Answer:
y = 4
Step-by-step explanation:
Given that y varies jointly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 16 when x = 4 and z = 
, that is
16 = k × 4 × = 2k ( divide both sides by 2 )
8 = k
y = 8xz ← equation of variation
When x = 2 and z = 
, then
y = 8 × 2 × = 16 × = 4
The first time I did it, I got an answer that's not one of the choices. The second time
I did it, I got an answer that IS . Here are both of my procedures. If all you want is
the answer, look down below at the second one. But if you could help me out, now
that you know how to do this stuff, please look at my first solution and tell me where
I messed up. I can't find it.
=======================================================
Here's what the problem tells you:
D = 10 log ( ' I ' / 10⁻¹² )
D = 60 . . . . . find ' I ' .
Here we go:
60 = 10 log ( ' I ' / 10⁻¹² )
Divide each side by 10 :
6 = log ( ' I ' / 10⁻¹² )
Raise 10 to the power of each side of the equation:
10⁶ = ' I ' / 10⁻¹²
Multiply each side by 10¹² :
10¹⁸ = ' I ' That's 10^18. It looks bad, because that isn't one of the choices.
Let's try a slightly different procedure:
============================================
After substituting 10⁺¹² for I₀ , we're working with this formula:
D = 10 log ( 'I' / 10⁺¹² )
Let's just look at the log part of that.
The log of a fraction is [ log(numerator) - log(denominator) ]
log of this fraction is [ log( 'I' ) - log(10⁻¹²) ]
But log(10⁻¹²) is just (-12) .
So the log of the fraction is [ log( 'I' ) + 12 ]
And the whole formula is now:
D = 10 [ log( 'I' ) + 12 ]
60 = 10 [ log( 'I' ) + 12 ]
Divide each side by 10 :
6 = log( 'I' ) + 12
Subtract 12 from each side :
-6 = log ( ' I ' )
' I ' = 10⁻⁶
That's choice-'B' .
==================================================
I'm going to leave the first solution up there, in hopes that you, or one
of the many aces, experts, and geniuses that prowl this site constantly,
can weigh in and show me my blunder on the first attempt.
Answer: After 6 Months Casey would have paid $450 at either gym.
Step-by-step explanation:
Since we're looking for these two gyms cost the same, we need to make the equation compare the two together:
35x + 240 = 75x (the 1st gym with a joining fee $240 and 35 monthly equals $75 monthly)
Subtract 35x from both sides:
35x - 35x + 240 = 75x - 35x
240 = 40x
Divide by 40:
240 / 40 = 6
6 = x
So they cost the same after 6 months
35 * 6+ 240 = 75 * 6
450 = 450
And you'll be spending $450 in total.
Volume of cylinders = pi x r^2 x height Simplifying the ratio: 1.6/3 = 16 / 30 (multiply and divide by 10 to remove the decimal) Volume Ratio = 512:27
