3 years ago

-4x – 4y = -8 -2x + 4y = –10

Mathematics

1 answer:

shusha [124]3 years ago

8 0

Answer:

–10

Step-by-step explanation:

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One number is 8 times another number. The numbers are both positive and have a difference of 70. Find the numbers.

Nat2105 [25]

Let one no. be x , Then according to question other number will be 8x
Now 8x - x = 70
7x = 70
x=10
hence one no is 10 and other 80

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Vesna [10]

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Step-by-step explanation:

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3 years ago

Because of Theorem 5.47 any function that is continuous on (0, 1) but unbounded cannot be uniformly continuous there. Give an ex

almond37 [142]

Answer:

$f: (0,1) \to \mathbb{R}$

$f(x) = \sin(1/x)$

Step-by-step explanation:

f is continuous because is the composition of two continuous functions:

$g(x) = \sin(x)$ (it is continuous in the real numbers)

$h(x) = 1/x$ (it is continuous in the domain (0,1))

It is bounded because $-1 \leq \sin(\theta) \leq 1$

And it is not uniformly continuous because we can take $\varepsilon = 1$ in the definition. Let $\delta > 0$ we will prove that there exist a pair $x,y\in \mathbb{R}$ such that $|x-y|< \delta$ and $|f(x) -f(y)|> \varepsilon = 1$ .

Now, by the archimedean property we know that there exists a natural number N such that

$\frac{1}{N} < 2\pi \delta$

$\Rightarrow \frac{1}{2\pi N} < \delta$ .

Let's take $x = \frac{1}{2\pi N + \pi/2}$ and $y = \frac{1}{2\pi N + 3\pi/2}$ . We can see that

$|x-y| = \frac{1}{2\pi N + \pi/2}-\frac{1}{2\pi N + 3\pi/2}$

And also:

$|f(x)- f(y)| = |f(2\pi N + \pi/2) - f(2\pi N + 3\pi/2)| = |1 - (-1)| = 2 > \varepsilon$

And we conclude the proof.

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3 years ago

Pregunta 14

IrinaK [193]

Answer:

sorry for points

Step-by-step explanation:

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3 years ago