If x=at^3 and y=bt^2 then find dy/dx

Answers

Answer 1
Answer: dy/dx = (dy/dt) / (dx/dt)

dy/dt = 2bt

dx/dt = 3at^2

therefore dy/dx = 2bt/3at^2
              dy/dx = 2b/3at

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The following graph represents a proportional relationship:A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, and 10. The values on the y axis are 0, 6, 12, 18, 24, 30. Points are shown on ordered pairs 0, 0 and 2, 6 and 4, 12 and 6, 18 and 8, 27. These points are connected by a line. The label on the x axis is Bunches of Thyme. The title on the y axis is Price of Bunches.

True

False

Answers

If points (ordered pairs) connected by a line are:
(0,0), (2,6), (4,12), (6,18) and (8,24) [If you did not make a mistake by typing a point (8,27)], THEN
it is a direct proportional relationship in question, defined by formula:
y = k*x
where k is coefficient of this proportion, and x and y are coordinates of points respectively.
So, if you check for EACH point:
0 = k*0,
6 = k*2,
12=k*4,
18=k*6,
24=k*8,
for each of these equations, it is obtained for k to has value of 3.
And the rule is for a proportion, that has to have SAME k value for each of its points on a line.
So the answer is TRUE.
But if you did not make a mistake by typing point (8,27), then k value for its equation
27=k*8, will not be 3 as for the rest of the points.
And then, the answer would be FALSE, it is NOT a proportional relationship.

Answer:

the answer is false, i took the test

What is the quotient (x^3+8)/(x+2)

Answers

Answer:

Step-by-step explanation:

The easiest way to do this is by using synthetic division (I really hope you know what I'm talking about!)

If the factor is x + 2 = 0, then the solution or the root is x = -2.  We will put -2 outside the "box" and the coefficients from the terms of the polynomial inside the "box":

-2|   1    0    0    8

Bring down the first number and multiply it by the -2.  Put the product up under the first 0 and add:

-2|   1    0    0    8

           -2

      1   -2  

Now multiply the -2 by the -2, put the product up under the next 0 and add:

-2|   1    0    0    8

           -2    4

      1    -2    4

Now multiply the 4 by the -2, put the product up under the 8 and add:

-2|   1    0    0    8

           -2   4    -8

     1    -2   4    0

Those bold numbers are the coefficients to the quotient, which is another polynomial, but is one degree less than the one you started with:

x² - 2x + 4 = 0

Since there is no remainder, then x = -2 is a zero of x³ + 8, and (x + 2) is a factor.

There is a whole world of stuff to learn about quadratics!!

Prove that sin(x) + tan(x) = 1 + sec(x)/csc(x) by using trigonometric identities.

Answers

Answer:

Step-by-step explanation:

sin(x) + tan(x) =sin(X) + sin(x)/cos(x)

=sinx(1+1/cosx)

=Sinx(1+secx)

=1+secx/cosecx. (Since sinx=1/cosecx)

Hence LHS=RHS proved

What is difference between 783 and366

Answers

If you mean subtraction, then its 417.
The answer would be 417



A student factors 3x2 – 12 to the following. 3(x2 – 4) Which statement about 3(x2 – 4) is true? A. The expression is equivalent, and it is completely factored. / B.The expression is equivalent, but it is not completely factored./ C. The expression is not equivalent, but it is completely factored./ D.The expression is not equivalent, and it is not completely factored.

Answers

Answer:

Option B is correct that is the expression is equivalent, but it is not completely  factored.

Step-by-step explanation:

We have given an expression

3x^2-12

when we take the common factor out which is 3 from the expression we will get

3(x^2-4)

This expression is equivalent but is not completely factored because the term

(x^2-4)\text{can be further factored as}(x-2)\text{and}(x+2)\text{from the formula}a^2-b^2=(a+b)(a-b)

Hence, Option B is correct.

Option C and D are discarded because given factor is equivalent  

Option A is discarded  because expression is not completely factored.

 

B. The expression is equivalent but not completely factored.

You can continue to factor

3 (x^2-4) =

3 (x+2)(x-2)

Х у -3 -1
0 0
3 1
6 2 Which equation describes the relationship expressed in the table? )) A) y = x C) y = ⅙x
B) y =3x D) y = ⅓x​

Answers

Answer:

D

Step-by-step explanation:

if y=2 then x=6, 2x3=6 ...if you multiple y with 3..you will get the answer of x

in that equation above..it will get x=3y...but there is no answer for it..so, you can convert it to, y=1/3x

Answer:

the answer is D

hope this will help you ❤️

Step-by-step explanation:

you can search in yt (how to find the slope of linear function)