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3 years ago

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The temperature at the core of the Sun is estimated to be more than 15,000,000 degrees Celsius. What is 15,000,000 written in sc

ientific notation.
A. 1.5 x 10^5
B. 1.5 x 10^6
C. 1.5 x 10^7
D. 1.5 x 10^8

1 answer:

Ronch [10]3 years ago

6 0

The answer is C because you would move the decimal 7 places to the right to get 15,000,000.

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Please calculate this limit <br>please help me

Tasya [4]

Answer:

We want to find:

$\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}$

Here we can use Stirling's approximation, which says that for large values of n, we get:

$n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n$

Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

$\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}$

Now we can just simplify this, so we get:

$\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\$

And we can rewrite it as:

$\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}$

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

Thus:

$\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}$

7 0

3 years ago

What is the vertical asymptote of f(x)=3/x+5

Rudiy27

Answer:

X = -5

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Pls help me, I really dont understand

Stella [2.4K]

Answer:

-2.5x-.5

$y=\frac{2}{3}x-1$

draw the dotted line (3/7)x-3 and shade below it

Step-by-step explanation:

First, we need the slope

Use the slope formula:

$\frac{Y_2-Y_1}{X_2-x_1}=\frac{2-(-8)}{-1-3}=\frac{10}{-4}=-2.5$

so we have

y= -2.5x+b

Solve for b by plugging in coordiantes

-8= -2.5(3)+b

-8= -7.5+b

b= -.5

Put it together and get -2.5x-.5

2.)

A line is parallel to another line if they have the same slope (and different y intercepts)

So in the formula y=mx+b we knowe that m= 2/3

Now it's just a matter of solving for B

plug in the required coordinate to do this

-1=(2/3)*0+b

-1= b

Put it all together to get

$y=\frac{2}{3}x-1$

3.)

put this into slope intercept form

3x-7y>21

3x-21 > 7y

(3/7)x-3 >y

To graph this just draw a dotted line with the equation (3/7)x-3 and shade everything below it (use de_smos if you're stuck)

7 0

3 years ago

For Jack's birthday, his mom is taking him and 12 friends to the zoo. If she pays $11 for each ticket using her credit card, wha

Gemiola [76]

Jack's mom is purchasing thirteen tickets at a price of $11 each. This equals a total of $143 in total spent. If Jack's mom has a credit card limit of $500, then after purchasing $143 with the card, her available amount to purchase additional things is $357. This impact on her available credit is due to credit cards working on an available balance system. When Jack's mom first received her credit card, a set balance or total amount she could purchase with the card was set. In this example, her total amount she could purchase with the card was $500. After her purchase of the tickets for $143 was completed, she subtracted that amount from her total available of $500 and that is why her available amount to purchase is now $357.

4 0

3 years ago

Read 2 more answers

Write the equation of the line in slope-intercept that has passes through the points (2,-5) and (8, 13).

const2013 [10]

Answer:

The equation of the straight line in Slope- intercept form

y = 3 x - 11

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given points are (2,-5) and (8, 13)

The Slope of the line

$m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{13-(-5)}{8-2} = \frac{18}{6} =3$

Equation of the line having slope 'm' and given point

$y - y_{1} = m (x - x_{1} )$

(x₁ , y₁) = ( 2, -5 )

$y - (-5) = 3 (x - 2 )$

y + 5 = 3x - 6

The equation of the straight line in slope intercept form

y = m x + c

y = 3 x - 6-5

y = 3 x - 11

<u><em>Final answer:</em></u>-

The equation of the straight line in Slope- intercept form

y = 3 x - 11

8 0

3 years ago