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jek_recluse [69]
3 years ago
14

Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a t

wo-sided scale by placing a certain combination of these weights onto that scale. What is the fewest number of weights you need, and what are their weights?
Mathematics
1 answer:
Archy [21]3 years ago
4 0

Answer:

You need 4 weights, and the weights are 1; 3; 9 and 27.

Step-by-step explanation:

<em>Since the scale has two plates, we can place weights on either side and also the object so it can be balanced. </em>

This is a key part of the problem, it's not only on the other side of the scale, but on both sides.

Let's do the math now.

If i get two weights, 1 and 3. I can form this combinations.

Object of 1lb = 1

Object of 2lb + 1 weight = 3 weight.

Object of 3lb = 3 weight

Object of 4lb = 1 weight + 3 weight.

So what if i want to add the next weight and that weight to add me the maximum amount of objects. The weight would have to have a difference with the last object plus one. So if i grab 9. 9 minus 4 is 5. And that is a difference with the last object plus 1.

With a weight of 9, now i can add all the integers up to 13lb.

And the next step? Lets add one more. Keeping the last rule, the weight would have to have a difference with the last object plus one. So if i grab 27, 27 minus 13 is 14. And that is a difference witht the last object plus 1.

The sum of all the weights adds up to 40 pounds. And i can balance any integer in the middle.

The formula we are using is p – n = n + 1

Where p is the new weight. and n is the last object we weighted. And the sum of the weights goes up to the last object we can place on the scale, and in this case is 40.

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7m + 2 = 6n - 5<br> Write a formula for f(m) in terms of m.
vlada-n [284]

Answer:  m = 6/7n-1

Step-by-step explanation: to get 7m alone dirst we must subtract 2 from both sides so 2-2 = 0 and -5 - 2= -7 so 7m= 6n-7 and divide both sides by 7 to get m alone so 6n divided by 7 = 6/7n and -7 divided by 7 equals -1 so we're left with m= 6/7n-1

8 0
3 years ago
3) This decimal is colored to show<br> 1
MAVERICK [17]
I believe it’s the first one. i’m very sorry if it’s wrong
3 0
3 years ago
Which equation is equivalent to
slega [8]

Answer:

B

Step-by-step explanation:

4 0
3 years ago
Charlotte is solving the following equation for X (x+3)^2-10=2 her first steps are given below (x+3)^2=12 x+3= + square root 12
Katarina [22]

The values of the x in the given equation are x = 6.46 and x = -0.46

<h3>Solving an equation </h3>

From the question, we are to solve the equation for x

The given equation is

(x+3)² -10 = 2

First, add 10 to both sides of the equation

(x+3)² -10 +10 = 2 +10

(x+3)²  = 12

Now, take the square root of both sides to get

x + 3 = ±√12

∴ x = 3 ± √12

x = 3+√12 OR 3-√12

x = 3 + 3.46 OR 3 - 3.46

x = 6.46 OR -0.46

Hence, the values of the x in the given equation are x = 6.46 and x = -0.46

Learn more on Solving an equation here: brainly.com/question/24334139

#SPJ1

7 0
2 years ago
How do I solve this?
Katena32 [7]
We’re the problem bro sorry can’t help you bud
3 0
3 years ago
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