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3 years ago

If it takes 4 years for an animal population to double, how many years will it take until the population triples?

Mathematics

2 answers:

Leto [7]3 years ago

8 0

Answer:

6 years

Step-by-step explanation:

i used a proportional approach

2 (the double)/ 4 years (the time it takes to double)

then compared it to

3(the triple)/ x amount of years

(like this)

$\frac{2}{4} \ \frac{3}{x}$

then cross multipled

4 times 3= 12

then divided the 12 by the remaining 2 above the 4

Shalnov [3]3 years ago

3 0

12! *boom* mental math XD

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Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter

Vaselesa [24]

We have been given a function $f(x)=2x^3+3x^2-336x$ . We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

$f'(x)=2(3)x^{2}+3(2)x^1-336$

$f'(x)=6x^{2}+6x-336$

$6x^{2}+6x-336=0$

$x^{2}+x-56=0$

$x^{2}+8x-7x-56=0$

$(x+8)-7(x+8)=0$

$(x+8)(x-7)=0$

$x=-8,x=7$

So $x=-8,7$ are critical points and these will divide our function in 3 intervals $(-\infty,-8)U(-8,7)U(7,\infty)$ .

Now we will find derivative over each interval as:

$f'(x)=(x+8)(x-7)$

$f'(-9)=(-9+8)(-9-7)=(-1)(-16)=16$

Since $f'(9)>0$ , therefore, function is increasing on interval $(-\infty,-8)$ .

$f'(x)=(x+8)(x-7)$

$f'(1)=(1+8)(1-7)=(9)(-6)=-54$

Since $f'(1)$ , therefore, function is decreasing on interval $(-8,7)$ .

Let us check for the derivative at $x=8$ .

$f'(x)=(x+8)(x-7)$

$f'(8)=(8+8)(8-7)=(16)(1)=16$

Since $f'(8)>0$ , therefore, function is increasing on interval $(7,\infty)$ .

(b) Since $x=-8,7$ are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

$f(-8)=2(-8)^3+3(-8)^2-336(-8)$

$f(-8)=1856$

$f(7)=2(7)^3+3(7)^2-336(7)$

$f(7)=-1519$

Therefore, $(-8,1856)$ is a local maximum and $(7,-1519)$ is a local minimum.

Let us find 2nd derivative.

$f''(x)=6(2)x^{1}+6$

$f''(x)=12x+6$

$12x+6=0$

$12x=-6$

$\frac{12x}{12}=-\frac{6}{12}$

$x=-\frac{1}{2}$

Therefore, $x=-\frac{1}{2}$ is an inflection point of given function.

3 0

3 years ago

On a coordinate plane, triangle R S T has points (negative 5, 6), (3, 4), and (negative 2, 2). Which expression can be used to f

pav-90 [236]

The area of a triangle is the amount of space on the triangle

The expression that represents the area of the triangle is $A = \frac 12|-5(2 -4) +3(2 -6) -2(4 -6)|$

The coordinates of the triangle are given as:

$R = (-5,6)$

$S = (3,4)$

$T = (-2,2)$

The area (A) of a triangle from its coordinates or vertices are:

$A = \frac 12|x_1(y_3 -y_2) +x_2(y_3 -y_1) + x_3(y_2 -y_1)|$

Substitute values for x's and y's

$A = \frac 12|-5(2 -4) +3(2 -6) -2(4 -6)|$

Hence, the expression that represents the area of the triangle is $A = \frac 12|-5(2 -4) +3(2 -6) -2(4 -6)|$

Read more about areas of triangles at:

brainly.com/question/9664477

6 0

2 years ago

Two shops, Tisco and Azda, sell the same brand of baked beans with the following deals.

andreev551 [17]

Answer:

Azda's price is better

Step-by-step explanation:

Tisco

3 for £1.29

12 for £1.29*4= £5.16

Azda

4 for £1.68

12 for £1.68*3= £5.04

Azda offers better price for 12 items

3 0

3 years ago

Read 2 more answers

Determine if f(x, y) = 10 − x^2 − y^2

Eva8 [605]

Answer:

Step-by-step explanation:

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. x is treat any other variable as a constant.

dz/dx=0-2x-0

dz/dx=-2x

Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.

Since this result is negative, it mrans as x increases z decreases.

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. y is treat any other variable as a constant.

dz/dx=0-0-2y

dz/dx=-2y

Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.

Since this result is positive it mrans as y increases z decreases.

8 0

3 years ago

Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each sale

yanalaym [24]

GIVEN:
<span>Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.
Salesman C does not earn any commission. His weekly salary is $900.

Salesman A: 1300 </span>≤ 65S
Salesman B: P = 40S + 300
Salesman C: P = 900

Salesman A can only have 20 sales. 1,300/65 = 20. It should not go beyond that because it will go beyond the limit of 1,300 per week.

Salesman B will earn 1,100 for 20 sales. P = 40(20) + 300 = 800 + 300 = 1,100.

Salesman C will earn 900 regardless if he had 0 or 20 sales for the week.

You can do your own graph using my equations.

3 0

3 years ago