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3 years ago

Prove: sin^2x (sec^2x + csc^2x)=sec^2x

1 answer:

4 0

Sin^2x (sec^2x + csc^2x) = sec^2x

I would convert the functions in the parentheses to their reciprocals.

sin^2x (1/cos^2x + 1/sin^2x) = sec^2x

Now distribute the sine.

sin^2x/cos^2x + sin^2x/sin^2x = sec^2x

Remember that sine divided by cosine is always tangent.

tan^2x + sin^2x/sin^2x = sec^2x

The remaining fraction is simply 1.

tan^2x + 1 = sec^2x

Use the Pythagorean identity to add the left side.

sec^2x = sec^2x

Q.E.D.

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What is centripetal acceleration?

Can an object accelerate if it's moving with constant speed? Yup! Many people find this counter-intuitive at first because they forget that changes in the direction of motion of an object—even if the object is maintaining a constant speed—still count as acceleration.

Acceleration is a change in velocity, either in its magnitude—i.e., speed—or in its direction, or both. In uniform circular motion, the direction of the velocity changes constantly, so there is always an associated acceleration, even though the speed might be constant. You experience this acceleration yourself when you turn a corner in your car—if you hold the wheel steady during a turn and move at constant speed, you are in uniform circular motion. What you notice is a sideways acceleration because you and the car are changing direction. The sharper the curve and the greater your speed, the more noticeable this acceleration will become. In this section we'll examine the direction and magnitude of that acceleration.

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8 0

4 years ago

PLS HELP ! NEED IT<br> GIVNG BRAINLIEST

qaws [65]

Answer:

21.75 or $21\frac{3}{4}$

Step-by-step explanation:

You have to convert from a mixed number to a decimal. You can follow the following steps: To do this:

1.) You must divide the fraction's numerator by the denominator.

2.) You must now add the quotient obtained to the part of the Whole number.

you will get:

${\large\boxed{\fcolorbox{7}{\frac{1}{4}=7+0.25=7.25 }}$

The scale of the image that maps "Figure a" to "Figure b" is:

${\large\boxed{\fcolorbox{1:7.25}}$

3.) You have to multiply by 7.25 the length of the corresponding side of "Figure A" in order to find the value "x."

The final result will be:

${\large\boxed{\fcolorbox{x=(3)(7.25)}}$

${\large\boxed{\fcolorbox{x=21.75}}$

4 0

3 years ago

Which of the equations shows an application of the Zero Property of Multiplication? A. 25+0=25 B. 13(3)= C. 0∙2=0 D. (34−2)−(34+

Montano1993 [528]

Answer:

0∙2=0

Step-by-step explanation:

Zero Property of multiplication is as follows :

The product of a number and 0 is equal to 0.

In option (c), 0 is multiplied by 2 and as a result, we get 0 as the answer.

It means,

0∙2=0

Hence, option (c) i.e. 0∙2=0 shows the Zero Property of Multiplication.

5 0

3 years ago

What percent of 272 is 34?

Morgarella [4.7K]

The answer is 12.5% this is the correct answer

6 0

3 years ago

Larry and Paul start out running at a rate of 5 mph. Paul speeds up his pace after 5 miles to 10 mph but Larry continues the sam

klasskru [66]

<h2>Hello!</h2>

The answer is:

They will be 10 miles apart after 3 hours.

To calculate how long after they start will they be 10 miles apart, we need to assume that after 1 one hour, they were at the same distance (5 miles), then, calculate the time when they are 10 miles apart, knowing that Paul increased its speed two times, running first at 5mph and then, at 10 mph.

The time that will pass to be 10 miles apart can be calculated using the following equation:

$TotalTime=TimeToReach5miles+TimeToBe10milesApart$

Calculating the time to reach 5 miles for both Larry and Paul, at a speed of 5 mph, we have:

$x=xo+v*t\\\\5miles=0+5mph*t\\\\t=\frac{5miles}{5mph}=1hour$

We have that to reach a distance of 5 miles, they needed 1 hour. We need to remember that at this time, they were at the same distance.

If we want to know how many time will it take for them to be 10 miles apart with Paul increasing its speed to 10mph, we need to assume that after that time, the distance reached by Paul will be the distance reached by Larry plus 10 miles.

So, for the second moment (Paul increasing his speed) we have:

For Larry:

$x_{L}=5miles+5mph*t$

Therefore, the distance of Paul will be equal to the distance of Larry plus 10 miles.

For Paul:

$x{L}+10miles=xo+10mph*t\\\\5miles+5mph*t+10miles=5miles+10mph*t\\\\5miles+10miles-5miles=10mph*t-5mph*t\\\\10miles=5mph*t\\\\t=\frac{10miles}{5mph}=2hours$

Then, there will take 2 hours to Paul to be 10 miles apart from Larry after both were at 5 miles and Paul increased his speed to 10 mph.

Hence, calculating the total time, we have:

$TotalTime=TimeToReach5miles+TimeToBe10milesApart$

$TotalTime=1hour+2hours=3hours$

Have a nice day!

3 0

4 years ago