Please help (I need a step by step explanation.)

Giving 13 points please put answer with step by step explanation

Answer: x = 1

Explanation: Correct me if I'm wrong

Answer: 17

Step-by-step explanation:

22-5=17

By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \cdot \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

So first differentiate both x and y with respect to t.

• dx/dt :

[tex]x = \dfrac{\sin^3(t)}{\sqrt{\cos(2t)}} = \sin^3(t) \left(\cos(2t)\right)^{-\frac12}[/tex]

By the product rule,

[tex]\dfrac{dx}{dt} = \dfrac{d(\sin^3(t))}{dt} \left(\cos(2t)\right)^{-\frac12} + \sin^3(t) \dfrac{d\left(\cos(2t)\right)^{-\frac12}}{dt}[/tex]

By the power and chain rules,

[tex]\dfrac{dx}{dt} = \dfrac{d(\sin(t))}{dt} 3\sin^2(t) \left(\cos(2t)\right)^{-\frac12} -\dfrac12 \sin^3(t) \left(\cos(2t)\right)^{-\frac32} \dfrac{d(\cos(2t))}{dt}[/tex]

[tex]\dfrac{dx}{dt} = 3\sin^2(t) \cos(t) \left(\cos(2t)\right)^{-\frac12} -\dfrac12 \sin^3(t) \left(\cos(2t)\right)^{-\frac32} (-2 \sin(2t))[/tex]

We can clean this up a bit and write

[tex]\dfrac{dx}{dt} = \dfrac{3\sin^2(t) \cos(t)}{\sqrt{\cos(2t)}} + \dfrac{\sin^3(t) \sin(2t)}{\sqrt{\cos^3(2t)}}[/tex]

[tex]\dfrac{dx}{dt} = \dfrac{\sin^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \cos(t) \cos(2t) + \sin(t) \sin(2t)\right)[/tex]

• dy/dt : (I'll skip some steps here, the derivative is nearly the same)

[tex]y = \cos^3(t) \left(\cos(2t)\right)^{-\frac12}[/tex]

[tex]\dfrac{dy}{dt} = 3\cos^2(t) (-\sin(t)) \left(\cos(2t)\right)^{-\frac12} + \cos^3(t) \left(-\dfrac12\right) \left(\cos(2t)\right)^{-\frac32} (-2 \sin(2t))[/tex]

[tex]\dfrac{dy}{dt} = -\dfrac{3\cos^2(t) \sin(t)}{\sqrt{\cos(2t)}} + \dfrac{\cos^3(t) \sin(2t)}{\sqrt{\cos^3(2t)}}[/tex]

[tex]\dfrac{dy}{dt} = -\dfrac{\cos^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \sin(t) \cos(2t) - \cos(t) \sin(2t)\right)[/tex]

Finally, we get dy/dx by dividing the two derivatives above:

[tex]\dfrac{dy}{dx} = \dfrac{-\frac{\cos^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \sin(t) \cos(2t) - \cos(t) \sin(2t)\right)}{\frac{\sin^2(t)}{\sqrt{\cos^3(2t)}} \left(3 \cos(t) \cos(2t) + \sin(t) \sin(2t)\right)}[/tex]

[tex]\dfrac{dy}{dx} = -\cot^2(t) \dfrac{3\sin(t)\cos(2t) - \cos(t)\sin(2t)}{3\cos(t)\cos(2t) + \sin(t)\sin(2t)}[/tex]

and by applying some trig identities,

[tex]\dfrac{dy}{dx} = -\cot^2(t) \dfrac{\sin(3t) - 2\sin(t)}{\cos(3t) + 2\cos(t)}[/tex]

[tex]\boxed{\dfrac{dy}{dx} = -\dfrac{\cos(3t)}{\sin(t) (2\cos(2t) + 1)}}[/tex]

Answer:

[tex]$\frac{dy}{dx}=-\cot (3 t)$[/tex]

Very important note!

Both answer are correct, the thing is: the expression can be more simplified  as

[tex]\sin(t)(2\cos(2t)+1) = \sin(3t)[/tex]

that will lead the the answer I just gave.

Step-by-step explanation:

The question is looking for [tex]\dfrac{dy}{dx}[/tex]

We have

[tex]x = \dfrac{\sin^3 (t)}{\sqrt{\cos(2t)}} \quad \text{ and } \quad y = \dfrac{\cos^3 (t)}{\sqrt{\cos(2t)}}[/tex]

One approach would be calculating [tex]\dot{x}[/tex] and [tex]\dot{y}[/tex] considering

[tex]\dfrac{dy}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

We would have

[tex]$\frac{dx}{dt}=\frac{3 \sin ^2(t) \cos(t)}{\sqrt{\cos (2 t)}} + \frac{\sin (2 t) \sin ^3(t)}{\cos ^{3/2}(2 t)} $[/tex]

[tex]$= \frac{\sin^{2} t}{\cos ^{3/2}(2 t)}(3\cos (t) \cos(2t)+2\sin^{2} (t) \cos(t))$[/tex]

[tex]$=\boxed{ \frac{\sin ^2(t) (2 \cos (t)+\cos (3 t))}{\cos ^{3/2}(2 t)}}$[/tex]

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

[tex]$\frac{dy}{dt}=\frac{\sin (2 t) \cos ^3(t)}{\cos ^{\frac{3}{2}}(2 t)}-\frac{3 \sin (t) \cos ^2(t)}{\sqrt{\cos (2 t)}}$[/tex]

[tex]$= \frac{\cos^{2} t}{(\cos ^{3/2}(2 t)} (-3\sin (t) \cos (2t)+2\cos^{2} (t) \sin (t))$[/tex]

[tex]$=\boxed{ \frac{\sin (t)-\sin (5 t)}{4 \cos ^{3/2}(2 t)}}$[/tex]

Finally,

[tex]$\frac{dy}{dx}= \frac{\sin (t)-\sin (5 t)}{4 \cos ^{3/2}(2 t)} \cdot \frac{\cos ^{3/2}(2t) }{ \sin ^2(t) (2 \cos (t)+\cos (3 t))}$[/tex]

[tex]$=\frac{\cos(t)(2\cos^{2} t-3(2\cos^{2} t-1))} {\sin(t)(2\sin^{2} t+3(1-2\sin^{2} t))} $[/tex]

[tex]$=-\frac{4\cos^{3} (t)-3\cos (t)}{3\sin (t)-4\sin^{3} (t)} $[/tex]

[tex]$=-\frac{\cos (3t)}{\sin (3t)}$[/tex]

[tex]=\boxed{-\cot (3t)}[/tex]

Answer:

What equation?

Step-by-step explanation:

Answer:

x-intercept: (1, 0)

Step-by-step explanation:

The x-intercept is the point on the graph where it crosses the x-axis, and has coordinates, (a, 0).  Looking at the two points on the graph, one of them crosses the x-axis at point (1, 0). This represents the x-intercept of the line.

Therefore, the x-intercept of the line is (1, 0).

Answer:

4

Step-by-step explanation:

its 4 because you have to convert ounces to pounds or pounds to ounces.

Answer:

4

Step-by-step explanation:

when we count ounces(Oz) to pound (ib) we should do

IB=Oz/16

IB=64/16

=4 this is your answer

Answer:

15 feet per minute.

Step-by-step explanation:

Answer:

All triangles measure 180 degrees. Angle B in Triangle BCD is congruent to angle D in triangle ABD. Angle D in triangle BCD is congruent with Angle B in triangle ABD.

Given these statements M<C= 50 degrees

Step-by-step explanation:

68+62=130

180-130=50

m<C= 50

Answer:

y=1/3(x-5)-3

graph is in attachment I added

Step-by-step explanation:

So you would subtract 3 from both sides which makes the equation look like this y=1/3(x-5)-3

And the graph is in the picture.

Answer:

hi can I be your best friend

Answer:

42 cups

Step-by-step explanation:

(C)

Step-by-step explanation:

The first condition states that the graph has 5 real zeros. Based on the choices, only (b) and (c) satisfy this condition because the other two choices contain 6 real zeros.

Now the second condition states that its end behavior approaches negative infinity as x approaches positive infinity. As you can see, graph (b) approaches positive infinity as x approaches positive infinity. This is clearly NOT the correct answer, which leaves us with (c) because we can see that it approaches negative infinity as x approaches positive infinity.

Answer:

A. [tex]\frac{rs-t}{2}[/tex]

Step-by-step explanation:

Given the expression [tex]s = \frac{2x+t}{r}[/tex] isolate [tex]x[/tex]

The first step is multiply both sides by [tex]r[/tex] then you have

[tex]sr = 2x + t[/tex]

know substract both sides by [tex]t[/tex]

[tex]sr - t = 2x[/tex]

The last step is multiply by [tex]\frac{1}{2}[/tex] both sides of the equation and get the answer

[tex]\frac{sr - t }{2} = x[/tex]

Answer:

-2

Step-by-step explanation:

If you want explanation lmk

Answer:

It was wrong but here is the correct answer

Step-by-step explanation:

Answer: I'm really late but here you go

Step-by-step explanation:

Answer:

it depends on how old the child is but theoretically yes because what if the child was ten the parent would be very young but would be thirty.

Step-by-step explanation:

[tex]\large\underline{\sf{Explanation-}}[/tex]

Given that

HOPE is a parallelogram.

It means,

Now, HE || PO & HP is transversal.

Now, In triangle HOP

We know, Exterior angle of a triangle is equals to sum of interior opposite angles.

It means, 40° + z = 70°

[tex]\longmapsto[/tex]"z" = 70° - 40° = 30°.

Now, OH || FE & HE is transversal.

So, we know, sum of Adjacent angles of a parallelogram is supplementary.

[tex]\rm \longmapsto\:z + 40\degree + x = 180 \degree[/tex]

[tex]\rm \longmapsto\:30\degree + 40\degree + x = 180 \degree[/tex]

[tex]\rm \longmapsto\:70\degree + x = 180 \degree[/tex]

[tex]\rm \longmapsto\:x = 180 \degree - 70\degree[/tex]

[tex]\longmapsto\:\bf{"x"} = 110 \degree [/tex]

Therefore, the measure of the following angle are:

Answer:

Step-by-step explanation:

y = mx + b

m = Δy/Δx = (9 - 9) / (8 - 4) = 0

y = 9

is a horizontal line nine units above the x axis.

choose any 3

(-3, 9) (-2, 9) (-1, 9) (0, 9) (1, 9) (2, 9) (3, 9) (4, 9) (5, 9) (6, 9) (7, 9)

Answer:

10.4

Step-by-step explanation:

Let the number be x

Sum of  x  and -3.2 : x + (-3.2) = x - 3.2

1/4 times the sum of a number and −3.2 = (1/4) * (x - 3.2)

[tex]\dfrac{1}{4}* \left( x - 3.2 \right) = 1.8\\\\\Multiply \ the \ whole \ equation \ by \ 4 \\\\4*\dfrac{1}{4} *(x - 3.2) = 1.8*4\\\\\\x - 3.2 = 7.2\\\\Add \ 3.2 \ to \ both \ sides\\\\\\x = 7.2 + 3.2\\[/tex]

x = 10.4

Answer:

10.4

ANSWER:

(10 2/5)

Step-by-step explanation:

k12

Answer: 1 / 52

Step-by-step explanation: Relating to what given card at the moment.

Answer:

See Below

Step-by-step explanation:

<4 and <8 are in corresponding positions in relations to the lines' intersection of the transversal, therefore they are corresponding angles.

<1 and <8 are on the outside, meaning they are exterior and on opposite sides. This means they are alternate exterior angles.

<1 and <5 are in corresponding positions in relations to the lines' intersection of the transversal, therefore they are corresponding angles.

<4 and <7  are on the inside, meaning they are interior and on the same side. This means they are same side interior angles.

Answer:

x + 3y = 55

-x -x

3y = -x + 55

3 3

y = -1/3x + 55/3

-x + 2y = 20

+x +x

2y = x + 20

2 2

y = 1/2x + 10

Espero que esto ayude :)

Por cierto, no soy un hablante nativo de español.

Answer:

[tex]f(x)=\frac{7}{2}x+10[/tex]

Step-by-step explanation:

These relations can be rewritten as ordered pairs.

Insert these ordered pairs into the slope formula to find the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-11-3}{-6-(-2)}\\\\m=\frac{-14}{-4}\\\\m=\frac{7}{2}[/tex]

Use the information found and insert it into the point-slope formula.

[tex]y-y_1=m(x-x_1)\\\\y-3=\frac{7}{2}(x-(-2))\\\\y-3=\frac{7}{2}x+7\\\\y=\frac{7}{2}x+10[/tex]