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3 years ago

A wire 8 meters long is cut into two pieces.

Mathematics

2 answers:

antoniya [11.8K]3 years ago

7 0

Each wire is now 4 meters long.

Mnenie [13.5K]3 years ago

5 0

x = radius of circle
y = side of triangle
Total length = 3y + 2πx = 8
total area = y²√3/4 + πx²

3y + 2πx = 8
y = (8–2πx)/3
A = y²√3/4 + πx²
A = [(8–2πx)/3]²√3/4 + πx²

A = √3/36(8–2πx)² + πx²
A = √3/9(4–πx)² + πx²
A = √3/9(16–8πx+π²x²) + πx²
A = (16/9)√3 – (8/9)√3πx + (√3/9)π²x² + πx²
A = (√3/9+1)π²x² – (8/9)√3πx + (16/9)√3

differentiate, set equal to zero and solve for x

A' = 2(√3/9+1)π²x – (8/9)√3π = 0
2(√3/9+1)πx = (8/9)√3

x = (8/9)√3 / 2(√3/9+1)π = 1.5396 / 7.492 = 0.205
check the arithmetic.

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Step-by-step explanation:

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3 years ago

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3 years ago

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function. (

Mrrafil [7]

Answer:

So, the first three nonzero terms in the Maclaurin series are:

$6, \, 27x^2, \, \frac{405x^4}{4}.$

Step-by-step explanation:

From exercise we have the next function y = 6 sec(3x).

We know that Maclaurin series for the function sec x, have the following form:

$\sec x=1+\frac{x^2}{2}+\frac{5x^4}{24}+...$

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So, the first three nonzero terms in the Maclaurin series are:

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3 years ago

If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra

bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be $l$ units.

Using pythagoras theorem, we can find out the value of $l$ .

As per theorem:

$Hypotenuse^{2} = Base^{2} + Height^{2}\\$

$\Rightarrow l^{2} = (\dfrac{w}{2})^{2} + y^{2}\\\Rightarrow l^{2} = (\dfrac{12}{2})^{2} + 8^{2}\\\Rightarrow l^{2} = {6}^{2} + 8^{2}\\\Rightarrow l^{2} = 36+64 = 100\\\Rightarrow l = 10\ units$

Lateral surface area of square prism = 4 $\times$ Area of triangular surface

$\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units$

Surface Area of 5 surfaces of the square prism =

$4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units$

So, total surface area of composite figure:

240 + 480 = 720 sq units.

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3 years ago

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Lelu [443]

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3 years ago