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Otrada [13]
3 years ago
15

A circle with radius ris inscribed inside a square with a side length s. Use 3. 14 for TT Round answer to the nearest hundredth

if necessary
If s = 10 millimeters and r = 5 millimeters, calculate the area of the shaded region
square millimeters

Mathematics
1 answer:
Dominik [7]3 years ago
4 0

9514 1404 393

Answer:

  21.46 mm^2

Step-by-step explanation:

The area of the square is ...

  A = s^2 = (10 mm)^2 = 100 mm^2

The area of the circle is ...

  A = πr^2 = π(5 mm)^2 = 25π mm^2 ≈ 78.54 mm^2

Then the shaded area is ...

  100 mm^2 -78.54 mm^2 = 21.46 mm^2 . . . shaded area

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3 0
3 years ago
Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)
Archy [21]

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P (x_0,y_0,z_0) is

z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\

Now the partial derivatives of f are

f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}

\\\\=\frac{1}{9-8}

= 1

Now

f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}

= -8

So, the tangent equation is

z - 0 = 1\times (x - 9) -8\times (y - 1)

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

4 0
3 years ago
What is the slope of a line that is parallel to y=3/4x+2
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8 0
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The table below shows the combination of a dry prepackaged mix and water to make concrete. The mix says for every 1 gallon of wa
egoroff_w [7]
Let's assign a variable x to the number of multiples for each pound of dry mix and water. With that being the said, the question for finding the total pounds would be:

Total pounds = x*Pounds of dry mix + x*Pounds of water
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Thus, the pounds of dry mix is 60*5/24 = 25/2 lbs, while the pounds of water is 8*5/24 = 5/3 pounds.

3 0
3 years ago
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