To subtract fractions, we need an lcd( lowest common denominator)
8. the lcd is 42 because it’s the smallest number that 6 and 7 are both factors of. the lcd is the bottom of the fraction
to make the denominator of (4/7) 42, we will multiply the top and bottom by 6 and we get (24/42)
to make the denominator of (3/6) 42, we will multiply the top and bottom by 7 and we get (21/42)
these two numbers now have the same denominator so we subtract them
24/42 - 21/42 = 3/42 which simplifies to 1/14
9. since these fractions already have a common denominator, we will make them mixed fractions
-5(2/7) as a mixed fraction. first multiply 5*7 which is 35. now add 2 which is 37. our mixed fraction is -37/7
-1(5/7) as a mixed fraction. multiple 1*7 which is 7. now add 5 which is 12. our mixed fraction is -12/7
now subtract (-37/7) - (12/7) and we get -49/7 which simplifies to -7
Considering the ballon to be spherical
It's volume is given by 4/3(π r^3) by differentiating volume with respect to time we get rate of change of volume hence,
4πr^2(dr/dt)=600÷60=10
Substituting r=30cm
4π(30)*(30)(dr/dt)=10
dr/dt=rate of increase in bullion's radius=1/(360π)cm/s
Subtract Harmony Trail from Mountain Trail so 844-528=316
(-7)^2 and 5^3 are your answers
