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1 year ago

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A garden store bought a fountain at a cost of $995.66 and marked it up 100%. Later on, the store marked it down 25%. What was th

e discount price?

2 answers:

Aliun [14]1 year ago

7 0

Answer:

Step-by-step explanation:

nexus9112 [7]1 year ago

3 0

Answer:

1493.49

Step-by-step explanation:

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Define a function sinc(x) (pronounced "sink of x") by: text(sinc)(x)={(sin(x)/x text(if)\ x != 0, 1 text(if)\ x = 0.) (This func

gayaneshka [121]

Answer:

Step-by-step explanation:

To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that

$\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}$

which is the taylor series expansion based at 0. Then for $x\neq 0$ , by dividing both sidex by x, we have that

$\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}$

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2 years ago

A student is raising money for cancer research. A local business agrees to donate an additional 25% of what the student raises,

bixtya [17]

Answer: 585 maybe??

Step-by-step explanation:

450/100 = 4.5

4,5 = 1 percent of the total amount.

4.5 x 25 = 112.5

112 = 25 percent of 450

4.5 x 5 = 22.5

22.5 = 5 percent of 450

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2 years ago

Find the volume of the right rectangular prism whose side lengths are 5 cm, 3 cm, and 13 cm

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2 years ago

Liam worked 5 hours 30minutes on Monday and 4 hours 45 minutes on Wednesday.How many total hours did Liam work on Monday and Wed

dangina [55]

5 hours + 4 hours = 9 hours
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2 years ago

Read 2 more answers

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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1 year ago