Answer:
a,d
Step-by-step explanation:
As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.
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:
$15.63 ≤ x ≤ $54.365
Step-by-step explanation:
Profit of the phone company is modeled by the equation,
p(x) = -50x² + 3500x - 2500
For the profit of at least $40000,
-50x² + 3500x - 2500 ≥ 40000
-50x² + 3500x ≥ 40000 + 2500
-50x² + 3500x ≥ 42500
-x² + 70x ≥ 850
x² - 70x + 850 ≤ 0
By quadratic formula,
x - intercept of the inequality will be,
x = 
x = 
x = 15.635, 54.365
Therefore, $15.635 ≤ x ≤ $54.365 will be the range of cost for which profit will be at least $40000.
