-3 3/4
Decimal form: -3.75
Answer:
See proof below
Step-by-step explanation:
show that
sinx/1+cosx=tanx/2
From LHS
sinx/1+cosx
According to half angle
sinx = 2sinx/2 cosx/2
cosx = cos²x/2 - sin²x/2
cosx = cos²x/2 - (1- cos²x/2)
cosx = 2cos²x/2 - 1
cos x + 1 = 2cos²x/2
Substitute into the expression;
sinx/1+cosx
= (2sinx/2 cosx/2)/2cos²x/2
= sinx.2/cos x/2
Since tan x = sinx/cosx
Hence sinx/2/cos x/2 = tan x/2 (RHS)
This shows that sinx/1+cosx=tanx/2
Answer:
Step-by-step explanation:
Considering the geometric sequence
As the common ratio '
' between consecutive terms is constant.
The general term of a geometric sequence is given by the formula:
where 
is the initial term and the common ratio.
Putting 
, 
and in the general term of a geometric sequence to determine the 12th term of the sequence.
∵ 
Therefore,
Answer:
Number of pounds of cashews = x = 14.96 pounds
Number of pounds of Brazil nuts = y = 19.04 pounds
Step-by-step explanation:
Let us represent:
Number of pounds of cashews = x
Number of pounds of Brazil nuts = y
The nut shack sells cashews for $6.00 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 34 pound mixture that sells for $5.44 per pound
Our system of equations is given as:
x + y = 34...... Equation 1
x = 34 - y
6x + 5y = 34 × 5.44
6x + 5y = 184.96.......Equation 2
Ww substitute : 34 - y for x in Equation 2
6(34 - y) + 5y = 184.96
204 - 6y + 5y = 184.96
Collect like terms
- 6y + 5y = 184.96 - 204
-y = -19.04
y = 19.04 pounds
Solving for x
x = 34 - y
x = 34 - 19.04
x = 14.96 pounds
Number of pounds of cashews = x = 14.96 pounds
Number of pounds of Brazil nuts = y = 19.04 pounds
Yes. For example x=-1 and y=-1/2
