Given that 14t = 2d, 5p = 2c, 4c = 9m, and 12p = 63t, what is 15d in the units of m? Can you show work on how to do this so I know what I missed or did wrong.
Thanks! :)
You know, it would have been MUCH better if you had shown your work and we could tell instantly what you did right or wrong. As it is, I don't know you did any work at all. Here is how you do it.
2d = [(14t x 12p)/63t] x (2c/5p) x (9m/4c) = ? then
multiply both side by 7.5 to get what 15 d is like this
7.5*2d = 7.5{[(14t x 12p)/63t] x (2c/5p) x (9m/4c)}
15d = ?m
Post your work if you get stuck.
Hey DrBob222
After I plugged in that into calculator I got -3. Does that sound about right?
To find the value of 15d in the units of m, we'll use the given equations and solve for the value of d in terms of m:
Given: 14t = 2d (equation 1)
Given: 5p = 2c (equation 2)
Given: 4c = 9m (equation 3)
Given: 12p = 63t (equation 4)
We'll begin by finding the value of p in terms of t:
From equation 4, divide both sides by 12:
12p/12 = 63t/12
p = 63t/12
p = 21t/4 (equation 5)
Next, find the value of c in terms of t:
From equation 2, multiply both sides by 2/5:
(2/5)c = (2/5)(5p)
(2/5)c = 2p
c = 2p/(2/5)
c = 5p (equation 6)
Substitute equation 5 into equation 6:
c = 5(21t/4)
c = 105t/4 (equation 7)
Substitute equation 7 into equation 3:
4(105t/4) = 9m
420t/4 = 9m
105t = 9m
m = (105t)/9 (equation 8)
Finally, substitute equation 1 into equation 8:
m = (105(14t)/9
m = 1470t/9
To find the value of 15d in terms of m, substitute equation 1 into the expression:
15d = 15(2d/14)
15d = 30d/14
Since we want to find the value of 15d in terms of m, substitute equation 8 into the expression:
15d = 30(1470t/9)/14
Simplifying further:
15d = 30(1470t)/9)/14
15d = (44100t/3)/14
15d = 14700t/14
15d = 7350t/7
Now, substitute m = 1470t/9 into the equation:
15d = 7350(1470t/9)/7
Simplifying further:
15d = (10795500t/9)/7
15d = 15365t/3
Therefore, 15d in the units of m is equal to 15365t/3.
To find the value of 15d in terms of meters (m), we can use the given equations. Let's work through the problem step by step:
Given equations:
1) 14t = 2d
2) 5p = 2c
3) 4c = 9m
4) 12p = 63t
First, let's solve equation 4) for p:
12p = 63t
Divide both sides by 12:
p = (63t) / 12
Simplify:
p = 21t / 4
Now, let's substitute this value of p in equation 2):
5p = 2c
5 * (21t / 4) = 2c
105t / 4 = 2c
Divide both sides by 2:
105t / 8 = c
Now, we can substitute this value of c in equation 3):
4c = 9m
4 * (105t / 8) = 9m
105t / 2 = 9m
Divide both sides by 105 to isolate t:
t / 2 = 9m / 105
t / 2 = m / 35
Now that we have the relation between t and m, let's go back to equation 1) involving d and t:
14t = 2d
Divide both sides by 2:
7t = d
Now, substitute the relation t = m / 35 in terms of d:
7 * (m / 35) = d
m / 5 = d
Finally, to find 15d in terms of m, we substitute the value of d we just found:
15d = 15 * (m / 5)
15d = 3m
Therefore, 15d in the units of m is equal to 3m.