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antiseptic1488 [7]
2 years ago
11

Given that

Mathematics
1 answer:
BaLLatris [955]2 years ago
8 0

Answer:

x=21/5

Step-by-step explanation:

5x:9 = 7:3

Turn the ratios into fractions:

5x/9 = 7/3

Then cross mutiply

15x=63

x=21/5

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Write the decimal as a fraction 0.272727
Oksana_A [137]
.272727 written as a fraction is 272727/1000000
7 0
2 years ago
If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have S_1=3\times2^{1-1}+2(-1)^1=3-2=1, which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}

and

S_k=3\times2^{k-1}+2(-1)^k

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}

From the given recurrence, we know

S_{k+1}=S_k+2S_{k-1}

so that

S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)

S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}

S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)

S_{k+1}=3\times2^k-2(-1)^k

S_{k+1}=3\times2^k+2(-1)(-1)^k

\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}

which is what we needed. QED

6 0
2 years ago
A super train travels 1,500 miles in 12.5 hours. How many miles does it travel in one hour?
katen-ka-za [31]
Let's treat the speed in one hour as a variable.
We can say that 1500=12.5x
Divide by 12.5
1500/12.5 = x
x = 120
120 mph is your answer.
6 0
2 years ago
What is the reasonable estimate for -3/2 x -5 1/4
Lady bird [3.3K]

Answer:

7.875......7.9.....or 8

Step-by-step explanation:

-3÷2×-21÷4= 7.875

63÷8=7.875

3 0
3 years ago
Read 2 more answers
What are the factors of 150 and 40? Please help me.​
posledela

Answer:

40: 1, 2, 4, 5, 8, 10, 20, 40

150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Step-by-step explanation:

6 0
3 years ago
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