f(x)=−5x^3−4x^2+8x and g(x)=−4x^2+8, find (f−g)(x) and (f−g)(−2).

Answer:

-1 and 1

Step-by-step explanation:

Reciprocal means "one divided by...".

1/-1 = -1 and 1/1 = 1

Answer: x < 28

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \bf \ \ k=320 \ \ }[/tex]

Step-by-step explanation:

Hello,

The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.

If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?

[tex]64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

105 years

Step-by-step explanation:

Given the function :

Q(t) = 4e^(-0.00938t)

Q = Quantity in kilogram of an element in a storage unit after t years

how long will it be before the quantity is less than 1.5kg

Inputting Q = 1.5kg into the equation:

1.5 = 4e^(-0.00938t)

Divide both sides by 4

(1.5 / 4) = (4e^(-0.00938t) / 4)

0.375 = e^(-0.00938t)

Take the ln of both sides

In(0.375) = In(e^(-0.00938t))

−0.980829 = -0.00938t

Divide both sides by 0.00938

0.00938t / 0.00938 = 0.980829 /0.00938

t = 104.56599

When t = 104.56599 years , the quantity in kilogram of the element in storage will be exactly 1.5kg

Therefore, when t = 105 years, the quantity of element in storage will be less than 1.5kg

Answer:

- At any time t, the population is:

P = 375t² + 3000t + 1000

- At time t = 3 days, the population is:

P = 13,375

Step-by-step explanation:

Given the rate of change of the population of bacteria as:

dP/dt = 3000/(1 + 0.25t)

we need to rewrite the given differential equation, and solve.

Rewriting, we have:

dP/3000 = (1 + 0.25t)dt

Integrating both sides, we have

P/3000 = t + (0.25/2)t² + C

P/3000 = t + 0.125t² + C

When t = 0, P = 1000

So,

1000/3000 = C

C = 1/3

Therefore, at any time t, the population is:

P/3000 = 0.125t² + t + 1/3

P = 375t² + 3000t + 1000

At time t = 3 days, the population is :

P = 375(3²) + 3000(3) + 1000

= 3375 + 9000 + 1000

P = 13,375

Answer:

B) x=80°

Step-by-step explanation:

This is a hexagon, so it has interior angles equaling 720°.  (N-2)*180

So the equation would be

78+134+136+132+2x+x=720

480+3x=720

3x=720-480

3x=240

x=80°

Answer:

The answer is 55, -275, 1375, -6875......

Step-by-step explanation:

Answer:

2x + 5y + 15

Step-by-step explanation:

add like terms

(x+x) + (y+y)+3y+15

2x+2y+3y+15

2x + 5y + 15

i hope this helps!

Answer:

√(x)

Step-by-step explanation:

(1)/(x^-(1/2)) that's 3 goes into -3 leaving 1 and goes into 6 leaving 2

1/2 is same as 2^-1

so therefore we can simplify the above as

x^-(-1/2)

x^(1/2)

and 4^(1/2)

is same as √(4)

so we conclude as

√(x)

Answer:

choice 1,2,4,5 from top to bottom

Step-by-step explanation:

1:the points given are in the line where both planes intersect

2:point H is not on any plane

3:in the diagram point F is on plane R so false

4:if you connect the points given they will intersect so not collinear

5:the points F and G are on the plane R

6:so F is on plane R but H is not on any do false

Answer:

The answer is:

C. [tex]\bold{x = -1.25h+220}[/tex]

Step-by-step explanation:

Given:

[tex]h=0.8( 220-x )[/tex]

Where [tex]h[/tex] is the heartbeats per minute and

[tex]x[/tex] is the age of person

To find:

Age of person in terms of heartbeats per minute = ?

To choose form the options:

[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]

Solution:

First of all, let us have a look at the given equation:

[tex]h=0.8( 220-x )[/tex]

It is value of [tex]h[/tex] in terms of [tex]x[/tex].

We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].

Let us divide the equation by 0.8 on both sides:

[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]

Now, subtracting 220 from both sides:

[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]

Now, multiplying with -1 on both sides:

[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]

So, the answer is:

C. [tex]\bold{x = -1.25h+220}[/tex]

This sequence converges to 0.

Proof: Recall that

[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]

is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].

Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then

[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]

[tex]\implies\dfrac1n<\varepsilon^2[/tex]

[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]

as required.

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

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

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

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

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

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

Answer:

137, 280 feet

Step-by-step explanation:

There are 5,280 feet in a mile.

26 * 5,280 = 137,280

There are 137, 280 feet in 26 miles.

There are 137,280 feet in 26 miles.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We know that there are 5,280 feet in a mile.

So, the solution would be;

26 x 5,280 = 137,280

Thus, There are 137,280 feet in 26 miles.

Learn more about the unitary method;

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[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

Answer:

Option (2)

Step-by-step explanation:

In an arithmetic progression,

[tex]a_1,a_2,a_3.........a_{n-1},a_n[/tex]

First term of the progression,

a = [tex]a_1[/tex]

Common difference 'd' = [tex](a_2-a_1)[/tex]

Recursive formula for the sequence,

a = [tex]a_1[/tex]

[tex]a_n=a_{n-1}+d[/tex]

By applying these rules in the recursive formula,

[tex]a_1=\frac{4}{5}[/tex]

[tex]a_n=a_{n-1}+\frac{3}{2}[/tex]

Common difference 'd' = [tex]\frac{3}{2}[/tex]

Therefore, Option (2) will be the answer.

Answer:

2 sqrt(41) = x

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10 ^2 = x^2

64+ 100 = x^2

164 = x^2

Take the square root of each side

sqrt(164) = sqrt(x^2)

sqrt(4) sqrt(41) = x

2 sqrt(41) = x

Answer:

E(w) = 1600000

v(w) = 240000

Step-by-step explanation:

given data

sequence = 1 million iid  (+1 and +2)

probability of transmitting a +1 =  0.4

solution

sequence will be here as

P{Xi = k } = 0.4              for k = +1

                  0.6              for k = +2

and define is

x1  + x2 + ................ + X1000000

so for expected value for W

E(w) = E( x1  + x2 + ................ +  X1000000 )   ......................1

as per the linear probability of expectation

E(w) = 1000000 ( 0.4 × 1 + 0.6 × 2)

E(w) = 1600000

and

for variance of W

v(w) = V ( x1  + x2 + ................ + X1000000 )    ..........................2

v(w) = V x1  + V x2 + ................  + V  X1000000

here also same as that xi are i.e d so cov(xi, xj ) = 0 and i ≠ j

so

v(w) = 1000000 ( v(x) )

v(w) = 1000000 ( 0.24)

v(w) = 240000

Answer:

Step-by-step explanation:

Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods

1/PV (FV) = (PV(1 + r^n)1/PV divide by PV

ln(FV/PV) = ln(1 + r^n) convert to natural log function

ln(FV/PV) = n[ln(1 + r)] by simplifying

n = ln(FV/PV) / ln(1 + r) solve for n

n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually

n = 9

n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly

n = 104 months or 8.69 years

n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily

n = 3163 days or 8.67 years

Alternatively

A = P e ^(rt)

Given that r = 8%

= 8/100

= 0.08

2 = e^(0.08t)

ln(2)/0.08 = t

0.6931/0.08 = t

t= 8.664yrs

t = 8.67yrs

Which ever approach you choose to use,you will still arrive at the same answer.

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]x=x(t)=2cos(t)\\\\dx=\dfrac{dx}{dt}dt=x'(t)dt=-2sin(t)dt[/tex]

and

[tex]y=y(t)=2sin(t)\\\\dy=\dfrac{dy}{dt}dt=y'(t)dt=2cos(t)dt[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The values of dx and dy are give as -2sin(t)dt and 2cos(t)dt respectively. The answer to the given problem can be stated as,

dy = 2cos(t)dt

And,  dx = -2sin(t)dt.

The integration can be defined as the inverse operation of differentiation. If a function is the integration of some function f(x) , then differentiation of that function is f(x).

The given integral over C is ∫ (x − y) dx + (x + y) dy.

And, the parameters for C are as follows,

x = 2cos(t)

y = 2sin(t)

0 ≤ t ≤ 2π

Now, on the basis of these parameters dx and dy can be found as follows,

x =  2cos(t)

Differentiate both sides with respect to t as follows,

dx/dt = 2d(cos(t))/dt

=> dx/dt = -2sin(t)

=> dx =  -2sin(t)dt

And, y = 2sin(t)

Differentiate both sides with respect to t as follows,

dy/dt = 2d(sin(t))/dt

=> dy/dt = 2cos(t)

=> dy = 2cos(t)dt

Hence, the value of dx and dy as per the given parameters is -2sin(t)dt and 2cos(t)dt respectively.

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Answer:

True

Step-by-step explanation:

The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.

Aswer:I am sure of the answer it is 6 and 42

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, first, let's use the product rule.

Derivative of uv is u'v + u v', so it gives:

[tex]f(x)=(x^3-2x+1)(x-3)=u(x) \cdot v(x)\\\\f'(x)=u'(x)v(x)+u(x)v'(x)\\\\ \text{ **** } u(x)=x^3-2x+1 \ \ \ so \ \ \ u'(x)=3x^2-2\\\\\text{ **** } v(x)=x-3 \ \ \ so \ \ \ v'(x)=1\\\\f'(x)=(3x^2-2)(x-3)+(x^3-2x+1)(1)\\\\f'(x)=3x^3-9x^2-2x+6 + x^3-2x+1\\\\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]

Now, we distribute the expression of f(x) and find the derivative afterwards.

[tex]f(x)=(x^3-2x+1)(x-3)\\\\=x^4-2x^2+x-3x^3+6x-4\\\\=x^4-3x^3-2x^2+7x-4 \ \ \ so\\ \\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

8

Step-by-step explanation:

Ham with or without cheese-2 choices

Bologna with or without cheese-2 choices

Bologna with cheese with water or juice-2 choices

Bologna without cheese with juice or water-2 choices

Ham with cheese with juice or water -2 choices

Ham without cheese with juice or water -2 choices

2+2+2+2=8

Kile has 8 choices for lunch

Answer:

486

Step-by-step explanation:

Hello!

To find the surface area of a cube we use the equation

[tex]S = 6a^{2}[/tex]

S is the surface area

a is the side length

Put what we know into the equation

[tex]S = 6*9^{2}[/tex]

Solve

S = 6 * 81

S = 486

Hope this Helps!

Answer:486[tex]ft^{2}[/tex]

Step-by-step explanation:

surface area= 6[tex]l^{2}[/tex]

l=9

sa=6 ([tex]9^{2}[/tex])= 6 x 81=486[tex]ft^{2}[/tex]

Answer:

Note that orthogonal to the plane means perpendicular to the plane.

Step-by-step explanation:

-1x+3y-3z=1 can also be written as -1x+3y-3z=0

The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).

Let us find a point on this  line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively

Therefore, the vector equation is given as:

-1(x-0) + 3(y-0) + -3(z-5) = 0

-x + 3y + (-3z+15) = 0

-x + 3y -3z + 15 = 0

Multiply through by - to get a positive x coordinate to give

x - 3y + 3z - 15 = 0

Answer: Find answer in the attached files

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

You have 10 tens not 1 ten

8 * 100 + 10 * 10 + 0*1

800 + 100 + 0

900

Answer:

[tex]900[/tex]

Step-by-step explanation:

[tex]8 \times 100 + 10 \times 10 + 0 \times 1 \\ 800 + 100 + 0 \\ = 900[/tex]