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3 years ago

The traditional way of writing a number.

Mathematics

1 answer:

Allushta [10]3 years ago

3 0

Step-by-step explanation:

In legal prose it is traditional to write every number twice, first in words, followed by the same number written in digits enclosed in brackets: That sentence contained twenty-five (25) words. Easy as one (1), two (2), three (3).

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10 binder; 60% off; 6% tax

laila [671]

Answer:

I'm going to assume that the binder is $10, and that the tax is applied after the 60% off, in which case the answer is $4.24

Step-by-step explanation:

10 * 10 = 100

6 * 10 = 60

10 - 6 = 4

6 / 25 = 0.24

4 + 0.24 = 4.24

Answer: $4.24

4 0

2 years ago

Consider the initial value problem y′+5y=⎧⎩⎨⎪⎪0110 if 0≤t<3 if 3≤t<5 if 5≤t<[infinity],y(0)=4. y′+5y={0 if 0≤t<311 i

rosijanka [135]

It looks like the ODE is

$y'+5y=\begin{cases}0&\text{for }0\le t$

with the initial condition of $y(0)=4$ .

Rewrite the right side in terms of the unit step function,

$u(t-c)=\begin{cases}1&\text{for }t\ge c\\0&\text{for }t$

In this case, we have

$\begin{cases}0&\text{for }0\le t$

The Laplace transform of the step function is easy to compute:

$\displaystyle\int_0^\infty u(t-c)e^{-st}\,\mathrm dt=\int_c^\infty e^{-st}\,\mathrm dt=\frac{e^{-cs}}s$

So, taking the Laplace transform of both sides of the ODE, we get

$sY(s)-y(0)+5Y(s)=\dfrac{e^{-3s}-e^{-5s}}s$

Solve for $Y(s)$ :

$(s+5)Y(s)-4=\dfrac{e^{-3s}-e^{-5s}}s\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}{s(s+5)}+\dfrac4{s+5}$

We can split the first term into partial fractions:

$\dfrac1{s(s+5)}=\dfrac as+\dfrac b{s+5}\implies1=a(s+5)+bs$

If $s=0$ , then $1=5a\implies a=\frac15$ .

If $s=-5$ , then $1=-5b\implies b=-\frac15$ .

$\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}5\left(\frac1s-\frac1{s+5}\right)+\dfrac4{s+5}$

$\implies Y(s)=\dfrac15\left(\dfrac{e^{-3s}}s-\dfrac{e^{-3s}}{s+5}-\dfrac{e^{-5s}}s+\dfrac{e^{-5s}}{s+5}\right)+\dfrac4{s+5}$

Take the inverse transform of both sides, recalling that

$Y(s)=e^{-cs}F(s)\implies y(t)=u(t-c)f(t-c)$

where $F(s)$ is the Laplace transform of the function $f(t)$ . We have

$F(s)=\dfrac1s\implies f(t)=1$

$F(s)=\dfrac1{s+5}\implies f(t)=e^{-5t}$

We then end up with

$y(t)=\dfrac{u(t-3)(1-e^{-5t})-u(t-5)(1-e^{-5t})}5+5e^{-5t}$

3 0

3 years ago

Solve for x. x − 4 1/6 = 9 1/3 A) −131 2 B) −51 6 C) 131 2 D) 51 6

lora16 [44]

I believe the answer is B

4 0

3 years ago

Read 2 more answers

What is the value of a?<br> a = ?

Tatiana [17]

Answer:

a = 15

Step-by-step explanation:

The Pythagorean theorem applies:

a² + 20² = 25²

a² = 625 - 400 . . . . . subtract 20²

a = √225 . . . . . . . . . . take the square root

a = 15

_____

You might recognize that the given measures (20, 25) are in the ratio 4:5. There is only one right triangle with sides in that ratio: the 3:4:5 right triangle. That is, the unknown side (a) matches

a : 20 : 25 = 3 : 4 : 5 . . . . numbers on the left are 5 times those on the right

a = 5·3 = 15

6 0

3 years ago

Read 2 more answers

Round 8,937.2546 to the nearest<br> hundred.

xeze [42]

Answer:

8,900

Step-by-step explanation:

Given Number: 8,937.2546

Determine the two consecutive multiples of 100 that bracket 8,937.2546

8,937.2546 is between 8,900 and 9,000

8,950 is the midpoint between 8,900 and 9,000

As illustrated on the number line, 8,937.2546 is less than the midpoint (8,950)

Therefore, 8,937.2546 rounded to the nearest hundred = 8,900

6 0

1 year ago