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4 years ago

Write the fraction 72/81 in simplest form.

Mathematics

2 answers:

wel4 years ago

6 0

Answer: 8/9

Hope it helped!

noname [10]4 years ago

5 0

Answer:

8/9

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 72 and 81 is 9

72 ÷ 9

81 ÷ 9

= 8/9

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A baseball team had 28 hime runs last year. This year they have 20 homeruns. What was the percent of change

dexar [7]

Answer:

28.57% drop

Step-by-step explanation:

Number of runs

Last year = 28
This year = 20

Change this year:

28 - 20= 8

Change %:

8/28*100 = 28.57% drop

8 0

3 years ago

Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

Does anyone else agree that the answer for this family of curves question is E, dy/dx = x + y?

neonofarm [45]

Yes this is the correct answer. The slope field shown is the differential equation dy/dx = x+y

All points along the line x+y = k, for some constant k, will have the same tangent slope k. For example, the line x+y = 0 will have every point with tangent slope 0 for the solution y(x). It may not be 100% clear, but this graph has horizontal tickmarks on the line x+y = 0, or the tickmarks are close to being horizontal. Using geogebra, I checked the others and they produced completely different graphs, which allowed me to rule them out.

6 0

4 years ago

A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the

aleksklad [387]

R = speed in still water
r + c = speed with current
r - c = speed against current

3.5(r + c) = 70
r + c = 20
c = 20 - r

4(r + c) = distance from pier to pier
5(r - c) = distance from pier to pier
4(r + c) = 5(r - c)
4(r + 20 - r) = 5(r - 20 + r)
80 = 10r - 100
180 = 10r
18 = r
The speed in still water is 18 km/hour

3 0

3 years ago

if one m&m is randomly selected from a dish containing 7 green, 4 red, 5 blue and 8 yellow m&ms, find the probability th

Bad White [126]

Answer:

1/6 = 16.67%

Step-by-step explanation:

There are a total of 24 m&ms. The probability of picking an m&m that has a quantity of 4 is 4/24 = 1/6 = 16.67%

6 0

3 years ago