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
What is Power rule, Product rule, Quotient rule and Chain rule? Detail please
Answers
When raising an exponential expression to a new power multiply the exponents.
For and Example|
Simplify: 7a^4 b^6)2
Solution: Each factor within the parentheses should be raised to the 2nd power.
7a^4 b^6)2 = 7^2(a4)2(b^6)2
You then simplify using the power Rule of Exponents.
7a^4 b^6)2 = 7^2(a4)2(b^6)2 = 49a^8 b^12
The power rule states that this derivative is n times the function raised to the (n-1) the power times the derivative of the function.
Product Rule|
When multiplying exponential expressions that have the same base, add the exponents.
Example:
Multiply: 4x^3 • -6x^2
Solution:
Multiply coefficients: 4 • -6 = -24
Use the product rule to multiply variables.
X^3 • x^2 = x^3 + 2 = x^5
4x^3 • -6x^2 = -24x^5
The power of product rule is a method for simplifying exponents and it states that a term raised to a power is equal to the product of its factors raised to the same power.
The product of two or more numbers is the result of multiplying these numbers.
Quotient Rule|
When dividing exponential expressions that have the same base, subtract the exponents.
Example:
Simplify: 8x^6/2x^3 = 4x^3
Solution:
Divide coefficients:
8 /2 = 4
Use the Quotient rule to divide variables:
X^6/x^3 = x6 - 3 = x^3
8x^6/ 2x^3 = 4x^3
The Quotient of two numbers is the result of the division of the numbers.
Chain Rule|
The general power rule is a special case of the chain rule. It is useful when finding the derivative of a function that is raised to the nth power.
((Hey I’m really tired so I hope this is good and helps you good luck!!))
Good Night fools!!!
7+x÷y is a ______( type of polynomial)
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I’m pretty sure this would be classified as a binomial
Hope this helps!
True or False (See Image)
The remainder theorem can be used to check if a binomial is a factor of a larger polynomial.
Answers
Answer: true
Step-by-step explanation:
Find the values of x and y that makes these triangles congruent by HL.
Answers
Answer:
What is HL? holey logic? hawk a loogy? half lies? honey lemon? heavenly lampshade? hand lotion?
Step-by-step explanation:
as AB = DE, the only options given where x = y - 1 are the the second and third.
as AC and AD are equal from ASA
3x - 2 = 2y + 1
3x - 3 = 2y
y = 1.5x - 1.5
the only x,y pair that fits is x = 5, y = 6
simplify (x^4-4x^3+9x^2-5x) (x^3-3x^2+7) -30x^2+25x^4
Answers
Answer:
x^7-7x^6+21x^5-13x^3+33x^2-35x
Step-by-step explanation:
there you go!
A steep mountain is inclined 74 degrees to the horizontal and rises 3150 feet above the surrounding plain. A cable for a cable car is to be installed from a point 725 feet from the base to the top of the mountain. Find the length of cable needed.
Answers
Answer:
3546 ft
Step-by-step explanation:
First find length of base to center of mountain.
(3150*sin 16 deg)/(sin 74 deg) = ~903 ft
Then dist of point from centre of mountain
903+725=1628 ft
Then cable length
(3150^2 + 1628^2)^0.5 = ~3546 ft
ANSWER FAST!!
Write the equation of a line that has a slope of -2/7 and passes through the point (5,-6)
Answers
Answer:
y = -2/7x - 32/7
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
The slope is -2/7
y = -2/7 x+b
We know a point on the line is (5,-6)
Substitute this into the equation
-6 = -2/7(5) +b
-6 = -10/7+b
Add 10/7 to each side
-6 +10/7 = b
-42/7 + 10/7 = b
-32/7 = b
y = -2/7x -32/7
MODELING REAL LIFE The table shows the amount y (in fluid Ounces) of carpet cleaner in a tank after x minutes of
cleaning.
x ll y
5 ll 108
10 ll 88
15 ll 68
a. Write an equation that represents the amount of cleaner in the tank after x minutes.
b. How much cleaner is in the tank when the cleaning begins?
C. After how many minutes is the tank empty?
Answers
Answer:
a. Write an equation that represents the amount of cleaner in the tank after x minutes
y= -4x + 128
b. How much cleaner is in the tank when the cleaning begins?
128
c. After how many minutes is the tank empty?
The tank is empty in 32 minutes
Find the quotient.
32 ÷ 0.08
Answers
Answer:
The quotient of the equation is 400
Answer:
hi
Step-by-step explanation:
the correct answer is 400
Simply:
3 (2x - 2) -2 (x - 2)
A: 3x -3
B: 3x -4
C: 4x -2
D: 4x -4
Answers
Answer:
4x-2
Step-by-step explanation:
6x-6-2x+4
=4x-2
Help help help help math please ASAP
Answers
Answer:
I think its 86
Step-by-step explanation:
As the two lines going in the same direction are parallel and angles within parallel lines add to 180.
so 180-94=86
94 + angle 5 = 180
angle 5 = 180 -94
angle 5 = 86
Hope this helps
If 3/4 of one of the acute angles of a right-angled triangle is 15 1/4 larger than 1/6 of the other, find the acute angles.
Answers
Answer:
Step-by-step explanation:
A + B = 90
A/6(15.25) = 3B/4
61A/18 = B
18A/18 + 61A/18 = 90
A = 90(18)/79
A = 20 40/79°
B = 90 -A = 69 39/79°
PLEASE HELP I WILL GIVE BRAINLEST AND 20 POINTS PLEASEEEE
Answers
Answer:
Question 4: Which equation is parallel to the above equation and passes through the point (35, 30)
[tex]y=[/tex] [tex]\frac{5}{7} x + 5[/tex] is the correct answer, I found this by inputting the x and y value of the coordinate (35, 30) onto the equation and solving for y-intercept since the slope of all equations is the same (since it's traveling parallel)
[tex]30 = \frac{5}{7} (35) + y\\30 = 25 + y\\5 = y[/tex]
so the equation would be [tex]y=[/tex] [tex]\frac{5}{7} x + 5[/tex]
Question 5: Which equation is perpendicular to the above equation and passes through the point (35, 30)
[tex]y=\frac{-7}{5} x+79[/tex] is the correct answer, I found this using the same method as before, input coordinate values into the equation and solve for the y-intercept (The only thing changed from the last answer is the opposite reciprocal slope).
[tex]30 = \frac{-7}{5}(35) + y \\30 = -49 + y \\79 = y[/tex]
so the equation would be [tex]y=\frac{-7}{5} x+79[/tex]
1) -4/3
2) -3/4
3) 10/17
4)17/10
Answers
Answer:
boom bam ba boom bam ba
Answer: -3/4
Step-by-step explanation:
The y value is decreasing by -0.75
-3.75 - 0.75 = -4.5
-4.5 - 0.75 = -5.25
-5.25 - 0.75 = -6
ect.
-0.75 in fraction form is -3/4
Given logv5 3 ≈ 0.6826 and logv5 8 ≈ 1.2920, evaluate the expressions.
A) logv5 2
B) logv5 (75/8)
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Sasha's SUV has a 17-gallon gas tank. The SUV gets an estimated 24 miles per gallon.
Approximately how many miles can the SUV run on half a tank of gas?
Answers
Answer:
The SUV can run 204 miles with half a gas of tank.
Step-by-step explanation:
Divide 17 by 2=8.5 gallons
Then do the formula for distance which is:
miles per gallon times gallon
24 times 8.5 would be 204
204 is your answer :3
an amount ogf $3700 id deposited into an account that pays 8.25% confounded semi-annually. how much money eill you receive in 15 years
Answers
Answer: The answer is seventeen
Step-by-step explanation:
i just answered this question
arithmetic sequence, can anyone help with this questions plz?
Answers
Answer:
Add 2/3
Step-by-step explanation:
2/3 + 2/3 = 4/3 + 2/3 = 6/3 (or 2) + 2/3 = 8/3 +2/3 = 10/3
What are the coordinates of A? someone help
Answers
Answer:
(7,10)
Step-by-step explanation:
The x coordinate is the first coordinate, it is how far you go across
X = 7
The next coordinate is the y coordinate, it is how for you go up or down
y = 10
(7,10)
What is the slope and y-intercept that represents this table?
Answers
Answer:
[tex]m=-2\ 000; q=17\ 000[/tex]
Step-by-step explanation:
First of all, whoever formatted that table is a criminal.
Now, slope first, it's the easiest: the slope in a table like that is the difference between two consecutive position: ie [tex]13\ 000 - 15\ 000[/tex] or [tex]11\ 000-13\ 000[/tex], being careful of subtracting the higher position (not value!) minus the lower, or right minus left. Your slope thus is [tex]-2 \ 000[/tex]. Intercept is found in two ways. One is writing the line in point slope form based on any two values and the slope we found, or since we're jumping integer to integer, you can look at the table in reverse and notice that if you go backwards (ie from 4 to 3 to 2 to 1) the value is increasing by 2000 every time. The intercept [tex]q[/tex]will be the value at 0, or 17 000
What is the solution to this equation? 1⁵+5²/25⁰-5¹=
Answers
Answer:
It is 21 first guy is no doubt correct.
Step-by-step explanation:
The expression results to 21.
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
1⁵+5²/25⁰-5¹
So, 1⁵ = 1
5² = 25
25⁰ = 1
5¹ = 5
Now, 1⁵+5²/25⁰-5¹
= 1+ 25 / 1 - 5
= 1 + 20
= 21
Hence, the expression results to 21.
Learn more about exponents and power here:
https://brainly.com/question/15722035
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1. The side of a square is 5 units long. What is the area of the square?
20 units?
25 units
10 units?
15 units?
Answers
Answer: 25 units squared
Step-by-step explanation:
1) A square has 4 equal sides.
2) The area of a square is length x width.
3) Therefore, 5x5 = 25 units squared (area is always reported in units squared).
A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be % confident that his estimate is in error by no more than percentage point Complete parts (a) through (c) below.
A) Assume nothing is known about the percentage of computers with new operating systems
n =
round up to the nearest integer
b) Assume that the recent survey suggest that about 96% of computers use a operating system.
n =
round up to the nearest integer
C) Does the additional survey information from part (b) have much of an effect on the sample size that is required?
A.
Yes, using the additional survey information from part (b) dramatically reduces the sample size.
B.
No, using the additional survey information from part (b) does not change the sample size.
C.
Yes, using the additional survey information from part (b) dramatically increases the sample size.
D.
No, using the additional survey information from part (b) only slightly increases the sample size.
Answers
Using the z-distribution, we have that:
a) A sample of 601 is needed.
b) A sample of 93 is needed.
c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
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]\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]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
For this problem, we consider that we want it to be within 4%.
Item a:
The sample size is n for which M = 0.04.There is no estimate, hence [tex]\pi = 0.5[/tex][tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
A sample of 601 is needed.
Item b:
The estimate is [tex]\pi = 0.96[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2[/tex]
[tex]n = 92.2[/tex]
Rounding up:
A sample of 93 is needed.
Item c:
The closer the estimate is to [tex]\pi = 0.5[/tex], the larger the sample size needed, hence, the correct option is A.
For more on the z-distribution, you can check brainly.com/question/25404151
PLEASE HELPP MEE ASAPP!!
Answers
Answer:
Step-by-step explanation:
each zero of the function will have a factor of (x - x₀)
h(x) = a(x + 3)(x + 2)(x - 1)
h(x) = a(x + 3)(x² + x - 2)
h(x) = a(x³ + 4x² + x - 6)
or the third option works if a = 1
however this equation gives us the points (0, -6) and (-1. -4), so "a" must be -2
h(x) = -2x³ - 8x² - 2x + 12
to fit ALL of the given points as it fits the three zeros and also h(0) and h(-1) so I guess that is why the given group is a partial set of solution sets
help please use picture
Answers
[tex]y = x + 4[/tex]
Step-by-step explanation:
Let [tex]P_1(-1, 3)[/tex] and [tex]P_2(0, 4)[/tex] and solve for the slope using the equation
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{4 - 3}{0 - (-1)} = 1[/tex]
Therefore, the general slope-intercept form of the equation of the line is
[tex]y = x + b[/tex]
where b is a constant. To solve for it, let's use one of the points. I'll use P2:
[tex]4 = (0) + b \Rightarrow b = 4[/tex]
Therefore, the slope-intercept form of the equation of the line is
[tex]y = x + 4[/tex]
heeelllppp meeee please
Answers
f(x)= 100.(0,9)^x
Express sin U as a fraction in simplest terms.
S
12
13
5
U
Answers
Answer:
12/13
Sine is opposite over hypotenuse. The opposite side of U is 12 and the hypotenuse is 13, so the answer is 12/13
What is the equation of the line that passes through the point (-6,8) and has an undefined slope?
Answers
Answer:
x = -6
Step-by-step explanation:
Slope is rise over run (change in y divided by change in x), and to have an undefined slope change in x must be zero. The line x = -6 is a vertical line that passes through the point (-6,8).
Fill in the blanks to solve 900 x 6
Answers
Answer:
The answer is 900 ×6= 5,400 u can use a calculator
A race director is preparing for an upcoming marathon and estimates that the mean time to
finish is 310 minutes. Assume
that the times are normally distributed, with a standard deviation of 50 minutes.
Use a standard normal table or a calculator to find the percentage of times that are longer than 236 minutes. For your
intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example
98.23%).
Answers
93.06% of the race is longer than 236 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]
Given that μ = 310, σ = 50
For x > 236:
[tex]z=\frac{236-310}{50}=-1.48[/tex]
From the normal distribution table:
P(x > 236) = P(z > -1.48) = 1 - P(z < -1.48) = 1 - 0.0694 = 0.9306 = 93.06%
93.06% of the race is longer than 236 minutes.
Find out more on z score at: https://brainly.com/question/25638875