Answers
Answer:
a) f'(x) = 12x
b) -120
c) 36
d) y = 36x -55
Step-by-step explanation:
The derivative is the limit of the average slope on an interval as the interval size approaches zero. The equation for a tangent line is conveniently written in point-slope form when the tangent point and the derivative there are known.
__
a)The derivative is ...
[tex]\displaystyle f'(x)=\lim_{h\to 0}{\dfrac{f(x+h)-f(x)}{h}}=\lim_{h\to 0}\dfrac{(6(x+h)^2-1)-(6x^2-1)}{h}\\\\=\lim_{h\to 0}\dfrac{(6x^2+12xh+6h^2-1)-(6x^2-1)}{h}=\lim_{h\to 0}\dfrac{12xh+6h^2}{h}=\lim_{h\to 0}(12x+6h)\\\\\boxed{f'(x)=12x}[/tex]
__
b)f'(-10) = 12(-10) = -120
__
c)f'(3) = 12(3) = 36
__
d)The point of tangency is ...
(3, f(3)) = (3, 6·3² -1) = (3, 53)
The slope there was found in part (c) to be 36. So, the point-slope equation for the tangent line can be written ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -53 = 36(x -3) . . . . equation of the tangent line at (3, 53)
This equation can be rearranged to slope-intercept form:
y = 36x -55 . . . . . add 53 and simplify
Related Questions
You are asked to find the space occupied by the shape below. Will you calculate its area or volume? A cube shape. area volume
Answers
Answer:
volume
Step-by-step explanation:
the amount of space enclosed by an object or shape, how much 3-dimensional space
If x = 3 (y + w) minus 1 what is the value of w in terms of x and y?
Answers
Answer:
Step-by-step explanation:
Discussion
The object of this is make w by itself on one side of the equation.
Equation
x = 3 (y + w) - 1 Add 1 to both sides of the equation.
x + 1 = 3(y + w) - 1 + 1 Combine
x + 1 = 3(y + w) Remove the Brackets
x + 1 = 3y + 3w Notice y and w are affected by the 3. Subtract 3y
x + 1 - 3y = 3y-3y + 3w Combine
x + 1 = 3w Divide both sides by 3
(x +1)/3 = 3w/3
(x + 1)/3 = w
Answer: (x + 1)/3 = w
A number a is a root of P(x) if and only if the remainder, when dividing the
polynomial by x + a, equals zero.
O A. True
O B. False
Answers is false
Answers
Answer: False
Reason: It should be x-a instead of x+a
how to get the perimeter and area.
Answers
2. Rewrite the expression below using the Associative Property of Multiplication: (ab)c
A. (ba)c
B. c(ab)
C. abc
D. a(bc)
E. All of the above
Answers
As long as the letters are all multiplying each other, the letters can be arranged in any way in accordance with the property
PROOF find the correct statements and reasons to complete the two column proof
Given: B is the midpoint of AC
D is the midpoint of BE
BC = BD
Prove: AC = BE
Answers
Answer: ac bd be 2bd
Step-by-step explanation: addion
Busi has a bag containing 20 balls. There are twice as much yellow balls than blue balls, but yellow balls are only a third of red balls. The green balls are the same number as the blue balls. How many of each of the ball
Answers
Answer:
12 red balls
4 yellow balls
2 blue balls
2 green balls
Step-by-step explanation:
set no. of yellow, blue, red and green ball as y, b, r, g respectively
y=2b
r=3y
g=b
y+b+r+g = 20 (translate all of them into b (smallest in qty)
2b + b + 3(2b) + b = 20
10b = 20
b =2
y = 4, r = 12, b =2, g =2
Which point is between points C and E?
A
B
D
S
Answers
Answer:
it's the 'D' ..............,..
Using negative numbers, what is 4+(-5) ?
Answers
Answer:
-1
Step-by-step explanation:
4+(-5) is basically 4-5 which is -1
Which choices are equivalent to the fraction below? Check all that apply.
6
12
A. 200%
B. 2/4
C. 2
D. 50%
E. 0.33
F. 0.5
Answers
Answer: 0.5 and 2/4
Step-by-step explanation:
How many matchs played in a 5 team round robin
Answers
[tex]\huge[\sum_{k=0}^{4}(k)][/tex] [tex] = 0+1+2+3+4=\boxed{10} [/tex]
=[tex]\huge(\binom {5}{2}) [/tex] [tex] =(5!)/(3! \times 2!) = (5\times 4)/(2)= \boxed{10}[/tex]
Since there are 5 teams..
The number of matches played in a 5 team round Robin is 10.
How does round robin tournament work for 5 teams?A round-robin tournament is a sports competition where each player or team competes against every other player or team; each contestant faces off against the other contestant in turn. A round-robin tournament differs from an elimination tournament in that participants are eliminated after a set number of losses.
From 5 teams we choose 2 to form combinations (need combinations of 2 different teams to play a match).
Here, 5C2 = 5!/2!(5-2)!
= 5×4×3×2!/2!×3!
= 10
Hence, the number of matches played in a 5 team round Robin is 10.
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answer please i need one fast
Answers
hope this helps!
Noah was given an assignment to build a rectangular prism with a volume of at least 32 cubic centimeters. If the area of the base is 4 squared centimeters, which inequality could represents the possible heights?
Answers
Answer:
h ≥ 8 cm
Step-by-step explanation:
Solving :
V ≥ 32 cm³
a = 4 cm²
h ≥ 32/4
h ≥ 8 cm
a combination lock is opened by setting each of five barrels to the correct digit. if digits are randomly chosen from the digits 0 through 9, how many unique combinations can be generated? repetition of numbers is allowed
Answers
Answer:
A. 0.3204
B. 0.59049
Step-by-step explanation:
Data:
The total number of combinations:
= [tex](10)^5=100000[/tex]
A.
The number of ways = [tex]10*9*8*7=30240[/tex]
[tex]\frac{30240}{100000}[/tex]
The probability for an event P taking place = [tex]=0.3024[/tex]
B.
Number of ways to arrange the subjects = [tex](9)^4=59049[/tex]
[tex]\frac{59049}{100000}[/tex]
The probability = [tex]=0.59049[/tex]
When Josiah buys a ticket at the local movie theater, he receives 100 reward points to use toward future purchases. He is offered a scratch-off card instead of the points, which will allow him to try for a higher point value. The three possible point awards on the scratch-off card are 25, 100, and 120. There is an equal number of cards for each point award in the stack he chooses the card from.
Which statement is true?
A
The best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points.
B
The best option is to take the scratch-off card because two of the three possible point values on the card are the same or greater than the 100 points.
C
The best option is to take the scratch-off card because the 120-point value that is on the card is greater than 100 points.
D
The best option is to take the 100 points because the probability of being awarded more than 100 points on the scratch-off card is zero.
Answers
The best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points option (A) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Since, there is an equal number of cards of point 25, 100, and 120
P(x =25) = P(x =100) = P(x =200) = 1/3
x: 25 100 120
P(x): 1/3 1/3 1/3
The expected value is:
E(x) = 25×(1/3) + 100×(1/3) + 125×(1/3)
E(x) = 245/3 < 300/3 = 100
Thus, the best option is to take the 100 points because the expected value of the points from the scratch-off card is less than 100 points option (A) is correct.
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P(S) = 3/5
P(T) = 1/3
If S and T are mutually exclusive events, find P(S or T).
Answers
Answer:
14/15
Step-by-step explanation:
P(S or T) = P(S) + P(T) = 3/5 + 1/3
= 9/15 + 5/15 = 14/15
[tex] \large\frak{ \orange{ Question}}[/tex]
The force of attraction (A) between two objects, whose masses are fixed, varies inversely with the square of their distance of separation (d). The force of attraction between them is 2 units when the dis- tance is 5 cm. What is the distance between the two objects, if the attraction between them is 8 units?
[tex] \pink \dag \: \pink{\large\rm{ No \: spam}}[/tex]
[tex] \red \dag \: \red{\large\rm{ With \: explanation }}[/tex]
Answers
Answer:
[tex]\boxed{\sf distance \: between \: the \: objects \: \: is \: 2.5 \: cm}[/tex]
Step-by-step explanation:
According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to
the product of their masses, given by standard formula.
[tex]A = G \cdot \frac{m_1.m_2}{ {d}^{2} } [/tex]
where A,d & G are force of attraction, distance of separation & proportionality constant respectively.
Given:
A1 = 2 units
d1= 5 cm
A2 = 8 units
To find:
Distance of separation when the force of attraction is 8 units d2 = ?
Solution:
Substituting the given values in above at each point,
[tex]A_1 = G \cdot \frac{m_1.m_2}{ {d_1}^{2} } \\ 2 = G \cdot \frac{m_1.m_2}{ {5}^{2} } \\ \sf similarly \: at \: second \: point \: of \: attraction \\ A_2 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ 8 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ \sf \: \: dividing \: both \: of \: the \: equation \\ \frac{2}{8} = \frac{G \cdot \frac{m_1.m_2}{ {5}^{2} }}{G \cdot \frac{m_1.m_2}{ {d_2}^{2} } } \\ \sf \: G \: m_1 and \: m_2 \: are \: \: constant \: hence \\ \sf they \: can \: be \: cancelled \: out \\ \frac{2}{8} = \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } } \\ \sf rearranging \: above \: equation \\ \frac{1}{4} = \frac{{d_2}^{2} }{ {5}^{2} } \\ {d_2}^{2} = \frac{ {5}^{2} }{4 } \\ {d_2}^{2} = \frac{25}{4} \\ {d_2}^{2} = 6.25 \\ \sqrt{{d_2}^{2} } = \sqrt{6.25} \\ \boxed{ \sf{d_2} = 2.5 \: cm}[/tex]
Answer: the distance between the two objects is 2.5 cm, if the attraction between them is 8 units.
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PLS ANSWER ITS FOR 20 POINTS!!!
The information in the table is displayed in the two graphs below.
If an employee wants to request a raise, which graph should that employee use to support his or her case?
Answers
A graph is a way to represent a lot of data in such a visual format. The correct option is C, he/she should use graph B.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
If an employee wants to request a raise, the graph he/she should use to support his or her case is graph B. Because that graph is showing all thought the company is earning good profit the salary of the employees is still reducing.
Hence, the correct option is C, he/she should use graph B.
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What is the value of n in the equation ?Solve the equation.
–9x + 1 = –x + 17
Answers
Answer:
-2
Step-by-step explanation:
→ -9x + 1 = -x + 17
→ -9x + x = 17 - 1
→ -8x = 16
→ x = -16/8
→ [ x = -2 ]
What are the zeros of the quadratic function f(x) = 6x- + 12x-7?
Answers
Answer:
Number 1
Step-by-step explanation:
Vertex is (−1,−13)
[tex]~~~~~6x^2 +12x -7 =0\\\\\implies x^2 +2x - \dfrac 76=0\\\\\implies x^2+2x = \dfrac76\\\\\implies x^2 +2x +1 = \dfrac 76 +1\\\\\implies (x+1)^2 = \dfrac{13}6\\\\\implies x+1 = \pm \sqrt{ \dfrac{13}6}\\\\\implies x = -1 \pm\sqrt{\dfrac{13} 6}\\\\\text{Hence,}~ x = -1 +\sqrt{\dfrac{13} 6}~~ \text{and}~~ x = -1-\sqrt{\dfrac{13} 6}[/tex]
( 9 × 10 2 ) + ( 7 × 10 3 )
Answers
Answer:
2/5 or 0.4
Step-by-step explanation: i'm smart
Let f(x)=x^2+4x+3 for what values of x will satisfy the equation f(x)=8
Answers
Explanation: If you plug in either 1 or -1 into the equation, it will satisfy the equation f(x) = 8.
A company is started by four friends. The company was Erica’s idea, so she wants to fill 70% of the orders. Jen, Heather, and Tonya each agree to fill 10% of the orders. After a successful first year, Erica wants to determine if the distribution of the number of orders filled is adhering to the agreed-upon percentages. She decides to test:
To do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. She finds that Erica filled 56 orders, Jen filled 18, Heather filled 14, and Tonya filled 12. The chi-square test statistic for goodness of fit is χ2 = 11.20 and the P-value is between 0.01 and 0.02.
Because the P-value is less than 0.05, Erica rejects the null hypothesis. Because the null hypothesis is rejected, she would like to know which term contributed the significance of the test. Complete a follow-up analysis. Which term contributed the most to the significance of this test? Were there more or fewer orders being filled by this person than expected?
Erica, more than expected
Erica, fewer than expected
Jen, more than expected
Jen, fewer than expected
Answers
The appropriate hypotheses for this test are
Erica filled 70
Jen filled 10
Heather filled 10
Tonya filled 10
A company is started by four friends.
The company was Erica’s idea,
So she wants to fill 70% of the orders. Jen, Heather, and Tonya each agree to fill 10% of the orders.
What is the meaning of the hypothesis?A hypothesis is a statement that proposes a result that will be tested to get a verified result.
A hypothesis is not hundred percent true, that is why it is always put to test.
The hypothesis is singular while the hypothesis is plural.
Making a hypothesis in this case is an attempt to predict an answer or result that will be verified by doing the experiment.
We can conclude by saying that a hypothesis is not hundred percent true.
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a local pizzaria offers 15 toppings for their pizzas you can choose any 4 of them for a fixed price how many different types of pizzas can you order with 4 toppings
Answers
Since we can choose 4 of the 15 toppings, we can order 1365 different types of pizzas with 4 toppings
Since the question says 'choose', it is a combination question and order is not important.
What is combination?This is the number of ways in which x objects can be selected from n objects.
It is given mathematically as ⁿCₓ = n!/[r!(n - r)!]
Number of different types of pizzasNow given that we have 15 toppings for pizza and we want to choose any 4, So, we are choosing 15 toppings in 4 ways. So,
n = 15 and r = 4So, ¹⁵C₄ = 15!/4!(15 - 4)!
= 15!/4!11!
= 15 × 14 × 13 × 12 × 11!/4!11!
= 15 × 14 × 13 × 12/24
= 15 × 7 × 13
= 1365 ways
So, we can order 1365 different types of pizzas with 4 toppings
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Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a 20-foot chimney in 1Five-sevenths hours. If it takes Kalon 4 hours to clean a 20-foot chimney by himself, how long does it take Marna to clean the same size chimney by herself?
Rate
(Chimneys per Hour)
Time
(Hours)
Fraction Completed
Kalon
One-fourth
1 and five-sevenths
Three-sevenths
Marna
x
1 and five-sevenths
StartFraction 12 x Over 7 EndFraction
3 hours
4 hours
5 hours
6 and six-sevenths hours
Answers
Answer:
3 hrs
Step-by-step explanation:
slope (12,-7) and (4,5)
Answers
[tex](\stackrel{x_1}{12}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{12}}}\implies \cfrac{5+7}{-8}\implies \cfrac{12}{-8}\implies -\cfrac{3}{2}[/tex]
Last year direct marketing had $122,222 in sales. This year direct marketing's sales are down by 9%. What are direct marketings sales this year
Answers
First, i will multiply 122,222 x 0.09 which is equal to 10,999.98 Then, i will subtract 10,999.98 from 122,222 which is equal to 111,222.02. so the direct marketing sales this year are 111,222.02.
Annie's rectangular garden is 5 feet long and 3 feet wide. What is the area of her garden?
Answers
Explanation: area is length multiplied by width.
we know that
the dimensions of the first garden are------> 5 ft x 3 ft
perimeter first garden=2*[5+3]-----> 16 ft
the dimensions of the second garden are---> (5*2) ft x (3*2) ft
10 ft x 6 ft
perimeter second garden=2*[10+6]-----> 32 ft
so
The answer is
32
if a rhombus has an area of 264 square units. If DB=12 units, find AC
Answers
Using the formula for calculating the area of a rhombus, the length of /AC/ is 44 units
Calculating the area of a RhombusFrom the question, we are to determine the length of AC
The area of a rhombus is given by
[tex]A = \frac{pq}{2}[/tex]
Where A is the area
p and q are the diagonals
Then, for the given diagram,
[tex]A = \frac{/DB/ \times /AC/}{2}[/tex]
From the given information,
A = 264 square units
/DB/ = 12 units
∴ [tex]264 = \frac{12\times /AC/}{2}[/tex]
[tex]264 = 6\times /AC/[/tex]
[tex]/AC/ = \frac{264}{6}[/tex]
/AC/ = 44 units
Hence, the length of /AC/ is 44 units
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Please show your work! I'll give you brainliest as well lol, thanks!
Answers
To know the area of a regular hexagon:
⇒ must know the formula:
[tex]Area = \frac{3\sqrt{3} }{2} s^2[/tex]
s: length of the sideConsider the information given:
Length of side ⇒ 5 cmLet's solve:
[tex]Area=\frac{3\sqrt{3} }{2} (5)^2=64.95cm^2[/tex]
Answer: 65.0 cm²
Hope that helps!
Answer:
64.1 cm²
Step-by-step explanation:
Central Angle = 360 °
∴ ∠AOB = 360 ° / 12
⇒ Tan 30° = AB/ 4 · 3
⇒ AB = 4.3 tan 30°
∴ (ΔAOB) = 1/2 × AB × OB
= 1/2 × 4.3 tan 30° × 4.3
= 5.34 cm
∴ Area of regular hexagon = 12 (a⊃(ΔAOB))
= 12 (5.34 cm²)
= 64.1 cm²