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3 years ago

Verify the identity sec^2(x)tan^2(x)+sec^2(x)=sec^4(x)

Mathematics

1 answer:

Natalija [7]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tan²x + 1 = sec²x ⇒ tan²x = sec²x - 1

Consider the left side

sec²x × tan²x + sec²x

= sec²x(sec²x - 1) + sec²x ← distribute and simplify

= $sec^{4}$ x - sec²x + sec²x

= $sec^{4}$ x = right side ⇒ verified

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It will take Adam four hours to drive to Disney Park, and 2.5 times less time if driving 45 mph faster. What is the distance Ada

Mashcka [7]

<h2>Hello!</h2>

The answer is:

The distance to over by Adam to get to the park is 108 miles.

To solve the problem, we need to write two equations using he given information about the times and his speed.

So,

For the first equation we have: Travel to Disney Park

$time=4hours$

$Distance=v*4hours$

For the second equation we have: Travel back from Disnery Park

$time=4hours-2.5hours=1.5hours$

$Speed=v+45mph$

$Distance=(v+45mph)*1.5hours$

Then, if Adam covered the same distance going and coming back, we have:

$v*4hours=(v+45mph)*1.5hours$

$v*4hours=v*1.5hours+45mph*1.5hours$

$v*4hours-v*1.5hours=45mph*1.5hours$

$v*2.5hours=67.5miles$

$v=\frac{67.5miles}{2.5hours}=27\frac{miles}{hour}=27mph$

We have that the speed when he was going to Disney Park was 27 mph.

Now, to calculate the distance, we need to substitute the obtained speed in any of the two first equations.

Therefore, substituting the speed into the second equation, we have:

$Distance=(v+45mph)*1.5hours$

$Distance=(27mph+45mph)*1.5hours=72mph*1.5hours=108miles$

Hence, we have that the distance that Adam should cover to get to the park is 108 miles.

Havea nice day!

8 0

3 years ago

How is this a non proportional relationship y=2x 4?

saveliy_v [14]

Y=2x +4 is non proportional because b does not equal 0
The b in the equation is 4
As long as the y intercept is not more or less than 0, than it will be proportional

5 0

3 years ago

5.676524687 in fraction

Ugo [173]

Answer:

5 7/10

Step-by-step explanation:

First, we need to round the number.

5.7

Now that we've rounded the number we can convert it to a fraction based on where the decimal is located.

5.7

Tenths

So, the decimal is in the tenths that means we have to put 7 over 10.

5 7/10

Hope this helps! :)

6 0

2 years ago

My brother is currently three times as old as me, but in five years, my brother

wolverine [178]

Answer: Your brother is 15 years old right now.

Step-by-step explanation:

Let be "m" your currently age and "b" your brother's currently age.

Knowing that right now he is three times (this indicates multiplication) as old as you, you can write the following equation:

$b=3m$

In five years your age will be:

$m+5$

And your brother's age will be:

$b+5$

Then, if in five years, your brother will be twice as old as you, you can set up the second equation:

$b+5=2(m+5)$

Then, the System of equations is:

$\left \{ {{b=3m} \atop {b+5=2(m+5)}} \right.$

Apply the Substitution method and substitute the first equation into the second one and solve for "m":

$3m+5=2(m+5)\\\\3m+5=2m+10\\\\m=10-5\\\\m=5$

Substitute the value of "m" into the first equation and evaluate in order to find "b":

$b=3(5)\\\\b=15$

4 0

3 years ago

What is 5/10 is the simplest form please help me

lesya [120]

1/2, try taking out the biggest number out of both of the numbers, in this case five can be taken out of both the numbers, leaving you with 1/2 :)

3 0

3 years ago