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.)
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
Interval Slope of secant lines
[1,2] 113.000
[1, 1.5] 75.000
[1, 1.1 ] 51.960
[1, 1.01] 47.482
[1, 1.001] 47.048
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = 16x^3 -x[/tex]
Now considering the intervals
For [1, 2]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(2) - f(1)}{2-1} = \frac{16(2)^3 - 2 - [16(1)^3 -1] }{2-1 } = 113.000[/tex]
For [1, 1.5]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.5) - f(1)}{1.5-1} = \frac{16(1.5)^3 - 1.5 - [16(1)^3 -1] }{1.5-1 } = 75.000[/tex]
For [1, 1.1]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.1) - f(1)}{1.1-1} = \frac{16(1.1)^3 - 1.1 - [16(1)^3 -1] }{1.1-1 } = 51.960[/tex]
For [1, 1.01]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.01) - f(1)}{1.01-1} = \frac{16(1.01)^3 - 1.01 - [16(1)^3 -1] }{1.01-1 } =47.482[/tex]
For [1, 1.001]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.001) - f(1)}{1.001-1} = \frac{16(1.01)^3 - 1.001 - [16(1)^3 -1] }{1.001-1 } =47.048[/tex]
Related Questions
show that the sequence with sum of the first n term sn=3n²+5n is an arithmetic sequence.
Answers
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.
у
is 100% more than x.
Circle the ratio
x : y
Answers
Answer:
1:2
Step-by-step explanation:
If John has drank three drinks per day how many will he have drank in 3 day's?
Answers
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
The table shows the relationship between the number of Calories Jacob burns while roller skating and the number of minutes he roller skates,
Minutes Calories Burned
40
200
80
400
120
600
160
800
How many calories will Jacob burn in 1 minute while roller-skating? Enter the answer in the box.
Answers
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.
Solve 7x-3+3x=4(4x-1)-5
Answers
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.
How many thousands are in 655,000
Answers
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!
A coin flipped 10 times and the results is recorded. What is the probability of getting at least 8 tails ?
Answers
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
A figure was created using a triangle and a semicircle. Use the ruler provided to measure the dimensions of the triangle and the semicircle to the nearest centimeter.
Which measurement is closest to the area of the figure in square centimeters?
A.
78 cm2
B.
81 cm2
C.
106 cm2
D.
53 cm2
Answers
Answer: D
Step-by-step explanation:
Find the area of the triangle with vertices: Q(-5,5,-3), R(-6,8,-4), S(-8,2,-4).
Answers
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
suppose that: (x-(x-y))-((x-y)-x)=14 what is x
Answers
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.
PLEASE HELP I WILL MARK YOU BRAINLIEST
A bread company makes 4 types of bread. A restaurant chain ordered 612 loaves of each kind of bread. How many loaves of bread in total did the restaurant chain order?
Mr. Ecker had $72 that he evenly split amongst his four children for their allowance. He then gave his eldest daughter an extra $5. How much money did Mr. Ecker’s eldest daughter get?
Answers
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
4 types of bread
612 loaves each kind
4 x 612 = 2448 loaves
3x - three other kids
x+ 5 - daughter
$72 - money
4x=72
4x/4 = 72/4
x= 18
x+5 = 23
He gave $23 to his daughter
9x+3x-10=3(3x+x) identity or solution
Answers
There is no solution. The output of this equation is equal to -10 = 0 which is obviously not true.
HELP ME!!
The square of the sum of seven times a number and
seven
Answers
7(n+7)^2
seven times the number and seven squared
A poll of 72 seniors, taken three weeks before the selection of the school Homecoming Queen, identified 60 who planned to vote for Jenny Wonderful. Unfortunately, a week after the poll was taken, the school newspaper ran an article that quoted Jenny slandering her opponents. Another poll of 80 seniors taken shortly after the article appeared showed that 56 planned to vote for Jenny.
Required:
Does this indicate a significant drop in support for Jenny?
Answers
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.
Determine the interval on which this function is constant. (1 point)
Answers
(-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.
Define Constant function.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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Which number completes the series: 1, 3, 6, 10, 15, ???
Answers
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!
The distance around a yard is 588ft. If the length of the yard is 2 more than 3 times the width, find the perimeter and width of the yard
Answers
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!
Determine how many solutions the equation has. If one solution, state the value of x.
x + 6 + 8 = 2x – x + 14
Group of answer choices
No Solution
One Solution, x=0
Infinite Many Solutions
One Solution, x=14
Answers
Answer:
x + 6 + 8 = 2x – x + 14 = True
Step-by-step explanation:
(all values of x are solutions)
Find the remaining trigonometric ratios. tan(α) = 2, 0<α<π/2the responses they want are:1. sine(α)=_2. cos(α)=_3. cot(α)=_4. sec(α)=_5. csc(α)=_
Answers
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
The price of jeans was reduced $15 per week for 6 weeks by how much did the price of the jeans change over the 6 weeks
Answers
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
-ayuda ¡¡¡ Se tiene previsto implantar un proyecto de "Caucho sintético" cuya inversión sería de S/ 2 500 000, para un tamaño de planta de 12 000 toneladas anuales. Luego de estudiar el proyecto, los promotores estiman que es más conveniente un tamaño de 19 200 toneladas por año. ¿A cuánto ascenderá la inversión total, si el exponente del factor de escala es α=0,63? ayuda !!!!!
Answers
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.
Alan owes $412.42 on his credit card. He returns two items, one for $48.38 and the other for $49.57. Then
he makes purchases of $34.10 and $37.06. What is the new balance on the card?
Answers
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.
Convert 2.38 km to dm.
Answers
Answer:
Step-by-step explanation:
2.38 km x 10^4 = 23,800 decimeters
Need help I don’t understand
Answers
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.
what value of x makes the equation 7x-2(3x+1)=4x-(3-x)-19 true?
Answers
Answer:
X=5
Step-by-step explanation:
Given the function k(t)=2t−1: a. Evaluate k(2). b. Solve(k)=7.
Answers
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]
Ten people ordered calculators. The least expensive was $29.95 and the most expensive was $89.95. Half of them ordered a $69.95 calculator. Select the best
estimate of the amount spent on calculators.
$490
$660
$550
$805
Choose the best estimate for the total amount spent for all 10 calculators.
O A. $805
OB. $490
OC. $550
OD. $660
Answers
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.
What is Mean?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,
Least expensive A=30Most expensive B=90half of order C=70Now, 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:
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0.95 bar as a simplified fraction
Answers
Answer:
95/99
Step-by-step explanation:
khan
Help me with this one too
Answers
Answer:
2 + 8 -7 = 3
Hope it helps.......
Congruent squares of length x are cut from the corners of an 8 inch by 12 inch piece of cardboard to create a box without a lid What is the... -Height of the box -Length of the box -Width of the box Write the function v(x) for the volumn of the box in terms of x. Leave in factored form.
Answers
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)