Identify the type of angel pair and solve for x

What is love represents the arithmetic sequence

Strike441 [17]

What subject is it then

6 0

3 years ago

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

Marrrta [24]

Split up the interval [0, 2] into <em>n</em> 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 <em>n</em> 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

Jim began a 165 mile bicycle trip to build up stamina for a triathlete competition unfortunately his bike chain broke so he fini

denpristay [2]

Answer: Approximately 4.7 hours.

Step-by-step explanation:

He rode the bicycle for some time before it broke down and he walked the remaining distance. This means that Jim covered a total of 165 miles by riding at a speed of 35 miles per hour and walking at a speed of 3 miles per hour.

Let x = the distance covered by riding the bicycle.

Let y = the distance covered by walking.

Time = distance /speed

Time he used in riding would be x/35

Time he used in walking would be y/3

Since the entire trip took 7 hours,

x/35 + y/3 = 7

3x + 35y = 735 - - - - - - - - 1

Total miles covered is 165. Therefore,

x + y = 165 - - - - - - - - -- - -2

Substituting x = 165-y into equation 1, it becomes

3(165-y) + 35y = 735

495-3y + 35y = 735

-3y + 135y = 735-495

132y = 240

y = 240/132

y = 1.81m

x = 165 - 1.81 = 163.19

Amount of time that he spent on the bicycle will be

x/35 = 163.19/35

= 4.66

Approximately 4.7 hours.

7 0

4 years ago

Five bikers join a race. In how many possible ways can they be arranged as

PolarNik [594]

Answer:

60 different possibilities

Step-by-step explanation:

Number of bikers = 5

Positions = first, second and third

First positions = all 5 riders can take the first spot = 5 possibilities

Second spot = position 1 has been filled hence number of possibilities = ( 5 - 1) = 4

Third spot = position 1 and 2 has been filled ; number of possibilities =. (5 - 2). = 3

Number of possible arrangements :

5 * 4 * 3 = 60 different possibilities

6 0

3 years ago

F(x) = x2+3x+2 x2+5x+4 Why is there no zero at x = –1?

dmitriy555 [2]

You could rewrite $F(x)$ as

$\dfrac{x^2+3x+2}{x^2+5x+4}=\dfrac{(x+1)(x+2)}{(x+1)(x+4)}$

and be tempted to cancel out the factors of $x+1$ . But this cancellation is only valid when $x\neq-1$ .

When $x=-1$ , you end up with the indeterminate form $\dfrac00$ , which is why $-1$ is not a zero.

7 0

4 years ago