Answer:
19 > 1083
Step-by-step explanation:
Given: The nth term of a sequence is given by .
let βn be the nth term.
then βn = 3n²
Let x be the term which is the first one with a value greater than 1000.
19 th term is the first one with a value greater than 1000 the sequence that is βx > 1000
3x² > 1000
divide by 3
3x²/3 > 1000/3
x² > 1000/3
x² > 333.33.....
to make x the subject of the formula, square root both sides
√x² > √333.333
the square cancel the square root at x
x > √333.333
x>18.257
x > 19 approximately
19 th term is the first one with a value greater than 1000 the sequence.
that is: β19 = 3(19)²
3(316)²
=1083.
Hope it will help.
You distribute the 30x to the equation in parenthesis
So basically you are doing (30x*x)+(30x*-3)
So you get 30x^2-90x
Hope this helps!
<span>D) 9.0 x 10^10 km
This is more an exercise in handling scientific notation than anything else. Since we have the distance that light travels in 1 second and we want to calculate how far it travels in 5 minutes, we must first calculate how many seconds are in 5 minutes. Simply multiplying 5 by 60 gives us 300 seconds. Now we need to multiply 300 by 3.0x10^8 km. So
300 * 3.0x10^8 = ?
We could first convert 300 into scientific notion, but it's easier to just leave it along and assume that it's 300 x 10^0. So 300 times 3 is 900. And since 0 plus 8 is 8, we have as the answer:
900 x 10^8
But we're not done. The significand has to be greater than or equal to 1 and less than 10. So let's divide 900 by 100 and add 2 to the exponent. So we get
9 x 10^10
Finally, since our data had 2 significant figures, our result should have that as well. So let's add the 2nd digit getting:
9.0 x 10^10
So we know that light travels 9.0x10^10 km in 5 minutes, and that answer matches option "D" from the available choices.</span>
Automobile insurance: 809.50
comprehensive coverage: 64
Based on the note:
subtract 64: 809.50 - 64 = 745.50
multiply by 150% : 745.50 x 1.5 = 1,118.25
add 64: 1,118.25 + 64 = 1,182.25
The new total is 1,182.25
