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anzhelika [568]
2 years ago
9

Choose the equation of a line that is perpendicular to the y-axis and passes through the point (5, -2).

Mathematics
1 answer:
Irina-Kira [14]2 years ago
5 0
It would moat likly be y=-2 due to it having to be perpendicular to the y axis and pass through the 5,-2 point
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The maximum value of 12 sin 0-9 sin²0 is: -​
jeka57 [31]

Answer:

4

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be \theta rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

f(\theta) = 12sin(\theta) - 9 sin^2(\theta)

Taking the first derivative of this with respect to \theta and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of f(\theta) w.r.t \theta is

                        12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)

And setting this = 0 gives

12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0

Eliminating cos(\theta) on both sides and solving for sin(\theta) gives us

sin(\theta) = \frac{12}{18} = \frac{2}{3}

Plugging this value of sin(\theta) into the original equation gives us

12(\frac{2}{3}) - 9(\frac{4}{9} ) = 8 - 4 = 4

This is the maximum value that the function can acquire. The attached graph shows this as correct

3 0
1 year ago
What is the equation of the line that is parallel to 8x-5y=2 and goes through the point (-5,-2)
Stella [2.4K]

Answer:

8x - 5y = - 30

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 8x - 5y = 2 into this form

Subtract 8x from both sides

- 5y = - 8x + 2 ( divide all terms by - 5 )

y = \frac{8}{5} x - \frac{2}{5} ← in slope- intercept form

with slope m = \frac{8}{5}

• Parallel lines have equal slopes, hence

y = \frac{8}{5} x + c ← is the partial equation of the parallel line

To find c substitute (- 5, - 2) into the partial equation

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y = \frac{8}{5} x + 6 ← in slope- intercept form

Multiply through by 5

5y = 8x + 30 ( subtract 5y from both sides )

0 = 8x - 5y + 30 ( subtract 30 from both sides )

8x - 5y = - 30 ← in standard form

3 0
3 years ago
A salesperson earns a flat monthly salary, plus a percentage of the items sold. Which of the following functions could model the
Sergeu [11.5K]
Option C. y = 0.06x + 1200

In that function 1200 represents the flat monthly salary, x is the value of the items sold and 0.06 means that teh percentage is 6%.
5 0
2 years ago
What is the answer?please help
White raven [17]

Answer:

d

Step-by-step explanation:

4 0
2 years ago
What is the missing coordinate of the square with corners at (4, 0), (6, 0) and (6, 2)?
Archy [21]
I think the answer is (4,2)
6 0
2 years ago
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