X^3 - y^3 = 218 where x and y are positive integers. Find x+y

Mathematics

1 answer:

finlep [7]2 years ago

8 0

The value of x + y is 12

<h3>How to solve for x + y?</h3>

The equation is given as:

x^3 - y^3 = 218

Make x^3 the subject

x^3 = 218 + y^3

The next cubic expression greater than 218 is 343.

So, we assume

x^3 = 343

This gives

x = 7

Substitute x^3 = 343 in x^3 = 218 + y^3

343 = 218 + y^3

Evaluate the like terms

y^3 = 125

This gives

y = 5

So, we have:

x + y = 7 + 5

Evaluate

x + y = 12

Hence, the value of x + y is 12

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Implicit differentiation of 1/x +1/y=5 y(4)= 4/19<br> y'(4)=?

Aneli [31]

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Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:

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3 years ago

In the figure above, quadrilateral ABCD is a parallelogram. Let x represent the measure of angle GBF, y represent the measure of

ira [324]

Answers:
measure angle x = 40°
measure angle y = 35°
measure angle z = 55°

Explanation:
Part (a): getting angle x:
In triangle BED, we have:
measure angle BED = 90°
measure angle BDE = 50°
Therefore:
measure angle DBE = 180 - (90+50) = 40°
Now, we have angle DBE and angle GBF vertically opposite angles.
This means that they are both equal. Therefore angle GBF = 40°
Since angle GBF is x, therefore:
x = 40°

Part (b): getting angle y:
We know that the sum of measures of angles on a straight line is 180.
This means that:
angle GBF + angle GBC + angle CBE = 180
We have:
angle GBF = 40°
angle GBC = 105°
angle CBE = y
Therefore:
40 + 105 + y = 180
y = 35°

Part (c): getting angle z:
In triangle BCE, we have:
measure angle BCE = z
measure angle BEC = 90°
measure angle CBE = 35°
Therefore:
z + 90 + 35 = 180
z = 55°

Hope this helps :)