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3 years ago

What are the domain and range of the function?

Mathematics

1 answer:

Nataliya [291]3 years ago

4 0

Answer:

Range: {0, 2, -4, -8}

Domain: {-2, -1, 0, 1, 2}

Step-by-step explanation:

The x-coordinate of each point on the graph (input values) = the domain

The y-coordinate of each point on the graph (output values) = the range

Thus:

Domain => {-2, -1, 0, 1, 2} (on the x-axis)

Range => {0, 2, -4, -8} (on the y-axis)

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The population of a town with a 20162016 population of 87 comma 00087,000 grows at a rate of 1.91.9% per year. a. Find the rate

SCORPION-xisa [38]

Answer:

Given,

The initial population, P = 87,000,

Annual rate of increasing, r = 1.9 %,

a) Thus, the population after t years,

$A=P(1+\frac{r}{100})^t$

$A=87000(1+\frac{1.9}{100})^{t}$

$=87000(1+0.019)^t$

$=87000(1.019)^t$

$87000(1.019)^t=87000e^{kt}$

Where, k is the rate constant,

By comparing,

$\implies k=log(1.019)=0.00817418400643\approx 0.00817$

Hence, the approximate value of k is 0.00817.

And, the exponential growth function would be,

$A=87000e^{0.00817t}$

b) If A = 145,000,

$145000=87000(1.019)^t$

By using graphing calculator,

We get,

$t=27.14\approx 27$

The year after 27 years from 2016 is 2043.

Hence, in 2043 the population reach 145,000.

6 0

4 years ago

What do the following two equations represent? -x-3y=-1 -x-3y=-1

densk [106]

Infanate solution I think???

4 0

4 years ago

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Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).

aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0

4 years ago

What is the slope, please 18,5 and -18, 5

ValentinkaMS [17]

Answer:

The slope is a zero slope. This means that the line is a straight, horizontal line.

Step-by-step explanation:

Use the slope formula.

$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$

5-5/-18-18 = 0/-36

8 0

3 years ago

Please help me happy new years

vodka [1.7K]

1) The quotient is 6.

2) The quotient is 9/10.

Hope it helps!

4 0

3 years ago

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