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3 years ago

The difference between 2 numbers is 8. The sum of the two numbers is 20. Find the number.

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

8 0

Answer:

14, 6

Step-by-step explanation:

x-y =8 =>x=y+8

x+y=20

y+8 +y=20

2y=20 - 8

2y=12

y=12 :2

y=6 (the second number

x=6 +8 =14 (the first number

Igoryamba3 years ago

3 0

Answer:

The numbers are 6 and 14

Step-by-step explanation:

Let the two numbers be x and y

x-y = 8

x+y = 20

Add the two equations

x-y = 8

x+y = 20

-----------------

2x = 28

Divide by 2

2x/2 = 28/2

x = 14

Subtract the two equations

x-y = 8

-x-y = -20

-----------------

-2y = -12

Divide by -2

-2y/-2 = -12/-2

y = 6

The numbers are 6 and 14

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3 years ago

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

3 years ago

The minute hand of a clock is 1.4 centimeters long. How far does the tip of the minute hand travel in 40 minutes? (Round your an

ozzi

Answer:

2.93cm

Step-by-step explanation:

I have to admit, this stumped me but I got o work and here's what I have for you. Hope this helps. TIP: remember it is the minute hand not any other hand.

For this one you will have to find the circumference of the clock because as the min hand goes round and round, it will act as a radius and it will go in a circular motion.

Formula will be π2r= 3.l4 * 2 * 1.4cm=8.792cm per every one revolution of the minute hand. Remembering that for the minute hand to revolve round the clock it has to cover 1 hr = 60min. For you to get the total circumference,

you'll have to take 8.792cm but since it is per every one revolution of the minute hand, multiply it by 40/60min. The answer will be 2.93066cm before rounding off. After rounding off you will have 2.93cm. Quite lengthy but I assure you after practicing you'll have at your fingertips.

3 0

2 years ago

The difference between 2 numbers is 8. The sum of the two numbers is 20. Find the number. ​

The difference between 2 numbers is 8. The sum of the two numbers is 20. Find the number.