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3 years ago

The function d(t)=300,000t represents the distance (in kilometer) that light travels in t seconds

Mathematics

1 answer:

aliina [53]3 years ago

8 0

Answer:21

Step-by-step explanation:21

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What is the area of a triangle with vertices (3,0) (9,0) (7,6)

Nezavi [6.7K]

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by the determinant of the following matrix:

$A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|$

In this question:

Vertices (3,0) (9,0) (7,6). So

$A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|$

$A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)$

$A = \pm 0.5*(63-21)$

$A = \pm 0.5*42 = 21$

The area of the triangle is of 21 units of area.

5 0

2 years ago

Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1

defon

I'm guessing the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}$

By the ratio test, the series converges if the following limit is less than 1.

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|$

The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|$

$|x^n|$ also cancels out and the remaining factor of $|x|$ can be pulled out of the limit (as it doesn't depend on $n$ ).

$\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0$

which means the series converges everywhere (independently of $x$ ), and so the radius of convergence is infinite.

3 0

3 years ago

Which line is a linear model for the data?

DochEvi [55]

Answer:

Bottom Left Choice

Step-by-step explanation:

If you look at the points, they are traveling up and to the right. So is the line in the graph. Also, the line in the graph is closer to more dots than the others.

5 0

2 years ago

Read 2 more answers

Use the given property to complete the statement

aleksklad [387]

Answer:

Step-by-step explanation:

your answer is A

8 0

2 years ago

I need to know the answer

ivanzaharov [21]