Elena's distances and times for a training run are given by the equation , where represents distance in miles and represents tim
1 answer:
Answer:
Elena's run for 1.17 miles in ten minutes
Step-by-step explanation:
From the question
y = 8.5 x ; where x is Distance in miles, and y is time in minutes
and y= 10 minutes
thus on substituting the respected values we get
10 = 8.5 x
⇒ x = = 1.17 miles
Therefore Elena's run for 1.17 miles in ten minutes
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Consider the picture attached.
From right triangle trigonometry:
tan(α)=(opposite side)/(adjacent side)=15/67=0.2239
using a scientific calculator we find that arctan(0.2239)=12.62°
thus α=12.62°, is the angle that the vector makes with the positive x-axis.
The angle made with the + y-axis is 12.62°+90°=102.62°.
The length of the vector v can be determined using the Pythagorean theorem:
Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.
This means that the x and y components will also be divided by 68.8, by proportionality.
So, the unit vector in the direction of v is:
<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>
Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j
From right triangle trigonometry:
tan(α)=(opposite side)/(adjacent side)=15/67=0.2239
using a scientific calculator we find that arctan(0.2239)=12.62°
thus α=12.62°, is the angle that the vector makes with the positive x-axis.
The angle made with the + y-axis is 12.62°+90°=102.62°.
The length of the vector v can be determined using the Pythagorean theorem:
Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.
This means that the x and y components will also be divided by 68.8, by proportionality.
So, the unit vector in the direction of v is:
<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>
Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j