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3 years ago

6.3 + |8.7 + (-6.8)|

Mathematics

1 answer:

mariarad [96]3 years ago

8 0

Answer:

8.2 & 4.4

Step-by-step explanation:

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Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function h(t)= -16

tangare [24]

Answer:

(d)

Step-by-step explanation:

Given

$h(t) = -16t^2 + 96t$

Required

The intercepts

The x intercepts are where the graph crosses x axis.

From the attached plot, they are:

$x = (0,0)$ and $x = (6,0)$

These represent the start and end of the ball that is launched.

Hence, (d) is true

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3 years ago

Write the quadratic function f(x) = 3x2 - 6x + 9 in vertex form.

Y_Kistochka [10]

The answer is y=3(x-1)^2+6

7 0

3 years ago

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You find a job that pays $11.25 per hour. You plan to work a 40 hour week. What will your weekly gross pay be?

KIM [24]

Gross pay is before taxes are taken out...
11.25(40) = 450 <== gross weekly pay

3 0

3 years ago

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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [0,5] into n equal subinterva

sergij07 [2.7K]

Given

we are given a function

$f(x)=x^2+5$

over the interval [0,5].

Required

we need to find formula for Riemann sum and calculate area under the curve over [0,5].

Explanation

If we divide interval [a,b] into n equal intervals, then each subinterval has width

$\Delta x=\frac{b-a}{n}$

and the endpoints are given by

$a+k.\Delta x,\text{ for }0\leq k\leq n$

For k=0 and k=n, we get

$\begin{gathered} x_0=a+0(\frac{b-a}{n})=a \\ x_n=a+n(\frac{b-a}{n})=b \end{gathered}$

Each rectangle has width and height as

$\Delta x\text{ and }f(x_k)\text{ respectively.}$

we sum the areas of all rectangles then take the limit n tends to infinity to get area under the curve:

$Area=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)$

Here

$f(x)=x^2+5\text{ over the interval \lbrack0,5\rbrack}$ $\Delta x=\frac{5-0}{n}=\frac{5}{n}$ $x_k=0+k.\Delta x=\frac{5k}{n}$ $f(x_k)=f(\frac{5k}{n})=(\frac{5k}{n})^2+5=\frac{25k^2}{n^2}+5$

Now Area=

$\begin{gathered} \lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{5}{n}(\frac{25k^2}{n^2}+5) \\ =\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{125k^2}{n^3}+\frac{25}{n} \\ =\lim_{n\to\infty}(\frac{125}{n^3}\sum_{k\mathop{=}1}^nk^2+\frac{25}{n}\sum_{k\mathop{=}1}^n1) \\ =\lim_{n\to\infty}(\frac{125}{n^3}.\frac{1}{6}n(n+1)(2n+1)+\frac{25}{n}n) \\ =\lim_{n\to\infty}(\frac{125(n+1)(2n+1)}{6n^2}+25) \\ =\lim_{n\to\infty}(\frac{125}{6}(1+\frac{1}{n})(2+\frac{1}{n})+25) \\ =\frac{125}{6}\times2+25=66.6 \end{gathered}$

So the required area is 66.6 sq units.

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1 year ago

Andy,Taylor and Ben share their team payment in a ratio of 1:3:4. What % dies Andy receive

matrenka [14]

Andy receives 1 share out of 8 total.

$\frac{1}{8} *100=12.5 \text{ percent}$

7 0

4 years ago

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​ 6.3 + |8.7 + (-6.8)|

6.3 + |8.7 + (-6.8)|