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3 years ago

Help me find area please asap

Mathematics

1 answer:

mart [117]3 years ago

7 0

You have to find the area of both the square and rectangle. use the formula A=wl
square = 3x3 = 9
rectangle = 10x3 = 30
area= 39 (i think)

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A news item is spreading by word of mouth through a population of size 12,000 people. After t days, the number of people (in tho

Lilit [14]

Answer:

a) 2.303

b) $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) 1.3609

e) $\frac{dy}{dx}=0.04y(12-y)$

f) 4.5 thousand people(smaller)

7.5 thousand people (larger)

e) t=7.93 days (smaller)

t=10.06 days (larger)

g) 1.44

Step-by-step explanation:

The given function is $y=f(t)=\frac{12}{1+75e^{-0.48t}}$

To find how many thousand people have heard the news after 6 days, we substitute to get:

$f(6)=\frac{12}{1+75e^{-0.48*6}}=2.303$ thousands.

b) We rewrite to get: $f(t)=12(1+75e^{-0.48t})^{-1}$

We differentiate using the chain rule to obtain:

$f'(t)=-12(1+75e^{-0.48t})^{-2}\cdot 75e^{-0.48t}\cdot -0.48$

This simplifies to:

$f'(t)=432e^{-0.48t}(1+75e^{-0.48t})^{-2}$

We rewrite as positive index to get:

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) To find the rate at which the news is spreading after 8 days, we substitute t=8 into $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$ to get:

$f'(8)=\frac{432e^{-0.48\cdot 8}}{(1+75e^{-0.48\cdot 8})^{2}}=1.3609$

d) The solution to the logistic differential equation:

$\frac{dy}{dt}=ky(M-y)$

$y=\frac{M}{1+be^{-Mkt}}$

By comparison, M=12, and $Mk=0.48$

$12k=0.48\\k=0.04$

The differential equation is:

$\frac{dy}{dx}=0.04y(12-y)$

e) To how many people have heard the news when its rate of spread is 1.35 thousand per day, we equate the differential equation to 1.35 and so for t first.

$\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}=1.35$

This gives us: t=10.06 ot t=7.93

We substitute the times into the function to get:

$f(7.93)=\frac{12}{1+75e^{-0.48\cdot7.93}}$ =4.5 thousand: smaller value

$f(10.06)=\frac{12}{1+75e^{-0.48\cdot10.06}}=7.5$ thousand: Larger value

f) The two times that the news is spreading at rate 1.35 thousand people per day are:

$t=7.93$ days: Smaller value

$t=10.06$ : Larger value

g) To find the fastest rate at which the news spread we take the second derivative and equate it to zero.

$f''(t)=0$

This corresponds to where the horizontal line is tangent to

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

From the graph the point of tangency is:

(8.99,1.44)

Therefore the fastest rate at which the news spread is 1.44

7 0

3 years ago

What - |3| math evaluate absolute value

EastWind [94]

The answer is -3, because the negative sign is outside of the absolute value. If the problem looked like this |-3|, then the answer would be 3. To clarify, your answer is -3.

7 0

3 years ago

If you have two triangles with the same shape but one is twice as large as the other, are the triangles similar?

Margarita [4]

The triangles are similar because of one triangle is 2x bigger than the other there seems to be a dilation. And since on triangle is 2x bigger the dilation between both triangles would be 2. I hope this helped :)

8 0

3 years ago

Which square root is between 4 and 5

shusha [124]

Answer:
I’m not sure what you mean by divided, but the square root of 24 would be between 4 and 5.

Explanation:
I translated 4 and 5 into square roots, being the square root of 16 (4^2) and the square root of 25 (5^2).
4 is equal to the square root of 16 just as 5 is equal to the square root of 25.
Of the given square roots in the answers, only the square root of 24 was between the square roots of 16 and 25. Therefore, the square root of 24 is between 4 and 5.

8 0

3 years ago

10.9 + (-15.6) + 2.1 write as a decimal

Delvig [45]

Answer:

-2.6

Step-by-step explanation:

10.9 + (-15.6) becomes 10.9 - 15.6 which equals -4.7. The last step is to add the 2.1 to the -4.7: -4.7 + 2.1 = -2.6

Therefore the answer is -2.6

5 0

3 years ago

Help me find area please asap​

Help me find area please asap