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4 years ago

Which statement is true about the ray passing through points B and C?

2 answers:

6 0

A. The definition of a ray states that it extends infinitely in one direction. (A line extends infinitely in both directions, and a line segment has two finite end points.) Anything that extends infinitely has an infinite number of points.

olchik [2.2K]4 years ago

5 0

Answer:

(a) The ray extends infinitely in one direction

Step-by-step explanation:

done the topic

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PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into n equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

3 years ago

Consider the equation below.

Kamila [148]

Answer:

Option (1)

Step-by-step explanation:

$\text{log}_4(x + 3)=\text{log}_2(2 + x)$

$\text{log}_4(x + 3)=\frac{\text{log}_{10}(x+3)}{\text{log}_{10}4}$

$\text{log}_2(2 + x)=\frac{\text{log}_{10}(2+x)}{\text{log}_{10}2}$

System of equations can be written as,

$y_1=\text{log}_4(x + 3)=\frac{\text{log}_{10}(x+3)}{\text{log}_{10}4}$

$y_2=\text{log}_2(2 + x)=\frac{\text{log}_{10}(2+x)}{\text{log}_{10}2}$

Therefore, system of equations given in Option (1) is the correct option.

4 0

3 years ago

Kayla invests $8,213 in a savings account with a fixed annual interest rate of 6% compounded continuously. What will the account

Nastasia [14]

It is 5913.36. You have to multiply all of them together except that you have to turn the percent to a decimal before multiplying.

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The pizza cost

ANSWER: D

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