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miv72 [106K]
3 years ago
11

While testing a new vaccine, a lab technician noticed that the number of bacteria reduced by half every minute. How long does it

take for 3,000 bacteria to reduce to 375?
Mathematics
1 answer:
ANTONII [103]3 years ago
7 0
As we know that 
x=x0*[1/2]n
putting the values 
375=3000*[1/2]n
375/3000=<span>[1/2]n
</span>1/8=<span>[1/2]n
simplify
[1/2]3=</span><span>[1/2]n
by cancelling them
so n=3
so it will take 3 minutes
hope it helps</span>
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Limit (sin4x-4sinx)/x^3 when x close to zero
BartSMP [9]

\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \  }

Step-by-step explanation:

Hello, please consider the following.

Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.

sin(x) \sim  \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}

Then,

\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10

Thank you

4 0
3 years ago
Read 2 more answers
I dont know what to do... im kinda not smart
myrzilka [38]

7.

10% = 6

25% = 15

50% = 30

20% = 12

_____________________

8.

a = 35

b = 105

c = 140

____________________________

9.

15 is 30% of 50.

_____________________________

10.

The punch recipe contains 25% lemonade:

24/6 = x/100

x=1/4 x 100 = 25%

_____________________________

11.

520

multiply 650 by 80 amd then divide by 100

or simply multiply 650 by 0.8

to get 520 students.

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12.

Number of items checked = 300

Defective items = 3%

Number of defective items =

Number of defective items =

Number of defective items = 9

Number of items worked = Total items - Number of defective items

Number of items worked = 300 - 9 = 291

291 items of checked items worked.

8 0
3 years ago
What is the difference between constructing a regular hexagon and constructing an equilateral triangle?
tresset_1 [31]

Answer:

Its not b since thats what i just got wrong on the test so your down to 3 options

Step-by-step explanation:

wadsdawdawf

4 0
3 years ago
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Subtracting mixed number 4_1 - 2_7 4 8 4
aleksandr82 [10.1K]

Answer:

4\frac{1}{4} - 2\frac{7}{8} = 1\frac{3}{8}

Step-by-step explanation:

Given

4\frac{1}{4} - 2\frac{7}{8} --- proper representation of the question

Required

Evaluate

Convert numbers to improper fractions

4\frac{1}{4} - 2\frac{7}{8} = \frac{17}{4} - \frac{23}{8}

Take LCM

4\frac{1}{4} - 2\frac{7}{8} = \frac{34 - 23}{8}

4\frac{1}{4} - 2\frac{7}{8} = \frac{11}{8}

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