Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
Answer:
Step-by-step explanation:
Possible:
Rolling a 1
Rolling a number less than 7
Rolling an even number
Impossible:
Rolling a number greater than 10
Rolling an 8
Answer:
0.44ft/hr
Step-by-step explanation:
Given parameters:
Quantity of rainfall = 8inches
1ft = 12inches
so;
= 0.67ft
Time = 
hr
Unknown:
Rate of rainfall expressed in ft/hr = ?
Solution:
The rate of the rainfall is given as;
Rate = 
Rate = 
= 0.44ft/hr
Complete question :
Sam knows that his MP3 player has 40% of its battery life left and that the battery
charges by an additional 12 percentage points every 15 minutes. What percent of
the mp3's battery will be charged when Sam and his family leave? If mp3 was plugged in an hour before his family plan to leave.
Answer:
88%
Step-by-step explanation:
Time before leaving = 1hour
Current percentage = 40%
Charge rate = 12% every 15 minutes
Therefore,
Charge rate per minute :
12% / 15 = 0.8% per minute
Charge recieved after one hour (60 minutes) :
0.8% * 60
= 48%
Therefore, total charge after just before leaving is:
Current percentage + percentage received
40% + 48%
= 88%
