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3 years ago

Idk how to do these problems cause I keep getting confused

Mathematics

1 answer:

melomori [17]3 years ago

8 0

Problem 5

x = number of songs downloaded

MyTunes charges $2.50 per song, so you pay 2.50*x dollars if you download x songs. If M is the cost of using MyTunes, then M = 2.50*x.

Let G be the cost of using Great Songs. The equation here is G = 1.50*x+50. We have 1.50*x representing the cost of downloading x songs (at 1.50 dollars a piece) plus the membership fee of $50. So the total cost here is 1.50x+50 dollars.

We want to find out when Great Songs is a better deal, so we want to determine what x values make G smaller than M

(Great Songs Cost) < (MyTunes Cost)

G < M

1.50x+50 < M ................................... replace G with 1.50x+50

1.50x+50 < 2.50x ............................. replace M with 2.50x

1.50x+50-1.50x < 2.50x-1.50x ....... subtract 1.50x from both sides

50 < 1.00x

50 < x

x > 50

If you download more than 50 songs, then Great Songs will be the better deal since it will be the cheaper plan.

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the pencil and the laptop computer are both tools that help writers accomplish their tasks. Follow the clues below to find the y

BartSMP [9]

What you do is divide the sum by 2. You will come out with and answer of 1891. Now, to figure out the years they were invented you take the difference of 192 and divide that in half also. It will come out to 96. Now, you subtract 1891 by 96 and that is the year the pencil was invented (1795=pencil) now with the other half (1891) you add on 96 and you’ll come out with the answer of 1987.

Pencil=1795
Laptop computer=1987.

Hope this helped!

5 0

3 years ago

Verify the identity. cot(x - pi/2) = -tan(x)

gizmo_the_mogwai [7]

Answer:

See below.

Step-by-step explanation:

$\cot(x-\frac{\pi}{2})=-\tan(x)$

Convert the cotangent to cosine over sine:

$\frac{\cos(x-\frac{\pi}{2} )}{\sin(x-\frac{\pi}{2})} =-\tan(x)$

Use the cofunction identities. The cofunction identities are:

$\sin(x)=\cos(\frac{\pi}{2}-x)\\\cos(x)=\sin(\frac{\pi}{2}-x)$

To convert this, factor out a negative one from the cosine and sine.

$\frac{\cos(-(\frac{\pi}{2}-x ))}{\sin(-(\frac{\pi}{2}-x))} =-\tan(x)$

Recall that since cosine is an even function, we can remove the negative. Since sine is an odd function, we can move the negative outside:

$\frac{\cos((\frac{\pi}{2}-x ))}{-\sin((\frac{\pi}{2}-x))} =-\tan(x)\\-\frac{\sin(x)}{\cos(x)} =-\tan(x)\\-\tan(x)\stackrel{\checkmark}{=}-\tan(x)$

8 0

3 years ago

During the first 3 days of the week, Mike read an average of 28 pages per day. During the next 4 days, Mike averaged 42 pages pe

Anestetic [448]

Answer:

36 pages per day on average

Step-by-step explanation:

Calculate the average.

3 * 28 (The first 3 days of the week where Mike reads 28 pages per day) = 84

4 * 42 (The next 4 days where Mike reads 42 pages per day ) = 168

168 + 84 = 252

To find the average using this total, divide it by the total amount of days of reading (seven days in this problem).

252 / 7 = 36

6 0

1 year ago

In the Diagram Lines M And N are Parallel M < 2 = 150 degress, Find the Measure of the following angles

Snezhnost [94]

<4= 150
<6=150
because the angels are parallel <4 & <2 are the exact same measurements and because 6 is perpendicular to <4 & <2 thus making it also 150 degrees

5 0

3 years ago

Given that tan θ ≈ −0.087, where 3 2 π < θ < 2 , π find the values of sin θ and cos θ.

elena-s [515]

Answer:

sin θ ≈ -0.08667
cos θ ≈ 0.99624

Step-by-step explanation:

Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

sin(-0.08678 radians) ≈ -0.08667

cos(-0.08678 radians) ≈ 0.99624

_____

<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

We have shown radians in the above answer because the restriction on the angle is written in terms of radians.

_____

<em>Alternate solution</em>

The relationship between tan and sin and cos in the 4th quadrant is ...

$\cos{\theta}=\dfrac{1}{\sqrt{1+\tan^2{\theta}}}\\\\\sin{\theta}=\dfrac{\tan{\theta}}{\sqrt{1+\tan^2{\theta}}}$

That is, the cosine is positive, and the sign of the sine matches that of the tangent.

This more complicated computation gives the same result as above.

4 0

3 years ago