Answer:
B
Step-by-step explanation:
find the the surface area of one corner
Answer:
Since Paula has her own business of making cakes for special occasions, and the total price (P) of one of Paula's cakes is represented by the equation P = 0.75S +10, where S is the number of people the cake serves, for determine what does the 0.75 represent in this situation and what does the 10 represent in this equation, the following mathematical reasoning must be carried out:
P is the price of the cake
S is the number of servings
Therefore, 0.75 is the value of each serving, which can be variable (the number of servings can vary)
In turn, 10 is the fixed cost of each cake.
Answer:
First: $65
Second: $115
Step-by-step explanation:
We write equations for each part of this situation.
<u>The Total Charge</u>
Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.
<u>The Sum of the Rates</u>
Since the first's rate is a and the second is b, we can write a+b=180 since their sum is 180.
We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.
For a+b=180, rearrange to b=180-a and substitute into 15a+5b=1550.
15a + 5 (180-a)=1550
15a+900-5a=1550
10a+900-900=1550-900
10a=650
a=$65 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
65+b=180
65-65+b=180-65
b= $115 was charged by the second mechanic
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
Solution: Let 
be the number of birds and 
be the number of cats.
Therefore, there were 14 birds at the shelter on Friday
