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Artist 52 [7]
3 years ago
10

How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … (

a) There are no other restrictions. (b) xi ≥ 3 for i = 1, 2, 3, 4, 5, 6 (c) 3 ≤ x1 ≤ 10 (d) 3 ≤ x1 ≤ 10 and 2 ≤ x2 ≤ 7
Mathematics
1 answer:
prohojiy [21]3 years ago
8 0

Answer:

The equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … Will have:

(a) 6 solutions where there are no other restrictions.

(b) 4 Solutions for xi ≥ 3 for i = 1, 2, 3, 4, 5, 6(x3 + x4 +x5 + x6 = 25)

(c) 4 Solutions for 3 ≤ x1 ≤ 10

( x3 + x4 + x5 + x6 = 25)

(d) 5 Solutions for 2 ≤ x2 ≤ 7

Step-by-step explanation:

The equation have 6 unknown variables . This means it will have 6 solutions when no condition is imposed as in (a) above. The number of unknown variables in the equation will give the numbers of solutions

When the conditions are imposed, the numbers of unknown variables will give the number of solutions.

In (b) and (c), the equation will reduce to x3 + x4 +x5 + x6 = 25) and the unknown variables are 4, giving 4 solutions

In (d), the equation will reduce be 5 unknown variables(x2 + x3 + x4 +x5 + x6 = 25) and the solution is 5

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Determine whether the following statements are true and give an explanation or counterexample.
Furkat [3]

Answer:

A) When using the shell​ method, the axis of the cylindrical shells is parallel to the axis of revolution. True.

The Shell method is a technique used to find the volume of a solid of revolution. Here, we take thin shells with axis coinciding with the axis about which the region whose volume is to be found, is revolved.

B) If a region is revolved about the​ y-axis, then the shell method must be used. False.

This method can be used with any axis of rotation.

C) If a region is revolved about the​ x-axis, then in principle it is possible to use the​ disk/washer method and integrate with respect to x or the shell method and integrate with respect to y. True.

The washer method uses thin disks with infinite width but the shell method uses thin concentric shells with infinite width about the axis of revolution. So, the statement is true.

5 0
3 years ago
Randy has 36 tiles. How should he arrange them so that he has the smallest perimeter?
Snezhnost [94]

Answer:

6by6

Step-by-step explanation:

3 0
4 years ago
A 0. 0427 kg racquetball is moving 22. 3 m/s when it strikes a stationary box. The ball bounces back at 11. 5 m/s, while the box
andreyandreev [35.5K]

To solve the question we must know about the conservation of momentum.

<h2>Conservation of Momentum</h2>

According to the law of conservation of momentum, when two bodies collide with each other then their momentum is conserved if no external force acts on the system. therefore, the combined momentum of the two objects before collision will be equal to the combined momentum of the two objects after the collision.

the momentum of the two objects before the collision

                       = momentum of the two objects after the collision

The mass of the box is 0.30141 kg.

<h2>Explanation</h2>

Given to us

  • Mass of racquetball, m = 0.0427 kg,
  • Velocity of racquetball before Collision,  \bold{u_1} = 22.3 m/s,
  • Velocity of box before Collision,\bold{ u_2}  = 0 m/s,
  • Velocity of racquetball after Collision, \bold{v_1} = 11.5 m/s,
  • Velocity of box after Collision, \bold{v_2} = 1.53 m/s,

<h3>Assumption</h3>

Let the mass of the box be M.

<h3>Conservation Of Momentum</h3>

Momentum before collision = Momentum after collision

mu_1 + Mu_2 = mv_1 + Mv_2

given, the box was stationary before the collision,

mu_1 + Mu_2 = mv_1 + Mv_2\\\\&#10;mu_1 + 0 = mv_1 + Mv_2\\\\&#10;mu_1  - mv_1 = Mv_2\\\\&#10;M= \dfrac{mu_1  - mv_1}{v_2}

Substituting the values,

M= \dfrac{mu_1  - mv_1}{v_2}\\\\&#10;M = \dfrac{(0.0427 \times 22.3)  - (0.0427\times 11.5)}{1.53}\\\\&#10;M = 0.30141\ kg

Hence, the mass of the box is 0.30141 kg.

Learn more about Conservation of Momentum:

brainly.com/question/2141713

3 0
3 years ago
Help<br> now please<br>ASAP<br>​
solong [7]

To find the answer, you must first turn the fractions into decimals. 4 ÷ 5 = 0.8 ; 1 ÷ 2 = 0.5 ; 1 ÷ 10 = 0.1. Then you must subtract 0.5 from 0.8. Then add 0.1 to 0.3 .

5 0
3 years ago
CAN SOMEONE PLEASE ANSWER!
belka [17]

Answer:

\frac{6}{5x^2}

Step-by-step explanation:

\sqrt{}\frac{72x^1^6}{50x^3^6}

Dividing the numerator and denominator by 2 gives;

\sqrt{}\frac{36x^1^6}{25x^3^6}

\sqrt{36x^1^6} = 6x^{4}

\sqrt{25x^3^6} = 5x^{6}

\frac{6x^4}{5x^6} = \frac{6}{5} × x^{4 - 6}

This gives \frac{6}{5} × x^{-2}

Which can also be written as \frac{6}{5x^2}

6 0
3 years ago
Read 2 more answers
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