Ahh sorry! i need help again! question 25! if you can, please include steps! thanks!

2

Step-by-step explanation:

2x^2 -3xy^3

Let x=-2 and y =-1

2 ( -2)^2 -3 (-2) (-1)^3

Using PEMDAS, we do exponents first

2 ( 4) - 3(-2) (-1)

Multiply nexy

8 - 6

2

In this question, we are required to find

When, x = -2 and y = -1

We just need to plug the values of x and y in the given polynomial to get our required answer.

Given, Polynomial in variable x and y,

Plugging values of x and y,

According to PEMDAS, we need to do the exponents first, So let's simplify the exponents,

Opening the parantheses and finding the answer,

This is our required answer !!

#CarryOnLearning

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f(x) represents the vertical height of the cannon

Step-by-step explanation:

The given function is presented as follows;

f(x) = -0.05·(x² - 26·x - 120)

Given that 'x' represent the horizontal path of the cannon and the function describes the path of the cannon, we have that the vertical height reached by the cannon as it moves along the horizontal path is given as the function f(x)

Therefore, we have;

f(0) = -0.05·(0² - 26×0 - 120) = -0.05 × -120 = 6

f(0) = 6

The starting height of the cannon = 6

The maximum height reached by the cannon is given as follows;

f'(x) = d(-0.05·(x² - 26·x - 120))/dx = -0.05·d(x² - 26·x - 120)/dx = -0.05×(2·x - 26)

f'(x) = -0.05×(2·x - 26)

f'(x) = 0 At maximum height, therefore, we have;

-0.05×(2·x - 26) = 0

(2·x - 26) = 0

2·x = 26

x = 26/2 = 13

x = 13

f(13) = -0.05·(13² - 26×13 - 120) = 14.45

The maximum height = 14.45

Therefore;

f(x) = The vertical height of the cannon