How to write the ratio of the amount of time spent playing video games to the amount of time spent watching television

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

8 0

You can write it just as given:

... (time spent in video games)/(time spent in television) = (10 minutes)/(1 hour)

However, the intent is to end with a pure number (no units), so we need to convert hours to minutes or vice versa. Most folks know that 1 hour is 60 minutes, so that is probably the easier conversion.

... = (10 minutes)/(60 minutes)

... = 10/60 . . . . . . . . . the units in numerator and denominator are the same, so cancel

... = 1/6 . . . . . . . . . . . .the fraction is reduced in the usual way

The ratio in simplest form is 1/6.

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Fill in Sin, Cos, and tan ratio for angle x. <br> Sin X = 4/5 (28/35 simplified)

Fantom [35]

Answer:

Given: $\sin(x) = (4/5)$ .

Assuming that $0 < x < 90^{\circ}$ , $\cos(x) = (3/5)$ while $\tan(x) = (4/3)$ .

Step-by-step explanation:

By the Pythagorean identity $\sin^{2}(x) + \cos^{2}(x) = 1$ .

Assuming that $0 < x < 90^{\circ}$ , $0 < \cos(x) < 1$ .

Rearrange the Pythagorean identity to find an expression for $\cos(x)$ .

$\cos^{2}(x) = 1 - \sin^{2}(x)$ .

Given that $0 < \cos(x) < 1$ :

$\begin{aligned} &\cos(x) \\ &= \sqrt{1 - \sin^{2}(x)} \\ &= \sqrt{1 - \left(\frac{4}{5}\right)^{2}} \\ &= \sqrt{1 - \frac{16}{25}} \\ &= \frac{3}{5}\end{aligned}$ .