Given that y = (e^x)/x, x > 0, find the range of values of x where y is a decreasing
function of x.

Answer:

The last one

Step-by-step explanation:

[tex]x^3+1=0[/tex]

Subtract 1 from both sides

[tex]x^3+1-1=0-1[/tex]

simplify

[tex]x^3=-1[/tex]

[tex]\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}[/tex]

[tex]x=\sqrt[3]{-1},\:x=\sqrt[3]{-1}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{-1}\frac{-1-\sqrt{3}i}{2}[/tex]

simplify

[tex]x=-1,\:x=\frac{1}{2}-i\frac{\sqrt{3}}{2},\:x=\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex]

(That's basically the last one but in a different way of writing it)

Answer:

The last one

Step-by-step explanation:

Subtract 1 from both sides

simplify

simplify

Answer:

[tex](1 + i\,3) \cdot (2 + i) = -1 + i\,7[/tex]

Step-by-step explanation:

We proceed to present the procedure by algebraic means:

1) [tex](1 + i\,3)\cdot (2 + i)[/tex] Given

2) [tex]2\cdot (1 + i\,3) + i\,(1+i\,3)[/tex] Distributive and Commutative Properties

3) [tex]2 + i\,6 + i + i^{2} \,3[/tex] Distributive, Commutative and Associative Properties

4) [tex]2 + i\,7 -3[/tex] Definition of imaginary number/Distributive, Commutative and Associative Properties

5) [tex]-1 + i\,7[/tex] Commutative and Associative Properties

Answer:

[tex]3(x+y)(x+y)[/tex]

Step-by-step explanation:

[tex]3x(x+y)+3y(x+y)[/tex]

[tex]3x^{2} +6xy+3y^{2}[/tex]

[tex]3(x+y)(x+y)[/tex]

hope this helps.....

Answer:

15 oz

Step-by-step explanation:

Answer:

r = 0.2

Step-by-step explanation:

Given

y = rx ( divide both sides by x )

[tex]\frac{y}{x}[/tex] = r

Use any of the ordered pairs from the table and substitute

Using (8, 1. 6 ) , then

r = [tex]\frac{1.6}{8}[/tex] = 0.2

Answer:

75%

Step-by-step explanation:

Each quartile is 25%; the answer asks for 70% and below, which is the first through third quartile.

Answer:

9

Step-by-step explanation:

If you want the number to be divisible by three make sure the sum of all the numbers are divisible by three. Add all the numbers you have to see what they make.

3+4+2+8+4=21

So we just need to find the greatest number we can add to that to have it remain divisible by three. A number divisible by three is 30, and we can add 9 to 21 to make 30. Of course, there are other numbers we could add, but nine is the largest one-digit number that would work. Other smaller numbers include 3 and 6.

3+4+2+8+4+9=30

Now we check to see if our number is divisible by three

342984÷3 = 114328

114328 is a whole number so we know it's divisible.

Answer:

62

Step-by-step explanation:

The sum of the angles in a triangle add to 180

L + M + N= 180

38+ 80 + N = 180

118+ N = 180

N = 180-118

N = 62

Answer:

hygiygtuvtyryfyrvvryfyvyvrvfyrvyvrvrvr.

Answer:

a= 45

Step-by-step explanation:

all angles equal 180 degrees so you take the angle given which is 45 and the other which is a right angle, or 90 degrees and subtract 45 from 90 and you get 45 so a = 45 and you add up 45 + 45 + 90 thats 180!  

Answer:

(x+4)² + (y-k) ² = 16

Step-by-step explanation:

The equation of the circumference is expressed as;  

(x-h) ² + (y-k) ² = r²

(h,k) is the centre

r is the radius

Given that diameter = 8

radius = 8/2

radius = 4units

Given that h = -4 and k = 2

(x-h) ² + (y-k) ² = r²

(x-(-4)) ² + (y-2) ² = 4²

(x+4)² + (y-k) ² = 16

This gives the required equation

Answer:

x = 4

Step-by-step explanation:

180° - 114° = 66°

15x - 6 = 66

15(4) - 6 = 66

60 - 6 = 54      

Statement is wrong because we can see another angle. so...

Final answers: x = 4   while 54 + 114° = 168°  then 180° - 168° = 12°

Answer:

x = 8

Step-by-step explanation:

15x - 6 = 114

Move the constant to the right-hand side and change its sign

15x = 114 + 6

15x = 120

Divide both sides of the equation by 15

x = 8

Answer:

The 3rd choice.

Step-by-step explanation:

The third choice has what it takes to be a scientific notation.

Answer:

there are 8 for any four leg creatures : there are 4 for a human

Step-by-step explanation:

Answer:

[tex]1.16\:\mathrm{rad/s}[/tex]

Step-by-step explanation:

Angular speed is given by [tex]\omega=\frac{\Delta \theta}{\Delta t}[/tex], where [tex]\Delta \theta[/tex] is angle change in radians and [tex]\Delta t[/tex] is elapsed time.

Since the baseball makes one fourth (one quarter) of a rotation in 1.35 seconds, it will take the baseball [tex]4\cdot 1.35=5.4[/tex] seconds to complete on rotation.

One rotation is 360 degrees or [tex]2\pi[/tex] radians. Therefore, the angular speed of the baseball is:

[tex]\omega =\frac{2\pi}{5.4}=1.16355283466\approx \boxed{1.16\:\mathrm{rad/s}}[/tex]

Answer:

???

Step-by-step explanation:

Where's the image?

Answer:

[tex]s(8)=2186[/tex]

Step-by-step explanation:

A particle is moving with acceleration modeled by the function:

[tex]a(t)=18t+16[/tex]

We are given that its position s(t) at t = 0 is 10 and that its velocity v(t) at t = 0 is 16.

And we want to find its position at t = 8.

Velocity is the integral of the acceleration. Hence:

[tex]\displaystyle v(t)=\int a(t)\, dt=\int 18t+16\, dt[/tex]

Find the velocity. Remember the constant of integration!

[tex]v(t)=9t^2+16t+C[/tex]

Since v(t) is 16 when t = 0:

[tex](16)=9(0)^2+16(0)+C\Rightarrow C=16[/tex]

Hence, our velocity is given by:

[tex]v(t)=9t^2+16t+16[/tex]

Position is the integral of the velocity. Hence:

[tex]\displaystyle s(t)=\int v(t)\, dt=\int 9t^2+16t+16\, dt[/tex]

Integrate:

[tex]\displaystyle s(t)=3t^3+8t^2+16t+C[/tex]

s(t) is 10 when t = 10. Hence:

[tex]C=10[/tex]

So, our position function is:

[tex]s(t)=3t^3+8t^2+16t+10[/tex]

The position at t = 8 will be:

[tex]s(8)=3(8)^3+8(8)^2+16(8)+10=2186[/tex]

Answer:

1. If x is under a square root then x cannot equal a negative number. If x is in the denominator of a fraction then x cannot equal zero.

2. ax2 + bx + c

Step-by-step explanation: Hope this helps :)

Answer:

B

Step-by-step explanation:

It is linear and increasing.

If it is linear, it is increasing at a constant rate with a straight line.

Exponential means it is a curved line and would have an equation like f(x)=5^x

If it was decreasing, it would have a negative slope, such as -2x +10

Answer:

x =180-(90+46)

=180-136

=44

Answer:

44°

Step-by-step explanation:

180-90-46=44

Answer:

64

Step-by-step explanation:

Okay, here it goes:

Where there is a g you insert -2 and where there is an h you insert 5

(2(-2)+9(5)-5)-(6(-2)-4(5)+2)

If two numbers are side-by-side with no other sign between them, you multiply

(-4+45-5)-(6(-2)-4(5)+2)

(-4+45-5)-(-12-20+4)

There is a subtraction sign between these equations. That means you must distribute the negative sign to the equation on the right.

Remember:

-4+45-5+12+20-4

Now just add them together. I recommend going left to right.

-4+45=41

41-5=36

36+12=48

48+20=68

68-4=64

Fill the 3L jug, then pour its contents into the 5L jug.

Fill the 3L jug again, then pour as much of it (2L) as you can into the 5L jug.

Now the 5L jug is full, and the 3L jug is carrying 1L of water.

Empty the 5L jug.

Pour the 1L of water from the 3L jug to the 5L jug.

Finally, fill up the 3L jug, then transfer its water into the 5L jug. It now has 4L of water.

Answer:

[tex]y = (x - 3)^2 - 12[/tex]

[tex](3,-12)[/tex]

Step-by-step explanation:

Given

[tex]y = x^2 - 6x - 3[/tex]

Solving (a): In vertex form

The vertex form of an equation is:

[tex]y = a(x - h)^2 + k[/tex]

To do this, we make use of completing the square method.

We have:

[tex]y = x^2 - 6x - 3[/tex]

------------------------------------------------------------------

Take the coefficient of x (i.e. -6)

Divide by 2; -6/2 = -3

Square it: (-3)^2 = 9

Add and subtract the result to the equation

------------------------------------------------------------------

[tex]y = x^2 - 6x - 3[/tex]

[tex]y = x^2 - 6x + 9 - 9 - 3[/tex]

[tex]y = x^2 - 6x + 9 - 12[/tex]

Factorize [tex]x^2 - 6x + 9[/tex]

[tex]y = x^2 - 3x-3x + 9 - 12[/tex]

[tex]y = x(x - 3)-3(x - 3) - 12[/tex]

Factor out x - 3

[tex]y = (x - 3)(x - 3) - 12[/tex]

Express as squares

[tex]y = (x - 3)^2 - 12[/tex]

Hence, the vertex form of [tex]y = x^2 - 6x - 3[/tex] is: [tex]y = (x - 3)^2 - 12[/tex]

Solving (b): State the coordinates of the vertex.

In [tex]y = a(x - h)^2 + k[/tex]; the vertex is: (h,k)

The vertex of [tex]y = (x - 3)^2 - 12[/tex] will be [tex](3,-12)[/tex]