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Ray Of Light [21]
3 years ago
10

Front-row tickets for a concert cost $60. After every 5 rows, the ticket price goes down by $5. What is the total amount of mone

y generated by a full house? Info: There are 20 rows that increase by 3 seats each time starting with 18.
Mathematics
2 answers:
Vladimir [108]3 years ago
7 0
N a 20 row theater, the number of seats increases by 3 with each successive row.  The first row has 18 seats.

a. Write an arithmetic series in summation notation to represent the number of seats in the theater,<span><span>∑<span>n=1</span>20</span>18+3(n−1)</span><span>b. What is the total seating capacity of the theater? </span>
930 seats

c. Front row seats cost $60.  After every 5 rows, the price drops $5.  What is the amount generated by a full house?
$46950

2.  An arithmetic series has a first term of 4.  The sum of the first 40 terms is 6080.  Find the value of the 40th term?
use the formula
<span>sum of first n terms = n/2 * (s1 + sn) </span>
<span>6080 = 40/2 * (4 + sn) </span>
arsen [322]3 years ago
3 0
I think I got it, but just in case...tell me the whole thing again. I wasn't listening.
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What is the solution if any, to the inequality 3-l4-nl&gt;1?
atroni [7]

Answer:

The solution to the inequality is all real values of n that respect the following condition: 2 < n < 6

Step-by-step explanation:

First, we need to separate the modulus from the rest of equation. So

3-l4-nl>1

-|4-n|>1-3

-|4-n|>-2

Multiplying everything by -1.

|4-n|<2

How to solve:

|x| < a means that -a<x<a

In this question:

|4-n|<2

-2<4-n<2

This means that:

4 - n > -2

-n > -6

Multiplying by -1

n < 6

And

4 - n < 2

-n < -2

Multiplying by 1

n > 2

Intersection:

Between n > 2 and n < 6 is 2 < n < 6

So the solution to the inequality is all real values of n that respect the following condition: 2 < n < 6

8 0
3 years ago
a triangle has a perimeter of 49 inches. the medium side is 7 more than the short side, and the longest side is 5 times the leng
slavikrds [6]
Short side length = x
Medium side = x + 7
Long side = 5x
Total 49, so
x + x + 7 + 5x = 49
If you combine like terms:
7x + 7 = 49
Subtract 7 from both sides
7x = 42
Divide both sides by 7
x = 6 inches
4 0
3 years ago
Read 2 more answers
Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 5t3dxdt+2x−2=05t3dx
uranmaximum [27]
Given the differential equation

5t^3 \frac{dx}{dt} +2x-2=0

The solution is as follows:

5t^3 \frac{dx}{dt} +2x-2=0 \\  \\ \Rightarrow5t^3 \frac{dx}{dt} =2-2x \\  \\ \Rightarrow \frac{5}{2-2x} dx= \frac{1}{t^3} dt \\  \\ \Rightarrow \int {\frac{5}{2-2x} } \, dx = \int {\frac{1}{t^3}} \, dt \\  \\ \Rightarrow- \frac{5}{2} \ln(2-2x)=- \frac{1}{2t^2} +A \\  \\ \Rightarrow\ln(2-2x)= \frac{1}{5t^2} +B\\  \\ \Rightarrow2-2x=Ce^{\frac{1}{5t^2}} \\  \\ \Rightarrow 2x=Ce^{\frac{1}{5t^2}}+2 \\  \\ \Rightarrow x=De^{\frac{1}{5t^2}}+1
3 0
3 years ago
Six more than three times a number w. <br> An expression for this phase is..? <br><br> (Please help)
satela [25.4K]

Answer:6+3w

Step-by-step explanation:

So, our number is "W"

SO, 6  more than three times w is

6+3w

Three times w=3w

Then, it says 6 more, so we add 6

8 0
3 years ago
Read 2 more answers
Simplify x + 4 - 5x - 2
Blababa [14]

Answer:

-2(2x-1)

Step-by-step explanation:

x+4-5x-2

1) collect like like terms

-4x+2

2) factor out the -2

-2(2x-1)

3) that gives you the final answer of

-2(2x-1)

7 0
3 years ago
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