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Wewaii [24]
2 years ago
6

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 21 N acts on

a certain object, the acceleration of the object is 7 m/s^2 . If the acceleration of the object becomes 10 m/s^2 , what is the force?
Mathematics
1 answer:
Marat540 [252]2 years ago
4 0

Answer:

21N:7m/s

? :10m/s

21x10=210

210÷7=30N

Your final answer is 30N

Step-by-step explanation:

This is called direct propotion

it involves close multiplication

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On average, there are 3 pages in every chapter of a James Patterson novel. Each book has approximately 79 chapters. James Patter
sdas [7]

Answer:13746

Step-by-step explanation:

3 * 79 = find amount of pages on average per book

= 237


237 * 58 = find amount of pages written for 58 books

=13746


James Patterson has written approximately 13,746 pages

6 0
3 years ago
An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of
Lilit [14]

Answer:

140

Step-by-step explanation:

20+4(s)=

20+4(30)=

20+ 120=

140

8 0
2 years ago
Find the smallest 4 digit number such that when divided by 35, 42 or 63 remainder is always 5
alex41 [277]

The smallest such number is 1055.

We want to find x such that

\begin{cases}x\equiv5\pmod{35}\\x\equiv5\pmod{42}\\x\equiv5\pmod{63}\end{cases}

The moduli are not coprime, so we expand the system as follows in preparation for using the Chinese remainder theorem.

x\equiv5\pmod{35}\implies\begin{cases}x\equiv5\equiv0\pmod5\\x\equiv5\pmod7\end{cases}

x\equiv5\pmod{42}\implies\begin{cases}x\equiv5\equiv1\pmod2\\x\equiv5\equiv2\pmod3\\x\equiv5\pmod7\end{cases}

x\equiv5\pmod{63}\implies\begin{cases}x\equiv5\equiv2\pmod 3\\x\equiv5\pmod7\end{cases}

Taking everything together, we end up with the system

\begin{cases}x\equiv1\pmod2\\x\equiv2\pmod3\\x\equiv0\pmod5\\x\equiv5\pmod7\end{cases}

Now the moduli are coprime and we can apply the CRT.

We start with

x=3\cdot5\cdot7+2\cdot5\cdot7+2\cdot3\cdot7+2\cdot3\cdot5

Then taken modulo 2, 3, 5, and 7, all but the first, second, third, or last (respectively) terms will vanish.

Taken modulo 2, we end up with

x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod2

which means the first term is fine and doesn't require adjustment.

Taken modulo 3, we have

x\equiv2\cdot5\cdot7\equiv70\equiv1\pmod3

We want a remainder of 2, so we just need to multiply the second term by 2.

Taken modulo 5, we have

x\equiv2\cdot3\cdot7\equiv42\equiv2\pmod5

We want a remainder of 0, so we can just multiply this term by 0.

Taken modulo 7, we have

x\equiv2\cdot3\cdot5\equiv30\equiv2\pmod7

We want a remainder of 5, so we multiply by the inverse of 2 modulo 7, then by 5. Since 2\cdot4\equiv8\equiv1\pmod7, the inverse of 2 is 4.

So, we have to adjust x to

x=3\cdot5\cdot7+2^2\cdot5\cdot7+0+2^3\cdot3\cdot5^2=845

and from the CRT we find

x\equiv845\pmod2\cdot3\cdot5\cdot7\implies x\equiv5\pmod{210}

so that the general solution x=210n+5 for all integers n.

We want a 4 digit solution, so we want

210n+5\ge1000\implies210n\ge995\implies n\ge\dfrac{995}{210}\approx4.7\implies n=5

which gives x=210\cdot5+5=1055.

5 0
2 years ago
Pleas Help!!!<br> |2s-7|≥-1
Paul [167]

Answer:

\frac{1}{2}s=\frac{7}{2}

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
What is the equation of the line that passes through the point (−1,−3) and has a slope of 3?
Tanya [424]

Answer:

y= 3x

Step-by-step explanation:

The slope is just read. It is 3. It is the value of m in the general equation.

y = mx + b

y = 3x + b

To find b, use (-1,-3)

x = -1

y = -3                  Substitute into the general equation

-3 = 3(-1) + b       Simplify the right side

-3 = -3 + b          Subtract -3 from both sides

b = 0

Answer: y = 3x

7 0
2 years ago
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