Since 3 < pi < 4,
<span>√9 < pi √16 </span>
<span>In fact, since pi^2 = 9.86, </span>
<span>√9 < pi < √10
</span>
One way would be to notice that both functions have the same derivative and then find out what the "constant" is by plugging in x=0
x
=
0
.
Here's another way. Look at
π2−2arctanx−−√=2(π4−arctanx−−√)=2(arctan1−arctanx−−√).
π
2
−
2
arctan
x
=
2
(
π
4
−
arctan
x
)
=
2
(
arctan
1
−
arctan
x
)
.
Now remember the identity for the difference of two arctangents:
arctanu−arctanv=arctanu−v1+uv.
arctan
u
−
arctan
v
=
arctan
u
−
v
1
+
u
v
.
(This follows from the usual identity for the tangent of a sum.) The left side above becomes
2arctan1−x−−√1+x−−√.
2
arctan
1
−
x
1
+
x
.
The double-angle formula for the sine says sin(2u)=2sinucosu
sin
(
2
u
)
=
2
sin
u
cos
u
. Apply that:
sin(2arctan1−x−−√1+x−−√)=2sin(arctan1−x−−√1+x−−√)cos(arctan1−x−−√1+x−−√)
sin
(
2
arctan
1
−
x
1
+
x
)
=
2
sin
(
arctan
1
−
x
1
+
x
)
cos
(
arctan
1
−
x
1
+
x
)
Now remember that sin(arctanu)=u1+u2−−−−−√
sin
(
arctan
u
)
=
u
1
+
u
2
and cos(arctanu)=11+u2−−−−−√
cos
(
arctan
u
)
=
1
1
+
u
2
Then use algebra:
2⋅(1−x√1+x√)1+(1−x√1+x√)2−−−−−−−−−−√⋅11+(1−x√1+x√)2−−−−−−−−−−√=1−x1+x.
Answer:
3:5 <em>the colon is needed to represent the ratio</em>
Step-by-step explanation:
r = 10
g = 4
y = 30 - 14 = 6
y = 6
so ratio of total balls is 10:4:6
and ratio of y:r is
6:10
simply by dividing by 2
3:5
A.) according to the graph, Austin appears to be burning 10 calories per minute. If you look at a perfect point on the graph, which I chose (50,5) and you do x over y or calories per minute, you get a unit rate of 10 calories per minute.
b.) Since you have already found the unit rate in question a, your slope would be 10.
Answer:
R = 9% per year
Step-by-step explanation:
