1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mazyrski [523]
3 years ago
10

Find two consecutive numbers whose cubes differ by 631

Mathematics
1 answer:
yan [13]3 years ago
4 0
Let the two numbers be x and y, in which x is larger than y. From these variables, we can formulate the following equations:

x = y + 1  --> eqn 1
x³ - y³ = 631 --> eqn 2

Since there are two unknowns and two independent equations, this system is solvable. Substitute equation 1 to equation 2, then solve for y.

(y + 1)³ - y³ = 631
Solving for y,
y = 14
x = y + 1  = 14 + 1 = 15

<em>Therefore, the two consecutive numbers are 14 and 15.</em>
You might be interested in
Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'
vodka [1.7K]

Answer:

a) v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9

a(t) = x''(t) = v'(t) =6t-12

b)  0

c) a(t) = x''(t) = v'(t) =6t-12

When the acceleration is 0 we have:

6t-12=0, t =2

And if we replace t=2 in the velocity function we got:

v(t) = 3(2)^2 -12(2) +9=-3

Step-by-step explanation:

For this case we have defined the following function for the position of the particle:

x(t) = t^3 -6t^2 +9t -5 , 0\leq t\leq 10

Part a

From definition we know that the velocity is the first derivate of the position respect to time and the accelerations is the second derivate of the position respect the time so we have this:

v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9

a(t) = x''(t) = v'(t) =6t-12

Part b

For this case we need to analyze the velocity function and where is increasing. The velocity function is given by:

v(t) = 3t^2 -12t +9

We can factorize this function as v(t)= 3 (t^2- 4t +3)=3(t-3)(t-1)

So from this we can see that we have two values where the function is equal to 0, t=3 and t=1, since our original interval is 0\leq t\leq 10 we need to analyze the following intervals:

0< t

For this case if we select two values let's say 0.25 and 0.5 we see that

v(0.25) =6.1875, v(0.5)=3.75

And we see that for a=0.5 >0.25=b we have that f(b)>f(a) so then the function is decreasing on this case.  

1

We have a minimum at t=2 since at this value w ehave the vertex of the parabola :

v_x =-\frac{b}{2a}= -\frac{-12}{2*3}= -2

And at t=-2 v(2) = -3 that represent the minimum for this function, we see that if we select two values let's say 1.5 and 1.75

v(1.75) =-2.8125< -2.25= v(1.5) so then the function sis decreasing on the interval 1<t<2

2

We see that the function would be increasing.

3

For this interval we will see that for any two points a,b with a>b we have f(a)>f(b) for example let's say a=3 and b =4

f(a=3) =0 , f(b=4) =9 , f(b)>f(a)

The particle is moving to the right then the velocity is positive so then the answer for this case is: 0

Part c

a(t) = x''(t) = v'(t) =6t-12

When the acceleration is 0 we have:

6t-12=0, t =2

And if we replace t=2 in the velocity function we got:

v(t) = 3(2)^2 -12(2) +9=-3

5 0
3 years ago
One morning the temperature is -28 degrees in Anchorage, Alaska, and +65 degrees in Miami, Florida. Which city is warmer in the
Alecsey [184]

Answer:

B. Miami is 93 degrees warmer than Anchorage.

Step-by-step explanation:

Miami-Anchorage is equal to 65-(-28) which is equal to 65+28 which is equal to 93. Thus, Miami is warmer by 93 degrees.

3 0
3 years ago
What is a coterminal angles
navik [9.2K]

Answer: Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

6 0
3 years ago
A rectangle is 13 centimeters wide and 18 centimeters long. how long is its diagonal
Naddika [18.5K]
You have to use the Pythagorean theorem a squared plus b squared is c squared so 13 squared plus 18 squared equals c squared. 13x13=169 18x18=324 169+324=493 so c squared is 493 to get c you square root 493 which equals 22.2 so the diagonal, c, is 22.2 centimeters long
7 0
3 years ago
Find the distance between the points (13,20) and (18,8)​
steposvetlana [31]

Answer:

(5,12)

Step-by-step explanation:

because 18-13=5 and 20-8=12

5 0
3 years ago
Read 2 more answers
Other questions:
  • three classmates spent money at the school supplies store mark spent 0.5 dollar, andre spent 0.45 dollar, and Raquel spent 0.52
    8·1 answer
  • You invest $2000 in a bank account that has 5% annual interest rate, compound ed continously. how much will you have in 5 years?
    14·1 answer
  • A total of 524 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t
    9·2 answers
  • Dry rectangle that has an area of a square you need any permitter of 12 units what are the silence of the rectangle
    9·1 answer
  • What is the scientific notation for 0.00064
    6·2 answers
  • Help me please<br> Solve the system algebraically using substitution.
    9·1 answer
  • 1 1/4×-1 1/3 is equals to?​
    15·1 answer
  • In TUV the measure of V=90 TU=88 and UV=43 feet. Find the measure of T to the nearest tenth of a degree​
    5·2 answers
  • Any help? I'm not sure how to answer this
    12·1 answer
  • = Homework: Special Right Triangles (8.2)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!