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3 years ago

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Mathematics Question - Billy played Clash Royale 16 times. Then her sister Karen played 9 times as much as Billy. How many times

Clash Royale has been played ? Also Explain your answer please

2 answers:

Zepler [3.9K]3 years ago

6 0

It has been used 160 times because 16+(16 x 9)= 160

DIA [1.3K]3 years ago

4 0

I will be 16+9=25 now you get how many times did she play and add them together

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What are the roots of x in -10x2 + 12x − 9 = 0?

hoa [83]

Answer:

$x_1=\frac{3(2+i\sqrt{6})}{10}$

$x_2=\frac{3(2-i\sqrt{6})}{10}$

Step-by-step explanation:

Use the Quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

You can identify that, in this case:

$a=-10\\b=12\\c=-9$

Now you need to substitute these values into the formula:

$x=\frac{-12\±\sqrt{12^2-4(-10)(-9)}}{2(-10)}$

$x=\frac{-12\±\sqrt{-216}}{-20}$

Remember that:

$i=\sqrt{-1}$

Therefore,rewriting and simplifying, you get:

$x=\frac{-12\±6i\sqrt{6}}{-20}$

$x=\frac{-6(2\±i\sqrt{6})}{-2(10)}$

$x=\frac{3(2\±i\sqrt{6})}{10}$

Then, you get the following roots:

$x_1=\frac{3(2+i\sqrt{6})}{10}$

$x_2=\frac{3(2-i\sqrt{6})}{10}$

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2 years ago

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3 years ago

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Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 10

WINSTONCH [101]

Answer:

The function for the outside temperature is represented by $T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$ , where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

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$A = \frac{100\º-70\º}{2}$

$A = 15\º$

Mean temperature

$\bar T = \frac{70\º+100\º}{2}$

$\bar T = 85\º$

Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:

$T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right]$

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$\bar T$ - Mean temperature, measured in degrees.

$A$ - Amplitude, measured in degrees.

$\tau$ - Daily period, measured in hours.

$t$ - Time, measured in hours. (where t = 0 corresponds with 5 AM).

If $\bar T = 85\º$ , $A = 15\º$ and $\tau = 24\,h$ , the resulting function for the outside temperature is:

$T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$

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