Answer:
x = 0
, y = 4
Step-by-step explanation:
Solve the following system:
{y = 4 - 3 x | (equation 1)
x + 2 y = 8 | (equation 2)
Express the system in standard form:
{3 x + y = 4 | (equation 1)
x + 2 y = 8 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{3 x + y = 4 | (equation 1)
0 x+(5 y)/3 = 20/3 | (equation 2)
Multiply equation 2 by 3/5:
{3 x + y = 4 | (equation 1)
0 x+y = 4 | (equation 2)
Subtract equation 2 from equation 1:
{3 x+0 y = 0 | (equation 1)
0 x+y = 4 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 0 | (equation 1)
0 x+y = 4 | (equation 2)
Collect results:
Answer: {x = 0
, y = 4
Answer:
∫₀² ln(x²) dx
Step-by-step explanation:
An integral is an improper integral if one or both endpoints is infinity, if the function is undefined at one or both endpoints, or if the function is discontinuous between the endpoints.
ln(x²) is undefined at x = 0.
Answer:
Either
(approximately
) or
(approximately
.)
Step-by-step explanation:
Let
denote the first term of this geometric series, and let
denote the common ratio of this geometric series.
The first five terms of this series would be:
First equation:
.
Second equation:
.
Rewrite and simplify the first equation.
.
Therefore, the first equation becomes:
..
Similarly, rewrite and simplify the second equation:
.
Therefore, the second equation becomes:
.
Take the quotient between these two equations:
.
Simplify and solve for
:
.
.
Either
or
.
Assume that
. Substitute back to either of the two original equations to show that
.
Calculate the sum of the first five terms:
.
Similarly, assume that
. Substitute back to either of the two original equations to show that
.
Calculate the sum of the first five terms:
.
Hey there! Every mile is 1760 yards, so multiply that by 4
1760 x 4 = 7040, so she walks 7040 yards.
Hope this helped!
Answer: 
You can write this as (-infinity, 7) if you aren't able to use the infinity symbol.
====================================================
Explanation:
Think of x < 7 as writing 
So x is between negative infinity and 7, excluding both endpoints.
To write
in interval notation, we write
The curved parenthesis tell us to exclude the endpoint.