Find the area of the CD. (I used P for pi, too lazy @
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A=Pr² - Pr²
radius of the small hole in the middle, 0.75cm
radius of the CD, 6cm
A=3.14*6²-3.14*0.75²
A=111.27375cm²
The Approximate area of the CD is 111.27cm²
Answer:
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Step-by-step explanation:
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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>
Answer:
2.1
Step-by-step explanation:
6.3 + 5.8(4 − 3.5(2)) + 6.6(2)
6.3+5.8(4−7)+(6.6)(2)
6.3+(5.8)(−3)+(6.6)(2)
6.3+−17.4+(6.6)(2)
-11.1+(6.6)(2)
−11.1+13.2
2.1
Answer: (2, 5)
Step-by-step explanation:
y = 2x + 1 y = 4x − 3
Eliminate the equal sides of each equation and combine.
2x + 1 = 4x − 3
Solve 2x + 1 = 4x − 3 for x.
Move all terms containing x to the left side of the equation.
Subtract 4x from both sides of the equation.
2x + 1 − 4x = −3
Subtract 4x from 2x.
−2x + 1 = −3
Move all terms not containing x to the right side of the equation.
Subtract 1 from both sides of the equation.
−2x = −3 − 1
Subtract 1 from −3.
−2x = −4
Divide each term by −2 and simplify.
x = 2
Evaluate y when x = 2.
Substitute 2 for x. y = 4 (2) − 3
Simplify 4 (2) − 3.
Multiply 4 by 2.
y = 8 − 3
Subtract 3 from 8.
y = 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
(2, 5)
The result can be shown in multiple forms.
Point Form:
(2, 5)
Equation Form:
x = 2, y = 5