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Korvikt [17]
3 years ago
10

Learning task 4: identify what kind of decimal number are the following choose the letter of the correct answer.

Mathematics
1 answer:
shusha [124]3 years ago
4 0

Answer:

a

Step-by-step explanation:

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A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re
bezimeni [28]

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force F and the distance d  that the object moves:

W=Fd

If F is measured in newtons and d<em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

W=\int\limits^b_a {f(x)} \, dx

Hooke’s Law states that the force required to maintain a spring stretched x    units beyond its natural length is proportional to

f(x)=kx

where k is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1

Thus F=x

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18

18 J is the work required to stretch a spring from 7 m to 13 m.

5 0
2 years ago
Find the distance between the points (0, 6) and (2, 3).
bogdanovich [222]
Distance= √((x2-x1)²+(y2-y1)²) = √((6-3)²+(0-2)²)=√(9+4)=√13  ≈ 3.61
7 0
3 years ago
Read 2 more answers
-3x - 6 = 2x - 14x - 6
Harman [31]

Answer:

x=0

Step-by-step explanation:

3 0
2 years ago
Help me lawd!!!!!!!jkdmfkfm
Klio2033 [76]
This is equivalent to:

(2.2533/2.59)(10^8/10^4)

(0.87)(10^4) which is:

0.87X10^4  which is equal to:  

0.87X10000 which is equal to:

8.7X1000  and since 1000=10^3 we can say:

8.7X10^3
6 0
2 years ago
What is 2 = y/5-8 plzzz answer!!!
umka2103 [35]
It's a simple linear equation in 'y'.  There is only one number that 'y' can be
that will make the equation a true statement.  That number is called the
'solution' to the equation.   Here's one way to find it:

You said that                         <u> 2  =  y/5 - 8</u>

Add  8  to each side:          10  =  y/5

Multiply each side by  5:  <em>  50  =  y</em>
3 0
3 years ago
Read 2 more answers
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