Calculate s75 for the arithmetic sequence defined by

The value of is -675 and this can be determined by using the formula of the sum of n terms in the arithmetic sequence and the given data.

Given :

  --- (1)

The following steps can be used in order to determine the value of :

Step 1 - Substitute the value of (n = 1) in the expression (1).

Step 2 - Substitute the value of (n = 75) in the expression (1).

Step 3 - Now, the formula of sum in an arithmetic sequence is given below:

where n is the total number of terms, is the first term, and is the last term.

Step 4 - Substitute the values of the known terms in the above expression.

Step 5 - Simply the above expression.

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The formula of a sum of an arithmetic sequence:

We have n = 75 and .

Calculate the first and seventy-fifth term:

Substitute:

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204