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dedylja [7]
2 years ago
9

24x²/5xy simplified fully

Mathematics
1 answer:
jarptica [38.1K]2 years ago
5 0

Step-by-step explanation:

exponents are subracted when divided

so next step is

24x/5y and this is the answer

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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
A car is traveling up a steep ramp to a parking garage.the ramp is 445 feet long and rises a vertical distance of 80 feet. What
Alecsey [184]
With the information provided in the problem, we can create a right triangle with the ramp as its hypotenuse, and  the vertical rise as its opposite side from its angle of elevation.
Let E be the angle of elevation from the car to the end of the ramp. We now know that the hypotenuse of our triangle measures 445 feet, and the opposite side measures 80 feet, so we need a trig function that relates our angle of elevation with the hypotenuse and the opposite side. That function is sine:
sine(E)= \frac{80}{445}
E=arcsine( \frac{80}{445} )
E=10.36

We can conclude that the angle of elevation from the car to the end of the ramp is 10.36°.

3 0
3 years ago
Read 2 more answers
What's the complex conjugate of 13-21i
Lubov Fominskaja [6]
The complex conjugate of 13-21i is 1.3+ 2i.

In general the conjugate of a+bi is a - bi
and the conjugate of a-bi is a + bi

3 0
3 years ago
To find how high school students feel about hot lunches, Adam walks to the nearest high When a=6 and b=22, c=33. If c varies dir
Delvig [45]

Answer:The equation that models the solution will be

33 = 22k / 6

Step-by-step explanation:

The two types of variation involved in this problem are direct variation and inverse variation.

In direct variation, when one item changes in the positive or negative direction, the other item also changes in the positive or negative direction.

In inverse variation, when one item changes in the positive or negative direction, the other item also changes in the negative or positive direction.

From the information given,

c varies directly with b

If we introduce a direct proportionality constant, k, then,

c = kb

c also varies inversely with a

If we introduce an inverse proportionality constant, k, then,

c = k/b

Therefore, c = kb / a

When a=6 , b=22 and c=33.

The equation that models the solution will be

33 = 22k / 6

8 0
3 years ago
Someone, please help me with this question.
Viefleur [7K]

Answer:

C.  95°

Step-by-step explanation:

Sumplementary angles sum 180°

144° + a = 180°

a = 180° - 144°

a = 36°

121° + b = 180°

b = 180° - 121°

b = 59°

The sum of internal angles of a triangle is 180°

a + b + c = 180°

36° + 59° + c° = 180°

c° = 180° - (36°+59°)

c° = 180° - 95°

c° = 85°

then:

c + n = 180°

85° + n = 180°

n = 180° - 85°

n = 95°

5 0
3 years ago
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