Did I get this right?

Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

An arithmetic sequence takes the form

$a_n=a_{n-1}+d$

where $d$ is the common difference between terms. You can solve for $a_n$ in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term $a_1$

$a_n=a_1+(n-1)d$

Given that the 4th term is $a_4=-6$ and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields $a_1=6$ and $d=-4$ .

So, the sequence is given explicitly by

$a_n=6+(n-1)(-4)=-4n+5$

3 0

3 years ago

A tennis ball has a radius of about 1.4 inches What is the volume of the tennis ball to the nearest half inch.? Use 3.14 as an a

Ilya [14]

Answer:

Volume of tennis ball = 11.49 inch³

Step-by-step explanation:

Given:

Radius of tennis ball = 1.4 inches

Value of π = 3.14

Find:

Volume of tennis ball

Computation:

Volume of sphere = [4/3][π][r]³

Volume of tennis ball = [4/3][π][Radius of tennis ball]³

Volume of tennis ball = [4/3][3.14][1.4]³

Volume of tennis ball = [1.333][3.14][1.4]³

Volume of tennis ball = [1.333][3.14][2.744]

Volume of tennis ball = [4.1856][2.744]

Volume of tennis ball = 11.4852

Volume of tennis ball = 11.49 inch³

6 0

3 years ago

4)

liberstina [14]

Arc length is the angle/360 times circumference. The diameter of the unit circle is 2. So the circumference of the unit circle is 2pi, if you use 3.14 for pi, then the circumference is 6.28. So your equation is
x/360 times 6.28=4.2, divide by 6.28, then multiply by 360
x=240.76432
Your answer rounded to the nearest thousanth is 240.764

6 0

2 years ago

A bag contains 7 green marbles and 4 white marbles you select a marble at random what are the odds in favor of picking a green m

dimaraw [331]

7/11 = 0.64 because 7+4 = 11 and then divid 7 by the total number

6 0

3 years ago

Bill spent 50% of his savings on school supplies, then he spent 50% of what was left on lunch. If he had $6 left after lunch, ho

Lera25 [3.4K]

If he spent half his savings on supplies and the other half on lunch he shouldn't have money left over. It's a trick question.

6 0

3 years ago

Read 2 more answers