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 =
[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]
which expression represents 100 less than 3 times the sum of 18 and 2
Answer: 3 times (18+ 2) - 100
3 (18+2) - 100 = -40
Step-by-step explanation:
1 5/8 ÷ (−1 3/5) Please help
Can someone pls help me!! And if u can explain how u do it I will very thankful for that..
Answer:
For the first question is 8y, and the second question would be 80
Step-by-step explanation:
The perimeter of a shape is calculated by adding it's sides together, and 2y+2y+2y+2y=8y. If y=10, we can substitute y for 10 in which 8*10 is 80.
The position of a scuba diver relative to the water surface was −22 1/3 feet. He saw something interesting beneath him and increased his depth by 12 1/2 feet.
What is the position of the scuba diver now relative to the water surface?
Enter your answer as a mixed number, in simplified form, in the box.
Answer:
-34 5/6
Step-by-step explanation:
Hope this helps
Have a blessed day
6(3x+12-4x)=2x+2+3x solve for x
Answer:
its 70/11 or 6.36
Step-by-step explanation:
What is x + 1 and x + 2
Answer:
I don't get what you're asking.
Do you want me to solve for x? :D
(✿◡‿◡) HAPPY HOLIDAYS!!!
Help me please I'm stuck on this question
Answer:
n= 2.9
1:2.9
Step-by-step explanation:
Divide by 15 on both sides
15 divided by 15 is 1
43 divided by 15 is 2.8666666666=>
It states "Give any decimals in your answer to 1 d.p.
Mean we round it to one decimal place
so it is 2.9
Thus the answer for n is 2.9
Hope this helps!
Unit 4 Solving Quadratic equations {and complex number}
HELP!!!!
Solve, 4/9 - 4/10
Answer:
[tex]\frac{2}{45}[/tex]
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
f(x)=2x 2 +8x Find f(−1)
Answer:
-6
Step-by-step explanation:
f(x)=2x^2+8x
f(-1)=2(-1)^2+8(-1)
f(-1)=2(-1)(-1)-8
f(-1)=2(1)-8
f(-1)=2-8
f(-1)=-6
Simplify 8 to the second power plus 2
8^2 + 2 = 64 + 2 = 66
The answer is 66 because 8 to the second power is 64 and then you add 2.
Answer:
66
Step-by-step explanation:
8^2 is equal to 64
64 +2 = 66
8^2 is 8x8
so 8x8= 64
64+2 is 66
why you always angry why you always quiet why do you sleep alone when I know you don't like it maybe you might be different will it kill you to tell me the truth what in the hell does a man have to do to be loved by you
Answer:
Beause you did love to be loved by you
Step-by-step explanation:
Maybe a spoon full of sugar will help but I'm not going to love you because love this pure is hard to find in world so scard from humanity and the hideous presence of me
Help pelsss thank you math sucks
Answer:
103
Step-by-step explanation:
180-77=103
Help I will give brainlest
The owner of a retail store is tracking his inventory for an annual report. The graph shows the remaining inventory for a particular item and the number of days that have passed since the stock was replenished. Which type of function best models the relationship between the number of days and the inventory remaining? A. a linear function with negative slopes
Two wheelchair ramps, each 10 feet long, lead to the two ends of the entrance porch of Mr. Bell's restaurant. The two ends of the porch are at the same height from the ground, and the start of each ramp is the same distance from the base of the porch. The angle of the first ramp to the ground is 24°.
Answer:
It must have an angle of exactly 24°.
Step-by-step explanation:
Answer:
It must have an angle of exactly 24°.
Step-by-step explanation:
I got a 100% on my mastery test
Solve. 9(8 - x) = 3x brainly EEE PLSS
Answer:
x=6
Step-by-step explanation:
9(8-x)=3x
9 x 8=72
72-9x=3x
72=12x
72/12=6
x=6
Select the graph of the equation y + x + 3 = 0.
Answer:
the fourth image
Step-by-step explanation:
y + x + 3 = 0
y = -x - 3
meaning slope = -1
and y-intercept is -3
answer: image attached
because they all look similar, it is the one that moves exactly one block per unit
Two angles are supplementary. The larger angle is 28∘ more than the smaller angle. Find the measure of the larger angle.
Supplementary means that the angles together equal 180°
So we simply do 180 - 28 = 152°
Hope this helps!
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?
Answer:
=$114.750
Step-by-step explanation:Length of new board cast tower=4.5 Inches
Cost of construction(per inch)=$25.50
To find cost=?
=25.50x4.5
=$114.750
...................................................................................
The required cost of the construction of a 4.5-inch tower is $114.75.
Given that,
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch, how much it cost to fund 4.5 inches of the construction is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 × 4.5 = $114.75.
Thus, the required cost of the construction of a 4.5-inch tower is $114.75.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ5
Use technology to find points and graph the line -4y=-x+20
plotting on a graph
Step-by-step explanation:
First we need to isolate the y, by dividing -4 on both sides. This will give you y = 1/4x - 5.
Now you can properly graph the equation:
Since -5 is the y-intercept (the point in which the line intercepts the y-axis), we will place our first point at (0,-5) on the graph.
In order to find the next point, we will use the slope of the line and do rise/run. So we will go upwards 1 unit and to the right 4 units.
(Image of graph will be attached above⤴⤴⤴)
Hope this helps you :)
help as soon as possible
The greatest common factor of y^4. y^6 and y^5 is
Answer:
Answer:GCF: y^4
Step-by-step explanation:
Factors of:
y^4= (y) (y) (y) (y) = y^4 (1)
y^5 = (y) (y) (y) (y) (y) = y^4 (y)
y^6 = (y) (y) (y) (y) (y) (y) = y^4(y^2)
What is the result of 3/ 1/6
2
9
18
27
Step-by-step explanation:
remember 3 things
1. 3 = 3/1 (any integer is also a fraction of itself divided by 1).
2. 3 / 1/6 = 3/1 / 1/6 = 3/1 × 6/1 (dividing by a fraction is the same as multiplying with the upside-down fraction).
3 a/b × c/d = ac / bd. in our case 3/1 × 6/1 = 18/1 = 18
What is the average rate of change on the interval from 3 to 9?
Enter your answer in the grid below. Make sure your answer contain
Answer:
5
Step-by-step explanation:
Mark used 14 bananas, 15 oranges, and 24 strawberries in his fruit salad.
Dani used 7 bananas, 9 oranges, and 12 strawberries. Did Mark and Dan
use the same ratio of bananas to strawberries? *
Answer:
yes-
Step-by-step explanation:
im not to sure if its right but
7+7=14
12+12=24
3. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach $800. Show your work. Answer:
Answer:
31.334... years
Step-by-step explanation:
Initial value = $500
r = 1.5%
t = ?
A = (500)[tex]e^{.015*t}[/tex]
I was unsure if the question was asking to express the equations in terms of t =, but i did those steps anyway just in case.
A/500 = [tex]e^{.015*t}[/tex]
ln A/500 = ln[tex]e^{.015*t}[/tex]
ln A/500 = .015*t
ln(A/500)/.015 = t
t = ln(A/500)/.015
To find the amount of time it takes for the account balance to reach $800, we plug in $800 for A in the equation that solves for t.
t= ln(800/500)/.015 = 31.334...(rounded) years
We also could have solved by plugging in $800 into the original equation and then solving for t, but i found it to be easier to find the equation for t prior to solving. Hope this helps!
Pls help!!!!!!!!!!!!!!!!!!!!!
Answer:
See below:
Step-by-step explanation:
First fill in:
180* . Every triangle has interior measurments of 180* total
Second fill in: Reason is definition of sum of triangle's interior angles
Third fill in: 2x. Everything in this equation is asking for the angles. First angle is 28, second angle is 2x, and third angle is x-4.
Fourth fill in: x=52
I found this by doing the following:
First, 180-28, so we can see how many degree we are left with.
152.
Now, make an equation:
152=2x+x-4
Simplify
152=3x-4
Add 4 to both sides to cancel out the -4.
156=3x
divide 156/3=52.
Now we know that x=52.
Although the question doesn't ask for this, you would now substitue 52 back into each of the equations to find that degree. For example, 2x=2(52), or 104*.
Answer:
See image
Step-by-step explanation:
All the angles of a triangle add up to 180°
The given diagram shows all the measures: 28°, x - 4° , and 2x
So add them up, set equal to 180 and solve for x. Combine like terms and subtract 24 from both sides of the equation. Divide both sides by 3. x = 52
3 + 6 x (5 + 4) ÷ 3 -7?
Answer:
Answer: 14
Step-by-step explanation:
[tex]{ \rm{3 + 6 \times (5 + 4) \div 3 - 7}} \\ \\ = { \rm{3 + (6 \times 9) \div 3 - 7}} \\ \\ = { \rm{3 + (54 \div 3) - 7}} \\ \\ = { \rm{14 }}[/tex]
Tomatoes that regularly sell for $0.55 per pound are on sale for 20% off the regular price. What is the sale price?
Answer:
$0.44
Step-by-step explanation:
lmk if you want an explanation