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3 years ago

How do you find the general solution for cos2A=cos^2A

Mathematics

1 answer:

eduard3 years ago

6 0

Answer:

A = 0 +/- nπ radians , where n is an integer.

Step-by-step explanation:

cos 2A = cos^2 A

Use the identity cos 2A = 2 cos^2 A -1 :

2cos^2 A - 1 = cos^2 A

cos^2 A = 1

Cos A = +/-1

When cos A = 1, A = 0 +/- 2nπ radians.

when cos A = -1, A = π +/- nπ radians.

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An athlete knows that when she jogs along her neighborhood greenway, she can complete the route in 10 minutes. It takes 20 minu

IgorLugansk [536]

Answer:

10 miles per hour.

Step-by-step explanation:

Let x represent athlete's walking speed.

We have been given that her jogging rate is 5 mph faster than her walking rate, so athlete's jogging speed would be $x+5$ miles per hour.

$\text{Distance}=\text{Rate}\cdot \text{Time}$

10 minutes = 1/6 hour.

20 minutes = 1/3 hour

While walking, we will get $D_{\text{walking}}=x\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{3}\text{hour}$

$D_{\text{walking}}=\frac{x}{3}$

While jogging, we will get $D_{\text{jogging}}=(x+5)\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{6}\text{hour}$

$D_{\text{jogging}}= \frac{(x+5)}{6}$

Since athlete is covering same distance while walking and jogging, so we can equate both expressions as:

$\frac{x}{3}=\frac{x+5}{6}$

Cross multiply:

$6x=3x+15$

$6x-3x=15$

$3x=15$

$\frac{3x}{3}=\frac{15}{3}\\\\x=5$

Therefore, athlete's walking speed is 5 miles per hour.

Jogging speed: $x+5\Rightarrow 5+5=10$

Therefore, athlete's jogging speed is 10 miles per hour.

3 0

3 years ago

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?

Fantom [35]

Answer:

<h2>If we placed the number 10 in the box, we obtain a system of equations with infinitely many solutions.</h2>

Step-by-step explanation:

The given system is

$y=2x-5\\2y-4x=a$

<em>It's important to know that a system with infinitely many solutions, it's a system that has the same equation</em>, that is, both equation represent the same line, or as some textbooks say, one line is on the other one, so they have inifinitely common solutions.

Having said that, the first thing we should do here is reorder the system

$y=2x-5\\2y=4x+a$

This way, you can compare better both equations. If you look closer, observe that the second equation is double, that is, it can be obtained by multiplying a factor of 2 to the first one, that is

$y=2x-5\\2y=4x-10$

So, by multiplying such factor, we obtaine the second equation. Observe that $a$ must be equal to 10, that way the system would have infinitely solutions.

Therefore, the answer is 10.

4 0

3 years ago

Pythagorean Theorem help please!

Sergio [31]

$14^2+48^2=c^2$
196+2304= $c^2$
2500= $c^2$
50 = c

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3 years ago

What is the geometric sequence?<br><br> 2,3,4.5?

kykrilka [37]

An=a12n-1 or an=(1)2n-1

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3 years ago

Give an example of a real-world situation involving two unknown quantities. Then write an algebraic expression to represent the

RUDIKE [14]

A real world expression would be Toby had makes 3 dollars per hour he wants to buy a ps4 for 40 dollars. he already has 10 dollars. how many hours does he have to work to afford his ps4. 3x+10=40

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3 years ago

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