Commutative Property of Addition <span />
Solutions
1) Find the least common denominator of 7/10 and 1/5.
10: 10
5 : 5 , 10
The least common denominator is 10.
2) Make the denominator of 1/5 to 10. Multiply numerator and denominator by 2.
1 x 2 = 2
5 x 2 = 10
3) New fraction
7/10 + 2/10
4) Add
7+2 = 9
9/10 is answer
9/10 can not be simplified. It is already in reduced form.
The difference between 100 and 75 is 25.
L
=
∫
t
f
t
i
√
(
d
x
d
t
)
2
+
(
d
y
d
t
)
2
d
t
. Since
x
and
y
are perpendicular, it's not difficult to see why this computes the arclength.
It isn't very different from the arclength of a regular function:
L
=
∫
b
a
√
1
+
(
d
y
d
x
)
2
d
x
. If you need the derivation of the parametric formula, please ask it as a separate question.
We find the 2 derivatives:
d
x
d
t
=
3
−
3
t
2
d
y
d
t
=
6
t
And we substitute these into the integral:
L
=
∫
√
3
0
√
(
3
−
3
t
2
)
2
+
(
6
t
)
2
d
t
And solve:
=
∫
√
3
0
√
9
−
18
t
2
+
9
t
4
+
36
t
2
d
t
=
∫
√
3
0
√
9
+
18
t
2
+
9
t
4
d
t
=
∫
√
3
0
√
(
3
+
3
t
2
)
2
d
t
=
∫
√
3
0
(
3
+
3
t
2
)
d
t
=
3
t
+
t
3
∣
∣
√
3
0
=
3
√
3
+
3
√
3
=6The arclength of a parametric curve can be found using the formula:
L
=
∫
t
f
t
i
√
(
d
x
d
t
)
2
+
(
d
y
d
t
)
2
d
t
. Since
x
and
y
are perpendicular, it's not difficult to see why this computes the arclength.
It isn't very different from the arclength of a regular function:
L
=
∫
b
a
√
1
+
(
d
y
d
x
)
2
d
x
. If you need the derivation of the parametric formula, please ask it as a separate question.
We find the 2 derivatives:
d
x
d
t
=
3
−
3
t
2
d
y
d
t
=
6
t
And we substitute these into the integral:
L
=
∫
√
3
0
√
(
3
−
3
t
2
)
2
+
(
6
t
)
2
d
t
And solve:
=
∫
√
3
0
√
9
−
18
t
2
+
9
t
4
+
36
t
2
d
t
=
∫
√
3
0
√
9
+
18
t
2
+
9
t
4
d
t
=
∫
√
3
0
√
(
3
+
3
t
2
)
2
d
t
=
∫
√
3
0
(
3
+
3
t
2
)
d
t
=
3
t
+
t
3
∣
∣
√
3
0
=
3
√
3
+
3
√
3
=
6
√
3
Be aware that arclength usually has a difficult function to integrate. Most integrable functions look like the above where a binomial is squared and adding the two terms will flip the sign of the binomial.
Be aware that arclength usually has a difficult function to integrate. Most integrable functions look like the above where a binomial is squared and adding the two terms will flip the sign of the binomial.
Answer: infinite answers, jk there is like a lot tho
Step-by-step explanation: The sum of x and y is 79. In other words, x plus y equals 79 and can be written as equation A:
x + y = 79
The difference between x and y is 23. In other words, x minus y equals 23 and can be written as equation B:
x - y = 23
Now solve equation B for x to get the revised equation B:
x - y = 23
x = 23 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 79
23 + y + y = 79
23 + 2y = 79
2y = 56
y = 28
Now we know y is 28. Which means that we can substitute y for 28 in equation A and solve for x:
x + y = 79
x + 28 = 79
X = 51
Summary: The sum of the two numbers is 79 and their difference is 23. What are the two numbers? Answer: 51 and 28 as proven here:
Sum: 51 + 28 = 79
Difference: 51 - 28 = 23
Please give me brainliest
