What is the playing surface called where the college basketball semi- finals are played

Svet_ta [12734]

To start, we will shift the non-repeating segment of the decimal to the left side by dividing by a power of 10.

Then we will assign a variable to represent the value and also shift the repeating segment to the left.

Essentially, the concept here is that we can denote the repeating portion with a variable, let's say "x", and move forward with the calculation;

$\bf 0.580\overline{80}\implies \boxed{\cfrac{5.80\overline{80}}{10}}\qquad \textit{now, let's say }x= 5.80\overline{80}\\\\
-------------------------------$

$\bf thus\qquad \begin{array}{llll}
100\cdot x&=&580.80\overline{80}\\
&&575+5.80\overline{80}\\
&&575+x
\end{array}\qquad \implies 100x=575+x
\\\\\\
99x=575\implies x=\cfrac{575}{99}\qquad therefore\qquad \boxed{\cfrac{5.80\overline{80}}{10}}\implies \cfrac{\quad \frac{575}{99}\quad }{10}
\\\\\\
\cfrac{\quad \frac{575}{99}\quad }{\frac{10}{1}}\implies \cfrac{575}{99}\cdot \cfrac{1}{10}\implies \cfrac{575}{990}\implies \stackrel{simplified}{\cfrac{115}{198}}$

you can verify that using your calculator.

4 0

2 months ago

Read 2 more answers

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Leona [12618]

Response:

a

f'(t) is negative

b

The unit is degC/min

c

At 35 minutes since the coffee was placed on the counter, the temperature is 68, and it will drop by approximately 0.75 in the next 30 seconds.

Detailed explanation:

According to the question, we are informed that

The temperature of a cup of coffee on a counter is represented by the equation

$H= f(t)$

where t indicates the time in minutes since the coffee was set on the counter.

In general, f(t)' denotes the derivative of f(t), indicating the change in temperature over time for the coffee

As the coffee rests on the counter, its temperature tends to decrease after a few minutes; thus, f(t)' is negative.

The temperature is measured in degrees Celsius while time is expressed in minutes.

Therefore, the change in temperature with respect to time, f(35)', will be given in degrees Celsius per minute (i.e., degC/min).

The question states that

$|f(35)'| = 1.5$

which means the rate of temperature change after 35 minutes is 1.5.

And

$|f(35)| = 68$

indicating that the coffee's temperature after 35 minutes is 67 degrees Celsius.

Subsequently, after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate at which the coffee's temperature changes is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

Thus

At 35 minutes since the coffee was placed on the counter, its temperature is 68 and will drop by roughly 0.75 in the next 30 seconds.

5 0

3 months ago

Marco wants to buy a new smartphone that costs $495, with some additional accessories. He has already saved $75. Write and solve

tester [12383]

Marco requires $420 to purchase a new smartphone along with accessories. The equation 75-495=420 demonstrates this while adding $75 to $420 yields a total of $495.

4 0

2 months ago