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3 years ago

Please help !! Solve: 4^3x = 4^2

Mathematics

1 answer:

sladkih [1.3K]3 years ago

5 0

Answer: x=1/4

Step-by-step explanation:

Simplify both sides of the equation.

$64x=16$

Simplify both sides of the equation

$64x/64=16/64$

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Need help with #8 & #14 PLEASE!!

juin [17]

Answer:

8 (see work)

14. 2x^2 -4x^2 +3

Step-by-step explanation:

There's attached work for explanation

8 0

3 years ago

Ginger wants to join a gym. She goes to the local gym and is told that there is a one-time fee of $100 to join and then a monthl

spin [16.1K]

She has paid $460 after joining the gym for a year. First there is the joining fee of $100. Then $30 a month for a year is 30 x 12 which equals $360.

4 0

4 years ago

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¿cual es la solucion de la siguiente ecuacion (10+2x +x= -x +18)?

n200080 [17]

Answer:

x=2

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

4 years ago

Suppose the CPI increases this year from 208 to 221. What is the rate of inflation for this year? Round your answer to the neare

guajiro [1.7K]

SOLUTION:

We are to find the rate of inflation in the given question;

The formula to be used is;

Inflation rate =

$\frac{\text{CPI}_{present}-CPI_{previous}}{CPI_{previous}_{}}\text{ X 100}$ $\begin{gathered} \frac{221-208}{208}\text{ X }\frac{100}{1} \\ \\ \frac{13}{208}X\frac{100}{1} \\ \\ 6.25\text{ \%} \\ 6.3\text{ \% (nearest tenth of a percentage)} \end{gathered}$

CONCLUSION

The inflation rate of CPI that increased from 208 to 221 to the nearest tenth of a percentage is 6.3%.

8 0

2 years ago