X=
Y=
Find the values of X and Y

Answer:

y = (7/4)x + 0

Step-by-step explanation:

yeah-ya....... right?

Answer:

(a) The particle is moving to the right in the interval  [tex](0 \ , \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2} \ , \ 2\pi)[/tex] , to the left in the interval [tex](\displaystyle\frac{\pi}{2}\ , \ \displaystyle\frac{3\pi}{2})[/tex], and stops when t = 0, [tex]\displaystyle\frac{\pi}{2}[/tex], [tex]\displaystyle\frac{3\pi}{2}[/tex] and [tex]2\pi[/tex].

(b) The equation of the particle's displacement is [tex]\mathrm{s(t)} \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3[/tex]; Final position of the particle [tex]\mathrm{s(2\pi)} \ = \ 3[/tex].

(c)  The total distance traveled by the particle is 9.67 (2 d.p.)

Step-by-step explanation:

(a) The particle is moving towards the right direction when v(t) > 0 and to the left direction when v(t) < 0. It stops when v(t) = 0 (no velocity).

Situation 1: When the particle stops.

[tex]\-\hspace{1.7cm} v(t) \ = \ 0 \\ \\ 5 \ \mathrm{sin^{2}(t)} \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.3cm} \mathrm{sin^{2}(t) \ cos(t)} \ = \ 0 \\ \\ \mathrm{sin^{2}(t)} \ = \ 0 \ \ \ \mathrm{or} \ \ \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.85cm} t \ = \ 0, \ \displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2} \ \ \mathrm{and} \ \ 2\pi[/tex].

Situation 2: When the particle moves to the right.

[tex]\-\hspace{1.67cm} v(t) \ > \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ > \ 0[/tex]

Since the term [tex]5 \ \mathrm{sin^{2}(t)}[/tex] is always positive for all value of t of the interval [tex]0 \ \leq \mathrm{t} \leq \ 2\pi[/tex], hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is positive in the first and third quadrant or when [tex]\mathrm{t} \ \epsilon \ (0, \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2}, \ 2\pi)[/tex] .  

*Note that parentheses are used to demonstrate the interval of t in which cos(t) is strictly positive, implying that the endpoints of the interval are non-inclusive for the set of values for t.

Situation 3: When the particle moves to the left.

[tex]\-\hspace{1.67cm} v(t) \ < \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ < \ 0[/tex]

Similarly, the term [tex]5 \ \mathrm{sin^{2}(t)}[/tex] is always positive for all value of t of the interval [tex]0 \ \leq \mathrm{t} \leq \ 2\pi[/tex], hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is negative in the second and third quadrant or  [tex]\mathrm{t} \ \epsilon \ (\displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2})[/tex].

(b) The equation of the particle's displacement can be evaluated by integrating the equation of the particle's velocity.

[tex]s(t) \ = \ \displaystyle\int\ {5 \ \mathrm{sin^{2}(t) \ cos(t)}} \, dx \ \\ \\ \-\hspace{0.69cm} = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx[/tex]

To integrate the expression [tex]\mathrm{sin^{2}(t) \ cos(t)}[/tex], u-substitution is performed where

[tex]u \ = \ \mathrm{sin(t)} \ , \ \ du \ = \ \mathrm{cos(t)} \, dx[/tex].

[tex]s(t) \ = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ \mathrm{sin^{2}(t)} \, du \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ u^{2} \, du \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5u^{3}}{3} \ + \ C \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ C \\ \\ s(0) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(0)} \ + \ C \\ \\ \-\hspace{0.48cm} 3 \ = \ 0 \ + \ C \\ \\ \-\hspace{0.4cm} C \ = \ 3.[/tex]

Therefore, [tex]s(t) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3[/tex].

The final position of the particle is [tex]s(2\pi) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(2\pi)} \ + \ 3 \ = \ 3[/tex].

(c)

[tex]s(\displaystyle\frac{\pi}{2}) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(\frac{\pi}{2})} \ + \ 3 \\ \\ \-\hspace{0.85cm} \ = \ \displaystyle\frac{14}{3} \qquad (\mathrm{The \ distance \ traveled \ initially \ when \ moving \ to \ the \ right})[/tex]

[tex]|s(\displaystyle\frac{3\pi}{2}) - s(\displatstyle\frac{\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(\frac{3\pi}{2})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | (-1) \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{10}{3} \\ \\ (\mathrm{The \ distance \ traveled \ when \ moving \ to \ the \ left})[/tex]

[tex]|s(2\pi) - s(\displaystyle\frac{3\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(2\pi})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{3\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | 0 \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{5}{3} \\ \\ (\mathrm{The \ distance \ traveled \ finally \ when \ moving \ to \ the \ right})[/tex].

The total distance traveled by the particle in the given time interval is[tex]\displaystyle\frac{14}{3} \ + \ \displaystyle\frac{5}{3} \ + \ \displaystyle\frac{10}{3} \ = \ \displaystyle\frac{29}{3}[/tex].

function!

Step-by-step explanation:

this was a function that the answer (y) is equal to 3

and the X is equal to (-2)

Answer:

This is about a function evaluated at a particular point.  You don't get a formula for the function, but there is enough information to say that the ordered pair (-2, 3) is part of the function.

The function's name is f.

The -2 in parentheses is a value for the independent variable ("input"), often designated by the variable  x.

The 3 is the corresponding value of the dependent variable ("output"), often designated by  the variable y.

The expression can be read as:

"f of negative two is equal to 3"

"the value of f at -2 is 3"

Answer:

Step-by-step explanation:

Find c if ∠PQR = 90°?

I will ASSUME you mean point P is at (3. c)

slope of PQ is (2 - c) / (9 - 3) = (2 - c) / 6

slope of QR is (11 - 2) / (3c - 9) = 9 / (3c - 9)

perpendicular lines have negative reciprocal slopes.

(2 - c) / 6 = -1(3c - 9)/9

9(2 - c) = -6(3c - 9)

18 - 9c = -18c + 54

       9c = 36

         c = 4

[tex]\dfrac{d}{dx} \left(\dfrac{x+9}{x+1}\right)\\\\\\=\dfrac{(x+1)\dfrac{d}{dx}(x+9) - (x+9) \dfrac{d}{dx}(x+1)}{(x+1)^2}\\\\\\=\dfrac{(x+1) - (x+9)}{(x+1)^2}\\\\\\=\dfrac{x+1-x-9}{(x+1)^2}\\\\\\=-\dfrac{8}{(x+1)^2}[/tex]

[tex]\text{Surface Area of Prism} = (2 \times \text{Base Area}) + (\text{Base perimeter} \times \text{height})\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=(2 \times 5)+(12\times 2)\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=10+24\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=34~~ \text{cm}^2[/tex]

Answer:

I think it's 33.

Hope that helps you.

Step-by-step explanation:

it will be 33 because the interquartile we give it by Q3 - q1

Q3 median of 84 plus 90 divided by 2 equal 87

q1 equal 54

Answer: The following triangles are congruent.

Answer:

put your equation into fractions and then see what or which 1mathces with the image

Step-by-step explanation:

Answer:

[tex]4^{12}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then

[tex]4^{9}[/tex] × [tex]4^{3}[/tex] = [tex]4^{(9+3)}[/tex] = [tex]4^{12}[/tex]

Answer:

A

Step-by-step explanation:

After doing long division we then know that 2,952 ÷24 = 123

We 1st follow pemdas knowing this we solve the equations in parenthesis 1st

(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)

2,400 ÷ 24 = 100

480 ÷ 24 = 20

72 ÷ 24 = 3

We can then rewrite the equation as

100 + 20 + 3   We then solve left to right

100 + 20 = 120

120 + 3 = 123

Answer:

The number of unique triangles that can be constructed from the given values is; Only one triangle

Step-by-step explanation:

We are given the 2 angles of a triangle as;  

∠1 = 50°  

∠2 = 80°  

Now, we know that sum of angles in a triangle is 180°. This means that if the third angle is denoted as ∠3, then we have;  

∠1 + ∠2 + ∠3 = 180°  

Thus;  

∠3 = 180 - (∠1 + ∠2)  

∠3 = 180 - (50 + 80)  

∠3 = 180 - 130  

∠3 = 50°  

Thus; ∠1 = ∠3 = 50°  

A triangle with two equal angles is called an isosceles triangle. Which means that it will also have 2 of its' sides to be equal.  

Thus, in conclusion, only one unique triangle can be drawn.

Answer:

Well the answer would be 865,920. Hope this helped! this is the way i learned it so if its wrong i'm super sorry!

Step-by-step explanation:

I = p x r x t

I = 82,000 x 8 x 11yrs

BUT WAIT! this is MONTHLY, so convert 11 x 12 = 132 and then move 8 back 2 spaces = 0.08 so the correct equation is

I = 82,000 x 0.08 x 132

I = 865,920

Answer:

<4 = 67 degrees

Step-by-step explanation:

Find <3

30+37+x=180

subtract 37 and 30

x = 180 - 30 - 37

x = 150 - 37

x= 113

Find <4

180 - 113

67

Answer:

6:4:3

Step-by-step explanation:

each can be divided by 7

Answer:

6 4 3

Step-by-step explanation:

Answer:

SOLUTION

HERE,

=X(P.2+Q)

=X(2P+Q)

Answer:

x(px+q) ( I took x as a common and the remaining are some

Answer:

2 50-pound bags

Step-by-step explanation:

[Conversions] 50-pound bags -> 800-ounce bags

[Total potatoes used] 200 mashed potato creations * 8 ounces of potatoes in each dish = 1,600 ounces of potatoes

[Bags used] 1,600 / 800 = 2 bags

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

0.670. M

Step-by-step explanation:

Molarity can be expressed like this:

molarity =  number of moles /volume (L)

We know the volume, which is  2.37 L , but we need to find the number of moles. We can do this by dividing  67.3 g  by the molar mass of  L i C l :

number of moles  = mass of sample /molar mass

number of moles  =  67.3 g /(6.94 + 35.45) g/mol  = 67.3 g /42.39 g/mol

number of moles = 1.59 mol

molarity = 1.59 mol /2.37 L =  0.670. M

====================================================

Work Shown:

x = number of windows purchased

The cost expression is 145.50x+3150 because the "145.50x" portion represents the $145.50 per window charge, then we tack on the fixed fee of $3150. Set this cost expression equal to the total charge ($5769) and solve for x.

[tex]145.50x+3150 = 5769\\\\145.50x = 5769-3150\\\\145.50x = 2619\\\\x = 2619/(145.50)\\\\x = 18\\\\[/tex]

They bought 18 windows.

Answer:

1

Step-by-step explanation:

correct on edge

sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =

0.893996664

Answer:

hope it helps

The question relates to the total number of pairs of feet ducks and a pigs

are known to have.

Reasons:

The length of the group of ducks and pigs = 40 feet

Number of ducks = Twice the number of pigs

Let x represent the number of pigs, and let y represent the number of ducks, we have;

y = 2 × x

4·x + 2·y = 40

Which gives;

4·x + 2 × (2·x) = 40

8·x = 40

x = 40 ÷ 8 = 5

y = 2 × x

Therefore;

y = 2 × 5 = 10

Learn more about solving word problems in mathematics here:

https://brainly.com/question/25272317

Equations are used to represent functions, and vice versa.

The equation of y as a function of x is [tex]y=\sqrt{6 - x^2[/tex]

The function is given as:

[tex]\sqrt{6-y^2}=x[/tex]

Square both sides

[tex]6-y^2=x^2[/tex]

Subtract 6 from both sides

[tex]-y^2=x^2 - 6[/tex]

Multiply both sides by -1

[tex]y^2=6 - x^2[/tex]

Take square root of both sides

[tex]y=\sqrt{6 - x^2[/tex]

Express as a function

[tex]f(x) = \sqrt{6- x^2[/tex]

Hence, the equation of y as a function of x is [tex]y=\sqrt{6 - x^2[/tex]

Read more about functions and equations at:

https://brainly.com/question/13336451

Answer

hi

Step-by-step explanation:

ok

Answer: a. y=3      slope = 0

b. x=-4 slope does not exist

Step-by-step explanation:

Answer: She should charge $10.50 for each box

Step-by-step explanation:

Total cookies = 960

Each box has 16 cookies

Her goal is $630

First, you want to find out how many boxes she made

960÷ 16 = 60

She made 60 boxes

Now you want to find the price for each box

630 ÷ 60 = 10.5

She should charge $10.50 for each box

I hope this helps!!!

Answer:

Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.

Step-by-step explanation:

can you mark me as brainlist

Answer:

4

Step-by-step explanation:

Well first you want to take 0.60 from the total amount which is $4 leaving you with $3.40

then you want to divide the remaining amount of money by the cost of a candy bar ($0.85)

So you do 3.40/0.85 which is equal to 4

Answer:

c) i^337 is equivalent to the expression i^137