There are many ways to solve simultaneous linear equations. One of my favorite for finding integer solutions is graphing. The attached graph shows the solution to be ...
... (x, y) = (4, 7)
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You can also use Cramer's Rule, or the Vedic math variation of it, which tells you the solution to
is given by
Here, that means
... x = (9·67-5·75)/(9·8-5·3) = 228/57 = 4
... y = (75·8-67·3)/57 = 399/57 = 7
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A (graphing) calculator greatly facilitates either of these approaches.
<h2>
Dimension of box is 2 m x 2 m x 1.33 m</h2>
Step-by-step explanation:
Let a be base side and h be the height.
Volume of box, V = a²h
The sides of the box will cost $3 per m² and the base will cost $4 per m². Cost for making is $48.
That is
4a² + 3 x 4 x a x h = 48
4a² + 12 a x h = 48
a² + 3 ah = 12
So volume is
At maximum volume we have derivative is zero,
Negative side is not possible, hence side of square base is 2m.
Substituting in a² + 3 ah = 12
2² + 3 x 2 x h = 12
h = 1.33 m
Dimension of box is 2 m x 2 m x 1.33 m
Try this solution (note, this is not the shortest way):
1. if the given length is 'l' and the width is 'w', then according to the condition 4*l=w;
2. according to the condition the perimeter is 30 ft. Formula of the perimeter is P=2(l+w), then 2(l+w)=30;
3. if to substitute '4*l' instead of 'w', the formula of the perimeter (from item no. 2) will be as 2(4*l+l)=30 or 10*l=30 ⇒ l=3 ft. The length is 3 ft.!
4. if l=3 ft., then w=4*3=12 ft. The width is 12 ft.!
5. Area is
A=w*l; A=12*3=<u>36 ft²</u>
Answer:
Step-by-step explanation:
a) We have 15! as the product of 1 to 15 natural numbers. Since 17 is prime there will be no factor common to these
By actual division we find
15! (mod 17) =16
From this we deduce
even 16! mod 17 = 16 = -1
According to Wilson theorem
(17-1)! = -1 mod 17
Thus verified 17 is prime
Hence 15! (mod 17) =-1=16
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b) 2(26!) is divided by 29
Since 29 is prime
(29-1)! = -1 mod 29
28! = -1 mod 29 = 28
When divided this gives 25 as remainder
Answer:
D is 107 and E is 38
Step-by-step explanation:
20x+40=180
20x=140
X=140/20
x=7
M<A=5(7)+3
38
m<a=m<e
15(7)+2
107
m<b=m<d
