Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for sine
sin2x = 2sinxcosx
Consider left side
cos20°cos40°cos80°
=
(2sin20°cos20°)cos40°cos80°
=
(2sin40°cos40°)cos80°
=
(sin80°cos80° )
=
(2sin80°cos80° )
=
. sin160°
=
. sin(180 - 20)°
=
. sin20°
=
= right side , thus proven
Answer:
50 degrees
Step-by-step explanation:
180-130=50
Relation Extremes equal means.
4×30÷22.
Or
(22)*2=4×30.=120.
484=120
484/120
111 yards
Explanation
Step 1
to solve this we need to know the equivalence
![\begin{gathered} 3\text{ ft= 1 yd} \\ 3\text{ ft}\leftrightarrow1\text{ yd} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%203%5Ctext%7B%20ft%3D%201%20yd%7D%20%5C%5C%203%5Ctext%7B%20ft%7D%5Cleftrightarrow1%5Ctext%7B%20yd%7D%20%5Cend%7Bgathered%7D)
Now, we can apply a rule of three
let x represents the number of yards in 333 ft, so
so
![\begin{gathered} if \\ 3\text{ ft}\rightarrow\text{ 1 yd} \\ \text{then} \\ 33\text{ ft}\rightarrow x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20if%20%5C%5C%203%5Ctext%7B%20ft%7D%5Crightarrow%5Ctext%7B%201%20yd%7D%20%5C%5C%20%5Ctext%7Bthen%7D%20%5C%5C%2033%5Ctext%7B%20ft%7D%5Crightarrow%20x%20%5Cend%7Bgathered%7D)
as the ratio is the same, we have a proportion
![\begin{gathered} \frac{3\text{ ft}}{1\text{ yd}}=\frac{33\text{ ft}}{x\text{ yd}} \\ \frac{3}{1}=\frac{33}{x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B3%5Ctext%7B%20ft%7D%7D%7B1%5Ctext%7B%20yd%7D%7D%3D%5Cfrac%7B33%5Ctext%7B%20ft%7D%7D%7Bx%5Ctext%7B%20yd%7D%7D%20%5C%5C%20%5Cfrac%7B3%7D%7B1%7D%3D%5Cfrac%7B33%7D%7Bx%7D%20%5Cend%7Bgathered%7D)
Step 2
now, solve for x
![\begin{gathered} \frac{3}{1}=\frac{333}{x} \\ \text{cross multiply} \\ 3\cdot x=333\cdot1 \\ 3x=333 \\ \text{divide both } \\ \frac{3x}{3}=\frac{333}{3} \\ x=111 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B3%7D%7B1%7D%3D%5Cfrac%7B333%7D%7Bx%7D%20%5C%5C%20%5Ctext%7Bcross%20multiply%7D%20%5C%5C%203%5Ccdot%20x%3D333%5Ccdot1%20%5C%5C%203x%3D333%20%5C%5C%20%5Ctext%7Bdivide%20both%20%7D%20%5C%5C%20%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B333%7D%7B3%7D%20%5C%5C%20x%3D111%20%5Cend%7Bgathered%7D)
so, the answer is 111 yards
I hope this helps you
Answer:
Thomas' real income now is half that it was (nominal income decreased by half or prices doubled)
Step-by-step explanation:
If you graph both cases you will see that the shift is parallel between one case and the other.
Changes in relative prices (this is, if only one of the goods change prices), would cause a rotation in the budget line