great day ahead ! :)
Answer:
No
Step-by-step explanation:
This is because it is a forever ongoing number. Here is an examples 7, pie, 5, and 2
tell me if this helped pls mark brainliest
Answer:
Length = 15.14, width = 7.14 and height = 2.43 inches.
( correct to the nearest hundredth).
Step-by-step explanation:
Let the lengths of the squares cut out be x inches.
Then the width of the box will be 12 - 2x and the length will be
20 - 2x inches.
The height of the box is x inches.
Volume V = x(20-2x)(12-2x)
To find the value of x when V is a maximum we find the derivative and equate it to zero.
V = x( 240 - 64x + 4x^2)
V = 4x^3 - 64x^2 + 240x
dV/dx = 12x^2 - 128x + 240 = 0
4(3x^2 - 32x + 60) = 0
This won't factor so we use the formula:
x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6
= 8.24, 2.43.
So one of these gives a maximum Volume.
The second derivative
d^2V/dx^2 = 24x - 128
When x = 8.24, this = 69.6 (positive) so this gives a minimum.
x = 2.43 gives a negative value ( -49.7) so this is the maximum
So the dimensions are:-
length = 20 - 2(2.43) = 15.14
width = 12 - 2(2.43) = 7.14
height = 2.43.
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Option I
(3x+4)cm =(2x+10)cm
3x-2x=6
x=6
Option II
(3x+4)= (x+12)
3x-x=12-4
2x=8
x=4
Option III
(2x+10)= (x+12)
2x-x=12-10
x=2
