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balu736 [363]
3 years ago
7

If the sum of the interior angles of a polygon is 3780° how many sides does it have ​

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
4 0

Answer:

the answer will be 23

Step-by-step explanation:

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Find the perimeter of a field that has length 2/x + 1 and width 5/x^2 -1.
Semmy [17]

Answer:

D)4x + 6/(x + 1)(x - 1)

Step-by-step explanation:

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

p=2(l+w)

where

p is the perimeter

l is the length

w is the width

We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so l=\frac{2}{x+1} and w=\frac{5}{x^2-1}.

Replacing values:

p=2(l+w)

p=2(\frac{2}{x+1} +\frac{5}{x^2-1})

Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula a^2-b^2=(a+b)(a-b) where a is the first term and b is the second term. We can infer that a=x^2 and b=1^2. So, x^2-1=(x+1)(x-1). Replacing that:

p=2(\frac{2}{x+1} +\frac{5}{x^2-1})

p=2(\frac{2}{x+1} +\frac{5}{(x+1)(x-1})

We can see that the common denominator of our fractions is (x+1)(x-1). Now we can simplify our fraction using the common denominator:

p=2(\frac{2(x-1)+5}{(x+1)(x-1)} )

p=2(\frac{2x-2+5}{(x+1)(x-1)} )

p=2(\frac{2x+3}{(x+1)(x-1)} )

p=\frac{4x+6}{(x+1)(x-1)}

We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).

3 0
3 years ago
Solve the equation. dy dx = ay + b cy + d , where a, b, c, and d are constants. (assume a ≠ 0 and ay + b ≠ 0.)
Reil [10]

 

It solves it in x. the solution for y includes heavy use of the product log function.

dy/dx                                = ay + b/cy +d

(cy +d/ ay + b) dy            = dx

∫ (cy +d/ ay + b) dy          = x (t) + C

 

Into solving the integral, integration by parts followed by u substitution and another integration by parts.

 

∫ (cy +d/ ay + b) dy

u            = cy + d dv          = dy/ay + b

du          = c dy v               = ln I ay + b l / a

 

Then, use u substitution for the new integral

 

u            = ay + b

du          = a dy

∫ ln l ay + b I dy                = ∫ ln IuI /a du    = 1/a ∫ ln luI du

 

Integrating the natural log includes thus far another integration by parts

r             = ln IuI ds            = du

dr          = du / u (s)           = du

∫ ln IuI / du                         = u ln IuI - ∫ du   = u ln IuI - ∫ a dy                                                                                   = (ay + b) ln Iay +bl – ay

 

The original integral of expression

∫ (cy +d/ ay + b) dy             = cy + d/a ln lay+bl – c/a² [(ay+b) ln lay+bl – ay]

Then simplify

∫ (cy +d/ ay + b) dy             = cy + d/a ln lay+bl – c/a²[(ay+b) ln lay+bl – ay]

                                           = a (cy + d)/a² ln lay+bl – c (ay+b)/ a²ln lay+bl +                                                               c/a² ay

                                           = cay + ad – cay – cb/ a² ln lay+bl + cay/a²

                                           = ad – cb/a²ln lay+bl + cy/a

 The final answer will be

x(t) + C                               = ad – cb/a² ln lay+bl + cy/a

x(t)                                     = ad – cb/a² ln lay+bl + cy/a + k

 

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3 0
3 years ago
During a period of 6 months, MegaCorp had monthly profits of $3.2 million, $1.8 million, and $6.4 million. Two months had losses
Feliz [49]
1. Add up all the profits:
3.2 + 1.8 + 6.4 = $11.4 million
2. Add up all the losses:
4.5 + 2.7 = $7.2 million
3. Profits - Losses = Total Profit so far
$11.4 million - $7.2 million = $4.2 million 
4. What happened in the last month?
The net profit is $7.5 million. This means the last month must have had a profitable month to equal $7.5 million. 
7.5 - 4.2 = $3.3 million profit in the last month

6 0
3 years ago
What is the volume of a cube with length 7 cm? V = lwh cm3
bonufazy [111]
343 Due to the fact that it is all the same length it will just multiply to 343 7*7*7=<span>343</span>
5 0
3 years ago
Read 2 more answers
55% of students voted for Mýa as class president if 78 students voted for Mýa as class president how many students are there in
Salsk061 [2.6K]

Answer:

Step-by-step explanation:

Let y represent students in the class

55% of y = 78

0.55y= 78

y = 142

5 0
3 years ago
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