help
a 2/3
b 1/6
c 2/9
d 1/3

Answer: it would be the first option. they are both the first letters of their little cluster of letters (don't judge, i have no idea what it's called haha) and the rest of them do not match up. so, it is the first answer.

Answer:

answer: A

Step-by-step explanation:

They are all incorrect besides A

Answer:

[tex]f(x)=\sqrt{\frac{1}{4x^2-3}}[/tex] for [tex](-\infty, -\sqrt {\frac 3 4 })[/tex] and [tex](\infty, \sqrt {\frac 3 4 })[/tex] .

Step-by-step explanation:

The given differential equation is [tex]\frac{dy}{dx}=-4xy^3[/tex]

Rearranging it as

[tex]y^{-3}dy=-4xdx \\\\\frac{y^{-3+1}}{-3+1}=-4\frac{x^2}{2}+C \\\\\frac{y^{-2}}{2}=4\frac{x^2}{2}+C \\\\y^{-2}=4x^2+C\cdots(i)[/tex]

where C is constant.

The initial condition is f(-1)=-1, i.e for x=-1, y=-1.

So, by using the initial condition to get the value of constant:

[tex](-1)^{-2}=4(-1)^2+C \\\\1=4+C \\\\C=1-4=-3[/tex]

From equation (i), we have

[tex]y^{-2}=4x^2+(-3) \\\\y^2=\frac{1}{4x^2-3} \\\\y=\sqrt{\frac{1}{4x^2-3}} \\\\[/tex]

As y=f(x), so the required particular solution

[tex]f(x)=\sqrt{\frac{1}{4x^2-3}}[/tex]

Now, determining the domain of the function

As for a real value output, the term under square root must be positive.

So,

[tex]\frac{1}{4x^2-3} >0 \\\\\Rightarrow 4x^2-3 >0 \\\\\Rightarrow x^2 > \frac 3 4 \\\\\Rightarrow |x|>\sqrt {\frac 3 4 } \\\\\Rightarrow x> \sqrt {\frac 3 4 } \; and \; x< -\sqrt {\frac 3 4 }[/tex]

Therefore, the domain of the function is

[tex](-\infty, -\sqrt {\frac 3 4 }) \;and\; (\infty, \sqrt {\frac 3 4 })[/tex]

Hence, [tex]f(x)=\sqrt{\frac{1}{4x^2-3}}[/tex] for [tex](-\infty, -\sqrt {\frac 3 4 })[/tex] and [tex](\infty, \sqrt {\frac 3 4 })[/tex] .

Answer:

10

Step-by-step explanation:

well you are multiplying -5 and -2. When multiplying two negative numbers you get a positive. 5x2= 10.

Answer:

I belive it would be D

Step-by-step explanation:

Answer:

D. 12) 25.68 = 2.14

Step-by-step explanation:

Given :

Divisor = 1.2

Dividend = 2.568

We can make the divisor a whole number by multiplying the divisor by 10,

i.e. Divisor = 1.2 x 10 = 12

Similarly , dividend = 2.568 x 10 = 25.68

Therefore,

         2.14            

 12 | 25.68

  (-)  24                        

           16

      (-) 12                      

             48

      (-)  48                

             0

Hence the answer is 2.14

cos(2A) + cos(2A) cot(2A) = cot(2A)

cos(2A) + cos(2A) cot(2A) - cot(2A) = 0

cot(2A) sin(2A) + cos(2A) cot(2A) - cot(2A) = 0

cot(2A) (sin(2A) + cos(2A) - 1) = 0

cot(2A) = 0   or   sin(2A) + cos(2A) - 1 = 0

cot(2A) = 0   or   sin(2A) + cos(2A) = 1

cot(2A) = 0   or   sin(2A) cos(π/4) + cos(2A) sin(π/4) = 1/√2

cot(2A) = 0   or   sin(2A + π/4) = 1/√2

[2A = cot⁻¹(0) + nπ]   or

[2A + π/4 = sin⁻¹(1/√2) + 2nπ   or   2A + π/4 = π - sin⁻¹(1/√2) + 2nπ]

(where n is any integer)

[2A = π/2 + nπ]   or

[2A + π/4 = π/4 + 2nπ   or   2A + π/4 = 3π/4 + 2nπ]

[A = π/4 + nπ/2]   or

[2A = 2nπ   or   2A = π/2 + 2nπ]

[A = π/4 + nπ/2]   or

[A = nπ   or   A = π/4 + nπ]

A = (1 + 2n) π/4   or   A = nπ   or   A = π/4 + nπ

Answer: It is B

Step-by-step explanation:

Just took the test

Answer:

a) y=5000e^{0.099t}

b) 11.097 hours

Step-by-step explanation:

a

Many systems exhibit exponential growth. These systems follow a model of the form [tex]y=ae^{kt}[/tex], where a represents the initial state of the system and k is a positive constant, called the growth constant.

So we have our value of which represents the initial state of the system, which is 5000.

We need to calculate k.

Now,

It says he doubling time of a population of bacteria is 7 hours there are 5000 present initially, which means at 0 hours there were 5000 bacteria (initially means at t = 0, and then after 7 hours it doubled so it became 10,000 at 07:00 hours then at 14:00 it became 20,000 and then at 21:00 it became 40,000 this is the doubling time. So to calculate the value of k we can use this data, lets take 10,000 bacteria at 07:00 hours and put in our equation.

[tex]y=ae^{kt} \\y=5000e^{kt}[/tex]

value of a is 5000 which was the initial value now we need the value of y which is the total amount of bacteria after t hours. So after 7 hours we have a total of 10,000 bacteria so our value of t becomes 7 and value of y becomes 10,000.

[tex]10000=5000e^{7k}[/tex]

[tex]2=e^{7k} \\[/tex]

Apply natural logarithm on both sides

[tex]ln2=lne^{7k}[/tex]

Ln e becomes 1 as we all know so we write 7k as it is.

[tex]ln2=7k[/tex]

[tex]k=\frac{ln2}{7} \\k=0.099[/tex]

Now our equation is

[tex]y=5000e^{0.099t}[/tex]

we can confirm this by inserting time t as 7 , 14 , 21 , 28 , 35  and we will get the exact bacteria we need which is y 10,000 , 20,000 , 40,000 , 80,000 , 160,000, respectively.

b)

It says how long will it take the population to triple which means the triple of 5000 is 15,000 and we set that to the value of y which is the amount of bacteria, and calculate t.

[tex]y=5000e^{0.099t} \\\\15000=5000e^{0.099t} \\\\3=e^{0.099t} \\ln3=lne^{0.099t} \\\\ln3=0.099t\\\\t=\frac{ln3}{0.099} \\\\t=11.097[/tex]

Which means it would take 11.097 hours for bacteria of 5000 to triple in size.

Answer:

a. 15L will last the cafe 3 days if they're using 4L every day

b. 15L will last them 7 days if they're using 2L every day

Step-by-step explanation:

division.

Answer:

I think it's 64, I'm not sure but I hope this helps

Step-by-step explanation:

IT'S NOT 64!! The real answer is 45%

Answer:

Step-by-step explanation:

1

find the amount of tax

2

find the amount of the tip

3

find the total cost by adding the cost of the meal, the tax, and the tip

RESULT

56.70

Answer:

7 minutes

Step-by-step explanation:

When Jay and Kevin work together to clear the driveway of snow it takes an average of 14 minutes. If Jay or Kevin works alone to clear the driveway he can clean it in 21 minutes. In total if Jay works alone then he can clean the driveway by spending additional 7 minutes.

Answer:

21

Step-by-step explanation:

Answer:

A. 3, 7, 9, 10, 12

Step-by-step explanation:

All of these numbers as x are less than 14.

Hope it helps!

Answer:

y=0

Step-by-step explanation:

So you would do -4(6y-3) and divide that by -4

then you would do 12 and divide that by -4

or

You could do

-6y-3 which equals -3

then

add three to both sides like this -6y-3+3=-3+3

then simplify it to -6y=0

then divide -6y over -6 and 0 over -6

then it will simplify to 0

Answer:

Net Worth

Step-by-step explanation:

Answer:

Amy

Step-by-step explanation:

amy completed a longer distance in a shorter amount of time

rather than john completed a shorter distance in a longer time

Answer:

negative twelve

Step-by-step explanation:

the slope is -1, so one must go down as the other goes up. since the x value has increased by 3, the y value must decrease by three

Answer:

y=-2/3x+3

Step-by-step explanation:

because -2/3 is the slope, y int 3

Answer:

20

Step-by-step explanation:

trust me.

Answer:

20

Step-by-step explanation:

The base square itself is 4 x 4 which is 16, then there are 4 halfs which makes 2 more and the other 2 in that 2 triangles so 20

Answer:

2 and 09 but if it's just one option, pick 2

Step-by-step explanation:

the others aren't rational i think

Answer:

sorry but their is no picture its black...

Answer:

Option D is correct

Step-by-step explanation:

For this question we would need the equation of line since this is a multiple choice question you wouldn't have enough time to find out the equation so we need to be FAST

If we see all the four options at first glance option C or option D seem correct because the line represents a rise in values of x and y respectively, which means x increases with respect to y. So the slope/gradient in other words m should be positive so option A and B are ruled out because the equation of line is written as

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept so seeing the graph our equation of line should be

[tex]y=mx-2[/tex]

where b = -2 because value of b corresponds to y-intercept which means the where the graph intersects the y-axis in this case its -2

where m is positive in this case 5 thus

[tex]y=5x-2[/tex]

if we try to rearrange the four choices option C and D give us the above equation and option A and B give us

[tex]y=-5x+2[/tex]

which is wrong !

Now, regarding the inequality sign the graph represents

[tex]y=5x-2[/tex]

and the area which is shaded in blue is the region lower the line which means it should be

[tex]y\leq 5x-2[/tex]

in this case its D if we rearrange it

I have two images so you understand it better visually

As you can see in both forms are shaded region is the same so option D is correct

Answer:

The value is 20.

Step-by-step explanation:

To solve this equation, you must use the method of PEMDAS.  In this order, you should multiply 8 by 2 first to get 16 for the first part of your answer.  Your equation should now be 7 + 16 - 6 + 3.  You can now solve this equation from left to right manually.  Add 16 from 7 to get 23, subtract 6 from that number to get 17 and add 3 to get your final answer which is 20.

Answer:

27 :)

Step-by-step explanation:

7+8=15

15x2=30

30-6=24

24+3=27

Answer:

1)=-80 | 2)=8,9,10 | 3)=12

Step-by-step explanation:

-80*3/4=-60

8+9+10=27

12*2-4=20

I hope this helps

Answer:

all girls are the same bro

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

An easy way is to just count the grids blocks, which are squares.

There are 18 of these.

For the rest, since they are in the shape of a triangle, they will count as a half grid block.

There are 4 of these, which are 4 halfs, which equal to 2 square blocks.

Add them, 18+2=20

Answer: the line is intercepting with 4 if that's what you're asking

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

Step-by-step explanation:

[tex]\qquad\quad {:}\leadsto\sf \dfrac {2x (x+7)}{\cancel{(x-3)}}\times {\dfrac {(x-9)\cancel{(x-3)}}{8x^2 (x+7)}}[/tex]

[tex]\qquad\quad {:}\leadsto\sf \dfrac {2x\cancel{(x+7)}}{x-3}\times {\dfrac {x-9}{8x^2 \cancel{(x+7)}}}[/tex]

[tex]\qquad\quad {:}\leadsto\sf \dfrac{2x (x-9)}{8x^2}[/tex]

[tex]\qquad\quad {:}\leadsto\sf \dfrac {\cancel{2x}^2-18x}{\cancel{8x}^2}[/tex]

[tex]\qquad\quad {:}\leadsto\sf \dfrac {18x}{4}[/tex]

[tex]\qquad\quad {:}\leadsto\sf \dfrac {9x}{2}[/tex]

[tex]\qquad\quad {:}\leadsto\sf 4.5x [/tex]

Answer:

Option C and D

Step-by-step explanation:

For a quadratic function having no x-intercepts the discriminant should be less than 0 .

[tex]D=b^2-4ac[/tex]

Now if this is less than zero if we plug in the values of a, b and c the square root of a negative number cannot be calculated thus giving us no real x-intercepts.

[tex]x=-b+-\frac{\sqrt{b^2-4ac} }{2a} \\\\x=-b+-\frac{\sqrt{D} }{2a}[/tex]

Here we can see that if we the value of D is less than zero the square would not be possible thus our correct choices are ,

Option C and D