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Neporo4naja [7]
3 years ago
11

What is the domain of the function h(w)=80/w

Mathematics
2 answers:
PtichkaEL [24]3 years ago
4 0
D: (-infinity, 0) U (0, infinity) because you cant have a zero in the bottom of the fraction
dybincka [34]3 years ago
4 0
The domain of the function would be, w>0.
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Consider a wire of length 16 ft. The wire is to be cut into two pieces of length x and 16 − x. Suppose the length x is used to f
Sophie [7]

Answer: x = 7.14ft

Step-by-step explanation:

First, the circle will have a perimeter P = x.

We know that the perimeter of a circle is:

P = 2*pi*r

where pi = 3.14 and r = radius of the circle.

Then we will have:

x = 2*pi*r

r = (x/(2*3.14)) = x/6.28

And the area of a circle of radius r is:

A = pi*r^2 = 3.14*(x/6.28)^2

Now, for the square, the perimeter will be:

P = 16ft - x

And we know that the perimeter of a square of sidelengt s is:

P = 4*s

then:

16ft - x = 4*s

s = (16ft - x)/4 = 4ft - x/4

And the area of a square is:

A = s^2 = (4ft - x/4)*(4ft - x/4).

Now, the total area of the circle + square will be:

Total area =  (4ft - x/4)*(4ft - x/4) + 3.14*(x/6.28)^2

We want to find the value of x that minimizes this.

First, let's rewrite the area equation as a quadratic equation:

Ta(x) = (4ft - x/4)*(4ft - x/4) + 3.14*(x/6.28)^2

        = 16ft + x^2/16  -2ft*x + 0.08*x^2

        =  (1/16 + 0.08)*x^2 - 2ft*x + 16ft^2

        = 0.14*x^2 - 2ft*x + 16ft^2

This is a quadratic equation with a positive leading coefficient, this means that the arms of the graph will open upwards, then the minimum will be at the vertex of the equation.

To find the vertex we can just take the first derivative, and find at what value of x is equal to zero.

Ta´(x) = 2*0.14*x - 2ft

Ta´(x) = 0.28*x - 2ft

Let´s find x such that this is equal to zero:

Ta´(x) = 0 = 0.28*x - 2ft

           x = 2ft/0.28 = 7.14ft

Then x = 7.14ft minimizes the area of the sum of the areas of the circle and square.

4 0
3 years ago
Help math help plzz no links or imma report u . Helps 20 points
PSYCHO15rus [73]

Answer:

its c .

Step-by-step explanation: :)

6 0
2 years ago
Are vectors parallel
kiruha [24]
"Two vectors are perpendicular if their dot product is zero, and parallel if their dot"
3 0
3 years ago
Identify the solution(s) of the system of equations, if any.<br> -2x - 2y = 4<br> 8y = -8x - 16
liubo4ka [24]
<span>-2x - 2y = 4|:(-2) 8y = -8x - 16|:(-8) 
x+y=-2 -y=x+2 x+y=-2x+y=-2 
</span>Ansfwer  :  x-2 y -2
4 0
3 years ago
Read 2 more answers
How many students can sit around a cluster of 7 square table? The tables in a classroom have square tops. Four students can comf
Sveta_85 [38]

Answer:

16 students can sit around a cluster of 7 square table.

Step-by-step explanation:

Consider the provided information.

We need to find how many students can sit around a cluster of 7 square table.

The tables in a classroom have square tops.

Four students can comfortably sit at each table with ample working space.

If we put the tables together in cluster it will look as shown in figure.

From the pattern we can observe that:

Number of square table in each cluster   Total number of students

                     1                                                                 4

                     2                                                                6

                     3                                                                8

                     4                                                                10

                     5                                                                12

                     6                                                                14

                     7                                                                16

Hence, 16 students can sit around a cluster of 7 square table.

8 0
3 years ago
Read 2 more answers
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