Answer:
original is 4 & 6.
for 54 sq inch= 6 & 9 and for 96 sq inch=8 & 12
Step-by-step explanation:
Given: The length is 1.5 times the width.
so the length is, l = 1.5w
----(a)
lw = 24 =1.5w(w)
lw = 54=
1.5w(w)
lw = 96
=1.5w(w)
Further simplifying it,
1.5
=24
1.5=54
1.5=96
so,
= 
=16
= 
36
= 
64
taking the square root, we get:
w = 4
w = 6
w = 8
By putting the above values in eq (a), we can find their corresponding lengths:
l = 1.5(4) = 6
l = 1.5(6) = 9
l = 1.5(8) = 12
So a few lengths could be:
(l, w)
(6,4)
(9,6)
(12,8)
Answer:
x = 12z + 1 and y = 10z - 1
Step-by-step explanation:
To solve the system of equations, we can use the substitution method
If we call
3x - 4y + 4z = 7 I
x - y - 2z = 2 II
2x - 3y + 6z = 5 III
Clearing II x = 2 + y + 2z
Now, replacing II in III
2(2 + y + 2z) - 3y +6z = 5
4 + 2y + 4z - 3y + 6z = 5
10z - y = 1 from here y = 10z - 1
Finally, replacing y in I
3x - 4(10z - 1) + 4z = 7
3x -40z + 4 + 4z = 7
3x - 36z = 3
3x = 36z + 3
x = 12z + 1
Done
Answer:
The Law of Cosine : cos C = 
Step-by-step explanation:
See the figure to understand the proof :
Let A Triangle ABC with sides a,b,c,
Draw a perpendicular on base AC of height H meet at point D
Divide base length b as AD = x -b and CD = x
By Pythagoras Theorem
In Triangle BDC And In Triangle BDA
a² = h² + x² ( 1 ) c² = h² + (x-b)²
c² = h² + x² + b² - 2xb ...(. 2)
From above eq 1 and 2
c² = (a² - x²) + x² + b² - 2xb
or, c² = a² + b² - 2xb .....(3)
Again in ΔBDC
cos C = 
Or, cos C = 
∴ x= a cos C
Now put ht value of x in eq 3
I.e, c² = a² + b² - 2ab cos C
Hence , cos C = Proved Answer
