B) multiplication of improper fractions: 4/3 x 4/3
expressed as improper fraction: 16/3
product expressed as mixed number: 5 1/3
why: 4 x 4 = 16, keeping the denominator (3) is 16/3. 16 isn't a multiple of 3, the closest is 15, and 15 / 3 is 5, but we since we have 16, we have one left, so it'd be 5 1/3
c) multiplication of improper fractions: 7/3 x 3/2
expressed as improper fraction: 21/6
product expressed as mixed number: 3 3/6 = 3 1/2
why: 7 x 3 = 21, 2 x 3 is 6, combine it, 21/6. multiple of 6 that is closest to 21 is 18. 18 / 6 = 3. we have 3 numbers left over. (21 - 18 = 3) so it's the 3 that we get, plus the 3 that we have left, is 3 3/6
d) multiplication of improper fractions: 11/6 x 7/5
expressed as improper fraction: 77/30
product expressed as mixed number: 2 17/30
why: 11 x 7 = 77, 6 x 5 = 30, combine it, 77/30. 77 goes into 30 twice. (30 x 6 = 60, can't add another 30, because its more than 77) we have 17 numbers left over, (77 - 60 = 17) so it's 2 17/30. can't reduce 17/30 because 17 doesn't have any common factors with 30. hope i helped!
Answer: The sides length are 8.32 cm
Step-by-step explanation:
An equilateral triangle has all his sides of the same lenght, so we assume that the triangle has an L lenght in his sides.
The area of a triangle is
where the base is L, the Area is 30 and an unknown height.
To determine the height, we cut the triangle in half and take one side. By simetry, one side has a base of
, a hypotenuse of L and a the unknown height.
Then we apply the <em>Pythagoras theorem</em>, this states that <em>in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides</em>, or,
Where one c is
and the other is the height.
Then we find one of the c of the equation wich will be the height.


Finally, we use the triangle area mentioned before an find the value of L.

The length of a curve
given parametrically by
over some domain
is

In this case,


So we have

and the arc length is

We have

where
is any integer; this tells us
on the interval
and
on
. So the arc length is



You would use the simple format SOH-CAH-TOA
SOH: sine = opposite/hypotenuse
CAH: cosine = adjacent/hypotenuse
TOA: tangent = opposite/adjacent
----
So for this problem to find c you would use this equation:
sin42= c/7
7sin42=c
c=4.68
Then for d you would use this equation:
tan48=d/4.68
4.68tan48=d
=5.197
Hope this helps :)