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3 years ago

What is the scientific notation of 42

Mathematics

2 answers:

RideAnS [48]3 years ago

8 0

Answer:

Step-by-step explanation: To write 49 in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.

So here we have 4.2. Next, count the number of places that we would need to move the decimal point in 4.2 to get back to the original number which is 42.

Since we would need to move the decimal point 1 place to the right to get back to the original number, we would need to multiply 4.2 by 10 to the 1st power. The exponent is positive because we need to move the decimal point to the right.

Therefore, 42 can be written in scientific notation as 4.2 × $10^{1}.$

Aleksandr-060686 [28]3 years ago

7 0

The answer is 7, because you multiply it by 6.

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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.

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3 years ago

Prove 2^n > n for all n equal to or greater than 1. I mostly need help with how to solve the problem when it is greater than

noname [10]

If $n$ is an integer, you can use induction. First show the inequality holds for $n=1$ . You have $2^1=2>1$ , which is true.

Now assume this holds in general for $n=k$ , i.e. that $2^k>k$ . We want to prove the statement then must hold for $n=k+1$ .

Because $2^k>k$ , you have

$2^{k+1}=2\times2^k>2k$

and this must be greater than $k+1$ for the statement to be true, so we require

$2k>k+1$

for $k>1$ . Well this is obviously true, because solving the inequality gives $3k>1\implies k>\dfrac13$ . So you're done.

If you $n$ is any real number, you can use derivatives to show that $2^n$ increases monotonically and faster than $n$ .

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3 years ago

Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebr

Aloiza [94]

Assume the smaller one is x, then the other ones will be x+2 and x+4

x(x+2) + 2 = 5(x+4)

x^2 + 2x - 5x - 18 = 0

-> x^2 - 3x - 18 = 0

-> (x-6)(x+3) = 0

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6 0

3 years ago

I need help please .

levacccp [35]

Answer:

Step-by-step explanation:

You know that anything to the zeroeth power is 1, so the equation is now

-7 * 1, or -7.

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3 years ago

What is the largest multiple of 36 that can be written with each digit 0-9 exactly once?

antoniya [11.8K]

Answer:

Not sure

Step-by-step explanation:

Sorry

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3 years ago

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