Answer:
Step-by-step explanation:
Step 1:-
We have c1(t) = e^ t i + (sin(t))j + t³k
and c2(t) = e^−t i + (cos(t))j − 6t³k.
By adding c1(t) and c2(t):
c1(t)+c2(t) = e^ t i + (sin(t))j + t³k + e^−t i + (cos(t))j − 6t³k
Now, employing the derivative formula:
Next, differentiate with respect to 't'
By factoring out i, j, and k terms, we arrive at:
The x intercept is at (12,0). To find it, start with the equation 1.5x + 4.5y = 18, and subtract 1.5x from both sides. This gives you 4.5y = -1.5x + 18. Next, divide everything by 4.5, resulting in y = -1/3x + 4. Hence, the slope of the line is -1/3, and the y intercept is at (0,4). To determine the x intercept, set y to 0. Plugging this into the equation yields: 1.5x + 4.5(0) = 18, simplifying to 1.5x = 18. Dividing both sides by 1.5 gives x = 12.
Complete question;
A booster club financed pizzas for an end-of-season celebration. The cost was $13 for each pepperoni pizza and $11 for each plain pizza. They purchased a
total of 18 pizzas for the event, totaling $212.
Organize the numbers into an equation that represents this scenario with x being the number of pepperoni pizzas and y being the number of plain pizzas purchased.
Answer:
13x + 11y = 212
Step-by-step explanation:
Two varieties of pizza were purchased: pepperoni and plain. The pepperoni variety cost $13 each while the plain one cost $11 each. In total, they bought 18 pizzas.
The overall expenditure on the pizzas was $212.
total number of pizzas = 18
total amount spent on pizzas = $212
x represents the number of pepperoni pizzas
y represents the number of plain pizzas
The cost of the pepperoni pizzas is derived by multiplying the number of pizzas by their individual price. The same calculation applies for the plain pizzas.
Therefore, by summing the costs of both pizza types, we arrive at the total price for the pizzas.
13x + 11y = 212
To find the unit rate, we simply divide 4 by 2.
4 ÷ 2 = 2
This means the artist can complete 2 paintings every hour, establishing the unit rate as 2 paintings per hour.
Hope this assists
-AaronWiseIsBae
