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katen-ka-za [31]
2 years ago
12

Work out the formula for the nth term of thequadratic sequence:5, 11, 19, 29​

Mathematics
1 answer:
Sladkaya [172]2 years ago
8 0

Answer:

n squared + 3n + 1

Step-by-step explanation:

5,11,19,29

Firstly look at the difference between each number. The first difference is 6 then 8 then 10 etc. After that you look at your created sequence - 6,8,10 etc. The difference is 2 each time. Then applying rules, you have to do the constant difference divided by 2 to get a coefficient of n squared. So in this case it's n squared because 2/2 = 1 so you don't have to place a 1 in front of the n squared. After you create a sequence from the n squared. That would be 1,4,9 etc. Then you need to see how to get from the sequence: 1,4,9 etc to your original sequence: 5,11,19 etc. So if you calculate it you will get 4,7,10 because firstly 5-1 = 4 then 11-4 = 7 etc. The sequence 4,7,10 is a linear sequence so the constant difference is 3 each time. So to get a nth term of a linear sequence you will start off as 3n then you will substitute 1 then 2 then 3 into the 3n. Therefore that would be 3,6 etc. So if you take the first substituted term, that would be 3 as said before then you will have to see how to get from the 3 to 4 so that is just adding 1. So the nth term of this linear sequence is 3n + 1. Check if it works at the end. So the overall nth term of the quadratic sequence is n squared as said before + 3n + 1.

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Step-by-step explanation:

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Polly’s Pasta and Pizza Supply sells wholesale goods to local restaurants. They keep track of revenue earned from selling kitche
dimaraw [331]

Complete question :

Polly’s Pasta and Pizza Supply sells wholesale goods to local restaurants. They keep track of revenue earned from selling kitchen supplies and food products. The function K models revenue from kitchen supplies and the function F models revenue from food product sales for one year in dollars, where t represents the number of the month (1 – 12) on the last day of the month.

K(t)=15t^3–312t^2+1600t+1100

F(t)=36t3–720t2+3800t–1600

In which month was her revenue from food products the greatest? The least?

Answer:

greatest revenue = 4384

Leat revenue = 400 ; October

Step-by-step explanation:

Using the model :

Claculating the revenue from. Food sales from January through December :

F(t)=36t^3–720t^2+3800t–1600

Put t = 1, 2, 3,.. 12 for January through December

t = 1

F(1)=36(1^3) - 720(1^2) + 3800(1) - 1600 = 1516

t = 2

F(2) = 36(2^3) - 720(2^2) + 3800(2) - 1600 = 3408

Inputting the t values up to 12 to cover for January thkorugh December :

We have the data:

t1 = 1516

t2 = 3408

t3 = 4292

t4 = 4384

t5 = 3900

t6 = 3056

t7 = 2068

t8 = 1152

t9 = 514

t10 = 400

t11 = 996

t12 = 2528

Hence, greatest revenue = 4384 (month of April)

Least revenue is at t10(October) ; Lowest revenue is at t 10 = 400

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2 years ago
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3 years ago
A photo 5 inches wide and 8 inches long is enlarged. How long is the new photo if it is How wide is the new photo if it is (1)12
ddd [48]

Answer:

1) 7.5 inches, 2) 12.5 inches, 3) 6.25 inches

Step-by-step explanation:

In the problem statement, it is stated that the original dimensions of the photo are 5 inches by 8 inches. The 3 parts of the problem are asking what the respective width of the new photo would be given a different length measurement.

Using the ratio (5:8) you can set up an equation with x representing the missing measurement, and cross multiply to calculate the new width.

1) If the length is 12 inches, the width is 7.5 inches

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2) If the length is 20 inches, the width is 12.5 inches

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3) If the length is 10 inches, the width is 6.25 inches

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50=8x

\frac{50}{8} =x

6.25 = x

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2 years ago
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