All categories

2 years ago

A wiring job requires 5,127 feet of cable. If the cable comes in 250-foot coils, how many coils of cable are required?

Mathematics

2 answers:

Zepler [3.9K]2 years ago

6 0

Answer:

20.58 (21)

Step-by-step explanation:

5127/250 = 20.58

if the coils are only be imported in full form your gonna need 21

natka813 [3]2 years ago

3 0

Answer:

21 cables

Step-by-step explanation:

Because the cables come in 250-foot coils, you cannot have a piece of one cable. So, if you take the total amount of cable you need (5,127 feet) and divide it by how long a single cable is (250 feet).

5,127 divided by 250 is 20.508, but you cannot have a piece of one cable. So, you round up to the nearest whole number, 21.

You might be interested in

Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects

Yuri [45]

Answer:

Area of triangle ADC is 54 square unit

Step-by-step explanation:

Here is the complete question:

Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .

Step-by-step explanation:

Please see the attachment below for an illustrative diagram

Considering the diagram,

BC = BD + DC = 14

Let BD be $x$ ; hence, DC will be $14-x$

and AD be $y$

To, find the area of triangle ADC

Area of triangle ADC = $\frac{1}{2} (DC)(AD)$

= $\frac{1}{2}(14-x)(y)$

We will have to determine $x$ and $y$

First we will find the area of triangle ABC

The area of triangle ABC can be determined using the Heron's formula.

Given a triangle with a,b, and c

$Area =\sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

For the given triangle ABC

Let $a$ = AB, $b$ = BC, and $c$ = CA

Hence, $a = 13, b= 14,$ and $c = 15$

∴ $s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21$

Then,

Area of triangle ABC = $\sqrt{(21)(21-13)(21-14)(21-15)}$

Area of triangle ABC = $\sqrt{(21)(8)(7)(6)}$ = $\sqrt{7056}$

Area of triangle ABC = 84 square unit

Now, considering the diagram

Area of triangle ABC = Area of triangle ADB + Area of triangle ADC

Area of triangle ADB = $\frac{1}{2} (BD)(AD)$

Area of triangle ADB = $\frac{1}{2}(x)(y)$

Hence,

Area of triangle ABC = $\frac{1}{2}(x)(y)$ + $\frac{1}{2}(14-x)(y)$

84 = $\frac{1}{2}(x)(y)$ + $\frac{1}{2}(14-x)(y)$

∴ $84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)$

$84 = 7y\\y = \frac{84}{7}$

∴ $y = 12$

Hence, $y =$ AD = 12

Now, we can find BD

Considering triangle ADB,

From Pythagorean theorem,

/AB/² = /AD/² + /BD/²

∴13² = 12² + /BD/²

/BD/² = 169 - 144

/BD/ = $\sqrt{25}$

/BD/ = 5

But, BD + DC = 14

Then, DC = 14 - BD = 14 - 5

BD = 9

Now, we can find the area of triangle ADC

Area of triangle ADC = $\frac{1}{2} (DC)(AD)$

Area of triangle ADC = $\frac{1}{2} (9)(12)$

Area of triangle ADC = 9 × 6

Area of triangle ADC = 54 square unit

Hence, Area of triangle ADC is 54 square unit.

5 0

3 years ago

For a certain bathtub, the hot water faucet can fill the tub in 12 minutes. The cold water faucet can fill the tub in 8 minutes.

Fofino [41]

If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.

<h3>What is the concept of time and work?</h3>

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.

When the amount of work is constant, efficiency is inversely proportional to the length of time required.

Important Time and Work Formula:

Work Done = Time Taken × Rate of Work.
Rate of Work = 1 / Time Taken.
Time Taken = 1 / Rate of Work.
If a piece of work is done in x number of days, then the work done in one day = 1/x.
Total Wok Done = Number of Days × Efficiency.
Efficiency and Time are inversely proportional to each other.

Calculation for the time taken by both faucet to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The filling rate for both faucets filling the tub at the same time is the sum of their rates.

Let 't' be the time taken by both faucets.

Then,

$\frac{1}{12} +\frac{1}{8} =\frac{1}{t}$

$\frac{8+12}{8*12} =\frac{1}{t}$

$\frac{1}{t} =\frac{20}{96}$

$\frac{t}{1} =\frac{96}{20}$

t = 4.8

Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.

To know more about the formula for calculating power, here

brainly.com/question/20290932

#SPJ4

3 0

2 years ago

18) What value of x makes R(x) = 10

Illusion [34]

<h3>Two Answers: <u>x = 2 and x = 10</u></h3>

========================================================

Explanation:

Draw a horizontal line through 10 on the y axis. This is because R(x) = 10 is the same as y = 10. The output of the function is the y value.

See the diagram below.

The horizontal line crosses the parabola at two locations. From those points, draw a vertical line straight down to the x axis. Note how we land at x = 2 and x = 10. This means that R(2) = 10 and R(10) = 10.