Answer:
Equation:(4 2/5)/2/5=? ; estimate: a
little more than 10 magazines; answer:
11 magazines in the stack.
Step-by-step explanation:
Answer:
102 1/3
Step-by-step explanation:
To find the 6th term, add the common difference to the 5th term:
103 + (-6 2/3) = 102 1/3
The statements which are correct about the equation of circle are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is .
Given the equation of circle be .
We are required to find the appropriate statements related to the equation .
can be written as under:
-9=0
Equation of a circle usually in the form in which a is radius.
From the comparison of both the equations we get that radius is 3 units.
From the equation point will be (1,0). It is on the x axis.
Hence the statements which are correct about the equation of circle are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is .
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Answer:
the critical points are (0,0) , (0, 20), (12, 0) , (4,16)
Step-by-step explanation:
To consider the autonomous system
The critical points of the above system can be derived by replacing x' = o and y' = 0.
i.e.
x = 0 or 24 - 2x - y = 0 ----- (1)
Also
y( 20 -y - x) = 0
y = 0 or 20 - y - x = 0 ----- (2)
By solving (1) and (2);
we get x = 4 and y = 16
Suppose x = 0 from (2)
y = 20
Also;
if y = 0 from (1)
x = 12
Thus, the critical points are (0,0) , (0, 20), (12, 0) , (4,16)
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