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amm1812
3 years ago
5

1,2,4,7,11,16,22, ___,____ What is the rule?

Mathematics
2 answers:
Paha777 [63]3 years ago
6 0
Find rates of change until you find a constant.

dy/dx=1,2,3,4,5,6

d2y/dx2=1,1,1,1,1  

So the acceleration, d2y/d2x, is constant.  This means that this is a quadratic sequence of the form a(n)=an^2+bn+c.  So we can set up a system of equations to solve for the values of a,b, and c.  Using the first three points, (1,1), (2,2), and (3,4) we have:

9a+3b+c=4, 4a+2b+c=2, and a+b+c=1  getting the differences...

5a+b=2 and 3a+b=1  and getting this difference...

2a=1, so a=1/2 making 5a+b=2 become:

2.5+b=2, so b=-1/2, making a+b+c=1 become:

1/2-1/2+c=1, so c=1  so the rule is:

a(n)=0.5x^2-0.5x+1  or if you prefer to not have decimals

a(n)=(x^2-x+2)/2
Mkey [24]3 years ago
3 0
The rule is to add each number like this 1,2,3,4,5,6,7 and so on to add to the numbers
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A turtle crawling at a rate of .1 (mi)/(h ) passess a resting bunny that rests for 30 minutes but moves 5 (mi)/(h ). How many fe
antiseptic1488 [7]

The bunny needs to run approximately 269.39 feet

<em><u>Solution:</u></em>

Let "x" be the number of hours passed since the turtle passed the buuny

Given that turtle crawls at a rate of 0.1 miles per hour

Then for "x" hours, distance traveled by turtle is 0.1x miles

Also given that bunny moves at 5 miles per hour but rests for 30 minutes

1 hour = 60 minutes

Therefore,

30 minutes = 0.5 hours

So the bunny rests for 0.5 hours

Thus the distance traveled by bunny is 5(x - 0.5) miles

To find when they will pass each, set the two distances equal to each other

0.1x = 5(x - 0.5)

0.1x = 5x - 2.5

5x - 0.1x = 2.5

4.9x = 2.5

x = 0.51

<em><u>Thus the distance ran by buuny is:</u></em>

Distance = 5(x - 0.5)

Substitute x = 0.51

Distance = 5(0.51020 - 0.5)

Distance = 5(0.010) = 0.05102 miles

Convert to feet

1 mile = 5280 feet

0.05102 miles = 0.05102 x 5280 feet = 269.39 feet

Thus the bunny needs to run approximately 269.39 feet

3 0
3 years ago
Find the interest on the loan if you borrowed $2,000 at 8% for 1 year.
kodGreya [7K]
Future Value = Present Value*(1 + interest rate)^(# of years)

Future Value = $2,000(1+0.08)^1

Future Value = $2,000(1.08) = $2,160

To find the interest on the loan, we need to do our Future Value - Present Value.

Future Value - Present Value = $2,160 - $2,000 = $160
7 0
3 years ago
Which expression uses the greatest common factor and the distributive property to rewrite the sum 75 + 45?
Vedmedyk [2.9K]
<span>75 + 45

First let's find the greatest common factor.
75: 1, 3, 5, 15, 25, 75
45: 1, 3, 5, 9, 15, 45
Their GCF is 15.

To get 75, you multiply 15 by 5.
To get 45, you multiply 15 by 3.

Therefore, 15(5 + 3) = 75 + 45.

</span><span>B. 15(5 + 3)
</span>
7 0
3 years ago
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How do you take the antiderivative of (sinxcosx)^2?
gtnhenbr [62]
<span>∫(sinx cosx)^2dx = ∫(1/2sin 2x)^2 dx = 1/4∫sin^2 2x dx = 1/4∫1/2(1 - cos 4x)dx = 1/8∫(1 - cos 4x) dx = 1/8[x - sin 4x / 4] + c = 1/32(4x - sin 4x) + c
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8 0
3 years ago
GUYS I SWEARRR I NEED HELP PLS IM BEGGING IMA FAIL MA TEST
liubo4ka [24]

Answer:

g

Step-by-step explanation:

3 0
3 years ago
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