Answer:
1/12
Steps:
1 - 2/3 = 1/3
1/3 / 4 = 1/3 × 1/4 = 1/12
<span> a∥e , m∥n , and m∠2 = 117°
<5 = 180 - <2
<5 = 180 - 117
<5 = 63
answer
</span><span>63°</span>
<span>In triangle XYZ,
angle X=46 degrees,
XZ = 10 units and
YZ=8 units.
We will find the length of XY using cosine rule:
According to cosine rule:
a² = b² + c² - 2bc cosA (the figure is attached)
Here, A = 46 degree.
a = 8 units.
b <span>= ?
</span>c = 10 units.
</span>⇒ b² = c² - a² -2bc cosA
⇒ b² = 100 - 64 - 160*cos(46)
⇒ b² = 100 - 64 - 160*0.69
⇒ b² = 100 - 64 - 110.4
⇒ b² = 100 - 64 - 110.4
⇒ b² = 74.4
or b = 8.62 units.
or b = 8 untis approximately.
Answer:
60 professors and 168 lecturers
Step-by-step explanation:
What you have is a 2 equations system with 2 unknown variables.
Let X be the number of professors and Y be the number of lecturers. As the total of both is 228:
X + Y = 228
Then, as there are 5 professors for every 14 lecturers:
5 X = 14 Y or X = (14/5) Y
Replacing this last value of X on the first equation:
(14/5) Y + Y = 228
(14/5) Y + (5/5) Y = 228
(19/5) Y = 228
Y = 228 * (5/19)
Y = (228*5)/19
Y = 1140 / 19
Y = 60
Then we can find X:
X = (14/5) Y = (14/5) * 60 = 168
X = 168
:)
Answer:
<h2><u>0.384</u></h2>
Step-by-step explanation:
By Pythagoras Theorem,
OM = √(4² + 3²) = √(16 + 9) = √25 = <u>5</u>
And,
OL = √(12² + 5²) = √(144 + 25) = √169 = <u>13</u>
Now,
sin L =
=
= <u>0.384</u>