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ser-zykov [4K]
3 years ago
6

How to multiply a scientific notation by a whole number?

Mathematics
1 answer:
Fantom [35]3 years ago
3 0

The best way to explain it is to provide a couple of examples.

<u>Example 1:</u>    1.111 x 10³  multiplied by 5

= (1.111 x 5) x 10³

= 5.555 x 10³

<u>Example 2:</u>    6.666 x 10³  multiplied by 5

= (6.666 x 5) x 10³

= 33.330 x 10³

= 3.3330 x 10⁴

Answer: multiply the numbers together and then include 10ⁿ. Convert answer into scientific notation afterward, if needed.

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Consider the ODE, dy dx = y 2 1 + x (2) subject to condition y = 1 when x = 0, use your Euler code from class (modified if neces
makkiz [27]

Answer:

Computation.

Step-by-step explanation:

I'm not really sure if that's the analytical solution of the inital value problem,

because y(0)=11-ln(1-0)(3)=11. Howevwer, let us procede with the given values...

Let us assume that we are going to use euler with n=2 (two steps) and h=0.2(the size of each step)

The update rules of the Euler Methode are

X_i = X_{i-1}+h=X_0+ih

m_i=\dfrac{dY}{dX} \biggr \rvert_{x_i} \\\\Y_{i+1}=m_i\cdot h+y_i

Since the initial value problem tells us that Y=1 when X=0, we know that

X_0=0 and that Y_0=1. Then, we have

X_0=0\\\\X_1=0.2\\\\X_2=0.4

and

Y_0=1\\\\m_0=21 \cdot Y_0 + X_0 \cdot 2=21 \cdot 1 + 0=21\\\\Y_1=0.2 \cdot 21 + 1 =5.2\\\\m_1=21 \cdot Y_1 + X_1\cdot 2=21 \cdot 5.2 + 0.2 \cdot 2=109.6\\ \\Y_2=m_1 \cdot h + Y_1 = 109.6 \cdot 0.2 + 5.2= 27.12

which gives us the points (0,1), (0.2, 5.2) and (0.4, 27.12).

Now, since we want to compare the analyticaland the Euler result, we first compute the value of y=11-ln(1-x)(3) for the values x=0, 0.2 and 0.4. We get that

y(0)=11-\ln(1-0)(3)=11-ln(1)(3)=11\\\\Y(1)=11-\ln(1-0.2)(3)=11.67\\\\Y(2)=11-\ln(1-0.4)(3)=12.53

and we compute Y(i)-Y_i for each i.

It holds

Y(0)-Y_0=11-1=10\\\\Y(1)-Y_1=11.67-5.2=6.47\\\\Y(2)-Y_2=12.53-27.12=-14.59

which tells us that we have a really bad approximation, as I already stated there must be a mistake in the analytical solution since the intial values don't coincide. Also note that the curve that we get using the euler methose is growing faster than the analitical solution.

4 0
3 years ago
Just before a referendum on a school​ budget, a local newspaper polls 402 voters to predict whether the budget will pass. Suppos
Sliva [168]

Answer:

21.21%

Step-by-step explanation:

Assume that proportion of support follows normal distribution.For resulting in defeat the proportion of support should less than 0.5.Given that the proportion of support is p= 0.52.

Sample size(n)= 402

We know that standard deviation is given as

\sigma = \sqrt {\dfrac {p(1-p)}{n}}

Now by putting the values

\sigma = \sqrt {\dfrac{0.52\times 0.48}{402}}

σ=0.0249

Proportion of support follows normal distribution with mean is 0.52 and standard deviation is 0.0249

We know that Z=\dfrac{\bar{X}-\mu }{\sigma }

So

Z=\dfrac{0.5-0.52 }{0.0249}

Z= -0.80

So P(Z<-.80) =0.2118 from standard table.

So the probability of news paper to predict defeat is 21.21%

7 0
3 years ago
Ruby and her friends are going into a restaurant. How much would it cost to buy 3
Gnoma [55]

Answer:

Step-by-step explanation:

3x2.25=6.75

4x4=16

16+6.75=22.75

8 0
3 years ago
HELP FIRST TO ANSWER ALL IS BRAINLEIST!!!!!!!!!​
andreev551 [17]

Answer:

1. D) 1 9/20

2. B) 7/12

4. D) $50.00

Step-by-step explanation:

The working is as follows :

1. Mrs. Lang bought 3/4 pound of red grapes and 7/10 pound of green grapes. To find out how many are in total we have to add both values total.

3/4 + 7/10

The LCM of 4 and 10 is 20.

3/4 * 5 = 15/20

7/10 * 2 = 14/20

15/20 + 14/20 = 29/20 = 1 9/20

2. 1/3 + 1/4

The LCM of 3 and 4 is 12

1/3 * 4 = 4/12

1/4 * 3 = 3/12

4/12 + 3/12 = 7/12

4. Sharon spent 2/3 of her clothing allowance; she was given $75. All we have to do is find 2/3 of $25 :

2/3 * $75 = $50.00

4 0
3 years ago
Simplify the given expression.
Gnom [1K]

Answer:

C. - 132x + 43y

Step-by-step explanation:

10x + 41y - 142x + 2y

Rearrange and put like terms together.

10x - 142x + 41y + 2y

= 10x - 142x

= - 132x

= 41y + 2y

= 43y

Now put all values together.

-132x + 43y

6 0
3 years ago
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