Answer: The person's speed is 8 miles per hour.
Step-by-step explanation:
To solve we want to convert the
and
proportionally for the number of miles per hour. We know that multiplying a fraction by its reciprocal will equal 1. So let's do that for the value of the hour.
×
Since we multiplied that to the number of hours we must also do that for the number of miles.
×
Exterior angle is equal to sum of interior opposite angles hence,
req. angle = 80 + 62 = 142
To find f(1), substitute 1 for x.
f(1) = (3(1)+7)²
f(1) = (3+7)²
f(1) = 10²
f(1) = 100
Answer:
5/12 of rain came, or 10 inches
Step-by-step explanation:
complete rain be 1
then, =1-(1/4+1/3)
=1-(3+4/12) take lcm
=1-7/12
=12-7/12 again lcm
= 5/12
or
1/4 of 24 inches means 1/4×24= 6 inches
1/3 of 24 inches, then 1/3×24= 8 inches
therefore, rest of the months get
= 24-(6+8)
=24-14
=10 inches
It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.
Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is
<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)
The cosine of the angle between the vectors can be obtained from the dot product identity,
<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>) ==> cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)
so that
<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)
For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is
<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))
==> <em>W</em> ≈ 5.12 J
(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).