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dolphi86 [110]
3 years ago
7

Sinxcosy = 1/2 (sin(x+y)+cos (x-y))

Mathematics
1 answer:
sasho [114]3 years ago
8 0
<span>(1/2) [SIN(X-Y)-SIN(X+Y)]= COS(X)SIN(Y)</span>
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There are 25 desks in a classroom. The number of rows is five less than twice the number of desks in each row. Find the number o
anastassius [24]
Let's say each row has x desks and there are y rows.

We then know that x*y =25

We also know that x*2-5=y (number number of rows is five less than twice the number of desks in each row)

So we substitute: x*(x*2-5)=25
putting numbers out of the brackets:
2x*x-5x=25

2x*x-5x-25=0
 
(2x+5)(x-5)=0 (this bracketing is true: you can check it by expanding it:
2x*x-10x+5x-25

So that means that either x=-2.5which can't be : there can't be a fractional number of benches,

or  x=5
so each row has 5 desks and there are 2*5-5 rows, or 5 rows.


6 0
3 years ago
If cotθ=1/<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%203%5C%5C" id="TexFormula1" title="\sqrt{x} 3\\" alt="\sqrt{x} 3\\" a
kobusy [5.1K]

\text{Given  that,}~\\\\\cot \theta = \dfrac 1{\sqrt 3} \\\\\\\text{So,}~~ \tan \theta = \dfrac 1{\cot \theta} = \sqrt 3\\\\\\\sec^2 \theta + \csc^2 \theta   \\\\=(1+\tan^2 \theta) + (1 + \cot^2 \theta)\\\\=1 +\left (\sqrt 3 \right)^2 + 1 + \left(\dfrac 1{\sqrt 3} \right)^2\\\\=1 +3 + 1 + \dfrac 13 \\\\= 5  + \dfrac 13 \\\\= 5 \dfrac 13

7 0
2 years ago
The revenue function for a sporting goods company is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=4
Zina [86]

The maximum revenue generated is $160000.

Given that, the revenue function for a sporting goods company is given by R(x) = x⋅p(x) dollars where x is the number of units sold and p(x) = 400−0.25x is the unit price. And we have to find the maximum revenue. Let's proceed to solve this question.

R(x) = x⋅p(x)

And,  p(x) = 400−0.25x

Put the value of p(x) in R(x), we get

R(x) = x(400−0.25x)

R(x) = 400x - 0.25x²

This is the equation for a parabola.  The maximum can be found at the vertex of the parabola using the formula:

x = -b/2a from the parabolic equation ax²+bx+c   where a = -0.25,  b = 400 for this case.

Now, calculating the value of x, we get

x = -(400)/2×-0.25

x = 400/0.5

x = 4000/5

x = 800

The value of x comes out to be 800. Now, we will be calculating the revenue at x = 800 and it will be the maximum one.

R(800) = 400x - 0.25x²

= 400×800 - 0.25(800)²

= 320000 - 160000

= 160000

Therefore, the maximum revenue generated is $160000.

Hence, $160000 is the required answer.

Learn more in depth about revenue function problems at brainly.com/question/25623677

#SPJ1

5 0
1 year ago
8.5cm squared = ...mm squared?<br><br> Please explain clearly
tekilochka [14]
1 centimeter = 10 milimeters.
Therefore, 8.5 centimeters squared = 85 millimeters squared.
6 0
3 years ago
Find the area for a triangle that has a base of 24 inches and a height of 4 inches.
nirvana33 [79]

Answer:

48in²

Step-by-step explanation:

to find the area of a triangle you first divide the base by 2 then multiply it by the height

7 0
3 years ago
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