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4 years ago

10

How many times will the digit '3' appear if we write all whole numbers from 1 to 9999?

1 answer:

Elan Coil [88]4 years ago

6 0

Answer:

1300

Step-by-step explanation:

Si unimos del 3XXX al 3999: 1000 treses. * En total le salen 1300 apariciones de la cifra 3. xd

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A weight suspended by a spring vibrates vertically according to the function D D given by D(t)=2sin(4π(t+18)) D ( t ) = 2 sin (

STALIN [3.7K]

Answer:

21.75 cm/s

Step-by-step explanation:

1 cm above central position means D = 1, so we plug in 1 into D(t) and find the time and which this occurs.

$D(t)=2Sin (4\pi(t+18))\\1=2Sin (4\pi(t+18))\\\frac{1}{2}=Sin(4\pi t +72\pi)\\4\pi t + 72 \pi = \frac{\pi}{6}\\4\pi t = \frac{\pi}{6}-72\pi\\t=\frac{\frac{\pi}{6}-72\pi}{4\pi}$

This is the time at which this occurs.

To find instantaneous rate of change, we differentiate D(t) and plug in this t we found. Remembering that d/dt (Sin t) = Cos t

$D(t)=2Sin (4\pi(t+18))\\D(t)=2Sin(4\pi t + 72\pi)\\D'(t)=2Cos(4\pi t + 72\pi)(4\pi)$

Now putting t:

$D'(t)=2Cos(4\pi t + 72\pi)(4\pi)\\D'(\frac{\frac{\pi}{6}-72\pi}{4\pi})=2Cos(4\pi (\frac{\frac{\pi}{6}-72\pi}{4\pi}) + 72\pi)(4\pi)\\=8\pi Cos(\frac{\pi}{6})\\=21.75$

Thus, the instantaneous rate would be around 21.75 cm/s

8 0

3 years ago

An athletic club buys car magnets and pom-poms for club members. The car magnets cost 4.95 each, and pom-poms cost each. The ath

VLD [36.1K]

Answer:

Each car magnet costs $4.95 and each pom-pom costs $0.425

The club spent $495 on 100 car magnets and $85 on 200 pom-poms.

Step-by-step explanation:

I guess that we have to calculate the price of pom-poms and how much money was spent purchasing car magnets and pom-poms.

x + y = 300

2x = y (now we replace y)

x + 2x = 300

3x = 300

x = 100

The club purchased 100 car magnets and 200 pom-poms.

To determine the price of each pom-pom:

($4.95 x 100) + 200P = $580

$495 + 200P = $580

200P = $85

P = $0.425

6 0

4 years ago

The system of equations is given:

Nutka1998 [239]

Answer:

x=-1/85; y=-283/85; z=2/17

Step-by-step explanation:

Using an algebraic method like elimination or substitution would take a lot of steps which could lead to mistake the calculations. In this case, I decided to use the Gaussian elimination. We can express the system in matrix form as follows:

$\left[\begin{array}{ccc}2&-4&6\\9&-3&1\\5&0&9\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}14\\10\\1\end{array}\right]$

To begin the calculations, we write the system in augmented matrix form and use the Gaussian elimination:

$\left[\begin{array}{ccccc}2&-4&6&|&14\\9&-3&1&|&10\\5&0&9&|&1\end{array}\right]$

By applying the Gaussian elimination, the final matrix is the following:

$\left[\begin{array}{ccccc}1&0&0&|&-1/85\\0&1&0&|&-283/85\\0&0&1&|&2/17\end{array}\right]$

In order to verify the results, it´s enough to substitute the calculated values in the original equations to see if the equalities are correct. Here you can see the verification for all of the equations:

$2(-1/85)-4(-283/85)+6(2/17)=14\\9(-1/85)-3(-283/85)+1(2/17)=10\\5(-1/85)+9(2/17)=1$

6 0

3 years ago

A cube with each face a different colour will fit exactly into a box in which it is packaged. In how many ways can the cube be p

dmitriy555 [2]

Answer:

362880 times

I hope this helps

4 0

3 years ago

A business has $10,000 in its bank account. In order to build an addition onto its office, it takes out a loan for $30,000 and d

ser-zykov [4K]

Answer:

The new account balance is $40000

Step-by-step explanation:

<em>The number line is not given. However, the question can be solved without it.</em>

Given

$Balance = \$10000$

$Loan = \$30000$

Required

Determine the new balance

$New\ Balance = Initial\ Balance + Loan\ Amount$

$New\ Balance = \$10000 + \$30000$

$New\ Balance = \$40000$

Hence:

<em>The new account balance is $40000</em>

7 0

3 years ago