Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2

The formula is given as;

P(t) = (t^2 + 100) ln (t + 2)

The rate of change refers to the first integral of the formula;

Thus we need to calculate this by the use of product formula;

The first differential of t^2 + 100 is 2t

while that of ln(t + 2) is 1/(t + 2)

P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)

Now, we substitute 2 for the value of t here.

P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))

P’(2) = 4 ln 4 + 104(1/4)

P’(2) = 4ln 4 + 26

P’(2) = 5.55 + 26 = 31.55 which is approximately 32

8 0

3 years ago

Find the equation of the least squares regression line. Show all calculations, and be sure to define any variables used.

spayn [35]

Steps
Step 1: For each (x,y) point calculate x2 and xy.
Step 2: Sum all x, y, x2 and xy, which gives us Σx, Σy, Σx2 and Σxy (Σ means "sum up")
Step 3: Calculate Slope m:
m = N Σ(xy) − Σx Σy N Σ(x2) − (Σx)2
Step 4: Calculate Intercept b:
b = Σy − m Σx N.
Step 5: Assemble the equation of a line.

3 0

3 years ago

Triangle and triangle are similar. What is the measure of side ?

snow_lady [41]

When two triangles are similar, they're sides are in proportion.

In order to find the unknown side, we first have to find the ratio of the larger triangle to the smaller triangle.

We can use the sides TV and LN to make the proportion.

$\frac{LN}{TV}$ = $\frac{21}{6}$