For the function f(x) = 16x^3 - x, make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at x = 1. Complete the table. (Round the final answer to three decimal places as needed. Round all intermediate values to four decimal places as needed.) An accurate conjecture for the slope of the tangent line at x = 1 is (Round to the nearest integer as needed.)

Answer:

1. sinα = +2√5/5 2.  cosα = +√5/5 3. cotα = +1/2 4. secα = +√5 5. cosecα = +√5/2.

Step-by-step explanation:

1. Since tan(α) = 2 and 1 + cot²α = cosec²α

1 + 1/tan²α = 1/sin²α

1 + 1/2² = 1/sin²α

1 + 1/4 = 1/sin²α

5/4 = 1/sin²α

sinα = ±√(4/5)

sinα = ±2/√5

sinα = ±2√5/5

Since 0<α<π/2, sinα = +2√5/5

2. sin²α + cos²α = 1

(2/√5)² + cos²α = 1

4/5 + cos²α = 1

cos²α = 1 - 4/5

cos²α = 1/5

cosα = ±1/√5

cosα = ±√5/5

Since 0<α<π/2, cosα = +√5/5

3. cotα = 1/tanα = 1/2

Since 0<α<π/2, cotα = +1/2

4. secα = 1/cosα = 1/±1/√5 = ±√5

Since 0<α<π/2, secα = +√5

5. cosecα = 1/sinα = 1/±2/√5 = ±√5/2

Since 0<α<π/2, cosecα = +√5/2

Answer:

3.16 square units

Step-by-step explanation:

Find the area of the triangle with vertices: Q(-5,5,-3), R(-6,8,-4), S(-8,2,-4).

Step 1

We find QR and QS

QR = R - Q

= R(-6,8,-4) - Q(-5,5,-3)

= (-1, 3, -1)

QS = S - Q

= S(-8,2,-4) - Q(-5,5,-3)

= (-3, -3, -1)

Step 2

QR × QS

(-1, 3, -1) × (-3, -3, -1)

Using the formula:

a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k

Where a = (a1, a2, a3)

b = (b1, b2, b3)

QR = a

QS = b

(-1, 3, -1) × (-3, -3, -1)

a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k

= ((3 × -1) – (-1×-3))i + ((-1)×-3) – (-1) × -1)j + (-1 × -3) – (3×-3)k

= (-3 - 3)i + (3 – 1)j + (3 – 9)k

= 0i + 2j - 6k = (0,2,-6)

QR × QS = (0,2,-6)

Area of the triangle = √0² + 2² + 6²/ 2

= √0 + 4 + 36/2

= √40/2

= 6.324555320336759 /2

3.1622776602 square units

Approximately = 3.16 square units

Answer: D

Step-by-step explanation:

Answer:

Perimeter = 588ft (given), Width of yard = 73ft

Step-by-step explanation:

The distance around a yard is the perimeter of the yard, so we know that the perimeter of the yard is 588ft. In order to find the length and width, we need to make an equation so we can solve for one of them. Since the length is 2 more than 3 times the width, we can represent it as 3w+2, where w is the width. This ensures we only have one unknown to solve for as we only have one equation. Since perimeter is the distance around the yard, it is calculated by adding the length of the 2 widths to the length of the 2 lengths, hence 588ft = 2w + 2l, the l we replace though as we can only solve for one unknown, so now we have:

2w + 2(3w+2) = 588

Now we can start solving for the width!

Firstly we need to expand the bracket which we do by multiplying the 2 by all the contents inside the bracket, so:

2w + 2*3w + 2*2 = 588

which equals:

2w +6w +4 = 588

Now we combine terms and move the 4 to the other side so we can solve for w:

8w + 4 -4 = 588 - 4

8w = 584

Now we just divide both sides by 8 to get:

w=73

The width of the yard is 73ft.

Hope this helped!

Answer:

x + 6 + 8 = 2x – x + 14 = True

Step-by-step explanation:

(all values of x are solutions)

7(n+7)^2

seven times the number and seven squared

Answer:

he now owes $385.63

Step-by-step explanation:

owes $412.42

returns an item for $48.38

-412.42 + 48.38 = -364.04

he now owes $364.04

returns an item for $49.57

-364.04 + 49.57 = -314.47

he now owes $314.47

makes a purchase of $34.10

-314.47 - 34.10 = -348.57

he now owes $348.57

makes a purchase of $37.06

-348.57 - 37.06 = -385.63

he now owes $385.63

Answer:

Nah you wrong

Step-by-step explanation:

You have got

to start thinking bee, my friend.

- Thinking bee!

- Me?

Hold it. Let's just stop

for a second. Hold it.

I'm sorry. I'm sorry, everyone.

Oan we stop here?

I'm not making a major life decision

during a production number!

All right. Take ten, everybody.

Wrap it up, guys.

Answer:

[tex]k(2) = 3[/tex]

[tex]t = 4[/tex]

Step-by-step explanation:

Given

[tex]k(t) = 2t - 1[/tex]

Solving (1): k(2)

Take t as 2 such that t = 2

This gives

[tex]k(2) = 2 * 2 - 1[/tex]

[tex]k(2) = 4 - 1[/tex]

[tex]k(2) = 3[/tex]

Solving (2): k(t) = 7

Substitute 7 for k(t)

[tex]7 = 2t - 1[/tex]

Add 1 to both sides

[tex]7 + 1 = 2t - 1 + 1[/tex]

[tex]2t = 8[/tex]

Divide both sides by 2

[tex]t = \frac{8}{2}[/tex]

[tex]t = 4[/tex]

Answer:

En caso de un tamaño de producción de 19,200 toneladas anuales, el costo de inversión total ascenderá a $3,999,936.

Step-by-step explanation:

Dado que la inversión inicial será de $ 2,500,000 para un tamaño de planta de 12,000 toneladas anuales, se estima que cada tonelada requiere una inversión de $208.33 (2,500,000 / 12,000).

Por lo tanto, en caso de una producción anual de 19,200 toneladas, el costo de inversión aumentará según lo establecido en la siguiente multiplicación:

208.33 x 19,200 = X

3,999,936 = X

Por lo tanto, en caso de un tamaño de producción de 19,200 toneladas anuales, el costo de inversión total ascenderá a $3,999,936.

Answer:

21

best of luck!

Answer:

21

Step-by-step explanation:

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

15 + 6 = 21

Hope it helps

Mark it as Brainliest!

Answer:

1. The height if the box is x.

2. The length of the box is 8 - 2x

3. The width of the box is 12 - 2x

4. The volume of the box is   4x(6 - x)(4 - x)

Step-by-step explanation:

1. Since the squares of length x are cut from the corners of the cardboard, the height of the box is the length of a square which is x.

2. Since we have 8 inch by 12 inch, its length is 8 inches and its width 12 inches.

Since squares of x length are cut from the corners of the cardboard, the length of the box is 8 - 2x

3. Since we have 8 inch by 12 inch, its length is 8 inches and its width 12 inches.

Since squares of x length are cut from the corners of the cardboard, the width of the box is 12 - 2x

4. The volume of the box is V(x) = length × width × height = (12 - 2x)(8 - 2x)x = 2 × 2x(6 - x)(4 - x) =  4x(6 - x)(4 - x)

Answer:

see below

Step-by-step explanation:

(2 · x) · 6 = 2 · (x · 6) → Associative property of multiplication, this property states that (a · b) · c = a · (b · c), basically, it doesn't matter what order you multiply in, the result will always be the same.

3(3x + 2) = 9x + 6 → Distributive Property, this property states that a(b + c) = a · b + a · c.

(7 + 1) + 5 = 5 + (7 + 1) → Commutative property of addition, this property states that a + b = b + a which means that you can "flip" or "switch the positions of" the quantities being added and you will still get the same result.

(7 · x · 3) = (7 · 3 · x) → Commutative property of multiplication, just like the commutative property of addition, this states a · b = b · a, in other words, you can "flip" or "switch the positions of" the quantities being multiplied and you will get the same result.

(9 + 2) + 3 = 9 + (2 + 3) → Associative property of addition, just like the associative property of multiplication, this property states that (a + b) + c = a + (b + c), in other words, it does not matter which order you add in, the result will always be the same.

Step-by-step explanation:

1. 7 (-6)=42

after 7 weeks the price will be reduced by 7 time

the price will be reduced $42

There is no solution. The output of this equation is equal to -10 = 0 which is obviously not true.

Answer:

X=5

Step-by-step explanation:

Answer:

1. 2448 do 612x4

2.she got $23 because he has four children and splits all do 72 divide by 4 and add 5 and thats ur answer

hope this helped

Answer:

95/99

Step-by-step explanation:

khan

Answer:

1:2

Step-by-step explanation:

Answer:

x = 0.

Step-by-step explanation:

(x-(x-y))-((x-y)-x)=14

Remove the parentheses from the inside out:

(x - x + y) - (x - y - x) = 14

x - x + y - x + y + x = 14

x - x - x + x + 2y = 14

0 + 2y = 14

x = 0 and y = 7.

Answer:

The formula says that the sum of the first n terms of our arithmetic sequence is equal to n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.

Answer:

Step-by-step explanation:

2.38 km x 10^4 = 23,800 decimeters

Answer:

310

Step-by-step explanation:

least money 19.95

Most money = 39.95

Mean = (least+most)/2 = 29.95

money for half people = 5 × (mean) 29.95

Amount of money for half people = 149.75

Lower limit for amount of the other half = 19.95 × 5 = 99.75

The Upper limit for the amount of the other half = 39.95 × 5 = 199.75

Mean = (99.75 + 199.75)/2 = 149.75

Total money spent (Mean) = 149.75 + 149.75 = 299.5

The Best estimate is B) 310 because it is closest to 295.5

A mean is an arithmetic average of a set of observations. The correct option is D.

A mean is an arithmetic average of a set of observations. It is given by the formula,

Mean = (Sum of observations)/Number of observations

To make the calculations easy let's round off the given numbers. Therefore, we can write the values as,

Now, the mean and the money for half the people can be written as,

Mean = (least + most)/2 = 60

money for half people = 5 × 60

Therefore, the amount of money for half people will be,

Amount of money for half people = 300

Lower limit for amount of the other half = 29.95 × 5 = 149.5

The Upper limit for the amount of the other half = 89.95 × 5 = 449.75

Mean = (149.75 + 449.75)/2 = 299.6

Total money spent (Mean) = 299.6 + 299.6 = 599.25

Hence, The Best estimate is $660. This is because it is closest to 599.25.

Learn more about Mean here:

https://brainly.com/question/15397049

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Answer:

Yes

Step-by-step explanation:

Initially it is provided that out of a total of 72 people 60 planned to vote for Jenny. This ratio as percentage shall be = [tex]\frac{60}{72} \times 100[/tex] = 83.33%

Later on the number of seniors polling in the survey increased to 80.

Now, out of 80 seniors, 56 planned to vote for Jenny.

In the percentage form this shall be

[tex]\frac{56}{80} \times 100 =[/tex] 70%

Thus, there is a change of 83.33% - 70% = 13.33%

This shall be considered a significant drop as it is more than 10% in an audience size of less than 100.

Answer: 9

do the 3 times table

Step-by-step explanation: if 3 in 1 than 9 in 3

hoped this helped let me know if it did

Answer: 5 calories

Step-by-step explanation:

Given the data:

Minute ____calorie burned

40__________200

80__________400

120_________ 600

160_________ 800

We need to find the rate at which calorie is burned :

Rate of burn = (Number of calorie burned/ time taken)

Take any of the points :

Time = 80 ; calorie burned = 400

Rate of burn = (400 calorie / 80 minute )

Rate of burn = 5calorie/minute

If time = 1 minute ; rate = 5

Calorie burned in 1 minute :

Amount of calorie = rate of burn × time taken

Amount burned in 1 minute = 5 × 1 = 5 calories

Hence, amount of calorie burned in one minute is 5 calories.

Answer:

5

Step-by-step explanation:

Maps Testing I have done it.

(-2,2)

Just took the quiz, this is 100% correct.

Please mark brainliest! :)

The constant function is - f(x) = -2 in the interval  x ∈ [-2, 4].

We have a graph of a function f(x).

We have to determine the interval on which this function is constant.

A constant function is a function having the same value of range for different values of the domain. Mathematically -

y = f(x) = k     [ k is constant ]

According to the question, we can see from the graph that -

The value of f(x) is constant, and is equal to f(x) = -2 between the points -2 and 4 on the x - axis.

The function in this interval can be given by -

f(x) = -2          where  x ∈ [-2, 4].

Hence, the constant function is - f(x) = -2 in the interval  x ∈ [-2, 4].

To learn more about constant functions, visit the link below-

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Answer:

2 + 8 -7 = 3

Hope it helps.......

Answer:

x=1

Step-by-step explanation:

Answer:

6=6x (x=1)

Step-by-step explanation:

7x-3+3x=4 (4x-1)-5

7x-3+3x=16x-4-2

So I have just multiplied out the brackets on the right side 4×4x and 4×1.

7x+3x=16x-4-2

Here I have just added the -3 from the left onto the right changing it to a positive and onto the -5 therefore getting -2.

10x=16x-3

Now I just added the numbers together on each side like 7x+3x and -4-2.

10x+6=16x

This is just moving the -6 onto the left side so we get a positive 6.

6=6x

I have simply done 16-10.

Answer:

55

Step-by-step explanation:

655,000 has 55 thousands. Hope this helps

There are 55 thousands in 655,000.

There are 6 hundred thousands, and 55 thousands. Hope this helps!

Answer: 0.0546875

Step-by-step explanation:

The number of times the coin landing head 8 out of 10 is simply:

C(10, 8)/2^10. At least 8 means, 8 or more. Since the events here are dependent on themselves the answer would be:

[ C(10, 8) + C(10, 9) + C(10, 10) ] / 2^10 = 56/1024 = 0.0546875