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Naddika [18.5K]
3 years ago
13

Dana ran 1/4 mile Trish ran 445 yards. Who ran the greater distance? Explain

Mathematics
2 answers:
Sonbull [250]3 years ago
7 0
Trish ran the greater distance because Dana ran a quarter of a mile and that is 440 yards. Trish ran 5 more yards than Dana.
alukav5142 [94]3 years ago
4 0
445 yards is equal to 0.253841 Miles

445 yards > 1/4 miles

Trish ran farther by 5 yards
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Step-by-step explanation:

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Write each of the following as a function of theta.<br> 1.) sin(pi/4 - theta) 2.) tan(theta+30°)
Paladinen [302]

Step-by-step explanation:

Let x represent theta.

\sin( \frac{\pi}{4} - x )

Using the angle addition trig formula,

\sin(x - y)  =  \sin(x)  \cos(y)  -  \cos(x)  \sin(y)

\sin( \frac{\pi}{4} )  \cos(x)  -  \cos( \frac{\pi}{4} )  \sin(x)

( \frac{ \sqrt{2} }{2})  \cos(x)  -  (\frac{ \sqrt{2} }{2}  )\sin(x)

Multiply one side at a time

Replace theta with x , the answer is

\frac{ \sqrt{2} \cos(x)  }{2}  -  \frac{ \sin(x) \sqrt{2}  }{2}

2. Convert 30 degrees into radian

\frac{30}{1}  \times  \frac{\pi}{180}  =  \frac{\pi}{6}

Using tangent formula,

\tan(x + y)  =  \frac{ \tan(x)  +  \tan(y) }{1 -  \tan(x) \tan(y)  }

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Tan if pi/6 is sqr root of 3/3

\frac{ \tan(x) +  ( \frac{ \sqrt{3} }{3} )  }{1 -  \tan(x)  (\frac{ \sqrt{3} }{3} )  }

Since my phone about to die if you later simplify that,

you'll get

\frac{(3 \tan(x) +  \sqrt{3} )(3 +  \sqrt{3}  \tan(x)  }{3(3 -  \tan {}^{2} (x) }

Replace theta with X.

4 0
2 years ago
Let ∠X and ∠Y be complementary. If sin(X) =
Lena [83]
<h3>Answer:</h3>

sin(Y) = 4/5

<h3>Step-by-step explanation:</h3>

The sine of one of a pair of complementary angles is equal to the cosine of the other. Given that ∠X and ∠Y are complementary, sin(Y) = cos(X) = 4/5.

_____

You can figure this from SOH CAH TOA, the mnemonic that reminds you of the definitions of the trig functions. The adjacent leg for one of the acute angles in the right triangle is the opposite leg for the other angle.

... Sin = Opposite/Hypotenuse

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