Answer:
B° = 46°
b = 23.8
c = 33.1
given:
- opposite: 23
- hypotenuse: c
- adjacent: b
- angle: 44°
Lets find B:
B + 90° + 44° = 180°
B = 180° - 134°
B = 46°
Lets find c:
using sine rule:
Lets find b:
using tan rule:
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Answer:
(a) P = 2x + 2r + 2πr
(b) x = ½(P - 2r - 2πr)
(c) x = 123 feet
Step-by-step explanation:
See Attachment for sketch of the track
Solving for (a): Perimeter of the track
This is calculated by adding the perimeter of the rectangle to the 2 semicircles as follows.
P = Perimeter of Rectangle + Perimeter of 2 Semicircles
P = 2(x + r) + 2 * πr
[Where r is the radius of both semicircles]
Open bracket
P = 2x + 2r + 2πr
Solving for (b): Formula for x
P = 2x + 2r + 2πr
Make x the subject of formula
2x = P - 2r - 2πr
Divide both sides by 2
x = ½(P - 2r - 2πr)
Solving for (c): the value of x when r = 50 and P = 660
Substitute the given values in the formula in (b) above
x = ½(P - 2r - 2πr)
x = ½(660 - 2 * 50 - 2π * 50)
x = ½(660 - 100 - 100π)
x = ½(560 - 100π)
Take π as 3.14
x = ½(560 - 100 * 3.14)
x = ½(560 - 314)
x = ½ * 246
x = 123 feet
Given problem;
Inequality equation;
< 6
Before we solve, let us first translate this problem.
It simply states that for what value(s) of x will the expression be less than 6.
To find this value, we can simply carry out the normal mathematical simplification.
Simply multiply both sides by 16 to reduce the fraction;
16 x () < 6 x 16
On the left hand side, 16 will cancel out;
x < 96
Any value for which x is less than 96 will make the solution of this problem less than 6.
For example, 95;
= 5.93
This value is less than 6