Answer:
n=288
Step-by-step explanation:
Rewrite the equation as
√
n
=
18
√
8
−
8
√
18
.
√
n
=
18
√
8
−
8
√
18
To remove the radical on the left side of the equation, square both sides of the equation.
√n
2
=
(
18
√
8
−
8
√
18
)
2
Simplify each side of the equation.
Use
n
√
a
x
=
a
x
n
to rewrite
√
n as n
1
2
.
(
n
1
2
)
2
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
n
1
2
)
2
.
Multiply the exponents in
(
n
1
2
)
2
.
Apply the power rule and multiply exponents,
(
a
m)n
=
a
m
n
.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Cancel the common factor of 2
Cancel the common factor.
n
1
2
⋅
2
=
(
18
√
8
−
8
√
18
)
2
Rewrite the expression.
n
1
=
(
18
√
8
−
8
√
18
)
2
Simplify.
n
=
(
18
√
8
−
8
√
18
)
2
Simplify
(
18
√
8
−
8
√
18
)
2
Simplify each term.
Rewrite
8 as 2
2
⋅
2
.
Factor
4 out of 8
n
=
(
18
√
4
(
2
)
−
8
√
18
)
2
Rewrite
4 as 2
2
n
=
(
18√
2
2
2
−
8
√
18
)
2
Pull terms out from under the radical.
n
=
(
18
(
2
√
2
)
−
8
√
18
)
2
Multiply
2 by 18
n
=
(
36
√
2
−
8
√
18
)
2
Rewrite
18
as
3
2
⋅
2
.
Factor
9
out of
18
.
n
=
(
36
√
2
−
8
√
9
(
2
)
)
2
Rewrite
9
as
3
2
.
n
=
(
36
√
2
−
8
√
3
2
⋅
2
)
2
Pull terms out from under the radical.
n
=
(
36
√
2
−
8
(
3
√
2
)
)
2
Multiply
3
by
−
8
.
n
=
(
36
√
2
−
24
√
2
)
2
Simplify terms.
Subtract
24
√
2
from
36
√
2
.
n
=
(
12
√
2
)
2
Simplify the expression.
Apply the product rule to
12
√
2
.
n
=
12
2
√
2
2
Raise
12
to the power of
2
.
n
=
144
√
2
2
Rewrite
√
2
2
as
2
.
Use
n
√
a
x
=
a
x
n
to rewrite
√
2
as
2
1
2
.
n
=
144
(
2
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
n
=
144
⋅
2
1
2
⋅
2
Combine
1
2
and
2
.
n
=
144
⋅
2
2
2
Cancel the common factor of
2
.
Cancel the common factor.
n
=
144
⋅
2
2
2
Rewrite the expression.
n
=
144
⋅
2
1
Evaluate the exponent.
n
=
144
⋅
2
Multiply
144
by
2
.
n
=
288
Answer:
How many miles does he ride his bike there and back?
6 miles.
What information is extra?
The hour at which he leaves his house.
Step-by-step explanation:
We know that he rides 3 miles each way.
Then he rides 3 miles from his house to his friend's house, and another 3 miles from his friend's house to his house.
So he rides 3 miles both times, if we add that, we get:
3 miles + 3 miles = 6 miles
So:
How many miles does he ride his bike there and back?
6 miles.
And to answer the other question, we need to look at the given information that we did not use in this calculation. In this case, is the hour at which he leaves his house.
Notice that we never did use the fact that he leaves his house at 4 p.m.
Then:
What information is extra?
The hour at which he leaves his house.
<span>first, we are going to define variables as the following:
a = 0
a = π/2
n = 4 rectangles
Δx = [ b - a ] / n ------>Δx = [ π/2 - 0 ] / 4 = π/8
right endpoints :
sum( seq( 4 cos(x) * π/8 , x , 0+π/8 , π/2 , π/8 ) ) = 3.163065 underestimate
left endpoints:
sum( seq( 4 cos(x) * π/8 , x , 0 , π/2-(π/8) , π/8 ) ) = 4.733861 overestimate
the reason because the actual estimate by integral as the following:
π/2
∫ 4cos(x) dx = 4
0</span>
Answer:
210cm cubed
Step-by-step explanation:
Width x length x height
3x7x10
That is an annuity and use the attached formula.
Total = 300 * [(1.055)^11 -1] / .055 -300
Total = 300 *
<span>
<span>
<span>
1.8020924036
</span>
</span>
</span>
-1 /.055 -300
Total = 300 *
<span>.8020924036 / .055 - 300
</span>Total = 300 *
<span>
<span>
<span>
14.5834982473
</span>
</span>
</span>
-300
Total =
<span>
<span>
<span>
4375.0494741818
</span>
</span>
</span>
-300
Total =
<span>4075.05
</span>
