The general formula for an arithmetic sequence is:
<span>a(n) = a + d(n - 1) </span>
<span>a : first term </span>
<span>d : common difference (6) </span>
<span>n : number of the term </span>
<span>In your example, you are told the 6th term is 22. </span>
<span>a(6) = a + 6(6 - 1) = 22 </span>
<span>a + 30 = 22 </span>
<span>a = 22 - 30 </span>
<span>a = -8 </span>
<span>So now you have the general formula: </span>
<span>a(n) = -8 + 6(n - 1) </span>
<span>If you like you can simplify it: </span>
<span>a(n) = -8 + 6n - 6 </span>
<span>a(n) = 6n - 14 </span>
<span>Then you can plug in n = 50: </span>
<span>a(50) = 6(50) - 14 </span>
<span>= 300 - 14 </span>
<span>= 286</span>
Answer:
x ≤ 1000 W
Step-by-step explanation:
Since the circuit becomes overloaded when the load exceeds 1800W and the toaster uses 800 W.
Let the additional watts be x
Therefore;
800 + x ≤ 1800
x ≤ 1800 -800
x ≤ 1000 W
Answer: 1406.25
Step-by-step explanation:
The soccer field at a park is 9,000 square yards. The soccer field takes up 6 2/5 square inches on the map of the park. How many square yards does 1 square inch on the map represent? Show your work. Help me pls
Given that:
Area of soccer field = 9000 sq yards
Soccer field takes up 6 2/5 square inches on the map of park
Hence,
9000 yd² = 6 2/5 in²
Let 1 in² on map = m
9000 yd² = 32/5 in² - - - (1)
m = 1 in² - - - (2)
Cross multiply ;
6.4 * m = 9000
m = 9000/6.4
m = 1406.25
Hence,
1 in² on map = 1406.25 feet²
900
Using integration, it is found that the area of the shaded region is of units squared.
<h3>How is the area of a shaded region found?</h3>
- The area of shaded region, between two curves and , considering , between x = a and x = b, is given by the following integral:
In this problem, the curves are:
The limits of integration are: .
Hence:
Applying the power properties of integration:
Finally, applying the Fundamental Theorem of Calculus:
The area of the shaded region is of units squared.
To learn more about integration, you can take a look at brainly.com/question/20733870
<span>y = 2x + 20. The answer is A. Explanation: Vlad spends a known amount of time on his history homework (20). On top of it, he also spends an unknown amount of time on solving a number of math problems (x). Each problem takes two minutes to solve, so the amount of time that he spends solving math problems is 2*x or 2x. In total (y), Vlad spends 20 + 2x amount of time on his homework. So y = 2x + 20, where y is clearly greater or equal to 20 and x is greater or equal to 0.</span>