Answer:
1. Arthur is about 54 meters away from Cameron.
2. Jamie is about 56 meters away from Cameron.
3. Arthur is closer to Cameron.
Step-by-step explanation:
We have been given the locations of Cameron (70,10), Arthur (20,30) and Jamie (45,60) on the the grid in meters.
1. To find the distances of Arthur and Jamie from Cameron we will use distance formula.
Therefore, the distance Arthur is about 54 meters away from Cameron.
2. Let us find the distance between Cameron and Jamie.
Therefore, Jamie is about 56 meters away from Cameron.
3. We can see that 56 is greater than 54, therefore, Arthur is closer to Cameron.
Answer
1946.8 cm
Step-by-step explanation:
you first need to find the circumference of the tire. to do this you use the formula C=d(3.14)
you plug in the 62 to the d
62 times 3.14 = 194.68
and multiply that by 10 because it is 10 revolutions to get 1946.8 cm
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Ksju [112]
Well, here's one way to do it at least...
<span>For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). </span>
<span>Let P=(4,0) be the projection of B onto the x-axis. </span>
<span>Let Q=(-3,0) be the projection of C onto the x-axis. </span>
<span>Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). </span>
<span>Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). </span>
<span>Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. </span>
<span>||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) </span>
<span>||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) </span>
<span>Using the Law of Cosines... </span>
<span>||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) </span>
<span>||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) </span>
<span>||a||^2 = 86 - 36 </span>
<span>||a||^2 = 50 </span>
<span>||a|| = sqrt(50) </span>
<span>Now apply the Law of Sines to find the other two angles. </span>
<span>||b|| / sin(B) = ||a|| / sin(A) </span>
<span>sqrt(41) / sin(B) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(41) / sqrt(50) = sin(B) </span>
<span>.8222 = sin(B) </span>
<span>asin(.8222) = B </span>
<span>55.305 = B </span>
<span>Two down, one to go... </span>
<span>||c|| / sin(C) = ||a|| / sin(A) </span>
<span>sqrt(45) / sin(C) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(45) / sqrt(50) = sin(C) </span>
<span>.8614 = sin(C) </span>
<span>asin(.8614) = C </span>
<span>59.470 = C </span>
<span>So your three angles are: </span>
<span>A = 65.225 </span>
<span>B = 55.305 </span>
<span>C = 59.470 </span>
By definition, the arc length is given by:
arc = (theta) * (R)
Where,
theta: central angle
R: radius
Substituting values we have:
arc = (π / 5) * (2.8)
Rewriting we have:
arc = ((3.14) / 5) * (2.8)
arc = 1.7584 cm
Round to the hundredth:
arc = 1.76 cm
Answer:
the arc length is:
arc = 1.76 cm
Hey!
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Solution:
Ratio is 4/1
Add.
4 + 1 = 5
Divide.
150 / 5 = 30
Multiply for Ivan.
30 x 4 = 120
30 x 1 = 30
Check.
120 + 30 = 150
Subtract.
120 - 30 = 90
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Answer:
Ivan has £90 more than Tanya has!
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Hope This Helped! Good Luck!
