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Zepler [3.9K]
2 years ago
10

Find the areas of these polygons

Mathematics
1 answer:
Zigmanuir [339]2 years ago
3 0
The area of triangle
=5*7/2
=35/2
17.5sq.units//

The area of parallelogram
=15*8
=120sq.units//
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Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini
Nat2105 [25]
By inspection, it's clear that the sequence must converge to \dfrac32 because

\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32

when n is arbitrarily large.

Now, for the limit as n\to\infty to be equal to \dfrac32 is to say that for any \varepsilon>0, there exists some N such that whenever n>N, it follows that

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|

From this inequality, we get

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}
\implies|2n-1|>\dfrac5{2\varepsilon}
\implies2n-1\dfrac5{2\varepsilon}
\implies n\dfrac12+\dfrac5{4\varepsilon}

As we're considering n\to\infty, we can omit the first inequality.

We can then see that choosing N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that N\in\mathbb N.
6 0
3 years ago
The value of a new truck decreases exponentially at a rate of 4.8% per year. If the purchase price of the new cars $42,000, how
Usimov [2.4K]

The worth of the car after it is paid off 5 years later given the rate of exponential depreciation is $32,842.34.

<h3>What is the worth of the car?</h3>

When the car declines in value, it means that the car is depreciating. The formula that can be used to determine the value of the car with the depreciationn rate is:

FV = P (1 - r)^n

  • FV = Future value
  • P = Present value
  • R = rate of decline
  • N = number of years

$42,000 x (1 - 0.048)^5 = $32,842.34

To learn more about future value, please check: brainly.com/question/18760477

7 0
2 years ago
56 projects 5:9 ratio divide
Alex Ar [27]
The answer is 4:4 it takes 4 of each





4 0
2 years ago
Write the ratio for sin P and cos Q
Gnom [1K]

Answer:

sin p -21/29

cos q 21/29 so here you go °~sohcahtoa~°

Step-by-step explanation:

sin means you find the soh part so you look for the oppisite over hyponuse

and for cos your looking for cah part so you find the adjsent over hypotnuse so the ansers is 21/29

4 0
3 years ago
Simplify 2x - 4) + 7(x + 2).<br> 9x + 6<br> 9x - 4<br> 09x - 6
d1i1m1o1n [39]
Answer:
Simplify 2x - 4) + 7(x + 2).
9x + 6
9x - 4
09x - 6
= 9x+10
6 0
2 years ago
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