Graph the line that passes through the points (3, -6) and (-6, -3) and determine
the equation of the line.

Answer:

[tex]\displaystyle \frac{dx}{d\theta}=5\text{ ft/rad}[/tex]

Step-by-step explanation:

Please refer to the diagram below.

We can use the sine function. Recall that the sine function is the ratio between the opposite side and the hypotenuse. Hence:

[tex]\displaystyle \sin(\theta)=\frac{x}{10}[/tex]

We want to find how fast x changes with respect to θ. So, we want to find dx/dθ. Therefore, let's take the derivative of both sides with respect to θ:

[tex]\displaystyle \frac{d}{d\theta}[\sin(\theta)]=\frac{d}{d\theta}\left[\frac{1}{10}x\right][/tex]

Differentiate. Since it's with respect to θ, we can differentiate the left-hand side like normal. On the right, we will implicitly differentiate. This yields:

[tex]\displaystyle \cos(\theta)=\frac{1}{10}\frac{dx}{d\theta}[/tex]

Multiply both sides by 10. So, dx/dθ is:

[tex]\displaystyle \frac{dx}{d\theta}=10\cos(\theta)[/tex]

We want to find dx/dθ when θ is π/3. Thus, substitute π/3 for θ:

[tex]\displaystyle \frac{dx}{d\theta}=10\cos\left(\frac{\pi}{3}\right)[/tex]

Evaluate:

[tex]\displaystyle \frac{dx}{d\theta}=10\left(\frac{1}{2}\right)=5\text{ ft/rad}[/tex]

So, x is changing with respect to θ at a rate of 5 feet per radian.

Answer:

16 songs.

Step-by-step explanation:

If Aaliyah has 50 songs, but her phone can only hold a third of those songs, to solve this problem, we will have to find a third of 50.

Divide 50 into 3:

[tex]50[/tex] ÷ [tex]3[/tex]

[tex]=16.6666...[/tex]

As this decimal does not terminate, we'll have to round down to [tex]16[/tex] since we cannot have a portion of the song downloaded.

Therefore, Aaliyah can download 16 songs on her phone.

Answer:

hatdogkajsidnevwjqo

Answer:

y=2x+5

Step-by-step explanation:

0,5

0,7

7-5 is 2

2/0 is 2

to check answer:

(2*0)+5

0+5

=5

See attachment for math work and answer.

The average speed exceeding the speed limit is mathematically given as

6.91 kilometers per hour

This is further explained below.

Let's assume that Erik maintains a steady pace during the whole trip.

Therefore, the following equation of motion may be used to compute the speed, which is expressed in terms of miles per hour:

Where: miles is the unit of measurement for distance.

t stands for time, which is measured in hours.

Kindly take into account that one hour is comprised of sixty minutes. If we assume so, then we can calculate Erik's speed as follows:

[tex]\begin{aligned}&v=\frac{19.2 m i}{0.267 h} \\\\&v=71.910 \frac{m i}{h}\end{aligned}[/tex]

In conclusion, That is 6.91 kilometers per hour faster than the allowed speed limit.

Read more about  average speed

https://brainly.com/question/12322912

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Answer:

The correct option is;

y = arcsinx and y = arctanx

Step-by-step explanation:

The given options are;

1) y = arcsinx and y = arccosx

Here, we have at the origin, where x = 0,  arccosx ≈ 1.57 while arcsinx = 0

Therefore arccosx does not intersect arcsinx at the origin for it to be symmetrical to arcsinx or the origin

2)  y = arccosxy and y = arctanx

Here arctanx = 0 when x = 0 and arcos x = 1.57 when x = 0 therefore, they are not symmetrical

3) y = arctanx and y = arccotx

Similarly, At x = 0, arccotx = 1.57 therefore, they are not symmetrical

4) y = arcsinx and y = arctanx

Both functions arcsinx and arctanx pass through the origin and their shapes are similar but inverted as they go from negative to positive.

The function are symmetric with respect to the origin is y = arcsinx and y = arctanx and this can be determined by using the trigonometric property.

The following steps can be used in order to determine which functions are symmetric with respect to the origin:

Step 1 - Check all the options given in order to determine which functions are symmetric with respect to the origin.

Step 2 - Substitute (x = 0) in option a), that is:

[tex]\rm y = sin^{-1}(0)=0[/tex]

[tex]\rm y = cos^{-1}(0)=1.57[/tex]

Step 3 - Substitute (x = 0) in option b), that is:

[tex]\rm y = cos^{-1}(0)=1.57[/tex]

[tex]\rm y = tan^{-1}(0)=0[/tex]

Step 4 - Substitute (x = 0) in option c), that is:

[tex]\rm y = tan^{-1}(0)=0[/tex]

[tex]\rm y = cot^{-1}(0)=1.57[/tex]

Step 5 - Substitute (x = 0) in option d), that is:

[tex]\rm y = tan^{-1}(0)=0[/tex]

[tex]\rm y = sin^{-1}(0)=0[/tex]

For more information, refer to the link given below:

https://brainly.com/question/13710437

Answer:

24/8 or 3

Step-by-step explanation:

19/8 + 5/8

=> 19 + 5 / 8

=> 24/8

=> 3

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

Answer:

.175 tons

Step-by-step explanation:

350 pounds converts to .175 tons.

Answer:

She paid $5.25

Step-by-step explanation:

You would multiply 15 times 0.65 and then subtract that from 15 or you could multiply 15 times 0.35 because 100-65 is 35.

Answer:

(x-3)(x-2)

Step-by-step explanation:

none cause you dont want one

Answer:

5m-4

Step-by-step explanation:

The product of 5 and a number is written as 5(m) <--- any variable you chose.

The solution is 4 less than 5m.

So: 5m-4

Hope this helps ^^

Answer:

60,72 - 12

45,81 - 9

Answer:

17

Step-by-step explanation:

I hope this helps!

See Explanation

Step-by-step explanation:

[tex] \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \\ \\ = 4 \times 1 - 3 \times 2 \\ \\ = 4 - 6 \\ \\ = - 2[/tex]

[tex] \begin{bmatrix} 4 & 2 & 6 \\ - 1 & - 4 & 5\\ 3 & 7 & 2 \end{bmatrix} \\ \\

=4(-4\times 2-5\times 7)\\ -2(-1\times 2-5\times 3)\\ +6(-1\times 7-(-4)\times 3)\\\\

= 4(-8-35) -2(-2-15) \\+6(-7+12)\\\\

= 4(-43) -2(-17) +6(5)\\\\

= - 172 + 34 + 30\\\\

= 64 - 172\\\\

= - 108 \\[/tex]

Answer:

-3x + y = 8 and 3y = 9x

Step-by-step explanation:

Answer:

1: x= 3

2:x=12

3:x= 6.7

4:x=3.6

Step-by-step explanation:

5 - 3n

I think sooooooo

Answer:

Its irrational since it’s never ending

Step-by-step explanation:

rational numbers are usually perfect squares and since that’s repeating it’s not A erfect square instead its irrational since it never ends

Answer:

0.584... is irrational

Step-by-step explanation:

This is because the decimal can't be made into a ratio or fraction because it doesn't terminate.

Answer:

49/30

Or

1 19/30

Step-by-step explanation:

Answer:

74t+(-24x)

Step-by-step explanation:

Answer:

Since 80 and 40 are both divisible by 40 and 10, 40 and 10 are factors of both 80 and 40.

Step-by-step explanation:

Answer:

$126

Step-by-step explanation:

Well first you would have to see how much the total sale of 700 chocolate bars is,

700*1.20=$840

Next you need to multiply the 15% thats going to club shirts,

$840*0.15=126

So your answer is $126

Answer:

The answer is 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

It is going by two's but with negative numbers so if we go backwards it would be -6, -4, -2, then the blue dot which would be 0.

Answer:

18 pieces of cheese

Step-by-step explanation:

3 slices x 6 grilled cheeses = 18 slices of cheese