I think you have to first separate the integral:1/(1+v^2) + v/(1+v^2),
so the integral of the first term is ArcTan (v) and for the integral of the second term i recommend you to do a change of variable:
y= 1+v^2
so
dy= 2v
and
v= dy/2and then you substitute:v/(1+v^2) = (1/2)(dy/y)
and the integral is
(1/2) (In y)finally you plug in the initial variables:
(1/2)(In [1+v^2])
so the total integral is:
ArcTan (y) + (1/2)(In [1+v^2])
Answer: PART A:
w-3.5 t=8
w-3.25t=24
PART B:
t=64
and w= 232
PART C:
It will take 64 minutes for both of the containers to have the same amount of water.
The amount of water in each container is:
232 gallons.
Step-by-step explanation:
PART A:
Let the water is filling in 't' minutes.
and 'w' denotes the amount of water in the container.
for container 1:
One begins with 8 gallons of water and is filled at a rate of 3.5 gallons per minute.
The equation is given by:
or
for container 2:
The other begins with 24 gallons and is filled at 3.25 gallons per minute.
The equation is given by:
or
PART B:
on solving equation (1) and equation (2) by method of elimination we get:
subtract equation (2) by equation (1) to obtain:
t=64
and putting the value of t in equation (1) to obtain:
w= 232
PART C:
Hence it will take 64 minutes for both of the containers to have the same amount of water.
The amount of water in each container is:
232 gallons.
Step-by-step explanation:
The answer is the 3rd one:)
Answer:
w>0.9
Step-by-step explanation:
7.2-3w<4.5
-7.2 -7.2
-3w<-2.7
/-3 /-3
w>0.9
The inequality switches when divided by a negative.
-hope it helps
Answer:
<em>Height of tomato plant is the </em><u><em>dependent variable</em></u>
<em>Presence of walnut leaves in the soil is the </em><u><em>independent variable</em></u>
<em>Tomato plants grown without walnut leaves is the </em><u><em>control</em></u>
<u><em></em></u>
Step-by-step explanation:
<em>An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment.</em> In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.
<em>A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment.</em> In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.
<em>A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time.</em> Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.