What are three expressions that are equivalent to -2(4-3x) + (5x-2)

Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

2 years ago

What values of x and y satisfy the system of equations {3x+2y=14x=4y−2? infinitely many solutions (5011,1811) (1811,5011) no sol

irinina [24]

3x+2y=14x=4y-2

(x,y)=(1/4,11/8)

8 0

3 years ago

A circle with radius 142.5 has an arc with a 24 degree angle. What is the length of the arc?

MissTica

Answer: 59.690260418206

The result is approximate. Round that value however you need to.

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Explanation:

For a circle with radius r = 142.5, the full distance around the edge (aka perimeter aka circumference) is found by using the formula below.

C = 2*pi*r

C = 2*pi*142.5

C = 895.353906273091

That value is approximate. I used my calculator's stored value of pi to get the most accuracy possible.

That value of roughly 895 represents the distance around a full circle of that radius, but we only want a 24 degree pizza slice.

In other words, we want 24/360 = 1/15 of the full perimeter

(1/15)*895.353906273091 = 59.690260418206

5 0

2 years ago

Read 2 more answers

Ms. Liebowitz has a choice of driving or flying from Morgantown, West Virginia to Washington, D.C. for a one-day business trip.

den301095 [7]

Answer:

Step-by-step explanation:

If she travels by air, she will be able to work seven hours in D.C. work four hours once there. Her expected income from each hour of work in D.C. is $40. This means that the total amount that she earns in 7 hours would be

40 × 7 = $280

if she drives, she will only have time to work four hours once there. This means that the total amount that she earns in 4 hours would be

40 × 4 = $160

The difference in both amounts would be

280 - 160 = $120

she will chose to fly if and only if the price differential (air cost minus driving cost) is less than $120

7 0

3 years ago

Please help

shtirl [24]

Answer:

Step-by-step explanation:

The slope of the line in question is the same as the slope of the line parallel to it. Using y = mx + b, where m is the slope, we find the slope of our line is -3.

Using the pt-slope form, y - y1 = m( x - x1), we get y - (-1) = -3( x - 2) or y + 1 = -3x + 6. Which leads us to y = -3x + 5. QED

4 0

2 years ago