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nalin [4]
3 years ago
14

Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. At​ 11:00 you plac

e a single bacterium in a​ bottle, and at​ 11:01 it divides into 2​ bacteria, which at​ 11:02 divide into 4​ bacteria, and so on. How many bacteria will be in the bottle at​ 11:30?
Mathematics
1 answer:
pychu [463]3 years ago
7 0

Answer:

we could work this out by geometric sequence

Step-by-step explanation:

G1=2, G2=4, we have a formula,Gn=G1r^n-1

G2=G1 (r)^1, 4=2r, r=2

G30=G1 (2)^29=1,073,741,824 bacterium

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A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner
algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by  using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

V=x(216-24x-36x+4x^{2})

V=x(4x^{2}-60x+216)

V=4x^{3}-60x^{2}+216x

So now we can find the derivative of the volume:

V'=12x^{2}-120x+216

and set it equal to zero, so we get:

12x^{2}-120x+216=0

and now we can solve. We can start by factoring the left side of the equation, so we get:

12(x^{2}-10x+18)=0

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}

so we substitute the corresponding values:

x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0
3 years ago
How to graph an exponential function
irina1246 [14]

Step-by-step explanation:

Exponential function is given by general form y=ab^x

Where a and b are constants.

say a=1 and b=2 then we can write function as :

y=1*2^x

or y=2^x

To graph this or any exponential function, we just need to find some points then join them by a curved line.

Like plug x=0, 1, 2,... into above function and find points:

plug x=1

y=2^x=2^1=2

Hence point is (1,2)

Find more points similarly then graph them to get the graph as shown below:


7 0
3 years ago
The Miguel traces a circle with the radius of 25 cm like the one shown. He will color the shade section what is the area of the
Scilla [17]

Answer: The area of shaded section is 491.07 cm²

Step-by-step explanation:

Given: Radius of the circle = 25 cm

Now as shown in figure the shaded region is a quadrant.

Therefore the central angle is 90°

Now as we know

Area of sector is given by

Area= \pi r^2 \dfrac{\theta}{360^\circ}  where r is radius and \theta is central angle

So we have

Area = \dfrac{22}{7} \times (25)^2\times \dfrac{90^\circ}{360^\circ} \\\\\Rightarrow Area=  \dfrac{22}{7} \times 625 \times \dfrac{1}{4} \\\\\Rightarrow Area=  \dfrac{11}{7} \times 625 \times \dfrac{1}{2} = 491.07cm^2

Hence, the area of shaded section is 491.07 cm²

5 0
3 years ago
Find the equatio of the line tht contains the point (5,6) and is perpendicualr to the line 4x+2y=2
anzhelika [568]
--------------------------------------------------------------
Find Slope
--------------------------------------------------------------
4x + 2y = 2
2y= -4x + 2
y = -4/2 x + 2
y = -2x + 2

Slope = -2
Perpendicular slope = 1/2

--------------------------------------------------------------
Insert slope into the general equation y = mx + c
--------------------------------------------------------------
y = 1/2x + c

--------------------------------------------------------------
Find y-intercept 
--------------------------------------------------------------
y = 1/2x + c
at (5,6)
6 = 1/2 (5) + c
6 = 5/2 + c
c = 6 - 5/2 
c = 7/2

--------------------------------------------------------------
Insert y-intercept into y = 1/2 x + c
--------------------------------------------------------------
y = 1/2 x + 7/2
2y = x + 7

--------------------------------------------------------------
Answer: 2y = x + 7
--------------------------------------------------------------
3 0
3 years ago
Find the slope between the following points:
bazaltina [42]

Answer:

1. y = -0.6x + 5.4.

2. The entered points belong to a vertical line. There is no slope.

Equation: x = 6

3.  y = 0.16667x + 5.5.

4. The entered points belong to a vertical line. There is no slope.

Equation: x = -8.

Step-by-step explanation:

7 0
3 years ago
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