3 years ago

Y=4 -2x у = -5 + 4х ||

Mathematics

1 answer:

kolezko [41]3 years ago

5 0

Answer:

y=1

Step-by-step explanation:

y= 4 - 2x

y= -5 + 4x

4 - 2x = -5 + 4x

4 + 5 = 4x +2x

9 = 6x

9/6 = x

3/2 = x

y= 4 -2(3/2)

y = 4 - 3

y = 1

You might be interested in

For the function given below, find a formula for the Riemann sum obtained by dividing the interval (0, 3) into n equal subinterv

Viktor [21]

Splitting up [0, 3] into $n$ equally-spaced subintervals of length $\Delta x=\frac{3-0}n = \frac3n$ gives the partition

$\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right]$

where the right endpoint of the $i$ -th subinterval is given by the sequence

$r_i = \dfrac{3i}n$

for $i\in\{1,2,3,\ldots,n\}$ .

Then the definite integral is given by the infinite Riemann sum

$\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}$