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givi [52]
3 years ago
7

(08.02)The coordinate grid shows the plot of four equations. A coordinate plane is shown with four lines graphed. Line A crosses

the x axis at negative 3.5 and the y axis at 7. Line B crosses the x axis at 6.5 and the y axis at 4.5. Line C is horizontal and crosses the y axis at 1. Line D crosses the x axis at 0.5 and the y axis at 1. Which set of equations has (−1, 5) as its solution? A and B B and D A and C B and C
Mathematics
1 answer:
Ganezh [65]3 years ago
3 0
The answer is A and B
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The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If
attashe74 [19]

Answer:

t=7.85 years

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

\frac{dP}{dt}=aP

Where a is proportional constant, P the population variable, and t the time.

\frac{dP}{P}=adt

Integrating each side of the equation.

\int \frac{dP}{P}=\int adt

ln(P)=at+c

P=e^{at+c}

P=e^{c}e^{at}=Ce^{at}

To find C we need to use the initial condiction, it means evaluae P at t=0.

P_{0}=Ce^{0}=C

P=P_{0}e^{at}

Now, we use the sentence  the population has doubled in 5 years.

2P_{0}=P_{0}e^{a5}

We can find "a" in this condition.

2=e^{a5}

ln(2)=a5

a=\frac{ln(2)}{5}

a=0.14

Finally, let's find how long will it take to triple.

3P_{0}=P_{0}e^{0.14t}

3=e^{0.14t}

t=\frac{ln(3)}{0.14}

t=7.85 years

I hope it helps you!

4 0
2 years ago
Given that p=9i+12j and q=-6i-8j. Evaluate |p-q|-{|p|-|q|}
krok68 [10]

Answer:

|p-q|-(|p|-|q|) = 20

Step-by-step explanation:

First let's find the value of 'p-q':

p - q = 9i + 12j - (-6i - 8j)\\p - q = 9i + 12j + 6i + 8j\\p - q = 15i + 20j\\

To find |p-q| (module of 'p-q'), we can use the formula:

|ai + bj| = \sqrt{a^{2}+b^{2}}

Where 'a' is the coefficient of 'i' and 'b' is the coefficient of 'j'

So we have:

|p - q| = |15i + 20j| = \sqrt{15^{2}+20^{2}} = 25

Now, we need to find the module of p and the module of q:|p| = |9i + 12j| = \sqrt{9^{2}+12^{2}} = 15

|q| = |-6i - 8j| = \sqrt{(-6)^{2}+(-8)^{2}} = 10

Then, evaluating |p-q|-{|p|-|q|}, we have:

|p-q|-(|p|-|q|) = 25 - (15 - 10) = 25 - 5 = 20

7 0
3 years ago
Factorise the following expressions 5x^2-25xy​
Natali [406]

Answer: 5x ( x - 5y )

Step-by-step explanation:

3 0
3 years ago
What’s the product of r and 9
Nina [5.8K]

Answer:

9r

Step-by-step explanation:

Multiply 9 and r together.

3 0
3 years ago
Read 2 more answers
Evaluate g(x) = 1.873 -0.0034x +0.5 for x = 1 and x = 2.
AlexFokin [52]

Answer:

g(1) = 1.8696

g(2) = 1.8662

Step-by-step explanation:

Simply plug in the x values into the equation in a calc and you should get your answer.

6 0
3 years ago
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