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svlad2 [7]
3 years ago
14

Which equation represents the sentence?

Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
7 0
<span>4x + 7 = 32
...................</span>
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A cable that weighs 8 lb/ft is used to lift 750 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approxim
Annette [7]

Answer:

13.8 × 10⁵ lb/ft

Step-by-step explanation:

Suppose the distance(ft) below the top of the shaft is represented by x

The weight of the cable = 8 lb/ft

Weight of the coal to be lifted from mine = 750 lb

Recall that:

The work done by a force f to move an object through a distance x can be expressed as:

W = force (f) × displacement (x)

So, the force implies the total weight which should be lifted at any height x

f(x) = 750 + 8x

Using Riemann sum

where; the coal is lifted from x = 0 to x = 500 i.e. [a,b] = [0,500]

Dividing the interval into n subintervals

\Deltax = \dfrac{b -a }{n}

\Deltax = \dfrac{500- 0 }{n}

Suppose [x_{i-1},x_i ] to represent the i^{th} subinterval, then the work done can be estimated as:

W_i = f(x_i) \Delta x

W_i =(750 + 8x_i) \Delta x

Therefore; the total work done in between all the n subintervals is:

W = \sum \limits ^n_{i=1} W_1

W = \sum \limits ^n_{i=1} f(x_i) \Delta x

W = \sum \limits ^n_{i=1}(750 +8x_I)\Delta x

Therefore;

dW = f(x) dx

\int \ dW = \int \ f(x) \ dx where x ranges from 0 to 500

W = \int ^{500}_{0} \ 750 + 8x \ dx

W =\bigg  [750x + 4x^2 \bigg ]^{500}_{0}

W =\bigg  [750(500) + 4(500)^2-0 \bigg ]

W = 375000 + 1000000

W = 1375000

Thus; the total work done W = 13.8 × 10⁵ lb/ft

5 0
3 years ago
To the nearest whole number, what is the surface area of a sphere with a volume of 140 cm3?
JulijaS [17]
We know that V= 4/3 pi r^3

So r^3= 140/ ((4/3) pi)= 33.422538

Hence r= 3.221166

SA = 4 pi r^2
= 4 pi 3.221166^2
= 130.39 cm^2
= 130 cm^2
6 0
3 years ago
Read 2 more answers
Factor 7x+35 PLEASE HELP
djyliett [7]

Answer:

7(x+5)

Step-by-step explanation:

The greatest common factor is 7

7*x + 7*5

Factor out the 7

7(x+5)

4 0
2 years ago
Read 2 more answers
If tan x is equal to 3/4 find the value of sin x + cos x/ cos x (1 - cos x) ​
Flauer [41]

Answer:

35/4 =8¾

Step-by-step explanation:

using pythagoras theorem

hyp²=opp²+adj²

recall that tanX= opp/adj

taking our opposite side to be 3 and the adjacent side to be 4 , the hyp² = 3²+4²

hypotenuse = 5

recall also that , sinX = opposite /hypotenuse

= 3/5

CosX= adjacent /hypotenuse

=4/5

so we've known tanx = 3/4 cosX = 4/5 sinx= 3/5

substitute these values into your equation

it will give us 3/5 + 4/5 divided by 4/5 ×(1-4/5)

=35/4 = 8¾

6 0
3 years ago
Fill in the blank and which goes where, drag and drop.. <br><br> 80%<br> 95%<br> 33 1/3%<br> 15%
scoundrel [369]
1. = 80 2 = 95 3 = 33 4 = 15
4 0
2 years ago
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