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
Set the number of chickens as x and number of cows as <span>y
</span>so the farmer has total 28 animals
so x+y=28
you know that since the animals are healthy
chickens will have 2 legs and
cows will have 4 legs
the total number of legs are 64
so 2x+4y=64
since you want to find the number of cows
so from the first equation <span>x+y=28
</span>we will get another equation <span>x=28-y
</span>then plug into <span>2x+4y=64
2(28-y)+4y=64
56-2y+4y=64
56+2y=64
-56 -56
2y=8
y=4
</span>
Answer:
28.3 centimeters and 21 centimeters
Step-by-step explanation:
28.3 + 0.05) cm, so 28.25 cm ≤ length < 28.35 cm.
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