Does anyone have the answers to Basic derivative rules: table on khan academy?

Answer:

100.

Step-by-step explanation:

100 + 0 = 100

100 ÷ 1 = 100

Immediately, by definition of cotangent, we find

tan(α) = 1/cot(α) = 1/(-√3)

⇒   tan(α) = -√3

Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.

Recall the Pythagorean identity,

cos²(α) + sin²(α) = 1

Multiplying both sides by 1/sin²(α) recovers another form of the identity,

cot²(α) + 1 = csc²(α)

Solving for csc(α) above yields

csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4

⇒   csc(α) = 2

⇒   sin(α) = 1/2

Solve for cos(α) using the first form of the Pythagorean identity:

cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)

⇒   cos(α) = -√3/2

⇒   sec(α) = -2/√3

Answer:

There are two stationary points

Note that 1/2 = 0.5

==========================================================

How to get those answers:

Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing (i.e. it's staying still at that snapshot in time).

Apply the derivative to get:

f(x) = 4x^3 - 3x + 3

f ' (x) = 12x^2 - 3

Then set it equal to zero and solve for x.

f ' (x) = 0

12x^2 - 3 = 0

12x^2 = 3

x^2 = 3/12

x^2 = 1/4

x = sqrt(1/4) or x = -sqrt(1/4)

x = 1/2 or x = -1/2

x = 0.5 or x = -0.5

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

Let's do the first derivative test to help determine if we have local mins, local maxes, or neither.

Set up a sign chart as shown below. Note the three distinct regions A,B,C

The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.

The reason why I split things into regions like this is to test each region individually. We'll plug in a representative x value into the f ' (x) function.

To start off, we'll check region A. Let's try something like x = -2

f ' (x) = 12x^2 - 3

f ' (-2) = 12(-2)^2 - 3

f ' (-2) = 45

The actual result doesn't matter. All we care about is whether if its positive or negative. In this case, f ' (x) > 0 when we're in region A. This tells us f(x) is increasing on the interval [tex]-\infty < x < -0.5[/tex]

Let's check region B. I'll try x = 0.

f ' (x) = 12x^2 - 3

f ' (0) = 12(0) - 3

f ' (0) = -3

The result is negative, so f ' (x) < 0 when [tex]-0.5 < x < 0.5[/tex]. The f(x) curve is decreasing on this interval.

The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.

Plug x = -0.5 into the original function to find its paired y coordinate.

f(x) = 4x^3 - 3x + 3

f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3

f(-0.5) = 4

The point (-0.5, 4) is a stationary point. More specifically, it's a local max.

Side note: This is the same as the point (-1/2, 4) when written in fraction form.

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

Let's check region C

I'll try x = 2

f ' (x) = 12x^2 - 3

f ' (2) = 12(2)^2 - 3

f ' (2) = 45

The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when [tex]0.5 < x < \infty[/tex]. The function f(x) is increasing on this interval.

Region B decreases while C increases. The change from decreasing to increasing indicates we have a local min when x = 0.5

Plug this x value into the original equation

f(x) = 4x^3 - 3x + 3

f(0.5) = 4(0.5)^3 - 3(0.5) + 3

f(0.5) = 2

The local min is located at (0.5, 2) which is the other stationary point.

The graph and sign chart are shown below.

The local min is located at (0.5, 2) which is the other stationary point.

Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing.

Apply the derivative to get:

f(x) = 4x^3 - 3x + 3

f ' (x) = 12x^2 - 3

Then set it equal to zero and solve for x.

f ' (x) = 0

12x^2 - 3 = 0

12x^2 = 3

x^2 = 3/12

x^2 = 1/4

x = 1/2 or x = -1/2

x = 0.5 or x = -0.5

The first derivative test to help determine if we have local mins, local maxes, or neither.

A = numbers to the left of -0.5

B = numbers between -0.5 and 0.5 excluding both endpoints

C = numbers to the right of 0.5

Thus, The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.

Let's try something like x = -2

f ' (x) = 12x^2 - 3

f ' (-2) = 12(-2)^2 - 3

f ' (-2) = 45

In this case, f ' (x) > 0 when we're in region A.

Let's check region B x = 0.

f ' (x) = 12x^2 - 3

f ' (0) = 12(0) - 3

f ' (0) = -3

The result is negative, so f ' (x) < 0 when f(x) curve is decreasing on this interval.

The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.

Substitute x = -0.5 into the original function to find its paired y coordinate.

f(x) = 4x^3 - 3x + 3

f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3

f(-0.5) = 4

The point (-0.5, 4) is a stationary point, it's a local max.

Let's check region C x = 2

f ' (x) = 12x^2 - 3

f ' (2) = 12(2)^2 - 3

f ' (2) = 45

The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when The function f(x) is increasing on this interval.

Susbtitute this x value into the original equation

f(x) = 4x^3 - 3x + 3

f(0.5) = 4(0.5)^3 - 3(0.5) + 3

f(0.5) = 2

Hence, The local min is located at (0.5, 2) which is the other stationary point.

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Answer: d. $8.04

Step-by-step explanation:

$4.05 + $3.99 = $8.04

Answer:

d. 8.04

Step-by-step explanation:

4.05+3.99=8.04

The company's expectation is $486.26.

Since the probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941, to determine, if an insurance company sells a one-year, $ 12,000 life insurance policy to such a person for $ 495, what is the company's expectation, the following calculation must be performed:

Therefore, the company's expectation is $486.26.

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Answer:

45215.31

Step-by-step explanation:

$596.6 is the interest will you earn if you deposit $4000 into an account compounded semi-annually at 2.8% for 5 years.

What is compounding?

Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid. Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time, the so-called “miracle of compounding.”

According to question,$4000 into an account compounded semi-annually at 2.8% for 5 years.

We have to find interest rate.

Formula for compound interest is [tex]P[(1+i)^n-1][/tex]

Since compounding is semi-annually,

[tex]i=\frac{0.028}{2}[/tex][tex]=0.014[/tex] (since compounding is semi-annually)

[tex]n[/tex]=number of years=[tex]5[/tex] ×[tex]2=10[/tex] years (since compounding is semi-annually)

So, compound interest

[tex]=[/tex][tex]P[(1+i)^n-1][/tex]

[tex]=4000((1+0.014)^{10} -1))[/tex]

[tex]=4000[/tex]×[tex]0.1491[/tex]

[tex]=596.6[/tex]

Hence we can conclude that,$596.6 is the  interest will you earn if you deposit $4000 into an account compounded semi-annually at 2.8% for 5 years.

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Answer:

12+26x=64

Step-by-step explanation:

64-12=52

52/2=26

$26 per pass

equation 12+26x=64

x=2 in this case x is representing the number of passes

12 is the ticket

and 64 is total cost

Answer:

Step-by-step explanation:

Mara has a 50% chance of getting the purple marble and 50% of getting an orange marble, since there's 2 marble; 1 purple and one orange; 1/2 = 50%

So she has a 50% chance of receiving $10 and a 50% chance of receiving the $200.

Step-by-step explanation:

x,y = 0,-15

for another you have to draw Cartesian plane

Answer:

The answer is:- Zero slope

Step-by-step explanation:

Hope it helps you ✌️

Answer:

Step-by-step explanation:

Answer:

7a + 6

Step-by-step explanation:

Expand the brackets and then collect like terms. 4a + 3a = 7a

Answer: B ( sorry if im wrong )

Step-by-step explanation:

if Conner begins lunch at 11:15am then we need to find out what it'll be in +60 minutes, which is . . . 12:15pm

so it's not A, C, E - which now leaves us B and D

( I used a time calculator btw )

the answer is D because B is 25 minutes for recess

Answer:

You add 5 each time so we just need to multiple 5 by 40  since we alredy have the first three terms.

40*5=200

21+200=221

Hope This Helps!!!

Answer:

See below

Step-by-step explanation:

Kinetic energy is basically energy that an object has while it moves. For example, a ball rolling down a hill will have kinetic energy as it rolls, or a bullet shot out of a gun.

Answer:

what are the measurements for 1 and 2?

Step-by-step explanation:

George Washington

Answer:

A

Step-by-step explanation:

You're looking for x-intercepts

From the graph you know that the x-intercepts are as follows:

x = -4, x = -2, x = 4

And this is when y or f(x) = 0

so you can rewrite each x-intercept as an equation

0 = x + 4

0 = x + 2

0 = x - 4

Now you know each of the terms

f(x) = (x-4)(x+2)(x+4)

Answer:

A choice.

Step-by-step explanation:

If you notice, you see the graph having x-intercepts which are x = 4, -2 and -4.

Because the graph passes through x = 4, -2 and -4, we have to find the function that satisfy x-values when f(x) = 0.

Finding x-intercepts, let f(x) = 0.

A choice

f(x) = (x-4)(x+2)(x+4)

Let f(x) = 0 to find x-intercepts.

0 = (x-4)(x+2)(x+4)

Then solve the equation like linear.

Hence, x = 4,-2,-4

Since the x-intercepts are (4,0),(-4,0) and (-2,0), it satisfies the graph and therefore A is correct.

Answer:

D

Step-by-step explanation:

You can infer to the solution of this problem by looking at the choices. Hope this helped :)

The pressure in a fluid flowing with laminar flow through a pipe is given by

Hagen-Poiseuille equation.

The correct responses are;

Reasons:

When the flow is a steady incompressible flow through pipe, the flow rate

can be derived from the Hagen-Poiseuille equation as follows;

[tex]\displaystyle \dot V = \mathbf{\frac{\left[\Delta P - \rho \cdot g \cdot L \cdot sin\left(\theta \right) \right] \cdot \pi \cdot D^4 }{128 \cdot \mu \cdot L}}[/tex]

ΔP = 135 kPa - 88 kPa = 47 kPa

The density of the oil, ρ = 876 kg/m³

μ = 0.24 kg/(m·s)

L = 15 m

The diameter of the pipe, D = 1.5 cm = 0.015 m

(a) When the pipe is horizontal, we have;

θ = 0°

Which gives;

[tex]\displaystyle \dot V = \mathbf{\frac{\left[47 \times 10^3 - 876 \, kg/m^3 \times 9.81 \, m/s^2 \times 15 \, m \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}}[/tex]

[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}[/tex]

[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4 \, Pa \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m} =\frac{0.002379357\cdot \pi}{460.8}[/tex]

[tex]\displaystyle \dot V=\frac{0.002379357\cdot \pi}{460.8} = \mathbf{1.622 \times 10^{-5}}[/tex]

(b) When the pipe is inclined 8°, we have;

[tex]\displaystyle \dot V = \mathbf{\frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(8^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}} = 1.003 \times 10^{-5} \, m^3/s[/tex]

(c) If the pipe is inclined 8° downward from the horizontal, we have;

[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(-8^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m} = 2.24\times 10^{-5} \, m^3/s[/tex]

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Answer:

No, there is no enough flour for each of his friends to get a cupcake

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ This recipe makes 2 dozen cupcakes

∵ Each dozen contain 12 cupcakes

∴ The number of cupcakes can the recipe make = 2  × 12

∴ The number of cupcakes can the recipe make = 30 cupcakes

∵ The recipe calls for 3 cups of flour

→ That means 3 cups of flour can make 30 cupcakes

∴ 3 cups of flour makes 30 cupcakes

∵ Anthony’s mother has only 1 cup of flour

→ By using the ratio method

→  flour  :  cupcake

→  3      :  30

→   1       :   x

→ By using cross multiplication

∵ 3 × x = 1 × 30

∴ 3 x = 30

→ Divide both sides by 3

∴ x = 9

∵ x represents the number of cupcakes  

∴ Anthony’s mother can make 9 cupcakes with 1 cup of flour

∵ Anthony has 12 friends at his daycare

∵ The number of the cupcakes = 9

∴ The number of cupcakes is not enough for each of his friends to

  get a cupcake

Step-by-step explanation:

Answer:

Tony’s birthday his mother is making cupcakes for his friends at his daycare that the recipe calls for 3 1/3 of flour I make 2 1/2 dozen cupcakes.Call me she’ll ask flower two dozen of cupcakes

Step-by-step explanation:

Hey there!

(5 * 6) * 4

= 30 * 4

= 120

So you’re basically looking for something that’s equivalent to 120

CHOICE A.

5 * (5 * 6)

= 5 * 30

= 150

So, Choice A is probably NOT the answer you’re looking for!

CHOICE B.

4 * (5 * 6)

= 4 * 30

= 120

Choice B. is probably the answer you’re probably looking for.

So, I recommend you to color it apricot. :)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

<6 = 158°

Step-by-step explanation:

we know a = 6

22 + a = 180

a = 180 - 22

a = 158

The exponential equation is given by y = 700(2)ˣ

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population of fish after x hours.

Given that he starts with 700 fishes, hence

a = 700

The population of the fish doubles every year, hence:

b = 2

The exponential equation becomes:

y = 700(2)ˣ

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Answer:

x<2

Step-by-step explanation:

You're answer is wrong because the circle on the number line is not closed. If it was closed, it would be x ≤ 2 , but because it is open, it would be just be x<2

Answer:

It will take 5 minutes to make one balloon structure. 7 balloons are used in 1 sculpture For part b the answer would be: Tom's unit rate for balloons used per minute would be 1.4

Step-by-step explanation:

Answer:

158.4

Step-by-step explanation:

Answer:

P = 106

A = 330

Step-by-step explanation:

= 2(l+w) (perimeter of rectangle)

= 2·(18+15)

= 66

picture below of perimeter of right angle triangle

Add both values

P= 66 + 40

P = 106

= w*l (Area of rectangle)

=15·18

= 270

= ab/2 ( Area of triangle )

= 8·15/2

=60

Add both values

A = 60 + 270

A = 330

I hope it helps

[tex]-5+\frac{i}{2i} = -5+\frac{1}{2}=-\frac{9}{2} =-4.5[/tex]

ok done. Thank to me :>

The equations and the number of hotdogs and sodas sold are:  x+ y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.

Two equations can be derived from this question:

2.25x + 1.50y = 225.75 equation 1

x + y = 126 equation 2

Where:

x = number of hotdogs sold

y = number of soda sold

In order to determine the value of y, multiply equation 2 by 2.25

2.25x + 2.25y = 283.50 equation 3

Subtract equation 1 from 3

57.75 = 0.75y

y = 77

Substitute for y in equation 2

x + 77 = 126

x = 49

To learn more about simultaneous equations, please check: brainly.com/question/23589883

Answer:

The correct answer is A) x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

Step-by-step explanation:

you know, a single side cannot be longer than the other 2 sides combined.

otherwise, the triangle cannot "close".

so, it starts with 12 cannot be longer than 5 + n.

therefore, n must be at least 7.

and n cannot be longer than 5+12 = 17

7 and 17 I would normally rule out a well, because in these cases the triangle would just be a flat line, when the 3rd side is as long as the other 2 combined.

so, in reality for a real, visible triangle, the range of valid values is 8 .. 16.

that is 9 positive integer values.

Answer:

Step-by-step explanation: I think it is c