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2 years ago

Please help with this question

Mathematics

1 answer:

lions [1.4K]2 years ago

8 0

Answer:

sin( -∅ )

- 1 / csc ( ∅ )

1 / csc ( -∅ )

Step-by-step explanation:

Since sin(x) is and odd function (a function where f(-a) = f(a) ).

-sin( ∅ ) = sin( -∅ )

On the other hand, we know that sin( ∅ ) = 1 / csc ( ∅ )

Another odd function, so the same as before applies.

-sin( ∅ ) = -1 / csc ( ∅ )

-sin( ∅ ) = 1 / csc ( -∅ )

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The data in the table represents a company’s profit based on the number of items produced

frutty [35]

Answer:

(A) y= -1.026x^2 + 1016.402x - 162075

Step-by-step explanation:

Here is the options to the question

Which equation best represents the data?

A) y= -1.026x^2 + 1016.402x - 162075

B) y= -1.036x^2 + 1024.771x - 163710

C) y= 298.214x - 66317.667

D) y= 196.2x – 18710

(A) y= -1.026x^2 + 1016.402x - 162075

The data above represents the company's profit based on number of items produced.

To get the equation which best represents the data, we have to substitute the value of x into the given equations

By substituting x=100 in first equation, we have:

y = -1.02x² + 1016.402x – 162075

y = -1.026(100)² + 1016.402(100) – 162075

y = -70500

Option A satisfies.

Using the second equation

When x = 100

y = -1.036x^2 + 1024.771x - 163710

y = -1.036(100)² + 1024.771(100) - 163710

y = -10360 + 102477.1 – 163710

y = -71592.9

Option B doesn’t satisfies

We can also replace the various values of x in the equations to check whether or not they satisfy.

4 0

3 years ago

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ollegr [7]

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2 years ago

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dalvyx [7]

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2 years ago

Math question for 30 points please answer correctly

joja [24]

Answer:

D. The rate of change for function B is greater than the rate of change for function A

Step-by-step explanation:

Function a has a slope (aka rate of change) of 3/3

I know this because we start at (-3, 0) then finish at (0, 3)

We added 3 to both the x value and the y value.

3/3 = 1, so we have a rate of change of 1 for function A

Now that we know this, we can write the equation out into slope intercept form.

We can get y = x + 3

The equation for function B is y = 5x + 5

The slope for function B is greater, therefore the rate of change for function B is greater than the rate of change for function A

4 0

2 years ago

Show that 1n^ 3 + 2n + 3n ^2 is divisible by 2 and 3 for all positive integers n.

Dmitry_Shevchenko [17]

Prove:

Using mathemetical induction:

P(n) = $n^{3}+2n+3n^{2}$

for n=1

P(n) = $1^{3}+2(1)+3(1)^{2}$ = 6

It is divisible by 2 and 3

Now, for n=k, $n > 0$

P(k) = $k^{3}+2k+3k^{2}$

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

P(k+1) = $(k+1)^{3}+2(k+1)+3(k+1)^{2}$

P(k+1) = $k^{3}+3k^{2}+3k+1+2k+2+3k^{2}+6k+3$

P(k+1) = $P(k)+3(k^{2}+3k+2)$

Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = $n^{3}+2n+3n^{2}$ is divisible by 2 and 3 for all positive integer n.

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3 years ago