Helppp pleasee it’s needed quick points

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

Archy [21]

Answer:

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

Step-by-step explanation:

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

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.

4 0

4 years ago

Ron walks 0.5 mile on a track in 10 minutes. Stevie walks 0.25 mile on the track in 6 minutes find the unit rate for each walker

Firlakuza [10]

Answer:

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

Step-by-step explanation:

Given:

Ron takes 10 minutes to walk on a track to cover a distance of 0.5 miles

Stevie takes 6 minutes to walk on a track to cover a distance of 0.25 miles

To find their unit rates in mile per hour and choose the faster one.

Solution:

Unit rate in miles per hour signifies their speeds. Thus, we will find out their speeds.

Ron:

Distance= 0.5 miles

Time = 10 minutes = $10\ min\times \frac{1\ hr}{60\ min}=\frac{1}{6}$ hours

Speed = $\frac{Distance}{Time}=\frac{0.5}{\frac{1}{6}}=0.5\times6=3\ miles/hour$

Stevie

Distance = 0.25 miles

Time = 6 minutes = $6\ min\times \frac{1\ hr}{60\ min}=\frac{1}{10}$ hours

Speed = $\frac{Distance}{Time}=\frac{0.25}{\frac{1}{10}}=0.25\times10=2.5\ miles/hour$

Thus, we have

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

4 0

3 years ago

The volume of a cone is 763.02. the radius and height of the cone are equal. What is the radius of the cone?

LUCKY_DIMON [66]

Answer:

The radius of the cone is 9cm

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

The volume of a cone is expressed as

V=1/3(πr²h)

We were told that the radius r and the height h are equal

I.e r=h

Substituting h=r in the formula we have

V= 1/3(πr²*r)

V =1/3(πr³)

To find the radius r let us substitute our given 763.02cm³ (note we assume unit in cm)

763.02= 1/3(3.142r³)

763.02= (3.142r³)/3

763.02*3=3.142r³

2289.06=3.142r³

r³=2289.06/3.142

r³= 728.54

r= ³√728.54

r= 8.99cm

≈r= 9cm

3 0

3 years ago

Solve the equation using square roots. 2x^2-98=0

Yuliya22 [10]

Step-by-step explanation:

2x²-98=0

2x²=98

x²=98/2

x²=49

x=root 49

so,x=7

if it is correct answer then please follow me

3 0

4 years ago

Solve the inequality 29-2(3-5w) 13

valentinak56 [21]

Answer:

29-2(2w)13

29-2(26w)

29-52w

w=52÷29

7 0

3 years ago