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il63 [147K]
2 years ago
14

If DE = X+1, EF = x-2, DF =15, and E is between D and F. then DE = ?

Mathematics
1 answer:
mart [117]2 years ago
8 0

Answer:

X =8

Step-by-step explanation:

DF = DE + EF

15 = X+1 + X-2

16 = 2X

X = 8

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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 25th of sequence 3,5,7,9,11
zubka84 [21]

Answer: The 25th term of the sequence is 75

Step-by-step explanation:

The given sequence depicts an arithmetic progression. The consecutive terms differ by a common difference. We will apply the formula for arithmetic progression.

Tn = a + (n-1)d

Tn = The value of the nth term of the arithmetic sequence.

a = first term of the sequence.

d = common difference (difference between a term and the consecutive term behind it)

n = number of terms in the sequence.

From the information given,

a = 3

d = 5-3 = 7-5 = 2

We want to look for the 25th term, T25

So n = 25

T25 = 3 + (25-1)2 = 3+ 24×2

T25 = 3 + 72 = 75

5 0
2 years ago
Simplify 3(tan^2 theta - sec^2 theta)
Nesterboy [21]

Answer:

sin ^2(x)

Step-by-step explanation:

3 0
2 years ago
Rick knows that 1 cup of glue weighs 1/18 pound. He has 2/3 pound of glue. How many cups of glue does he have?
Basile [38]
\begin{array}{ccc}1\ cup&-&\frac{1}{18}\ lb\ (pound)\\\\x\ cup&-&\frac{2}{3}\ lb\ (pounds)\end{array}\ \ \  \ \ \ cross\ multiply\\\\\\\frac{1}{18}x=1\times\frac{2}{3}\\\\\frac{1}{18}x=\frac{2}{3}\ \ \ \ \ \ |multiply\ both\ sides\ by\ 18\\\\18\times\frac{1}{18}x=18\times\frac{2}{3}\\\\x=6\times2\\\\\boxed{x=12}\\\\Answer:He\ has\ 12\ cups\ of\ glue.
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3 years ago
How do u write 3:4 and 6:8 as a fraction proportion
faltersainse [42]

3/4=6/8

hope this helps :)

3 0
2 years ago
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