We note that the area of the square is given by: $A(x) = x^2$ but we aim to find $\frac{dA}{dt}$ . But we can use the chain rule to pull out that dA/dt. Doing so gives us:

$\frac{dA}{dt} = \frac{dA}{dx} \times \frac{dx}{dt}.$

Now, $\frac{dA}{dx} = 2x$ (by the power rule and $\frac{dx}{dt} = 3.$

But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.

So, finally, we see that:

$\frac{dA}{dt} = 2(7) \times 3 = 14 \times 3 = 42.$

7 0

2 years ago

The floor plan of a ballroom is shown at the right. The scale is 3 centimeters: 4 meters. what are the length and width of the b

astraxan [27]

Length = 16
Width = 12
Area = 192

3 0

2 years ago

Given the points J(4,-7) and L(-2,13), find the coordinates of point k on JL such that the ratio of jk is 1:4

Irina-Kira [14]

Answer:

The coordinates of point k are (-2.8,-3)

Step-by-step explanation:

we shall use the internal division formula to find the coordinates of point k

Mathematically, the formula is as follows;

Let’s call the coordinates of point k (x,y)

(x , y) = mx2 + nx1/(m + n) , my2 + ny1/(m + n)

From the question;

m = 1 , n = 4

x1 = 4, x2= -2

y1 = -7 , y2 = 13

Substituting these values in the equation, we have the following;

1(-2) + 4(4)/(1 + 4) , 1(13) + 4(-7)/(1+4)

(-2+16)/5, (13 -28)/5

= -14/5, -15/5

= (-2.8, -3)

3 0

2 years ago