Answer:
q=26.92 p=31.13
Step-by-step explanation:
![p^{2} +16q=1400\\\\q=\frac{1400-p^{2} }{16} ;\\\\700-p^{2} +10q=0\\\\q=\frac{p^{2}-700 }{10} ;\\\\](https://tex.z-dn.net/?f=p%5E%7B2%7D%20%2B16q%3D1400%5C%5C%5C%5Cq%3D%5Cfrac%7B1400-p%5E%7B2%7D%20%7D%7B16%7D%20%3B%5C%5C%5C%5C700-p%5E%7B2%7D%20%2B10q%3D0%5C%5C%5C%5Cq%3D%5Cfrac%7Bp%5E%7B2%7D-700%20%7D%7B10%7D%20%3B%5C%5C%5C%5C)
![q=q\\\\\frac{1400-p^{2} }{16} =\frac{p^{2}-700 }{10} \\\\10(1400-p^{2})=16(p^{2}-700)\\\\14000-10p^{2}=16p^{2}-11200\\\\14000+11200=16p^{2}+10p^{2}\\\\25200=26p^{2}\\\\p^{2}=\frac{25200}{26} \\\\p=+\sqrt{\frac{25200}{26}} \\\\p=31.13](https://tex.z-dn.net/?f=q%3Dq%5C%5C%5C%5C%5Cfrac%7B1400-p%5E%7B2%7D%20%7D%7B16%7D%20%3D%5Cfrac%7Bp%5E%7B2%7D-700%20%7D%7B10%7D%20%5C%5C%5C%5C10%281400-p%5E%7B2%7D%29%3D16%28p%5E%7B2%7D-700%29%5C%5C%5C%5C14000-10p%5E%7B2%7D%3D16p%5E%7B2%7D-11200%5C%5C%5C%5C14000%2B11200%3D16p%5E%7B2%7D%2B10p%5E%7B2%7D%5C%5C%5C%5C25200%3D26p%5E%7B2%7D%5C%5C%5C%5Cp%5E%7B2%7D%3D%5Cfrac%7B25200%7D%7B26%7D%20%5C%5C%5C%5Cp%3D%2B%5Csqrt%7B%5Cfrac%7B25200%7D%7B26%7D%7D%20%5C%5C%5C%5Cp%3D31.13)
replace p in any equation and
![q=\frac{1400-p^{2} }{16} \\\\q=\frac{1400-(31.13)^{2} }{16}\\\\q=26.92](https://tex.z-dn.net/?f=q%3D%5Cfrac%7B1400-p%5E%7B2%7D%20%7D%7B16%7D%20%5C%5C%5C%5Cq%3D%5Cfrac%7B1400-%2831.13%29%5E%7B2%7D%20%7D%7B16%7D%5C%5C%5C%5Cq%3D26.92)
Answer:
$936
Step-by-step explanation:
Simple interest is money you can earn by initially investing some money (a.k.a the principal). In return, a percentage (a.k.a the interest) of the initial money invested is added to the principal, this is what makes your initial investment grow.
The equation for simple interest is:
I = P x r x t
P = Principal, $2600
r = interest rate, 12%
t = time involved, 3 years
Fill in the values:
2600 × 0.12 × 3 = $936.00
D and F and C are all equal D.360 F. 10yards = 360inches C. 30 feet = 350inches.
Answer: TRUE:
_____________________
It is TRUE that the product of 21 (twenty-one) negative integer is a negative number; because you are multiplying an ODD NUMBER of NEGATIVE INTEGERS.
________________________
Answer:
![\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7Bx%5E4%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B1%7D%7B5%7D%28%20%5Carctan%28x%5E5%29%29%20%2B%20c)
Step-by-step explanation:
Given
![\int\ {\frac{x^4}{1 + x^{10}}} \, dx](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7Bx%5E4%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20dx)
Required
Integrate
We have:
![\int\ {\frac{x^4}{1 + x^{10}}} \, dx](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7Bx%5E4%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20dx)
Let
![u = x^5](https://tex.z-dn.net/?f=u%20%3D%20x%5E5)
Differentiate
![\frac{du}{dx} = 5x^4](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%205x%5E4)
Make dx the subject
![dx = \frac{du}{5x^4}](https://tex.z-dn.net/?f=dx%20%3D%20%5Cfrac%7Bdu%7D%7B5x%5E4%7D)
So, we have:
![\int\ {\frac{x^4}{1 + x^{10}}} \, dx](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7Bx%5E4%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20dx)
![\int\ {\frac{x^4}{1 + x^{10}}} \, \frac{du}{5x^4}](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7Bx%5E4%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20%5Cfrac%7Bdu%7D%7B5x%5E4%7D)
![\frac{1}{5} \int\ {\frac{1}{1 + x^{10}}} \, du](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%5Cint%5C%20%7B%5Cfrac%7B1%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20du)
Express x^(10) as x^(5*2)
![\frac{1}{5} \int\ {\frac{1}{1 + x^{5*2}}} \, du](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%5Cint%5C%20%7B%5Cfrac%7B1%7D%7B1%20%2B%20x%5E%7B5%2A2%7D%7D%7D%20%5C%2C%20du)
Rewrite as:
![\frac{1}{5} \int\ {\frac{1}{1 + x^{5)^2}}} \, du](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%5Cint%5C%20%7B%5Cfrac%7B1%7D%7B1%20%2B%20x%5E%7B5%29%5E2%7D%7D%7D%20%5C%2C%20du)
Recall that: ![u = x^5](https://tex.z-dn.net/?f=u%20%3D%20x%5E5)
![\frac{1}{5} \int\ {\frac{1}{1 + u^2}}} \, du](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%5Cint%5C%20%7B%5Cfrac%7B1%7D%7B1%20%2B%20u%5E2%7D%7D%7D%20%5C%2C%20du)
Integrate
![\frac{1}{5} * \arctan(u) + c](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%2A%20%5Carctan%28u%29%20%2B%20c)
Substitute: ![u = x^5](https://tex.z-dn.net/?f=u%20%3D%20x%5E5)
![\frac{1}{5} * \arctan(x^5) + c](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%2A%20%5Carctan%28x%5E5%29%20%2B%20c)
Hence:
![\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7Bx%5E4%7D%7B1%20%2B%20x%5E%7B10%7D%7D%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7B1%7D%7B5%7D%28%20%5Carctan%28x%5E5%29%29%20%2B%20c)