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Stells [14]
3 years ago
10

SALES Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39,000 more than three times the num

ber of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.
​
Mathematics
1 answer:
Talja [164]3 years ago
8 0

Given :

Miki has 104 nickels and 88 dimes. She wants to divide her coins into groups where each group has the same number of nickels and the same number of dimes.

There were 216,000 cars sold last year.

To Find :

Equation that can be used to find the number of trucks, t, sold last year.

Solution :

Let , number of truck sold is t and number of car sold is c.

It is given that the number of cars sold was 39,000 more than three times the number of trucks sold.

So ,

c=3t+39000\\\\t=\dfrac{c-39000}{3}

Putting value of c = 216000 in above equation , we get :

t=\dfrac{c-39000}{3}\\\\t=\dfrac{216000-39000}{3}\\\\t=59000

Hence , this is the required solution .

​

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The definite integral of a continuous function <em>f</em> over the interval [a,b] denoted by \int\limits^b_a {f(x)} \, dx, is the limit of a Riemann sum as the number of subdivisions approaches infinity. That is,

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To evaluate the integral

\int\limits^{0}_{-2} {7x^{2}+7x } \, dx

you must:

Find \Delta x

\Delta x = \frac{b-a}{n}=\frac{0+2}{n}=\frac{2}{n}

Find x_i

x_i=a+\Delta x\cdot i\\x_i=-2+\frac{2i}{n}

Therefore,

\lim_{n \to \infty}\frac{2}{n} \sum_{i=1}^{n} f(-2+\frac{2i}{n})

\int\limits^{0}_{-2} {7x^{2}+7x } \, dx=\lim_{n \to \infty}\frac{2}{n} \sum_{i=1}^{n} 7(-2+\frac{2i}{n})^{2} +7(-2+\frac{2i}{n})

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\lim_{n \to \infty}\frac{14}{n} \sum_{i=1}^{n} \frac{4i^2}{n^2}-\frac{6i}{n}+2\\\\\lim_{n \to \infty}\frac{14}{n}[ \sum_{i=1}^{n} \frac{4i^2}{n^2}-\sum_{i=1}^{n}\frac{6i}{n}+\sum_{i=1}^{n}2]\\\\\lim_{n \to \infty}\frac{14}{n}[ \frac{4}{n^2}\sum_{i=1}^{n}i^2 -\frac{6}{n}\sum_{i=1}^{n}i+\sum_{i=1}^{n}2]

We can use the facts that

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\sum_{i=1}^{n}i=\frac{n(n+1)}{2}

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\frac{14}{3}\cdot \lim _{n\to \infty \:}\left(\frac{n^2-3n+2}{n^2}\right)\\\\\mathrm{Divide\:by\:highest\:denominator\:power:}\:1-\frac{3}{n}+\frac{2}{n^2}\\\\\frac{14}{3}\cdot \lim _{n\to \infty \:}\left(1-\frac{3}{n}+\frac{2}{n^2}\right)\\\\\frac{14}{3}\left(\lim _{n\to \infty \:}\left(1\right)-\lim _{n\to \infty \:}\left(\frac{3}{n}\right)+\lim _{n\to \infty \:}\left(\frac{2}{n^2}\right)\right)\\\\\frac{14}{3}\left(1-0+0\right)\\\\\frac{14}{3}

Thus,

\int _{-2}^07x^2+7xdx=\frac{14}{3}

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