What is the numberpattern in 4-14-30-?

Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish i

ICE Princess25 [194]

There would be 173,535 lionfish after 6 years.

Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:

A)
8000 x 1.67 ^ n = f
B)
8000 x 1.67 ^ 6 = X
8000 x 21.691961596369 = X
173,535.692770952 = X
C)
(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f

Therefore, there would be 173,535 lionfish after 6 years.

Learn more about maths in brainly.com/question/25851847

4 0

1 year ago

calculate the side lengths a and b to two decimal places angle a is 64 angle b is 85 and line ab is 9.3? PLEASE HELP ASAP

qaws [65]

∠C = 180° - (∠A + ∠B) = 180° - (64° + 85°) = 180° - 149° = 31°
$AC= \frac{9.3*sin(85)}{sin(31)} = \frac{9.3*0.9962}{0.515} =17,99 \\ \\ BC=\frac{9.3*sin(64)}{sin(31)} = \frac{9.3*0.8988}{0.515} =16,2$

4 0

3 years ago

Given the function g(x) = (5 - x)^3 , what is the value of g(2)?

11111nata11111 [884]

Answer:

g(2) = 27 is the answer.

Step-by-step explanation:

If the function is g(x) = (5 - x)³

By expanding (5 - x)³ = 5³-3.5²x + 15x² -x³

g(x) = 125 - 75x + 15x² - x³

Now g(2) = 125 - 75×2 + 15×(2)² - 2³

g(2) = 125 - 150 + 60 - 8

= -25 + 60 - 8

= 35 - 8 = 27

Or directly putting the value x = 2 in g(x) we get

g(2) = (5 - 2)³ = 3³ = 27

Therefore g(2) = 27 is the answer.

3 0

2 years ago

Read 2 more answers

Find the absolute maximum and minimum values of f(x, y) = x+y+ p 1 − x 2 − y 2 on the quarter disc {(x, y) | x ≥ 0, y ≥ 0, x2 +

Andreas93 [3]

Answer:

absolute max: f(x,y)=1/2+p1 ; at P(1/2,1/2)

absolute min: f(x,y)=p1 ; at U(0,0), V(1,0) and W(0,1)

Step-by-step explanation:

In order to find the absolute max and min, we need to analyse the region inside the quarter disc and the region at the limit of the disc:

Region inside the quarter disc:

There could be Minimums and Maximums, if:

∇f(x,y)=(0,0) (gradient)

we develop:

(1-2x, 1-2y)=(0,0)

x=1/2

y=1/2

Critic point P(1/2,1/2) is inside the quarter disc.

f(P)=1/2+1/2+p1-1/4-1/4=1/2+p1

f(0,0)=p1

We see that:

f(P)>f(0,0), then P(1/2,1/2) is a maximum relative

Region at the limit of the disc:

We use the Method of Lagrange Multipliers, when we need to find a max o min from a f(x,y) subject to a constraint g(x,y); g(x,y)=K (constant). In our case the constraint are the curves of the quarter disc:

g1(x, y)=x^2+y^2=1

g2(x, y)=x=0

g3(x, y)=y=0

We can obtain the critical points (maximums and minimums) subject to the constraint by solving the system of equations:

∇f(x,y)=λ∇g(x,y) ; (gradient)

g(x,y)=K

Analyse in g2:

x=0;

1-2y=0;

y=1/2

Q(0,1/2) critical point

f(Q)=1/4+p1

We do the same reflexion as for P. Q is a maximum relative

Analyse in g3:

y=0;

1-2x=0;

x=1/2

R(1/2,0) critical point

f(R)=1/4+p1

We do the same reflexion as for P. R is a maximum relative

Analyse in g1:

(1-2x, 1-2y)=λ(2x,2y)

x^2+y^2=1

Developing:

x=1/(2λ+2)

y=1/(2λ+2)

x^2+y^2=1

So:

(1/(2λ+2))^2+(1/(2λ+2))^2=1

$\lambda_{1}=\sqrt{1/2}*-1 =-0.29$

$\lambda_{2}=-\sqrt{1/2}*-1 =-1.71$

$\lambda_{2}$ give us (x,y) values negatives, outside the region, so we do not take it in account

For $\lambda_{1}$ : S(x,y)=(0.70, 070)

and

f(S)=0.70+0.70+p1-0.70^2-0.70^2=0.42+p1

We do the same reflexion as for P. S is a maximum relative

Points limits between g1, g2 y g3

we need also to analyse the points limits between g1, g2 y g3, that means U(0,0), V(1,0), W(0,1)

f(U)=p1

f(V)=p1

f(W)=p1

We can see that this 3 points are minimums relatives.

Conclusion:

We compare all the critical points P,Q,R,S,T,U,V,W an their respective values f(x,y). We find that:

absolute max: f(x,y)=1/2+p1 ; at P(1/2,1/2)

absolute min: f(x,y)=p1 ; at U(0,0), V(1,0) and W(0,1)

4 0

2 years ago

What is the area of a rectangular driveway measuring 20 feet long and 15 feet wide?

alukav5142 [94]

Answer:

300 square feet

Step-by-step explanation:

Area is found by multiplying the length and width of a surface

5 0

3 years ago