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2 years ago

How many solutions does the system have? y= -5x - 1 y = -5.2 + 7

Mathematics

1 answer:

mote1985 [20]2 years ago

4 0

Answer: y= -5x - 1

y = -5.2 + 7

Step-by-step explanation: y= -5x - 1 has 3. y = -5.2 + 7 has 1

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Solve the equation 10x^4-81x^2+164=0 on the real number system

rusak2 [61]

I got -2,2....................

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3 years ago

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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 11 feet and

Inessa [10]

Answer: The percentage ≅ 48.4%

Step-by-step explanation:

* Lets revise how to find the volume of a container shaped cylinder

- The volume of any container = area of its base × its height

- The base of the cylinder is a circle, area circle = 2 π r,

where r is the length of its radius

* In container A:

∵ r = 13 feet , height = 13 feet

∴ Its volume = π (13)² × (13) = 2197π feet³

* In container B:

∵ r = 9 feet , height = 14 feet

∴ Its volume = π (9)² × (14) = 1134π feet³

* So to fill container B from container A, you will take from

container A a volume of 1134π feet³

- The volume of water left in container A = 2197π - 1134π = 1063π feet³

* To find the percentage of the water that is full after pumping

is complete, divide the volume of water left in container A

by the original volume of the container multiplied by 100

∴ The percentage = (1063π/2197π) × 100 = 48.3841 ≅ 48.4%

8 0

2 years ago

Find the perimeter of rectangle whose length is 5m 20 cm and breadth 3.5m

Mrac [35]

Answer:

17.4

5.2x2

3.5x2

17.4

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2 years ago

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Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find

inna [77]

Best guess for the function is

$\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}$

By the ratio test, the series converges for

$\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1$

When $x=1$ , $f(x)$ is a convergent $p$ -series.

When $x=-1$ , $f(x)$ is a convergent alternating series.

So, the interval of convergence for $f(x)$ is the closed interval $\boxed{-1 \le x \le 1}$ .

The derivative of $f$ is the series

$\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n$

which also converges for $|x|$ by the ratio test:

$\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1$

When $x=1$ , $f'(x)$ becomes the divergent harmonic series.

When $x=-1$ , $f'(x)$ is a convergent alternating series.

The interval of convergence for $f'(x)$ is then the closed-open interval $\boxed{-1 \le x < 1}$ .

Differentiating $f$ once more gives the series

$\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)$

The first series is geometric and converges for $|x|$ , endpoints not included.

The second series is $f'(x)$ , which we know converges for $-1\le x$ .

Putting these intervals together, we see that $f''(x)$ converges only on the open interval $\boxed{-1 < x < 1}$ .

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1 year ago

If 2 Lemons cost 15 cents, how many can be bought for 60 cents

mamaluj [8]

The answer is 8 lemons
What you do is divide 0.15 by 2 into a calculator.
you will get 0.075 which you would then divide by 8 and get 0.6 which is 60 cents, hope this helped!!

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3 years ago

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