Please Help - Suppose f(t)=6t−8−−−−√.
(a) Find the derivative of f.
f′(t) =
-3/(sqrt(t-8)(t-8))
(b) Find an equation for the tangent line to the graph of y=f(t) at the point (t,y)=(33,6/5).
Tangent line: y =
Answers
[tex](a)\\\\\\\text{Given that,}~~\\\\ f(t) =\dfrac 6{\sqrt{t-8}}\\\\\\\\\implies f'(t) = 6\left[\dfrac{\left(\sqrt{t-8}\right) \cdot 0 - \dfrac 1{2\sqrt{t-8 }}}{\left(\sqrt{t-8}\right)^2}\right]\\\\\\\\\implies f'(t) = -6\left(\dfrac {\dfrac 1{2\sqrt{t-8}}}{t-8}\right)\\\\\\\implies f'(t) = -6\left(\dfrac{1}{2\sqrt{t-8} (t-8)}\right)\\\\\\\implies f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}[/tex]
(b)
[tex]\text{Given that,}\\\\y=f(t)\\\\\text{Slope of y,} ~~ f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}\\\\\text{At point (33, 6/5)}\\\\\\f'(t) = -\dfrac 3{(33-8)^{\tfrac 32}} = - \dfrac 3{ (25)^{ \tfrac 32}} = - \dfrac 3{5^3} = -\dfrac 3{125}\\\\\\\text{Equation with given points,}\\\\y - \dfrac 65 = -\dfrac 3{125} ( t - 33)\\\\\\\implies y =-\dfrac 3{125} t +\dfrac{99}{125} + \dfrac 65\\\\\\\implies y = -\dfrac 3{125} t +\dfrac{249}{125}[/tex]
Related Questions
A circle P is circumscribed about a regular hexagon ABCDEF
If segment AE is drawn, triangle AEF is a/n ____________ triangle. Select one:
a. isosceles
b. scalene
c. equilateral
d. right
i’ll mark u as brainliest:))
Answers
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Answer:
a. isosceles
Step-by-step explanation:
Segments EF and FA of the hexagon are the same length, so the triangle is an isosceles triangle.
Find hypotenuse,perpendicular and base
Answers
Answer:
Hypotenuse = XY = 17 cm
Base = YZ = 15 cm
Perpendicular = XZ = 8 cm
Mr. E bought 3 drinks and 5 sandwiches for $25.05 and Mr. E bought 4 drinks and 2 sandwiches $13.80. how much does each drink cost?
Answers
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Answer:
drink: $1.35sandwich: $4.20Step-by-step explanation:
Let d and s represent the cost of a drink and a sandwich, respectively. The two purchases give rise to the equations ...
3d +5s = 25.05
4d +2s = 13.80
Dividing the second equation by 2 gives ...
2d + s = 6.90
Subtracting the first equation from 5 times this, we get ...
5(2d +s) -(3d +5s) = 5(6.90) -25.05
7d = 34.50 -25.05 = 9.45
d = 1.35
The cost of each drink is $1.35.
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Additional comment
Using the simplified 2nd equation, we can find the cost of a sandwich.
s = 6.90 -2d = 6.90 -2.70 = 4.20
The cost of each sandwich is $4.20.
The prices of paperbacks sold at a used bookstore are approximately Normally distributed, with a mean of $7.85 and a standard deviation of $1.25.
Use the z-table to answer the question.
If the probability that Joel randomly selects a book in the D dollars or less range is 56%, what is the value of D?
$4.46
$7.75
$8.04
$8.10
(C) 8.04
Answers
Answer:
The answer you want is indeed, (C).
8.04
ED2021
Answer:
C) 8.04
Step-by-step explanation:
edge 2023
Can someone help me find the answer?
Answers
Answer:
a. x = 3/a
Step-by-step explanation:
Add all like terms on left hand side of the equation:
5 ax + 3 ax => 8 ax
Bring like term 4ax on left hand side
8ax - 4ax
=> 4ax
Therefore we get 4ax = 12
ax = 12/4
ax = 3
x = 3/a
There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?
Answers
Answer:
60
Step-by-step explanation:
To begin, we can look at combinations and permutations. A permutation or combination is when we need to find how many possibilities there are to choose a certain amount of objects (in this case, candidates) given an array of options (members on the board)
Combinations are when the order doesn't matter, and permutations are when the order does matter. Here, we know that we care whether someone is chairperson or secretary. If we were to just choose three for an "elite" board, and there were no specific positions in the board, then order would not matter. However, because it does matter which person gets which role, order does matter.
Assuming that someone cannot have more than one role, we know that this is a permutation without repetition. The formula for this is
(n!) / (n-r)!, where we have to choose from n number of people and choose r number of people. We have 5 members to choose from, and 3 people to choose, making our equation
(5!) / (5-3)! = 120 / 2! = 120/2 = 60
Triangles ABC and DEF are similar. Find the
perimeter of triangle DEF.
a. 34.7 cm
b. 25.3 cm
c. 15 cm
d. 38 cm
Please show work to help me understand.
Answers
If Both triangles are similar the ratio of sides will be same
[tex]\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}[/tex]
[tex]\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}[/tex]
[tex]\\ \sf\longmapsto 8DF=120[/tex]
[tex]\\ \sf\longmapsto DF=\dfrac{120}{8}[/tex]
[tex]\\ \sf\longmapsto DF=15cm[/tex]
Now
[tex]\\ \sf\longmapsto Perimeter=DF+DE+EF[/tex]
[tex]\\ \sf\longmapsto Perimeter=15+11+12[/tex]
[tex]\\ \sf\longmapsto Perimeter=38cm[/tex]
Solve 3(5x + 7) = 9x + 39.
O A. X=-3
B. X= -10
O c. x = 10
O D. x= 3
Answers
Answer:
x=3
Step-by-step explanation:
3(5x + 7) = 9x + 39
15x + 21 = 9x + 39
15x - 9x = 39 - 21
6x = 18
x = 3
In a die game, you roll a standard 6-sided die twice. If the second number rolled is the same as the first number rolled, you win $25. Otherwise, you lose $2. If you were to play the game 100 times, how much money can you expect to make
Answers
Answer:
You can expect to make $250.
Step-by-step explanation:
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Probability of the second number rolled being the same as the first number rolled:
6 outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
Out of 36, thus:
[tex]p = \frac{6}{36} = \frac{1}{6}[/tex]
Expected value of 1 game:
1/6 probability of earning $25.
5/6 probability of losing $2.
Thus:
[tex]E = 25\frac{1}{6} - 2\frac{5}{6} = \frac{25 - 10}{6} = 2.5[/tex]
100 games:
100*2.5 = 250
You can expect to make $250.
Find the slope of the line (4,0) (9,11) Help plsss!!!!
Answers
Answer:
m= 11/5 (11 over 5)
Hope this helps! :)
The population of a town is decreasing exponentially according to the formula
P = 7,285(0.97)t, where t is measured in years from the present date. Find the population in 2 years, 9 months. (Round your answer to the nearest whole number.)
Answers
Answer: 6669
Step-by-step explanation:
I hope I did this right... anyways,
t, is represented by years, which is given to us by 2 years and 9 months. Assuming you would put 2.9 for t.
Additionally, as you can't have a decimal for a person, and they've asked for it to be rounded to the nearest whole number, there would be 6669 people in 2 years and 9 months.
The formula used is:
[tex]7285(0.97)^2^.^9[/tex]
Which equation has a graph that is a parabola with a vertex at (-2, 0)?
y= -2x^2
y = (x + 2)^2
y= (x – 2)^2
y= x^2 – 2
Answers
Of the respondents, 502 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment?
Answers
Answer:
The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]
Step-by-step explanation:
Incomplete question, so i will suppose this is a sample of 1000.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of the n respondents, 502 replied that America is doing about the right amount.
Supposing [tex]n = 1000[/tex], so [tex]\pi = \frac{502}{1000} = 0.502[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 - 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.461[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 + 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.543[/tex]
The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]
data
find the range between 14, 15, 16, 14,23,13
15, 24, 12, 23, 14; 20, 17, 21, 22, 1031, 19, 20,
17, 16, 15, 11, 12, 21, 20, 17, 18, 19, 23
Answers
the lowest is 11 and the highest is 1031 then subtract it you are going to have 1020
) How many different three-letter initials can people have: , (b) How many different three-letter initials with none of the letters repeated can people have: , (c) How many different three-letter initials with letters repeated begin with an X: , (d) How many different three-letter initials begin with a F and end in a D:
Answers
Solution :
a).
The different three letter initials that people have is :
= 26 x 26 x 26
= [tex]26^3[/tex]
= [tex]17576[/tex]
b). The first place to be fill in26 ways.
The second place to be filled in 25 ways
The third place to be filled in 24 ways.
Therefore, total number of three letter initial with no repetition is :
= 26 x 25 x 24
= [tex]15600[/tex]
c). The total number of three letter initial begin with X = 1 x 26 x 26
= [tex]676[/tex]
d). The total number of the three letter initials that begin with letter 'F' an end with letter 'D' is = 1 x 26 x 1
= [tex]26[/tex]
A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work
Answers
Answer:
The answer is 1,000
SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)
write your answer in simplest radical form
Answers
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Answer:
4√2
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratio of side lengths is ...
1 : √3 : 2
That is, the hypotenuse (c) is double the short side (2√2).
c = 4√2
Find the area of each figure one of the sides are 8.3cm it’s a square btw
Answers
Answer:
68.89 cm
Step-by-step explanation:
8.3 X 8.3 would equal 68.89 cm. We can see that one side is 8.3 cm, and the other sides don't say their sides, so the only number we will use for multiplying is 8.3, and all sides of the square will be 8.3. The equation is L X W, where L is the length, and W is the width. Since 8.3 is on all four sides, it will also be the length and the width on the equation. As a result, 68.89 cm would be the final answer.
Answer:
I don't real know if this is right, but I think its this:
68.89 cm2 is the area.
For f(x) = 4x2 + 13x + 10, find all values of a for which f(a) = 7.
the solution set is ???
Answers
Answer:
f(7)=109
Step-by-step explanation:
Since f(a)=7 then you just imput 7 on each x like this f(7)=8+13(7)+10= 109
Question 7
In circle P below, angle OPM equals 124 degrees and line segments ON and MN are tangents to the circle
What is the measure of Angle ONM?
A 56
B 62
С 74
D 90
Answers
Answer:
B) 62 is the answer. I'm sure
A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups. Using the data provided below, conduct an F-test to determine whether you believe there is an association between race and average age at marriage.
Race N Mean
Black 113 25.39
White 904 22.99
Other 144 23.87
All Groups 1,161 23.33
Answers
Answer:
The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )
Step-by-step explanation:
Conducting an F-test to determine association between race and average age at marriage
step 1 : State the hypothesis
H0 : ц1 = ц2 = ц3
Ha : ц1 ≠ ц2 ≠ ц3
step 2 : determine the mean square between
Given mean value of all groups = 23.33
SS btw = 113*(25.39 - 23.33)² + 904*(22.99 - 23.33)² + 144*(23.89 - 23.33)^2 = 113(4.2436) + 904(0.1156) + 144(0.3136)
= 629.1876
hence: df btw = 3 - 1 = 2
df total = 1161 - 1 = 1160
df within = 1160 - 2 = 1158
SS within = 36.87*1158 = 42695.46
Therefore the MS between = 629.19 / 2 = 314.60
The F-ratio = 314.59 / 36.87 = 8.53
using the values for Btw the P-value = 0.00021
The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
Answers
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Answer:
(b) 7x + 2y = 1
Step-by-step explanation:
You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)
7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does
The equation is ...
7x +2y = 1
__
Additional comment
The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.
Answer:
b
Step-by-step explanation:
A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?
Answers
I need to know this answe ASAP
Answers
Answer:
The function is always increasing
Step-by-step explanation:
To be increasing, the y value needs to be getting bigger as x gets bigger
This is true for all values of x
The function is increasing for all values of x
Answer pleaseeeeeeee
Answers
Answer:
17x^2-9x-9 -->B
Step-by-step explanation:
7x^2 -12x +3 +10x^2+3x-12
Leonard made some muffins. He gave 5/8 of them to his grandmother and 10 muffins to his aunt. He then had 11 muffins left. How many muffins did he have at first?
Answers
Answer:
56
Step-by-step explanation:
x = number of muffins in total at the beginning.
x - 5/8 x - 10 = 11
x - 5/8 x = 21
8/8 x - 5/8 x = 21
3/8 x = 21
3x = 168
x = 56
One leg of a right angle has a length of 3m. The other sides have lengths
Answers
2^17+2^14 chia hết cho 9
Answers
Answer:
ABC
Step-by-step explanation:
= 2^14.2^3 + 2^14
= 2^14. (2^3 +1)
= 2^14 . 9
Vì 2^14.9 chia hết cho 9 nên 2^17 + 2^14 chia hết cho 9
(. là dấu nhân)
Answer:
đúng
Step-by-step explanation:
Suppose (-13,2) is a point on the graph of y=f(x). What is a point that will be on the graph of y=9f(x)-5
Answers
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Answer:
(x, y') = (-13, 13)
Step-by-step explanation:
At the given value of x, f(x) = 2. Then 9f(x)-5 = 9(2) -5 = 13.
The point on the scaled, translated graph will be ...
(x, y') = (-13, 13)
_____
The graph shows a function f(x) with a distinct feature (vertex) at (-13, 2). It also shows where that distinct feature moves to when the function is scaled and translated.
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find. (F o G) (-5)
26
3
–59
–6
Answers
Answer:
-59
Step-by-step explanation:
f(x) = -2x - 7 and g(x) = -4x + 6.
f(g(x)) =
Replace x in the function f(x) with g(x)
= -2(-4x+6) -7
= 8x -12 -7
= 8x - 19
Let x = -5
f(g(-5) = 8(-5) -19
= -40 -19
= -59
