Answer:
a) Eva will need 2 bags of clay to make both pieces of pottery.
b) She will have leftover
pounds of clay.
Step-by-step explanation:
Hi
a) We have to find the total amount of clay, as she needs
and
, so
, is the total amount of clay. Then as we Know that one bag of clay has
, It isn´t enough, but with two bags
, It is enough clay.
b) She will have leftover
of the second bag, then we add the third one, so
are leftover.
x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is 
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.
I = PRT
P (principal) = 6000
R (rate) = 3.7%.....u need decimal form = 0.037
T (time) = 5
I = (6000)(0.037)(5)
I = 1110.00 <===
u dont need years as a decimal...u need rate as a decimal
Answer:
C
Step-by-step explanation:
The number is 225.
It square roots are +15 and -15 .
They are 30 apart on the number line.