Find and simplify each of the following for fx = 6x -3. (A) f(x+ h) (B) f(x +h) - f(x) (C) f(x + h) - f(x)/h

Answer:

-14

Step-by-step explanation:

[tex] \boxed{gradient = \frac{y1 - y2}{x1 - x2} } [/tex]

Using the above formula, slope

[tex] = \frac{8 - ( - 6)}{ - 4 - ( -3 )} \\ = \frac{8 + 6}{ - 4 + 3} \\ = \frac{14}{ - 1} \\ = - 14[/tex]

Answer:

√ 96

log

( 7 )

6 ! /3 !

Step-by-step explanation:

Answer:

A)

[tex]f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.[/tex]

B) Continuous but not differentiable.

Step-by-step explanation:

So we have the piecewise function:

[tex]f(x) = \left\{ \begin{array}{lIl} \frac{1}{2}x+5 & \quad x >2 \\ 6& \quad x =2\\x +4&\quad x<2 \end{array} \right.[/tex]

A)

To write the differentiated piecewise function, let's differentiate each equation separately. Thus:

1)

[tex]\frac{d}{dx}[\frac{1}{2}x+5}][/tex]

Expand:

[tex]\frac{d}{dx}[\frac{1}{2}x]+\frac{d}{dx}[5][/tex]

The derivative of a linear equation is just the slope. The derivative of a constant is 0. Thus:

[tex]\frac{d}{dx}[\frac{1}{2}x+5}]=\frac{1}{2}[/tex]

2)

[tex]\frac{d}{dx}[6][/tex]

Again, the derivative of a constant is 0. Thus:

[tex]\frac{d}{dx}[6]=0[/tex]

3)

We have:

[tex]\frac{d}{dx}[x+4][/tex]

Expand:

[tex]\frac{d}{dx}[x]+\frac{d}{dx}[4][/tex]

Simplify:

[tex]=1[/tex]

Now, let's substitute our original equations for the differentiated equations. The inequalities will stay the same. Therefore:

[tex]f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.[/tex]

B)

For a function to be differentiable at a point, the function must be a) continuous at that point, and b) the left and right hand derivatives must be equivalent.

Let's first determine if the function is continuous at the point. Remember that a function is continuous at a point if and only if:

[tex]\lim_{x \to n^-} f(n)= \lim_{x \to n^+}f(n)=f(n)[/tex]

Let's find the left hand limit of f(x) at it approaches 2.

[tex]\lim_{x \to 2^-}f(x)[/tex]

Since it's coming from the left, let's use the third equation:

[tex]\lim_{x \to 2^-}f(x)\\=\lim_{x \to 2^-}(x+4)[/tex]

Direct substitution:

[tex]=(2+4)=6[/tex]

So:

[tex]\lim_{x \to 2^-}f(x)=6[/tex]

Now, let's find the right-hand limit:

[tex]\lim_{x \to 2^+}f(x)[/tex]

Since we're coming from the right, let's use the first equation:

[tex]\lim_{x \to 2^+}(\frac{1}{2}x+5)[/tex]

Direct substitution:

[tex](\frac{1}{2}(2)+5)[/tex]

Multiply and add:

[tex]=6[/tex]

So, both the left and right hand limits are equivalent. Now, find the limit at x=2.  

From the piecewise function, we can see that the value of f(2) is 6.

Therefore, the function is continuous at x=2.

Now, let's determine differentiability at x=2.

For a function to be differentiable at a point, both the right hand and left hand derivatives must be equivalent.

So, let's find the derivative of the function as x approahces 2 from the left and from the right.

From the differentiated piecewise function, we can see that as x approaches 2 from the left, the derivative is 1.

As x approaches 2 from the right, the derivative is 1/2.

Therefore, the right and left hand derivatives are not the same.

Thus, the function is continuous but not differentiable.

Answer:

1.17.9

2. 120.61

Step-by-step explanation:

Answer:

17.9

120.61

Step-by-step explanation:

Answer:

y-3 = 2/9 (x-8)

Step-by-step explanation:

Answer:

The volume of the solid = 1444

Step-by-step explanation:

Given that:

The region of the solid is bounded by the curves [tex]y = 38 \sqrt{cos \ x}[/tex] and the axis on [tex][-\dfrac{\pi}{2}, \dfrac{\pi}{2}][/tex]

using the slicing method

Let say the solid object extends from a to b and the cross-section of the solid perpendicular to the x-axis has an area expressed by function A.

Then, the volume of the solid is ;

[tex]V = \int ^b_a \ A(x) \ dx[/tex]

However, each perpendicular slice is an isosceles leg on the xy-plane and vertical leg above the x-axis

Then, the area of the perpendicular slice at a point [tex]x \ \epsilon \ [-\dfrac{\pi}{2},\dfrac{\pi}{2}][/tex] is:

[tex]A(x) =\dfrac{1}{2} \times b \times h[/tex]

[tex]A(x) =\dfrac{1}{2} \times(38 \sqrt{cos \ x})^2[/tex]

[tex]A(x) =\dfrac{1444}{2} \ cos \ x[/tex]

[tex]A(x) =722 \ cos \ x[/tex]

Applying the general slicing method ;

[tex]V = \int ^b_a \ A(x) \ dx \\ \\ V = \int ^{\dfrac{\pi}{2} }_{-\dfrac{\pi}{2}} (722 \ cos x) \ dx \\ \\ V = 722 \int ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}} cosx \dx[/tex]

[tex]V = 722 [ sin \ x ] ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}[/tex]

[tex]V = 722 [sin \dfrac{\pi}{2} - sin (-\dfrac{\pi}{2})][/tex]

[tex]V = 722 [sin \dfrac{\pi}{2} + sin \dfrac{\pi}{2})][/tex]

[tex]V = 722 [1+1][/tex]

[tex]V = 722 [2][/tex]

V = 1444

∴ The volume of the solid = 1444

Answer:

3x =24

x = 24 -3

x = 21 (ans)

Answer:

X=8

Step-by-step explanation:

3x=24

divide each side by 3 to isolate x

x=8

Answer:

w = 4

Step-by-step explanation:

13w-8w =20

Combine like terms

5w = 20

Divide each side by 5

5w/5 = 20/5

w = 4

Answer:

w=4

Step-by-step explanation:

13w-8w=20

5w=20

w=4

No.

Here is why:

If you mean equally divided then no because of the little 5 in the ones's place. If that 5 was a 0, it would definitely be divided equally.

Hope this makes sense!

Answer:

no

Step-by-step explanation:

Don’t know the answer

Answer:

5.58×10²⁴ atoms.

Step-by-step explanation:

From the question given above, the following data were obtained:

1 mole of silver = 107.9 g

Number of atoms in 1 mole of silver = 6.02×10²³ atoms.

Number of atoms in a kilogram of silver =.?

Next, we shall convert 1 kg of silver to grams (g). This can be obtained as follow:

1 kg = 1000g

Therefore, 1 kg of silver is equivalent to 1000g.

Finally, we shall determine the number of atoms in 1 kg (i.e 1000 g) of silver as follow:

107.9 g of silver contains 6.02×10²³ atoms.

Therefore, 1000 g of silver will contain = (1000 × 6.02×10²³) / 107.9 = 5.58×10²⁴ atoms.

Thus, a kilogram of silver contains 5.58×10²⁴ atoms.

Answer:

u=-1

Step-by-step explanation:

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

u= -1

Answer:

-16

Step-by-step explanation:

4 + 5(8-10)2

4 + 5(-2)2

4 + 10(-2)

4 - 20

-16

The answer is: 24

I assume this is a question from k12

  4 + 5(8 - 10)^2

  4 + 5(-2)^2

  4 + 5(4)

  4 + 20

= 24

Hope this helps ^^

Steps to solve:

2(n + 3) = 2n + 3

~Distribute left side

2n + 6 = 2n + 3

~Subtract 6 to both sides

2n = 2n - 3

~Subtract 2n to both sides

n = -3

Best of Luck!

Answer:

1 metric ton is = to 1000 kilograms

Answer:-0.5

Step-by-step explanation:

Greetings from Brasil....

The intersection of two sets is given by the elements that are common - present in both - to the sets.

A = {2; 5}

B = {5; 7; 9}

Element in both sets = 5.... So

Answer:

[tex]f^{-1}(x)=\frac{1}{6}\ln(x+9)[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=e^{6x}-9[/tex]

To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:

[tex]x=e^{6f^{-1}(x)}-9[/tex]

Add 9 to both sides:

[tex]x+9=e^{6f^{-1}(x)}[/tex]

Take the natural log of both sides:

[tex]\ln(x+9)=\ln(e^{6f^{-1}(x)})[/tex]

The right side cancels:

[tex]\ln(x+9)=6f^{-1}(x)[/tex]

Divide both sides by 6:

[tex]f^{-1}(x)=\frac{1}{6}\ln(x+9)[/tex]

And we're done!

Answer: x = -1/2y + 2

Step-by-step explanation:

12x + 6y = 24  To solve for x  first start by subtracting 6y from both sides

      - 6y    -6y

12x =  24 - 6y    Now divide each side by 12

x= 2 - 1/2y

21.406 in standard form

Answer:

21406 X 10^3

Answer:

0.966

Step-by-step explanation:

Given that:

Probability of DVD player breaking down before the warranty expires = 0.034

To find:

The probability that the player will not break down before the warranty expires = ?

Solution:

Here, The two events are:

1. The DVD player breaks down before the warranty gets expired.

2. The DVD player breaks down after the warranty gets expired

In other words, the 2nd event can be stated as:

The DVD does not break down before the warranty gets expired.

The two events here, have nothing in common i.e. they are mutually exclusive events.

So, Sum of their probabilities will be equal to 1.

[tex]\bold{P(E_1)+P(E_2)=1}\\\Rightarrow 0.034+P(E_2)=1\\\Rightarrow P(E_2)=1-0.034\\\Rightarrow P(E_2)=\bold{0.966}[/tex]

Answer:

Yes

Step-by-step explanation:

(5*2)x = 10x

5*2 = 10 so

10x = 10x

They are equal.

Answer:

Yes

Step-by-step explanation:

5 x 2 is 10, and so 5(2)x is 10x

Answer:

n=-1

Step-by-step explanation:

3n-5=-8(6+5n)

3n-5=-48-40n

add 40n to both sides

43n-5=-48

n=-1

Step-by-step explanation:

Answer:

y' = -4eˣ sin⁵(eˣ)

Step-by-step explanation:

Part 1 of the Fundamental Theorem of Calculus simply says that the definite integral of a function is equal to the antiderivative evaluated between the limits.

∫ₐᵇ f(x) dx = F(b) − F(a), where F(x) = ∫ f(x) dx.

y = ∫ₑₓ⁰ 4 sin⁵(t) dt

To integrate, use Pythagorean identity.

y = 4 ∫ₑₓ⁰ (1 − cos²(t))² sin(t) dt

Ignoring the limits for the moment, let's say u = cos(t) and du = -sin(t) dt.

y = 4 ∫ (1 − u²)² (-du)

y = -4 ∫ (1 − 2u² + u⁴) du

y = -4 (u − ⅔u³ + ⅕u⁵) + C

y = -4 (cos(t) − ⅔ cos³(t) + ⅕ cos⁵(t)) + C

Evaluate between t = eˣ and t = 0.

y = -4 (cos(0) − ⅔ cos³(0) + ⅕ cos⁵(0)) + C − [-4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ)) + C]

y = -4 (1 − ⅔ + ⅕) + 4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ))

Now take derivative with respect to x.

y' = 0 + 4 (-sin(eˣ) eˣ − 2 cos²(eˣ) (-sin(eˣ) eˣ) + cos⁴(eˣ) (-sin(eˣ) eˣ))

y' = -4eˣ sin(eˣ) (1 − 2 cos²(eˣ) + cos⁴(eˣ))

y' = -4eˣ sin(eˣ) (1 − cos²(eˣ))²

y' = -4eˣ sin⁵(eˣ)

This can be more easily calculated using the Second Fundamental Theorem of Calculus.

Answer:

I think it's 352. 02 g/mol

Step-by-step explanation:

googled it :)

Answer:

352.02 g/mol

In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles.

Answer:

$1,079.04

Step-by-step explanation:

multiply: 89.92x12=1078.04

Turn the percentage into a decimal.

8.25% / 100 = 0.0825

Multiply.

39.89 * 0.0825 ≈ $3.29

Subtract.

39.89 + 3.29 = $43.18

Best of Luck!

Answer:

375 miles

Step-by-step explanation:

m=miles

I set it up as an equation.                                                    $75+.60m=.80m                      

And solved from there                                                                                                                                                                                                                                                                                

Answer:

375 miles :D

Step-by-step explanation:

Answer:

a).To break even

They need to enroll 87 student

B) Profit=$100000

C) yeah they can think of that.

Profit= $70000

Step-by-step explanation:

Initial start up cost = $350000

Cost from adminstrative bodies

= 12000 for first 100 student

= $1200000

Total cost =$1200000+$350

Totral cost =$ 1550000

Tuition cost

= $18000 per student

To break even

The college needs to enroll

1550000/18000= 86.1

They need to enroll 87 student

B) if they enroll 75 students

Adminstrative cost = 12000*75

Adminstrative cost= 900000

Total cost= 350000+900000

Total cost =$ 1250000

Tuition fee= $18000*75

Tuition fee=$ 1350000

Their profit= 1350000-1250000

Profit=$100000

C).if tuition is $24000 and enrollment number= 35

Adminstrative cost = 35*12000

Adminstrative cost = $420000

Total cost= $770000

Tuition fee= $24000*35

Tuition fee= $840000

Profit= $840000-$770000

Profit= $70000