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3 years ago

Cot(x)=square root three ty!!

Mathematics

1 answer:

julia-pushkina [17]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tanx = $\frac{1}{cotx}$ , then

tanx = $\frac{1}{\sqrt{3} }$

x = $tan^{-1}$ ( $\frac{1}{\sqrt{3} }$ ) = $\frac{\pi }{6}$

Hence x = $\frac{\pi }{6}$ + kπ ( k ∈ Z )

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Collins has a part-time job as a dog walker. The table below shows the amount of money Collins earned for different numbers of h

solmaris [256]

Answer:

Step-by-step explanation:

Part A:

For Dog walking, he earns $30 for 5 hours of work.

He earns $36 for 6 hours of work.

$30/5 hours = $6/hour

$36/6 hours = $6/hour

He earns $6/hour dog walking.

For 8 hours, he earns 8 hours * $6/hour = $48

To earn $66, he works 66/6 = 11 hours.

5 30

6 36

8 48

11 66

Part B:

He earns $7/hour for yard work, so multiply the number of hours by 7 to find the money he earns.

Table for yard work

Hours Money

5 $35

6 $42

8 $56

Part C:

For 5 hours, he earns $35 for yard work and $30 as a dog walker.

$35 - $30 = $5

8 0

3 years ago

Find the equation of the linear function passing through (2,3) and (5,12)

Elis [28]

y = 3x - 3 is the equation of the linear function passing through (2, 3) and (5, 12)

<em><u>Solution:</u></em>

Given that we have to find the equation of linear function passing through (2, 3) and (5, 12)

The formula y = mx + b is said to be a linear function

Where "m" is the slope of line and "b" is the y - intercept

Let us first find the slope of line

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=2 ; y_{1}=3 ; x_{2}=5 ; y_{2}=12$

Substituting values we get,

$m=\frac{12-3}{5-2}=\frac{9}{3}=3$

Thus slope of line is m = 3

To find the y - intercept, substitute m = 3 and (x, y) = (2, 3) in y = mx + b

3 = 3(2) + b

3 = 6 + b

b = 3 - 6

b = -3

Thus the required equation of linear function is:

Substitute m = 3 and b = -3 in formula

y = mx + b

y = 3x - 3

Thus the equation of linear function is found

6 0

3 years ago

Graph y−5=−23(x+9) using the point and slope given in the equation.

Mashcka [7]

Answer:

Plot (-9,5) then you do rise over run and go down 2 and to the right 3

Step-by-step explanation:

So your points would be (-9,5) and(-6,3)

6 0

3 years ago

A function y(t) satisfies the differential equation dy dt = y4 − 9y3 + 20y2. (a) What are the constant solutions of the equation

Darya [45]

Answer:

a) y = 0, y = 4 and y = 5

b) y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)

c) y ⊂ (4,5)

Step-by-step explanation:

Data provided in the question:

function y(t) satisfies the differential equation:

$\frac{dy}{dt}$ = y⁴ − 9y³ + 20y²

Now,

a) For constant solution

$\frac{dy}{dt}$ = 0

y⁴ − 9y³ + 20y² = 0

y² (y² - 9y + 20 ) = 0

y²(y² -4y - 5y + 20) = 0

y²( y(y - 4) -5(y - 4)) = 0

y²(y - 4)(y - 5) = 0

therefore, solutions are

y = 0, y = 4 and y = 5

b) for y increasing

$\frac{dy}{dt}$ > 0

y²(y - 4)(y - 5) > 0

y²

y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)

c) for y decreasing

$\frac{dy}{dt}$ < 0

y²(y - 4)(y - 5) > 0

y²

y ⊂ (4,5)

8 0

4 years ago

A homeowner wants to build a circular patio. if the diameter of the patio is 20 feet, what is its area to the nearest whole numb

andreyandreev [35.5K]

We are asked to find the area of patio. It is circular so formula used for area is given by:
$A= r^{2} \pi$
Where
r = radius = diameter / 2 = 20 / 2 = 10 feet

$A = 10^{2} \pi =100 \pi$
When we round this to the nearest whole number:
$A =100 \pi = 314.159=314ft^{2}$

5 0

4 years ago