The ODE is linear. Multiplying both sides by
allows you to condense the left hand side as the derivative of a product.
![\dfrac{\mathrm d}{\mathrm dt}\left[e^{7t}x\right]=5e^{7t}\cos2t](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Be%5E%7B7t%7Dx%5Cright%5D%3D5e%5E%7B7t%7D%5Ccos2t)
Integrating both sides with respect to
yields
The integral can be done by parts. You should get
With the given initial condition, you have
So the particular solution to the ODE is
9x-7 = -7
step 1 = add 7 to each side
9x = 0
step 2 divide both sides by 9
x = 0/9 = 0
I believe the correct answer from the choices listed above is option B. <span>If a < b, then a/c < b/c is always true. No matter what the value of c would it is clear that the value of b/c will always be higher than a/c. Hope this helps. Have a nice day.</span>
Answer:
She can put the rocks into groups of 19.
That would give her 2 groups.
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
The 4 sides of a rhombus are congruent.
(i)
2y + x - 4 = 2x - y ( subtract 2x - y from both sides )
3y - x - 4 = 0 ( add 4 to both sides )
3y - x = 4 → (1)
and
= 2x - y ( multiply both sides by 2 to clear the fraction )
4x - 3y + 5 = 4x - 2y ( subtract 4x - 2y from both sides )
- y + 5 = 0 ( subtract 5 from both sides )
- y = - 5 ( multiply both sides by - 1 )
y = 5
substitute y = 5 into (1)
3(5) - x = 4
15 - x = 4 ( subtract 15 from both sides )
- x = - 11 ( multiply both sides by - 1 )
x = 11
(ii)
then
2x - y = 2(11) - 5 = 22 - 5 = 17
perimeter = 4 × 17 = 68 cm
