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VashaNatasha [74]
3 years ago
13

Can someone please help me?

Mathematics
2 answers:
qwelly [4]3 years ago
8 0
A ) sin x ( \frac{sinx}{cosx}*cosx- \frac{cosx}{sinx}+*cos x)= \\ sinx(sinx- \frac{cos^{2} x}{sin^{2} x})=
sin^{2}x-cos^{2} x=1-cos^{2}x-cos^{2} x= \\ 1-2cos^{2}x
b ) 1 +  \frac{1}{cos^{2} x} *sin^{2} x=1+ \frac{sin^{2} x}{cos^{2} x} = \\  \frac{cos {2} x+sin x^{2} x}{cos^{2} x} = \frac{1}{cos^{2} x} =sec^{2} x
c)\frac{sinx}{1-cosx} + \frac{sinx}{1+cosx}= \frac{sin x ( 1+cosx)+sinx(1-cosx)}{1-cos^{2} x} = \\  \frac{sinx+sinxcosx+sinx-sinxcosxx}{1-cos^{2}x }= \\  \frac{2sinx}{sin^{2} x}   =  \frac{2}{sinx}=2 csc x
d) -tan ^{2}x+sec ^{2}x=- \frac{sin ^{2} x}{cos ^{2} x} + \frac{1}{cos^{2} x} = \\  \frac{1-sin^{2x} }{cos ^{2}x }= \frac{cos^{2} x}{cos^{2}x }  =1
sattari [20]3 years ago
4 0

Answer:

a ) sin x ( \frac{sinx}{cosx}*cosx- \frac{cosx}{sinx}+*cos x)= \\ sinx(sinx- \frac{cos^{2} x}{sin^{2} x})=
sin^{2}x-cos^{2} x=1-cos^{2}x-cos^{2} x= \\ 1-2cos^{2}x    

b ) 1 +  \frac{1}{cos^{2} x} *sin^{2} x=1+ \frac{sin^{2} x}{cos^{2} x} = \\  \frac{cos {2} x+sin x^{2} x}{cos^{2} x} = \frac{1}{cos^{2} x} =sec^{2} x

c) \frac{sinx}{1-cosx} + \frac{sinx}{1+cosx}= \frac{sin x ( 1+cosx)+sinx(1-cosx)}{1-cos^{2} x} = \\  \frac{sinx+sinxcosx+sinx-sinxcosxx}{1-cos^{2}x }= \\  \frac{2sinx}{sin^{2} x}   =  \frac{2}{sinx}=2 csc x  

d) -tan ^{2}x+sec ^{2}x=- \frac{sin ^{2} x}{cos ^{2} x} + \frac{1}{cos^{2} x} = \\  \frac{1-sin^{2x} }{cos ^{2}x }= \frac{cos^{2} x}{cos^{2}x }  =1  

Step-by-step explanation:

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If the cheetah sprinted at maximum speed, how far would the cheetah have traveled?
saveliy_v [14]

Answer:

a. D = 1.167t miles per minute

b. 11.67 miles

c. 9.33 miles

d. 5.33 miles

e. 4 miles

f. Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.

Step-by-step explanation:

<u>Complete Question</u>

<em>"A cheetah sitting under a tree sprints toward its prey at 70 mph. It runs back to its initial spot by the tree at a modest 40 mph. The cheetah has embarked on a round-trip. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.</em>

<em>If the cheetah sprinted at maximum speed, how far would the cheetah have traveled? </em>

<em>a. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.</em>

<em> </em>

<em>b. Let t = 10 and solve for the distance the cheetah covered in 10 minutes. </em>

<em> </em>

<em>Suppose the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes. </em>

<em />

<em>c. How far would the cheetah have traveled in the first 8 minutes? Show how you arrived at your answer. </em>

<em> </em>

<em>d. How far would the cheetah have traveled in the next 8 minutes? Show how you arrived at your answer. </em>

<em> </em>

<em>e. How much farther did the cheetah travel in the first 8 minutes than in the second 8 minutes? </em>

<em> </em>

<em>f. The cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. Was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes? Show the calculation to justify your answer."</em>

<em />

Solution:

a.

The distance equation is D = RT, where

D is distance

R is rate (speed)

T is time

If cheetah travels at max speed, 70 mph, we can say D = 70t

There are 60 minutes in 1 hours, so the distance in miles per minute is:

D=\frac{70}{60t}=1.167t

D = 1.167t miles per minute

b.

Given t = 10 minutes, the distance covered using formula would be

D = RT

D = 1.167 * 10 = 11.67 miles

c.

Since Cheetah traveled at max speed (70mph) for the first leg of 8 minutes, the distance covered would be:

D = RT

D = 1.167 * 8

D = 9.33 miles

d.

Next leg of 8 minutes would be at 40mph, to get that in minutes, we divide by 60, so rate would be 40/60. Hence, distance covered is:

D = RT

D = (40/60) * 8 = 5.33 miles

e.

The distance traveled in first 8 minutes is 9.33

The distance traveled in second 8 minutes is 5.33,

Hence, the more distance is 9.33 - 5.33 = 4 miles

f.

To justify if 9.33 is actually 1.75 times that of 5.33, we multiply 5.33 by 1.75 and see if it is 9.33. So

1.75 * 5.33 = 9.33 [in fact, it is!]

Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.

4 0
3 years ago
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