Answer: 179.93
Step-by-step explanation:
1) Change radical forms to fractional exponents using the rule:The n<span>th root of "</span>a number" = "that number" raised to the<span> reciprocal of n.
For example </span>
![\sqrt[n]{3} = 3^{ \frac{1}{n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7B3%7D%20%3D%20%20%203%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%20%7D)
.
The square root of 3 (

) = 3 to the one-half power (

).
The 5th root of 3 (
![\sqrt[5]{3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B3%7D%20)
) = 3 to the one-fifth power (

).
2) Now use the product of powers exponent rule to simplify:This rule says

. When two expressions with the same base (a, in this example) are multiplied, you
can add their exponents while keeping the same base.
You now have

. These two expressions have the same base, 3. That means you can add their exponents:
3) You can leave it in the form
or change it back into a radical ![\sqrt[10]{3^7}](https://tex.z-dn.net/?f=%20%5Csqrt%5B10%5D%7B3%5E7%7D%20)
------
Answer:
or
The equation must equal 84, so you can eliminate B and D.
Chin charges a rate for 2 hours, then charges a reduced rate for 4 hours. There are no discounts present in his rate, so you can eliminate A.
The equation for Chin's charges can be found by the equation C. 2x + 4y = 84.
Answer: The required solution is

Step-by-step explanation: We are given to solve the following differential equation :

Let us consider that
be an auxiliary solution of equation (i).
Then, we have

Substituting these values in equation (i), we get
![m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.](https://tex.z-dn.net/?f=m%5E2e%5E%7Bmt%7D%2B10me%5E%7Bmt%7D%2B25e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%5E2%2B10y%2B25%29e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B10m%2B25%3D0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bsince%20%7De%5E%7Bmt%7D%5Cneq0%5D%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B2%5Ctimes%20m%5Ctimes5%2B5%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%2B5%29%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20m%3D-5%2C-5.)
So, the general solution of the given equation is

Differentiating with respect to t, we get

According to the given conditions, we have

and

Thus, the required solution is
