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.
To get the value of x, you have to divide 810.75 by 15. You should get x=54.04
The angle of NPR is 130°
First, set up an equation to find x.
Then, solve the equation for x.
Then, substitute 25 in for x in 2x
50
Finally, subtract 50 from 180 to find the angle of NPR
130°
Hi, I think the answer should be $4.26
7.25% × $24 = $1.74
$24 +1.74 = $25.74
Change is the difference between the amount tendered and this total amount:
$30.00 -25.74 = $4.26
