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3 years ago

The original price of the DVD is nine dollars the sale price is 80% of the price what is the sale price of the DVD?

Mathematics

2 answers:

Bas_tet [7]3 years ago

8 0

multiply $9 by 80%

80% = 0.80

9 * 0.8 = 7.20

subtract that from original price

9 - 7.20 = 1.80

Sale price is $1.80

Vilka [71]3 years ago

3 0

Let's rewrite the information then figure out the answer.

DVD: $9.00 originally but on sale with an 80% discount.
80%=0.80
9.00(0.80) = $7.20
$9.00 - $7.20 = $1.80

Thus, the sales price is: $1.80

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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.

3 0

1 year ago

1. Rachel borrowed $1000. The interest rate for her loan is 8%. What is the difference in the interest she’ll pay if she pays it

PIT_PIT [208]

Answer:

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Step-by-step explanation:

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3 years ago

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Tom [10]

Answer:

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0.98

Step-by-step explanation:

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3 years ago

Which are correct representations of the inequality -3(2x-5) <5(2 - x)? Select two options.

kogti [31]

Answer:

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Step-by-step explanation:

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3 years ago

Compute using significant digits. What is the area of a parallelogram with length 17.25 mm and width 5.065 mm?

Dmitriy789 [7]

Answer: Option 'a' is correct

Step-by-step explanation:

Since we have given that

Length of parallelogram =17.25 mm

Width of parallelogram =5.065 mm

As we know the formula for " Area of parallelogram"

Area of parallelogram is given by

$Area= length \times breadth\\\\17.25\times 5.065=87.03 \ mm^2$

Hence, option 'a' is correct .

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3 years ago