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LenKa [72]
3 years ago
14

Consider the equation 0.75⋅10^w/3=30

Mathematics
1 answer:
Nastasia [14]3 years ago
5 0

Answer:

The value of w is:

w=3\cdot log_{10}(40)

Step-by-step explanation:

We have to calculate w from the equation

0.75\cdot 10^{w/3}=30

The solution has to be expressed as a logarithm in base 10.

We can solve it like:

0.75\cdot10^{w/3}=30\\\\10^{w/3}=30/0.75=40\\\\(w/3)log_{10}(10)=log_{10}(40)\\\\w/3=log_{10}(40)\\\\w=3\cdot log_{10}(40)

The value of w is:

w=3\cdot log_{10}(40)

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Each football is sold for $9.95. To make one of these football costs $7.10.
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A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is
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Answer:

Trail Mix costs $2.50 per pound, and Jelly Beans cost $1.50 per pound.

Step-by-step explanation:

Using x for trail mix and y for jelly beans, we have a system of equations being

\left \{ {{5x+3y=17} \atop {2x+12y=23}} \right.

We can solve this system using substitution

5x+3y=17

Divide by 5 to have a coefficient of 1 before x

x+\frac{3}{5} y=\frac{17}{5}

Subtract \frac{3}{5} y from each side to single out one variable to one side

x=\frac{17}{5} -\frac{3}{5} y

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2(\frac{17}{5} -\frac{3}{5} y)+12y=23

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6.8+10.8y=23

Separate numerical values from variables

10.8y=16.2

Divide by 10.8 in order to have a coefficient of 1

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Now that we have one of the values, we know that a pound of jelly beans costs $1.50. We can now plug in 1.5 for y into one of our equations to find x.

5x+3(1.5)=17

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Divide by 5 to have a coefficient of 1 before x

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7 0
3 years ago
It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel
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The length of train is 120 meters

The speed of train is 25 meter per second

<u><em>Solution:</em></u>

The speed is given by formula:

speed = \frac{distance}{time}

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

<em><u>The total distance travelled by the train across the bridge is given by:</u></em>

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

<em><u>Therefore, the speed is given as:</u></em>

speed = \frac{2x+ 1260}{60}

<em><u>The total distance travelled by the train through the tunnel is given by:</u></em>

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

<em><u>Therefore, the speed is given as:</u></em>

speed = \frac{2x+ 2010}{90}

The speed of the train was the same in both cases.

Equate both speeds

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3 years ago
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