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Karolina [17]
2 years ago
5

Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 28, the sum of the square

s is 65, and the sum of the cubes of the numbers is 407.
Mathematics
2 answers:
fgiga [73]2 years ago
4 0

Answer:

Step-by-step explanation:

1) f(x) = x+y , xy = 49 --> f(x) = x+49/x

f '(x) = 1-49/x2 , x = ±√49 , choose x = +7

y = 49/x = 7

smaller = 7

larger = 7

2) Vertical Distance is difference between the two functions

V(x) = x+56 - x2, V '(x) = 1 -2x --> x = 1/2 --> V(1/2) = 56.25 <---Max Vertical distance

Boundary at -7 and 8 are less

3) I googled the equation, it is really y(n) = kn/(49+n2)

y '(n) = (k(49+n2) - 2kn2)/(49+n2) , Setting to zero, k(49+n2) -2kn2 = 0 , n = 7

4) Let x and y be the sides of the rectangle. A = xy = 37.5 Million or y = 37.5/x

The length of the fences is f(x) = 2x + 3y = 2x+112.5/x

f '(x) = 2-112.5/x2 --> x = √56.5 = 7.5 and y = 37.5/7.5 = 5 then scale by √Million

smaller = 5000 ft and larger = 7500 ft

this took me ages to work out so hopefully it helped

yanalaym [24]2 years ago
3 0

Answer:

x + y = 11

Step-by-step explanation:

xy = 28

x² + y² = 65

x³ + y³ = 407

(x + y)(x² - xy + y²) = x³ + y³

(x + y)(x² + y² - xy) = x³ + y³

(x + y)(65 - 28) = 407

37(x + y) = 407

x + y = 407÷37

x + y = 11

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Nita uses 1/3 of a carton of 12 eggs how many eggs does she use
Valentin [98]
What's 1/3 of 12?

Mulitply 1/3 times 12 = 4

Nita uses 4 eggs.
5 0
2 years ago
A sound wave travels through iron at a rate of 5120\,\dfrac{\text{m}}{\text{s}}5120 s m ​ 5120, start fraction, start text, m, e
klio [65]

Answer:

18432 km/h

Step-by-step explanation:

It is given that a sound wave travels through iron at a rate of 5120 m/s.

We know that

1 km = 1000 m

1 hour = 60 minutes

1 minutes = 60 second

Using these conversions we get

1 m = 0.001 km

1 hour  = 3600 second

5120\text{ m/s }=5120\times 0.001\times 3600\text{ km/h}

5120\text{ m/s }=18432\text{ km/h}

Therefore, the sound wave travels through iron at a rate of 18432 km/h.

6 0
3 years ago
Find the ratio of 5 degree and (pi/6)^c​
Nataly_w [17]
Lemme just say this real quick, Ratio
3 0
3 years ago
50+x(greater than or equal to)300
nikdorinn [45]

Answer:

x ≥ 250

Step-by-step explanation:

Note that "greater than or equal to" looks like ≥

50 + x ≥ 300

Isolate the variable. What you do to one side, you do to the other. Subtract 50 from both sides.

x + 50 (-50) ≥ 300 (-50)

x ≥ 300 - 50

x ≥ 250

x ≥ 250 is your answer.

~

4 0
3 years ago
Help me please it’s due by today
anyanavicka [17]

Answer:

D

Step-by-step explanation:

Lateral SA = area of the 4 triangles

Formula to be used :-

Area (triangle) = 1/2bh

=> 4 x 1/2 x 9 x 12

=> 108 x 2

=> 216 cm²

Total SA = LSA + area of the square

Formula to be used :-

Area (square) = side length x side length

=> 216 + 9 x 9

=> 216 + 81

=> 297 cm²

<u>The correct option is (D).</u>

4 0
2 years ago
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