Answer:
The solution of the equation are x = - 1 , y = 0 and z = 3
Step-by-step explanation:
Given three linear equation as :
6 x - y + z = - 3 ......A
4 x - 3 z = - 13 ......B
2 y + 5 z = 15 ......C
Solving eq A and C
I.e 2× (6 x - y + z ) = -3 ×2
or, 12 x - 2 y + 2 z = - 6
So, ( 12 x - 2 y + 2 z ) + ( 2 y + 5 z) = - 6 + 15
Or, 12 x + 7 z = 9 ......D
Solving eq B and D
I.e 3 × ( 4 x - 3 z ) = - 13 × 3
or, 12 x - 9 z = - 39
So, ( 12 x + 7 z ) - ( 12 x - 9 z ) = 9 + 39
or, 16 z = 48
∴ z = 
i.e z = 3
put the value of z in eq D
So, 12 x + 7×3 = 9
Or, 12 x = 9 - 21
or, 12 x = - 12
∴ x = - 
I.e x = - 1
Now, Put The value of z in eq C
or, 2 y + 5 z = 15
or, 2 y + 5 × 3 = 15
Or, 2 y = 15 - 15
or, 2 y = 0
∴ y = 0
Hence The solution of the equation are x = - 1 , y = 0 and z = 3 Answer
We are given the statement that the strength, S, of a beam of width w andheight h is proportional to wh2. hence using k as the proportionality constant, the equation is S = k wh2. the exact width and height can be determined by applying optimization to the problem. optimization is taking the first derivative of an equation and equating then to zero
Answer: 1150 turns
Step-by-step explanation: radius of wheel is 0,9 m
In one turn wheel moves 2·pi·0,9 m = 5,652 m
You divide 6500 m : 6,652 m = 1150
Answer:
5. 2¯⁶ or 1/2⁶
6. 2⁹
Step-by-step explanation:
5. Simplify 2⁴ ÷ 2¹⁰
The above expression can be simplified as follow:
2⁴ ÷ 2¹⁰
Recall
Aⁿ ÷ Aᵐ = Aⁿ¯ᵐ
Thus,
2⁴ ÷ 2¹⁰ = 2⁴ ¯ ¹⁰
2⁴ ÷ 2¹⁰ = 2¯⁶
Recall:
A¯ⁿ = 1/Aⁿ
Thus,
2¯⁶ = 1/2⁶
Therefore,
2⁴ ÷ 2¹⁰ = 2¯⁶ or 1/2⁶
6. Simplify 2³ × (2²)³
2³ × (2²)³ can be simplified as follow:
2³ × (2²)³
Recall
(Aⁿ)ᵐ = Aⁿ*ᵐ
Thus,
(2²)³ = 2²*³
(2²)³ = 2⁶
2³ × (2²)³ = 2³ × 2⁶
Recall
Aⁿ × Aᵐ = Aⁿ⁺ᵐ
2³ × 2⁶ = 2³⁺⁶
2³ × 2⁶ = 2⁹
Therefore,
2³ × (2²)³ = 2⁹
