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3 years ago

FInd the value of C.

Mathematics

1 answer:

My name is Ann [436]3 years ago

6 0

Answer:

The side C equals to 10. hence the answer is letter A

Step-by-step explanation:

To solve this, we need to use trigonometric functions.

we know that sin (α) = Lo / H for a triangle. Being Lo : Length of the opposite side and H: Length of the hypotenuse.

Given α= 45º and Lo= 5√2 and replacing in the equation:

sin (45º) = 5√2 / C (1)

Using trigonometric identities we know that sin(45º) =(√2)/2. Replacing in equation (1):

sin (45º) = (√2)/2 = 5√2 / C ⇒ C = 2 *5 *√2 / (√2) ⇒ C=10

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3 years ago

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Answer:

(e) csc x − cot x − ln(1 + cos x) + C

Step-by-step explanation:

(e) ∫ (1 + sin x) / (1 + cos x) dx

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∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx

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∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx

Divide.

∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx

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3 years ago

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3 years ago

Miguel wants to build a container out of sheet metal that has a volume of about 320 cubic inches . He

ZanzabumX [31]

Answer:

cylinder, has the least surface area

Step-by-step explanation:

We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.

We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.

<h3>Rectangular Prism</h3>

The relevant formulas are ...

V = LWH

A = 2(LW +H(L +W))

for length L, width W, and height H.

<u>a)</u><u> prism 1</u>

The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...

V = (8 in)(8 in)(5 in) = 320 in³

A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²

<u>b)</u><u> prism 2</u>

The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...

V = (10 in)(8 in)(4 in) = 320 in³

A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²

<h3>Cylinder</h3>

The relevant formulas are ...

V = πr²h

A = 2πr(r +h)

for radius r and height h.

c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...

V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³

A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²

<h3>Square Pyramid</h3>

The relevant formulas are ...

V = 1/3s²h

A = s(s +2H)

for base side dimension s, vertical height h, and slant height H.

d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...

V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³

A = (10 in)(10 in + 2×14 in) = 380 in²

<h3>Summary</h3>

The proposed figures have volume and area (rounded to the nearest unit) as follows:

$\begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}$

The proposed <em>cylinder</em> requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.

_____

<em>Additional comment</em>

For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.

3 0

2 years ago