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3 years ago

Which value of x is a solution of the inequality 25x - 100 < 250?

Mathematics

1 answer:

Leona [35]3 years ago

5 0

Answer:

inequality form: x<14

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

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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

3 years ago

What is the answer for 9=Y=?

musickatia [10]

(5,4)

x=5

y=4

hope this helped

mark brainliest :)

you question did not make sense so i assumed this is what you meant and needed.

6 0

3 years ago

What is the answer of -3 2/3 + 1.1 as a fraction?

pickupchik [31]

$- 3 \frac{2}{3} + 1.1 = - \frac{11}{3} + \frac{11}{10} = - \frac{110}{30} + \frac{33}{30} \\ = -\frac{77}{30} = -2 \frac{17}{30}$

7 0

3 years ago

15/16 divided by 3/4 = ?

Dmitry [639]

5/4

(15/16)(4/3) The 4/3 is the reciprocal of 3/4

=5/4

8 0

3 years ago

How does the 3 in 350 compare to the 3 in 403

Alexandra [31]

3 in 350 is 300 the 3 in 403 is 3

7 0

3 years ago