Slope is (change in y)/(change in x). If you have a slope of -2/3 the change in y is -2 and the change in x is 3. Find the point (-2, 1) on the xy plane. Change the y component by -2 (move down 2 grid lines) then change the x component by 3 (move to the right 3 grid lines). If you repeat this process in both directions then draw a line through the points you'll have a line with slope -2/3 which passes through the point (-2, 1). The equation of this line is: y=-2/3x-1/3
16=1/4 d+2.5
Where d is diameter of larger gear
16-2.5=1/4d
D=74 cm
We are told that the principle is the same for both investments so we can say:
315=P(r+4)/100 and 175=Pr/100 solving both for P you have:
P=31500/(r+4) and P=17500/r since P=P:
17500/r=31500/(r+4)
175(r+4)=315r
175r+700=315r
-140r+700=0
-140r=-700
r=5
So the rates are 5% and (5+4)=9%
check...
P(9/100)=315 and P(5/100)=175
P=31500/9 and P=17500/5
P=157500/45 and P=157500/45
So P=P
note: P=$3500
3500(9/100)=$315
3500(5/100)=$175
Answer: Yeheheheheheuejehe
Explanation
Sol. (1) Prime factors of 26 = 2 x 13
Prime factors of 91 = 7 x 13
Hence, HCF = Common factors between 26 and 91 =13 and LCM=13x2x7=182
Now product of numbers 26 and 91
= 26 x 91 = 2366 and Product of HCF and LCM = 13 x 182 = 2366
So, it verify that product of two numbers = Product of HCF and LCM.
(2) Prime factors of 510 = 2 x 3 x 5 x 17
Prime factors of 92 = 2 x 2 x 23
Hence,HCF=2 and LCM=2×2×3 × 5×17×23 =23460
Now product of Numbers 510 and 92 = 46920 and product of HCF and LCM = 2 x 23460= 46920
Hence, verified that product of two numbers 18 equal to product of their HCF and LCM.
(3) Prime factors of336 = 2 x 2 x 2 x 2 x 3 x 7
Prime factors of 54 = 2 x 3 x 3 x 3
Hence, HCF (Product of common factors of 336 and 54)
=2 x 3=6
And LCM (Product of all common factors with remaining factors)
=(2 x 3)x 2 x 2 x 2 x 3 x 3 x 7=3024
Now, product of numbers 336 and 54 = 336 x 54 = 18144
and product of HCF and LCM = 6 x 3024 = 18144
Hence, product of two numbers: Product of HCF and LCM.
