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2 years ago

11

If it takes 3,127 feet of computer cable to wire an office building, how much cable will be left if the wire is taken from a 5,0

00 foot reel?

2 answers:

anyanavicka [17]2 years ago

6 0

This is one of the most complex problems I've seen on Brainly. If you don't understand after reading my lengthy explanation, just tell me.

You have 5000 feet of reel. The office building uses 3127 feet of cable.
So you do 5000-3127 to find the remaining amount of reel.

5000 - 3127 = 1873

Whew! That was quite difficult, wasn't it?

Alexxandr [17]2 years ago

5 0

5000 - 3127 = 1873 feet

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1.5s+2.5p<20

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What is the quotient of StartFraction negative 8 x Superscript 6 Baseline Over 4 x Superscript negative 3 Baseline EndFraction?

scZoUnD [109]

Answer:

Option D.

Step-by-step explanation:

We need to find the quotient of

$\dfrac{-8x^6}{4x^{-3}}$

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$\dfrac{-8}{4}\times \dfrac{x^6}{x^{-3}}$

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2 years ago

Given the following right triangle, find cosθ, sinθ, tanθ, secθ, cscθ, and cotθ. Do not approximate: Find exact answers. Show al

Viktor [21]

Answer:

See below for explanation

Step-by-step explanation:

A related question can be found at chegg. Find attached the diagram.

The triangle is a right angled triangle. The 3 sides are named opposite, adjacent and hypotenuse.

The opposite is the vertical side facing angle theta (θ)

The adjacent is horizontal side

The angle between opposite and adjacent = 90°

The hypotenuse is the longest side

The relationship between the 3 sides:

Hypotenuse² = opposite ² + adjacent²

The relationship between theta (θ)

and the lengths of the sides of the triangle:

Applying SOHCAHTOA in trigonometry

Sine ratio:

Sinθ = opposite/hypotenuse

Cosine ratio:

Cosθ = adjacent/hypotenuse

Tangent ratio:

Tanθ = opposite/adjacent

Applying the Pythagorean theorem to find the third side of the triangle

Hypotenuse² = opposite ² + adjacent²

Hypotenuse = 7, opposite = 4

adjacent² = Hypotenuse² - opposite ²

adjacent² = 7²-4² = 49-16

adjacent² = 33

Adjacent = √33

Write out the six trigonometric functions in exact form related to theta.

cosθ = adjacent/hypotenuse = (√33)/7

sinθ = opposite/hypotenuse = 4/7

tanθ = sinθ/cosθ = opposite/adjacent

sinθ/cosθ = 4/7 ÷ (√33)/7

= 4/7 × 7/(√33) = 4/(√33)

opposite/adjacent = 4/(√33)

tanθ = 4/(√33)

secθ = 1/cosθ = 1/(√33)/7

= 7/√33

cosecθ = 1/sinθ = 1/(4/7)

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cotθ = 1/tanθ = 1/[4/(√33)]

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6 0

2 years ago

The sum of an infinite geometric sequence is seven times the value of its first term.

Radda [10]

Answer:

a). r = $\frac{6}{7}$

b). At least 5 terms should be added.

Step-by-step explanation:

Formula representing sum of infinite geometric sequence is,

$S_{\inf}=\frac{a}{1-r}$

Where a = first term of the sequence

r = common ratio

a). If the sum is seven times the value of its first term.

$7a=\frac{a}{1-r}$

$7=\frac{1}{1-r}$

7(1 - r) = 1

7 - 7r = 1

7r = 7 - 1

7r = 6

r = $\frac{6}{7}$

b). Since sum of n terms of the geometric sequence is given by,

$S_{n}=\frac{a(1-r^{n})}{1-r}$

If the sum of n terms of this sequence is more than half the value of the infinite sum.

$\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}$ > $\frac{7a}{2}$

$\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}$

$\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}$

$1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}$

$1-(\frac{6}{7})^{n}> \frac{1}{2}$

$-(\frac{6}{7})^{n}> -\frac{1}{2}$

$(\frac{6}{7})^{n}< \frac{1}{2}$

$(0.85714)^{n}< (0.5)$

n[log(0.85714)] < log(0.5)

-n(0.06695) < -0.30102

n > $\frac{0.30102}{0.06695}$

n > 4.496

n > 4.5

Therefore, at least 5 terms of the sequence should be added.

8 0

2 years ago