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Gennadij [26K]
2 years ago
8

The rate of people entering a safari tour is modeled by the equation p(t) = 200e ^ (- t) for the first 5 hoursEstimate the popul

ation density on a 2.000 km ^ 2 animal reserve for t = 2 to t = 4usir using the midpoint sum approximation with 6 subintervals . Round to the nearest person .
Mathematics
1 answer:
aivan3 [116]2 years ago
4 0

Answer:23

Step-by-step explanation:

You might be interested in
Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).
Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0
3 years ago
HELP PLEASE!!! I DONT UNDERSTAND
g100num [7]
A is 10 and 12

C is 4 and 8
4 0
3 years ago
Read 2 more answers
Help pleaseee and explain how , I’m confused thanks
docker41 [41]

Answer:

The rope is worth 13.

The shoe is worth 5.

The clock is worth 3.

Step-by-step explanation:

We know that the weights are 8 so we will use 8 for the weights.

Let s = show

Let r = rope

Let c = clock

We have three unknowns so we need three equations.

8 + s = r                      c + s = 8                                 s= c +2

There are a number of ways that we can approach this.  Let's substitute

c + 2 for s in the first 2 equations.

8 + s = r

8 + c + 2 = r

10 + c = r

c + s = 8

c + c + 2 = 8

2c + 2 = 8  

2c = 6

c = 3  we found the value of the clock.

Now, let's substitute 3 in for 3 in the bold equation above.

10 + c = r

10 + 3 = r

13 = r we found the value of the rope.

We can use any of the equations to find the shoe.

s= c + 2

s = 3 + 2

s = 5

This is tricky.  It takes a lot of practice.  Don't give up!

7 0
1 year ago
Read 2 more answers
(b) The globe has a radius of 28.5 cm. Find the surface area of the globe. Round your answer to two decimal places. Use:
damaskus [11]

Answer:

\boxed {\boxed {\sf  10,207.03 \ cm^2}}

Step-by-step explanation:

Surface area is the total area of the surface of an object. A globe is a sphere and the formula for calculating a sphere's surface area is:

SA= 4 \pi r^2

The radius (r) of the globe is 28.5 centimeters. Substitute this value into the formula.

  • r= 28.5 cm

SA= 4 \pi ( 28.5 \ cm)^2

Solve the exponent. Multiply the number by itself.

  • (28.5 cm)²= 28.5 cm * 28.5 cm = 812.25 cm²

SA= 4 \pi (812.25 \ cm^2)

Multiply 4, pi and 812.25 centimeters together.

SA= 12.56637061  (812.25 \ cm^2)

SA= 10207.03453 \ cm^2

Round to two decimal place or the hundredth place. The 4 in the thousandth place to the right (10207.03453) tells us to leave the 3 in the hundredth place (10207.0<u>3</u>453).

SA \approx 10207.03 \ cm^2

The surface area of the globe is approximately <u>10,207.03 centimeters squared.</u>

3 0
2 years ago
Read 2 more answers
W−2+2w=6+5w please helppp
Lerok [7]

Answer:

Step-by-step explanation:

Simplifying

W + -2 + 2w = 6 + 5w

Reorder the terms:

-2 + W + 2w = 6 + 5w

Solving

-2 + W + 2w = 6 + 5w

Solving for variable 'W'.

Move all terms containing W to the left, all other terms to the right.

Add '2' to each side of the equation.

-2 + W + 2 + 2w = 6 + 2 + 5w

Reorder the terms:

-2 + 2 + W + 2w = 6 + 2 + 5w

Combine like terms: -2 + 2 = 0

0 + W + 2w = 6 + 2 + 5w

W + 2w = 6 + 2 + 5w

Combine like terms: 6 + 2 = 8

W + 2w = 8 + 5w

Add '-2w' to each side of the equation.

W + 2w + -2w = 8 + 5w + -2w

Combine like terms: 2w + -2w = 0

W + 0 = 8 + 5w + -2w

W = 8 + 5w + -2w

Combine like terms: 5w + -2w = 3w

W = 8 + 3w

Simplifying

W = 8 + 3w

6 0
3 years ago
Read 2 more answers
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