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denpristay [2]
2 years ago
5

In the diagram, what is the value of x?

Mathematics
2 answers:
Katen [24]2 years ago
5 0

Answer:

i believe its C

LuckyWell [14K]2 years ago
3 0

Answer:

D

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1-6
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6 0
3 years ago
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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
3 years ago
Help please I don’t understand any of this
sveta [45]

The two angles form a straight line which is equal to 180 degrees. This makes the angles supplemtary.

To find x, add the two angles together to equal 180:

7x + x+20 = 180

Combine like terms:

8x + 20 = 180

Subtract 20 from both sides:

8x = 160

Divide both sides by 8:

X = 20

6 0
2 years ago
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A portable electronic typewriter cost £180 in 1988. Its price rose by 5% in 1989. What was the new price?
elena-s [515]

\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 180}}{\left( \cfrac{5}{100} \right)180}\implies 9~\hfill \stackrel{\textit{new price}}{180+9\implies 189}

5 0
3 years ago
Which expression is equivalent to –2(5x – 0.75)?
Zinaida [17]

Answer:

5(5x - 0.34

Step-by-step explanation:

3 0
3 years ago
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