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ankoles [38]
3 years ago
5

How would i solve this problem using log base 10

Mathematics
1 answer:
Archy [21]3 years ago
8 0

First isolate the power of 10 on the right side by dividing both sides by 5:

100=5\cdot10^{0.3t}\implies20=10^{0.3t}

Now you're free to take the logarithm and simplify where you can:

\log_{10}20=\log_{10}10^{0.3t}=0.3t\log_{10}10=0.3t

Then solve for t:

t=\dfrac{\log_{10}20}{0.3}\approx4.34

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Make a conjecture about the next item in the sequence 1, -4, 9, -16
Snezhnost [94]
To get -4 from 1, we must either subtract 5 from 1 or mult. 1 by -4.  Unfortunately subtracting 5 from -4 does not result in 9, and mult -4 by -4 does not result in -16.  So neither "works"  in predicting the next term.

Can you think of any other experiments to do that would help you discover the pattern 1, -4, 9, -16?  


4 0
3 years ago
Read 2 more answers
Lydia graphed ΔXYZ at the coordinates X (0, −4), Y (2, −3), and Z (2, −6). She thinks ΔXYZ is a right triangle. Is Lydia's asser
katrin [286]

Answer:

Option (4)

Step-by-step explanation:

Vertices of the triangle are X(0, -4), Y(2, -3) and Z(2, -6).

Slope of XY (m_{1}) = \frac{y-y'}{x-x'}

                            = \frac{-3+4}{2-0}

                     (m_{1}) = \frac{1}{2}

Similarly, slope of XZ (m_{2}) = \frac{-6+4}{2-0}          

                                   (m_{2}) = (-1)

m_{1}\times m_{2}=-\frac{1}{2}

Which should be (-1) if XY and XZ are perpendicular to each other.

Now we can say that XY and XZ are not perpendicular.

Therefore, Lydia's assertion that ΔXYZ is a right triangle is not correct.

Option (4) will be the answer.

5 0
2 years ago
I need to increase the number of customers by 20% daily, I talk to an average of 8 customers per hour during an 8 hour shift so
MA_775_DIABLO [31]

Before we figure out how many customers you will need to talk per day to reach your goal, let's calculate what is 20% of how many customers you normally talk to a day.


current no. = 8

goal = 8 + 20%

20% = 8 x 0.20

(a percent is really just a fraction with the percent number over 100)

20% = 1.60

goal = 8 + 1.60

goal = 9.60


However, there is no such thing as .60 of a person so we will have to round up. You will need to talk to 10 customers per day.

6 0
3 years ago
Read 2 more answers
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