Use following substitutions:
<span>r cosθ = x </span>
<span>r sinθ = u </span>
<span>r² = x² + y² </span>
<span>r = 8 cosθ + 4 sinθ </span>
<span>Multiply both sides by r </span>
<span>r² = 8 r cosθ + 4 r sinθ </span>
<span>x² + y² = 8x + 4y </span>
<span>This is equation of circle. We can put in standard form: </span>
<span>x² − 8x + y² − 4y = 0 </span>
<span>x² − 8x + 16 + y² − 4y + 4 = 16 + 4 </span>
<span>(x − 4)² + (y − 2)² = 20 </span>
<span>Circle centered at point (4, 2) with radius = √20</span><span />
Answer:
7 people purchase the items and they used 53 coins
Step-by-step explanation:
Let x represent the number of people.
Let y be the number of coins needed to purchase the items.
If each person pays 8 coins, the surplus is 3 coins. This is illustrated below:
8x = y + 3 (1)
if each person gives 7 coins, the deficiency is 4 coins. This is illustrated below:
7x = y — 4 (2)
Solving by elimination method: subtract equation(2) from equation (1). This is illustrated below:
8x = y + 3 (1)
— (7x = y — 4) (2)
x = 7.
Next, Substituting the value of x into any of the equation to obtain y. In this case I will be using equation 1 as illustrated below:
8x = y + 3 (1)
8(7) = y + 3
56 = y + 3
Collect like terms
y = 56 — 3
y = 53
Therefore, 7 people purchase the items and they used 53 coins
If he turns clockwise half a turn, he would be face north east
A bar graph is a chart that uses bars to show comparisons of different types of data. The bars can either be horizontal or vertical. They are always straight if I’m not mistaken
