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3 years ago

Find the square meters

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

5 0

Answer:

17 square meters

Step-by-step explanation:

Begin by finding the area of the whole rectangle without the cut out. The area is A = l*w = 4*5 = 20.

Now find the area of the cut out and subtract it from 20.

A = l*w = 3*1 = 3

20 -3 = 17

The area of the figure is 17.

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2. Jamie bought a computer for $856.35 including tex He received an interest-free loan for the exact poor of the computer. If Ja

Ksju [112]

Answer:

57.09

Step-by-step explanation:

856.35/15. total amount divided by number of payments

5 0

3 years ago

A manufacturer produces bearings, but because of variability in the production process, not all of the bearings have the same di

Lena [83]

Answer:

Proportion of all bearings falls in the acceptable range = 0.9973 or 99.73% .

Step-by-step explanation:

We are given that the diameters have a normal distribution with a mean of 1.3 centimeters (cm) and a standard deviation of 0.01 cm i.e.;

Mean, $\mu$ = 1.3 cm and Standard deviation, $\sigma$ = 0.01 cm

Also, since distribution is normal;

Z = $\frac{X -\mu}{\sigma}$ ~ N(0,1)

Let X = range of diameters

So, P(1.27 < X < 1.33) = P(X < 1.33) - P(X <=1.27)

P(X < 1.33) = P( $\frac{X -\mu}{\sigma}$ < $\frac{1.33 -1.3}{0.01}$ ) = P(Z < 3) = 0.99865

P(X <= 1.27) = P( $\frac{X -\mu}{\sigma}$ < $\frac{1.27 -1.3}{0.01}$ ) = P(Z < -3) = 1 - P(Z < 3) = 1 - 0.99865

= 0.00135

P(1.27 < X < 1.33) = 0.99865 - 0.00135 = 0.9973 .

Therefore, proportion of all bearings that falls in this acceptable range is 99.73% .

7 0

3 years ago

Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions

monitta

I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take $z=y'$ , so that $z'=y''$ and we're left with the ODE linear in $z$ :

$y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2$

Now suppose $y$ has a power series expansion

$y=\displaystyle\sum_{n\ge0}a_nx^n$
$\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}$
$\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}$

Then the ODE can be written as

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0$

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0$

$\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0$

All the coefficients of the series vanish, and setting $x=0$ in the power series forms for $y$ and $y'$ tell us that $y(0)=a_0$ and $y'(0)=a_1$ , so we get the recurrence

$\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}$

We can solve explicitly for $a_n$ quite easily:

$a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}$

and so on. Continuing in this way we end up with

$a_n=\dfrac{a_1}{n!}$

so that the solution to the ODE is

$y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x$

We also require the solution to satisfy $y(0)=a_0$ , which we can do easily by adding and subtracting a constant as needed:

$y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}$

4 0

2 years ago

What is 7 1/5 - 6 2/5 =?

poizon [28]

Answer:

0.8

Step-by-step explanation:

7 1/5 - 6 2/5 = 0.8

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3 years ago

What is the standard form of 3+5x-4x^2<br>and what is the standard form of 8x+x+5+x^3

harina [27]

Answer:

1. -4x^2 + 5x + 3

2. x^3 + 9x + 5

Step-by-step explanation:

hope this helps

4 0

2 years ago