x = liters of 40% solution
y = liters of 70% solution
Gabe needs 30 liters, so
x + y = 30
Each liter of 40% solution contributes 0.4x liter of acid; each liter of 70% solution contributes 0.7y liter of acid. Gabe needs a solution with concentration 60%, which from 30 liters amounts to a net volume of 0.6*30 = 18 liters of acid. So
0.4x + 0.7y = 18
Solve the system however you like. By substitution, we have
y = 30 - x
0.4x + 0.7(30 - x) = 18
0.4x + 21 - 0.7x = 18
3 = 0.3x
==> x = 10 ==> y = 20
Answer:
10Oz = 7 , 14Oz = 16, 20 OZ = 6
Step-by-step explanation:
There three equations that can be made here based on given data
Let number of 10 Oz cup be x
Let number of 14 Oz cup be y
Let number of 20 Oz cube be z
we can see that
x+y+z=29 ----- (i)
.95x + 1.15y + 1.5z = 34.05 ---- (ii)
10x+ 14y + 20z = 414 ---- (iiI)
We can solve these equations together to get the value of x and y and z (Done through calculator 3 variable equation function)
x= 7
y=16
z=6
It's equal to the exponent, 2 to what power = x^3 y^5
Answer:
24x-2
Step-by-step explanation:
Perimeter is 2(L+w)
(10x-3)+(2x+2)
Combine like terms
12x-1
2(12x-1)
24x-2
Sounds like a physics problem
basically we can simlpify it to this:
we toss something straight up with initial velocity 10ft/sec, assuming gravity kicks in, what is max height?
we can use the kinematic equation
![v_{f}^2=v_{0}^2+2ad](https://tex.z-dn.net/?f=v_%7Bf%7D%5E2%3Dv_%7B0%7D%5E2%2B2ad)
![v_f](https://tex.z-dn.net/?f=v_f)
is final velocity
![v_0](https://tex.z-dn.net/?f=v_0)
is initial velocity
a is acceleration due to gravity
d=distance traveled
if we say he tosses it straight up then when it reaches max height,
![v_f=0](https://tex.z-dn.net/?f=%20v_f%3D0)
and
![v_0=10 \frac{ft}{s}](https://tex.z-dn.net/?f=v_0%3D10%20%5Cfrac%7Bft%7D%7Bs%7D)
and we know that
![a=-32.174 \frac{ft}{s^2}](https://tex.z-dn.net/?f=a%3D%3Cspan%3E-32.174%20%5Cfrac%7Bft%7D%7Bs%5E2%7D)
so solving for d
<span>
![v_{f}^2=v_{0}^2+2ad](https://tex.z-dn.net/?f=v_%7Bf%7D%5E2%3Dv_%7B0%7D%5E2%2B2ad)
</span><span>
![v_{f}^2-v_{0}^2=2ad](https://tex.z-dn.net/?f=v_%7Bf%7D%5E2-v_%7B0%7D%5E2%3D2ad)
</span><span>
![\frac{v_{f}^2-v_{0}^2}{2a}=d](https://tex.z-dn.net/?f=%5Cfrac%7Bv_%7Bf%7D%5E2-v_%7B0%7D%5E2%7D%7B2a%7D%3Dd)
plug the numbers in
</span>
![\frac{(0)^2-(10 \frac{ft}{s})^2}{2(-32.174 \frac{ft}{s^2})}=d](https://tex.z-dn.net/?f=%5Cfrac%7B%280%29%5E2-%2810%20%5Cfrac%7Bft%7D%7Bs%7D%29%5E2%7D%7B2%28%3Cspan%3E-32.174%20%5Cfrac%7Bft%7D%7Bs%5E2%7D%29%7D%3Dd)
![1.5540498539193137315845092310561 ft=d](https://tex.z-dn.net/?f=1.5540498539193137315845092310561%20ft%3Dd)
we add that to the initial 6ft
so total of 7.5540498539193137315845092310561 ft max height
about 7.6ft