If you round 75 to the nearest tenth it would be 80
Answer:3
x
−
2
y
=
7
Explanation:
Write the standard form of the line that goes through
(
3
,
1
)
and is perpendicular to
y
=
−
2
3
x
+
4
.
The equation
y
=
−
2
3
x
+
4
is in slope intercept form
y
=
m
x
+
b
where
m
= slope and
b
= the
y
intercept.
The slope of this line is then
m
=
−
2
3
A perpendicular slope is the opposite sign reciprocal. So, we change the sign of
−
2
3
and switch the numerator and denominator.
Perpendicular slope
m
=
3
2
To find the equation of the new line, use the point slope equation
y
−
y
1
=
m
(
x
−
x
1
)
where
m
=
slope and
(
x
1
,
y
1
)
is a point.
The slope is
3
2
and the point is the given point
(
3
,
1
)
.
y
−
1
=
3
2
(
x
−
3
)
a
a
a
Distribute
y
−
1
=
3
2
x
−
9
2
Standard form is
a
x
+
b
y
=
c
where
a
,
b
and
c
are integers and
a
is positive.
a
a
2
(
y
−
1
=
3
2
x
−
9
2
)
a
a
a
Multiply the equation by
2
a
a
a
a
a
2
y
−
2
=
3
x
−
9
−
3
x
a
a
a
a
a
a
a
−
3
x
a
a
a
Subtract
3
x
from both sides
−
3
x
+
2
y
−
2
=
−
9
a
a
a
a
a
a
a
a
+
2
a
a
a
+
2
a
a
a Add 2 to both sides −
3
x
+
2
y
=
−
7
−
1
(
−
3
x
+
2
y
=
−
7
)
a
a
a
Multiply the equation by −
1
3
x
−
2
y
=
7
Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Answer:
Your exact value should be 10h
Step-by-step explanation:
I put it into the calculator and that's what came out.
