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m_a_m_a [10]
2 years ago
10

Help please, try to explain it in steps for me if u can't that's fine, ty!

Mathematics
1 answer:
Iteru [2.4K]2 years ago
3 0

Answer:

B

Step-by-step explanation:

We are given that Expression One is:

2\cdot 10^x

And Expression Two is:

4\cdot 10^{x+y}

We are given that the value of Expression Two is 20,000 times greater than the value of Expression One. And we want to find the value of <em>y.</em> In other words:

4\cdot 10^{x+y}=20000(2\cdot 10^x)

We can divide both sides by four:

10^{x+y}=10000\cdot 10^x

Recall that:

x^a\cdot x^b=x^{a+b}

Therefore:

10^x\cdot 10^y=10000\cdot 10^x

Divide both sides by 10ˣ:

10^y=10000

Solve for <em>y: </em>

<em />\displaystyle y = \log_{10}10000 = 4<em />

Our answer is B.

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Use Euler's method with each of the following step sizes to estimate the value of y(0.4), where y is the solution of the initial
sergey [27]

Answer:

h=0.4--> 15

h=0.2 --> 14.06

h=0.1 --> 13.71

Step-by-step explanation:

This is a numerical solution using Euler's method. Euler's method enables us to numerically approch a solution with a suitable  step size. As the step size gets smaller, the approximation will be more accurate. Euler's method is as the following.

y_{i+1}=y_{i}+h*y_{first derivation}

Here, h is the step size. The reason why first derivation used here is to make an appriximation with using the rate of increase or decrease. As the step size is smaller, the icreases or decreases are followed more accurately. Now, let's solve the question:

for h= 0.4:

y(0.4)=y(0)+0.4*y'

The trick here is y' is equal to y, thus we can write that y'=y(0.4) and our starting point y(0) is given as 9 in the question and the equation becomes:

y(0.4)=9+0.4*y(0.4) and this is easy to solve.By replacing y(0.4) functions to be at the same side of the equation, we get:

0.6*y(0.4)=9 and by solving this equation, y(0.4) is found to be 15.

for h=0.2:

This will be similar to the previous question, but since the step size is 0.2, we will first calculate y(0.2) and then y(0.4).

y(0.2)=y(0)+0.2*y(0.2) and y(0) is 9.

0.8*y(0.2)=9 and y(0.2)=11.25. Now, we will replace this value into the next iteration o the formula istead of y(0). The equation is like:

y(0.4)=y(0.2)+0.2*y(0.4) and y(0.4) is found to be 14.06.

for h=0.1:

This is also similar to the above solutions but will be longer and have 4 iterations.

first iteration: y(0.1)=9+0.1*y(0.1) --> y(0.1)=10

second iteration: y(0.2)=y(0.1)+0.1*y(0.2) --> y(0.2)=11.11

third iteration: y(0.3)=y(0.2)+0.1*y(0.3) --> y(0.3)=12.34

fourth iteration: y(0.4)=y(0.3)+0.1*y(0.4) --> y(0.4)=13.71

As the step size gets smaller, the answer also gets smaller and more accurate. With even smaller step sizes, there will be a better approximation. However, in case you have more complex equations or smaller step sizes, it is recommended to use a computer software to make an approximation.

6 0
3 years ago
Principle = $15,500 Interest Rate = 8.75% Time = ? Years Simple Interest = $5425.00
amid [387]
We must find time by using the simple interest formula:

I = P x i x t

I is the interest
P is the total principal 
i is the rate of interest per year
t is the total time in years

In this example, when we plug our known values in, our formula looks like this: 

t = \frac{I}{i*p}

t = \frac{5425}{0.0875 * 15500}

t = 4

So time (in years) would be 4 years. 
7 0
3 years ago
What property does the number sentence show? 8+0=8
zubka84 [21]
Identity Property of Zero!
I hope this helps xD
7 0
3 years ago
Read 2 more answers
If ( 43.65 ) ( 8.79 ) / x = ( 0.4365 ) ( 87.9 ) then value of x is:
strojnjashka [21]

Answer:

  (d)  10

Step-by-step explanation:

Multiply by x and divide by its coefficient:

  (43.65)(8.79) = (0.4365)(87.9)x

  (43.65)(8.79)/((0.4365)(87.9)) = x

At this point, any calculator can give you the answer. It is, perhaps, more satisfying to work out the answer without a calculator.

  x = (43.65)/(0.4365) × (8.79)/(87.9)

In the first quotient, the numerator is 100 times the denominator; in the second, the denominator is 10 times the numerator.

  x = (100) × (1/10) = 100/10

  x = 10

_____

Moving the decimal point to the right 1 place multiplies the numerical value by 10.

5 0
3 years ago
Help I've got 5min to figure it out 20 points for 1st actual answer and brainlyist​
VARVARA [1.3K]
Chronological order
Hoped this help
4 0
2 years ago
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