x = number of adult tickets
y = number of children tickets
9x + 6y = 1053
x+y = 127 so x = 127 - y
replace x = 127 - y into 9x + 6y = 1053
9(127 - y) + 6y = 1053
1143 -9y + 6y = 1053
-3y = 1053 -1143
-3y = -90
y = 30
x = 127 - 30
x = 97
answer: 97 adults and 30 children
Answer:
The first occurence of t for which x = 0 is t = 0.5.
Step-by-step explanation:
The harmonic motion is described by the following equation.

What is the first occurrence of a value of t for which x = 0?
This is t when
. So




The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.





The first occurence of t for which x = 0 is t = 0.5.
Answer:
500 pounds
Step-by-step explanation:
Let the pressure applied to the leverage bar be represented by p
Let the distance from the object be represented by d.
The pressure applied to a leverage bar varies inversely as the distance from the object.
Written mathematically, we have:

Introducing the constant of proportionality

If 150 pounds is required for a distance of 10 inches from the object

Therefore, the relationship between p and d is:

When d=3 Inches

The pressure applied when the distance is 3 inches is 500 pounds.
($3.91)(0.09) = $0.3519
$3.91 + 0.3519 = $4.2619 per gallon
if you're looking for the total expense next year:
($4.2619)(370 gallons) = $1,576.903