Answer:
Step-by-step explanation:
<u>1 and 2/3 minus 4/5</u>
- 1 2/3 - 4/5 =
- 5/3 - 4/5 =
- 25/15 - 12/15 =
- 13/15
Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"
Suppose n is even. That means n = 2k where k is any integer.
Square both sides
n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)
The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even.
So this contradicts the initial statement which forces n to be odd.
Answer:
h=4/3 r Base area =27(pi)/16 h^2
Step-by-step explanation:
The Volume of the following solids are
Cylinder: (pi)r^2 h
Sphere:4/3 (pi) r^3
Pyramid: 1/3(base area) h
Assuming that the Volume is the same in all three solids
(pi)r^2 h= 4/3 (pi) r^3
Simplify
h=4/3 r
(pi) r^2 h= 1/3(Base area)h
Simplify
(pi) r^2= 1/3 base area
substitute r=3/4 h
(pi) 9/16 h^2=1/3 base area
Base area =27(pi)/16 h^2
Well $16 times 16 would be $256.
If each shirt costs $1 then she could buy 16 shirts.
Answer:
sin θ/2=5√26/26=0.196
Step-by-step explanation:
θ ∈(π,3π/2)
such that
θ/2 ∈(π/2,3π/4)
As a result,
0<sin θ/2<1, and
-1<cos θ/2<0
tan θ/2=sin θ/2/cos θ/2
such that
tan θ/2<0
Let
t=tan θ/2
t<0
By the double angle identity for tangents
2 tan θ/2/1-(tanθ /2)^2 = tanθ
2t/1-t^2=5/12
24t=5 - 5t^2
Solve this quadratic equation for t :
t1=1/5 and
t2= -5
Discard t1 because t is not smaller than 0
Let s= sin θ/2
0<s<1.
By the definition of tangents.
tan θ/2= sin θ/2/ cos θ/2
Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.
cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2
Solve for s.
s/-√1-s^2 = -5
s^2=25(1-s^2)
s=√25/26 = 5√26/26
Therefore
sin θ/2=5√26/26=0.196....
