Given was <span><span>cotθ</span>=−<span>21</span></span> and cot is the reciprocal of tan
therefore
<span><span>tanθ</span>=<span>1<span>−2</span></span></span>
solve for the hypotenuse c since t he opposite side <span>a=1</span> and the adjacent sides <span>b=−2</span> were already given. that is,
<span><span>c2</span>=<span>a2</span>+<span>b2</span></span>
<span>c=<span>√<span><span><span>(1)</span>2</span>+<span><span>(−2)</span>2</span></span></span></span>
<span>c=<span>√5</span></span>
Solving for <span>sinθ</span>
<span><span>sinθ</span>=<span><span>oppositesides</span><span>hypoteνse</span></span>=<span>ab</span></span>
<span><span>sinθ</span>=<span>1<span>√5</span></span></span> need to rationalize
<span><span>sinθ</span>=<span>(<span>1<span>√5</span></span>)</span>×<span><span>√5</span><span>√5</span></span></span>
<span><span>sinθ</span>=<span><span>√5</span>5</span></span>
Note that the adjacent side of the angle is <span>−2</span> so the angle
θ is found in the <span>2nd</span> quadrant.
It is currently 03:00 PM, the family will reach at 03:00+4.5 = 07:30 PM
Step-by-step explanation:
We have to calculate the speed first to find the time it will take the family to complete the trip.
Given
Distance = d = 25 miles
Time = t = 1/2 hours = 0.5 hours
Now,
Distance remaining = 225 miles
Speed = 50 miles per hour
As we see that the time required to complete the journey is 4.5 hours.
It is currently 03:00 PM, the family will reach at 03:00+4.5 = 07:30 PM
Keywords: Speed, Distance
Learn more about speed at:
#LearnwithBrainly
This an { } solution because the absolute value is always a positive number unless there is a negative sign in front of the brackets.
hope this helps :)
Step-by-step explanation:
Given the average of 8 numbers = 56.
Then the Total sum of 8 numbers = 56 * 8
= 448.
Sum of 1st three numbers = 49 + 57 + 72
= 178.
So, the total = 448 - 178
= 270.
Average of the other 5 numbers = 270/5
= 54.
Verification:
178 + 270 = 448/8
= 56.
