A and b are legs
a^2+b^2=c^2
lets say
a>b
so
a=13+3b
c=14+3b
a^2+b^2=c^2
(13+3b)^2+b^2=(14+3b)^2
9b^2+78b+169+b^2=9b^2+84b+196
10b^2+78b+169=9b^2+84b+196
minus 9b^2 both sides
b^2+78b+169=84b+196
minus 84b both sides
b^2-6b+169=196
minus 196 both sides
b^2-6b-27=0
factor
(b+3)(b-9)=0
set to zero
b+3=0
b=-3, false, dimentions cannot be negative
b-9=0
b=9
shorter leg is 9
a=13+3b
a=13+3(9)
a=13+27
a=40
c=14+3b
c=14+27
c=41
side legnths are
9in, 40in, 41in
We know that
if cos x is positive
and
sin x is negative
so
the angle x belong to the IV quadrant
cos x=5/13
we know that
sin²x+cos²x=1-------> sin²x=1-cos²x------> 1-(5/13)²---> 144/169
sin x=√(144/169)-------> sin x=12/13
but remember that x is on the IV quadrant
so
sin x=-12/13
Part A) <span>cos (x/2)
cos (x/2)=(+/-)</span>√[(1+cos x)/2]
cos (x/2)=(+/-)√[(1+5/13)/2]
cos (x/2)=(+/-)√[(18/13)/2]
cos (x/2)=(+/-)√[36/13]
cos (x/2)=(+/-)6/√13-------> cos (x/2)=(+/-)6√13/13
the angle (x/2) belong to the II quadrant
so
cos (x/2)=-6√√13/13
the answer Part A) is
cos (x/2)=-6√√13/13
Part B) sin (2x)
sin (2x)=2*sin x* cos x------> 2*[-12/13]*[5/13]----> -120/169
the answer Part B) is
sin(2x)=-120/169
Answer: The answe would be 26.70
Step-by-step explanation:
15% of 178
convert: 0.15 x 178
=26.70
:>
Answer:
B) 43.758
Step-by-step explanation:
Starting from the right side of the decimal point, the places are:
tenths
hundredths
thousands
Each time, you add a zero to the previous number (10 to 100 to 1000, etc), therefore the third decimal would be the thousandths place. If the next figure is a 5 or above, you round up, to the next decimal.
It is in form (x,y) (ususally)
7.5 and 12
there is something called a coordinate system where a line called the y axis runs vertically for infinity and a line perpendicular to it, crosses it. the other line is called the x axis which also extends for infinity
the point where they cross is point (0,0) or the origin
basically the numbers tell you how far you are from the axises
on the y axis, + numbers are up and - numbers are down
on the x axis, + numbers are to the right and - numbers are to the left
7.5=x and 12=y
+7.5 is positive
7.5 means that the point is 7.5 units to the right of the origin in relation to the x axis
12 is positive
12 means that the point is 12 units up from the origin in relation to the y axis
hope this helped. feel free to ask if its too confusing
