Answer:
different answers in step-by-step
Step-by-step explanation:
100 mph
100mi:1hr
100mi/1hr
Answer:
13) Angle A is 30°
14) Angle A is 45°
15) Angle A is 40°
16) Angle A is 40.5°
Step-by-step explanation:
By the angle sum theorem for the interior angles of a triangle, we have;
13) 130° + 2·x + 3·x = 180°
∴ 2·x + 3·x = 180° - 130° = 50°
2·x + 3·x = 5·x = 50°
x = 50°/5 = 10°
∠A = 3·x = 3 × 10° = 30°
∠A = 30°
14) 3·x + 9 + 4·x + 9 + 78° = 180°
7·x + 18 + 78° = 180°
7·x = 180° - (18 + 78)° = 180° - 96° = 84°
x = 84°/7 = 12°
∠A = 3·x + 9 = 3 × 12° + 9 = 45°
∠A = 45°
15) 90° + x + 51 + x + 61 = 180°
∴ x + 51 + x + 61 = 180° - 90° = 90°
2·x + 112 = 90°
2·x = (90 - 112)° = -22°
x = -22°/2 = -11°
x = -11°
∠A = x + 51 = -11° + 51 = 40°
∠A = 40°
16) x + 79 + x + 49 + 70° = 180°
x + x = (180 - 70 - 79 - 48)° = -17°
2·x = -17°
x = -17°/2 = -8.5°
x = -8.5°
∠A = x + 49 = (-8.5 + 49)° = 40.5°
∠A = 40.5°.
I've answered your other question as well.
Step-by-step explanation:
Since the identity is true whether the angle x is measured in degrees, radians, gradians (indeed, anything else you care to concoct), I’ll omit the ‘degrees’ sign.
Using the binomial theorem, (a+b)3=a3+3a2b+3ab2+b3
⇒a3+b3=(a+b)3−3a2b−3ab2=(a+b)3−3(a+b)ab
Substituting a=sin2(x) and b=cos2(x), we have:
sin6(x)+cos6(x)=(sin2(x)+cos2(x))3−3(sin2(x)+cos2(x))sin2(x)cos2(x)
Using the trigonometric identity cos2(x)+sin2(x)=1, your expression simplifies to:
sin6(x)+cos6(x)=1−3sin2(x)cos2(x)
From the double angle formula for the sine function, sin(2x)=2sin(x)cos(x)⇒sin(x)cos(x)=0.5sin(2x)
Meaning the expression can be rewritten as:
sin6(x)+cos6(x)=1−0.75sin2(2x)=1−34sin2(2x)
The simplified form would be -4×^2-13x+9
In order to convert centimeters to inches, you use the following equation:
1 inches = 2.54 cm
If you have to convert, for example, 4 inches, you proceed as follow:
4 inches* (2.54cm/1 inches) = 10.16 cm
That is, you multiply the quantity that you want to convert, by the quotient between 2.54cm and 1 inches.
