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andrezito [222]
3 years ago
5

Warm-up for you! Get your brain ready! 50 points! You got this!

Mathematics
1 answer:
3241004551 [841]3 years ago
6 0

Answer:

A

Step-by-step explanation:

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A. What is the explicit definition for this sequence?<br><br>b. How far does she run on day 19?​
creativ13 [48]

Answer:

(a) a_n=1+\frac{1}{6}(n-1)

(b) 4 miles

Step-by-step explanation:

Given:

The sequence of run is an arithmetic sequence.

Miles traveled on day 1 = 1 mile

Miles traveled on day 7 = 2 miles

(a).

Explicit formula for an arithmetic sequence is given as:

a_n=a_1+(n-1)d\\a_n\to n^{th}\ term\\a_1\to first\ term\\n\to number\ of\ terms\\d\to \textrm{common difference}

Here, a_1=1,a_7=2

So,

a_7=a_1+(7-1)d\\2=1+6d\\6d=2-1\\d=\frac{1}{6}

Therefore, the explicit definition of the above sequence is given as:

a_n=1+\frac{1}{6}(n-1)

Where, a_n is the miles covered on n^{th} day.

(b)

In order to find the distance covered by her on day 19, we plug in 19 for n in the above formula. This gives,

a_{19}=1+\frac{1}{6}(19-1)\\\\a_{19}=1+\frac{1}{6}(18)\\\\a_{19}=1+3=4\ mi

Therefore, the number of miles covered by her on day 19 is 4 miles.

3 0
3 years ago
the area of a rectangular field is x^2-x-72 m^2. The length of the field is x+8 cm. What is the width of the field meters.
Gre4nikov [31]
Hello,


A(x)=x²-x-72 (m²)
L=(x+8) (cm)= (x+8)/100 (m)

We suppose here x≠-8
(in reality x²-x-72>0 ==>x<-8 or x>9
but x+8>0 ==> x>-8
 then
only x>9 are solutions)

W=A(x)/ ((x+8)/100 )=100*(x²-x-72)/(x+8)= 100*(x-9)(x+8)/(x+8)=100*(x-9)

5 0
2 years ago
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Lynna [10]
I gotchu my guy let me know what you need help with I’d gladly revive those free points
3 0
2 years ago
Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x , with ini
Svetach [21]
For this case we have the following difference equation:
 dy / dx = 3xy&#10;
 Applying separable variables we have:
 dy / y = 3xdx&#10;
 Integrating both sides we have:
 \int\ ({1/y}) \, dy =  \int\ {3x} \, dx
 ln (y) = (3/2) x ^ 2 + C&#10;
 applying exponential to both sides:
 exp (ln (y)) = exp ((3/2) x ^ 2 + C)&#10;&#10; y = C * exp ((3/2) x ^ 2)
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 C = 1 / (exp ((3/2) * 1 ^ 2))&#10;&#10;C = 0.2
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 y = 0.2 * exp ((3/2) x ^ 2)&#10;
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6 0
3 years ago
31/8 as a mixed number?
Katyanochek1 [597]
\frac{31}{8}=\frac{24}{8}+\frac{7}{8}=3+\frac{7}{8}=\boxed{3 \frac{7}{8}}
5 0
3 years ago
Read 2 more answers
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