Find f'(a) f(t)=2t+1/t+3

Answers

Answer 1
I'm going to rewrite f(t) to make it a little easier to use the power rule:
[tex]f(t)=2t+t^{-1}+3[/tex]

Now just take the derivative using the power rule:
[tex]f'(t)=2-t^{-2}[/tex]

Since they ask for f'(a), we need to replace the t's with a's:
[tex]f'(a)=2-a^{-2}[/tex]

Related Questions

one hundred times the quantity seven plus nine

Answers

100(7 + 9) = 
100(16) =
1600 <=

In Sean's fish tank there are 6times as many goldfish as guppies that's are a total of 21 fish in the tank how many more goldfish are there than guppies

Answers

18 - 3 = 15 Answer =15. Use a BAR MODEL  21 divided by 7 = 3. 3x6 = 18   3x1= 3







There are 126 goldfish

Thirty students are eating lunch at 5 tables. Each table has the same number of students. How many students are sitting at each table

Answers

30 ÷ 5
6 students at each table

Hope this helps!
There are 6 students sitting at each table, just divide 30 by 5.

gregs gas station sells three different kinds of gasoline:regular,plus,and premium


mr.adams spent $36.25 on 12.5 gallons of regular gasoline at gregs gas station.determine the cost per gallon for regular gasoline,showing each step in the process.

Answers

To find the amount he spent of each gallon, you would have to divide the price by the number of gallons to set the number of gallons in the equation to 1.

36.25/12.5 = $2.90

Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline. To find the cost per gallon, divide the total cost by the number of gallons, resulting in a cost of $2.90 per gallon of regular gasoline at Greg's gas station.

To determine the cost per gallon for regular gasoline, we need to divide the total amount spent by Mr. Adams at Greg's gas station by the number of gallons of gasoline he purchased. In this case, Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline.

Step-by-step calculation:

Write down the total cost of gasoline: $36.25.

Write down the total gallons of gasoline purchased: 12.5 gallons.

Divide the total cost by the number of gallons to find the cost per gallon: $36.25 \/ 12.5 gallons.

Perform the division: $36.25 \/ 12.5 gallons = $2.90 per gallon.

Therefore, the cost per gallon for regular gasoline at Greg's gas station is $2.90.

How many times can 36 go into 83??

Answers

Only 2 times!

36*2 = 72

86-72 = 14 which is less than 36

So only 2 times.

How many milligrams are in 5 grams

Answers

5000 milligrams are in 5 grams.
There are 5,000 milligrams in 5 grams

What is 1 more ten than 11?

Answers

 one  more ten than 11 is 21

your answer is 21

hope this helps

The length of a rectangle is 1 less than twice the width. The area of the rectangle is 28 square feet. Which equation represents the situation?

Answers

x=1-56 is the equation  that represents the situation

Answer:

2W²-W-28 = 0

Step-by-step explanation:

Write 720,080 in expanded form with exponents

Answers

700,000 + 20,000 + 80


there are no exponents

hope this helps

A carpenter is making a brace for a chair. To do so she intersects two pieces of wood to make two sets of vertical angles. The ostuse angles formed are each 145 . What is the measurement of each acute angle formed

Answers

In this question, there are two pieces of wood that crossed together. It will form 2 line that cut each other in the middle, looked like X.
In this case, the angles will be divided into 4 and two of the adjacent angel will result in 180° if you add them. Then the answer to this question would be: 180°-145°= 35°
The acute angle formed will be 35°

Eva has 2 apples in her basket she eats 1 apple and gives 1 apple to her friend how many apples does Eva have now

Answers

She has zero apples now. Since there was 2 at the start, then she eats one (1 apple) then again another apple is subtracted, leaving Eva with zero apples.

16x+x =12 solve justify each step with algebraic property

Answers

Here are some things you should know when solving algebraic equations.
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand. The distributive property is used mostly for simplifying parentheses in expressions/equations. 
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6

16x + x = 12
17x = 12 <-- Combine like terms
x = [tex]\frac{12}{17}[/tex]

So, x is equal to 12/17 or approximately to 0.7.

You bought a magazine for $6 and some notepads for $3 each. You spent a total of $18. How many notepads did you buy?

Answers

These are possible answers:

We can get 1 magazine and 4 notepads with $18 
6 + (3×4) = 6 + 12 = 18

We can get 2 magazines and 2 notepads with $18
(6 × 2) + (3 × 2) = 12 + 6 = 18


\Final answer:

To find the number of notepads bought, we can set up an equation by subtracting the cost of the magazine from the total cost and equating it to the cost of the notepads. By solving the equation, we find that you bought 4 notepads.

Explanation:

To solve this problem, we can start by setting up an equation. Let's assume the number of notepads bought is 'x'. We know the magazine cost $6, so the cost of the notepads is $18 - $6 = $12. Since each notepad costs $3, the equation becomes 3x = 12. To find the value of 'x', we can divide both sides of the equation by 3. So, x = 12/3 = 4.

Therefore, you bought 4 notepads.

Which function represents g(x), a reflection of f(x) =1/2(3)x across the y-axis?

Answers

g(x) = (1/2)3^-x  reflection over y axis yields (-x,y)                                            

Answer:

The required function -  [tex]g(x)=\frac{1}{2}(3)^{-x}[/tex]

Step-by-step explanation:

Given : Function represents g(x), a reflection of [tex]f(x) =\frac{1}{2}(3)^x[/tex] across the y-axis

To find : Which function represents the g(x)?

Solution :

The function [tex]f(x) =\frac{1}{2}(3)^x[/tex]

The function f(x) reflected across y-axis to form g(x)

The reflection of the point (x,y) across  the y-axis is the point (-x,y).

f(x,y)→f(-x,y) , the graph of f(x) is reflected across y-axis.

Let [tex]y=\frac{1}{2}(3)^x[/tex]

After reflection across y-axis is

[tex]g(x)=\frac{1}{2}(3)^{-x}[/tex]

The required function.

Refer the attached graph below.

What is the square root of 25 over 36

Answers

The square root of 25/36 is 5/6

for √25 =5
and √36= 6

hope this helps

Help Please?? 12. Of the following, which one is an observational study? A. Asking hearing-impaired people to try a new style of earphone to get their opinion B. Comparing survival rates between treating bone cancer with surgery versus treating it with radiation C. recording the daily output of a balloon factory for 6 months D. polling people on their favorite color I believe it would be 'C', yes?

Answers

the answer to your question is d

Final answer:

Option 'C' is an example of an observational study because it involves recording data without manipulation from the researcher, fitting the definition of observing the natural state or habits of a situation over time.

Explanation:

You have correctly identified option 'C' as an example of an observational study. In an observational study, researchers merely observe and record data without manipulating or intervening in the study environment or subjects. Option 'C', which involves recording the daily output of a balloon factory for 6 months, fits this description as it simply measures and records data over time without any intervention from the researcher.

It is different from a controlled experiment where variables are manipulated to assess the effect of treatments, as in option 'B', which compares survival rates between different treatments for bone cancer. Similarly, options 'A' and 'D' involve asking for opinions, which might be part of a broader observational study but are not observational studies by themselves.

In summary, an observational study is characterized by the purposeful absence of manipulation by the researcher and is designed to observe the natural state or habits of the subject or situation being studied.

Type the number 1340000 in scientific notation. express your answer using scientific notation.

Answers

The answer is 1.34 X 10^ 6, It is 1.36 times ten to the sixth power
Final answer:

To convert the number 1,340,000 into scientific notation, move the decimal point 6 places to the left to get 1.34, then place this as an exponent on 10 to get 1.34 x 10^6.

Explanation:

In scientific notation, large numbers are simplified by moving the decimal point to the left until we have a number between 1 and 10. We then use an exponent on 10 to indicate how many places the decimal point has been moved. If you take a look at the number 1,340,000, the decimal point is technically at the end of the number right now. In order to express this number in scientific notation, we move the decimal point 6 places to the left, which gives us 1.34. The number of places we moved the decimal point to the left becomes the exponent on 10. Therefore, 1,340,000 in scientific notation is 1.34 x 10^6.

Learn more about Scientific Notation here:

https://brainly.com/question/16936662

#SPJ6

Is the point (8'10), a solution of the equation y=16x-3

Answers

Lets find out...
(8,10)...x = 8 and y = 10

y = 16x - 3
10 = 16(8) - 3
10 = 128 - 3
10 = 125....nope...incorrect
therefore, (8,10) is not a solution to this equation

what’s the y and x intercept of 4/5x-2y=3

Answers

I would first solve for y
4/5x - 2y = 3
-4/5x -4/5x
-2y = -4/5x + 3
----- -----
-2 -2
Y= -4/5x + 3
-----------
-2

Now to find the y intercept, plug 0 in for x

Y=-4/5(0) + 3
--------------
-2
This gets you 3/-2 as your y intercept

To find x intercept, plug 0 in for y

0= -4/5x + 3
----------
-2
This gets x to be 3 and 3/4


The Waist to Hip Ratio (WHR) is a ratio commonly expressed as a decimal that has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Kevin has a WHR greater than 1, he is considered to be “high risk” for cardiovascular problems. Calculate Kevin’s WHR with a waist measurement of 42 inches and a hip measurement 2 inches less.

Answers

[tex]\bf \cfrac{waist}{hip}\qquad \cfrac{42}{\stackrel{two~less}{42-2}}\implies \cfrac{42}{40}\implies \cfrac{21}{20}\implies \stackrel{\ \textgreater \ 1}{1.05}[/tex]

That means Kevin need to ease off on the sloppy joes.
42 / 42-2= 40 = 42/ 40 = 21/20 =   >1 / 1.05

99 POINTS POSSIBLE!!!! I have a lot of math problems.....Please show your work also:) I will give Brainiest too!

1.Chase picked three buckets of blackberries that weigh: 2.79 pounds, 2.45 pounds, and 2.62 pounds. What is the average weight for the three buckets?

2. Ashley is baking cookies for math class. The recipe calls for 4 4/5 cups of flour. Ashley has to make 1 1/3 times the recipe to feed the whole class. How much flour does Ashley need?

3. Jordan finished her homework in 1 1/2 hours. It took Kasey 3/4 an hour longer than Jordan to finish her homework. How long did it take Kasey?

4. 32.5 divided by -0.08

5. 4.3x= 81.7 (Decimal Equation)

Thank you for helping me if you did!!!!!!!! I really appreciate it very much!!!!!!!

Answers

1) average weight=the sum of weights divided by number of buckets
average weight=(2.79+2.45+2.62)÷3
=2.62

2) recipe calls for 4 4/5=4+(4÷5)
=4.8
1 1/3=1+(1÷3)=4/3
So 4.8 times 4/3=6.4

3) Jordan took 1+1/2=1.5 hours
Kasey 3/4 an hour longer than Jordan
So Kasey took 1.5+(3÷4)=2.25 hours

4) 32.5÷(−0.08)=−406.25

5) 4.3x= 81.7
Solve for x by dividing both sides by 4.3 to get
X=81.7÷4.3
X=19

Hope it helps!

Hello!

1) 2.62

2) 4.8

3) 6.4

3) 2.25 hours

4) −406.25

5) X=19

I hope it helps!

A violin student records the number of hours she spends practicing during each of nine consecutive weeks. 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 what is the interquartile range (iqr) for this data?

Answers

We need to put the data set in ascending order

1.2     4.3     5.0     5.8     6.2     6.3     7.2      7.4     8.4

Interquartile range is given by upper quartile - lower quartile

Location of lower quartile = 1/4 of the data set
Location of upper quartile = 3/4 of the data set

Lower quartile = 1/4 of 9 = 2.25th (rounded down to 2nd  value) = 4.3
Upper quartile = 3/4 of 9 = 6.75th (rounded up to 7th value) = 7.2

Interquartile value = 7.2 - 4.3 = 2.9

To calculate the interquartile range (IQR) of the data set, the ordered values are split by the median to find Q1 and Q3. The difference between Q3 and Q1 gives the IQR which is 2.65 for this data set.

The interquartile range (IQR) is the measure of the middle 50 percent spread in a data set and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the IQR for the provided data set (6.2, 5.0, 4.3, 7.4, 5.8, 7.2, 8.4, 1.2, 6.3), we first need to order the data from smallest to largest and then identify Q1 and Q3. Using the median to split the ordered data into two halves and finding the medians of these two halves gives us Q1 and Q3, and their difference gives us the IQR.

Ordered data: 1.2, 4.3, 5.0, 5.8, 6.2, 6.3, 7.2, 7.4, 8.4Median (also Q2): 6.2Lower half (for Q1 calculation): 1.2, 4.3, 5.0, 5.8Upper half (for Q3 calculation): 6.3, 7.2, 7.4, 8.4Q1: (5.0 + 4.3) / 2 = 4.65Q3: (7.4 + 7.2) / 2 = 7.3IQR: 7.3 - 4.65 = 2.65

litter along a 15 mile stretch road will be picked up by 6 different groups of students which equation shows how to find the number of miles each group needs to clean

a.15 divided by 6=6/15
b. 6 divided by 15=6/15
c. 15 divided by 6=15/6
d. 6 divided by 14 =15/6

Answers

c) 15 divided by 6 = 15/6

What is the value of t? t−122=3t2−3 –3 –1 1 3

Answers

If your equation is ...

[tex]t-122=3t^2-3[/tex]

then it has no real solutions, and certainly no integer solutions.

_____

The attached graph show the left side is never equal to the right side of this equation for any real values of t.

the correct answer is actually 3

i just got done with the quiz and the answer was 3

if bx-2=k then x equal

Answers

bx - 2 = k
bx = k + 2
x = (k+2)/b

Hope this helps!

what is -4.15 as a fraction

Answers

-83/20 or -4 3/20. The first one is an improper fraction and the second on is the mixed fraction.

To solve the equation t² - t = 12 by factoring, you would use

Answers

Hello,

[tex]t^2-t=12\\ t^2-t-12=0\\ t^2-4t+3t-12=0\\ t(t-4)+3(t-4)=0\\ (t-4)(t+3)=0\\ t=4\ or\ t=-3 [/tex]

Factor the expression completely:
2x² + 5x - 12

Answers

Using the slip and slide method:

2x^2+5x-12
x^2+5x-24
(x+8)(x-3)

(x+8/2)(x-3/2)
(x+4)(2x-3)

Final answer: (2x-3)(x+4)
see attached picture for the answer:

Use the formula d = rt to find the distance d a long-distance runner can run at a rate r of 9 1/2 miles per hour for time t of 1 3/4 hours.

Answers

multiply the 2 numbers

9 1/2 * 1 3/4 =

19/2 * 7/4 = 133/8 = 16 5/8 miles

Markia saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?

Answers

35% would be the same as .35
So multiply 270 by .35 and you woild get $94.50

Then you take 270 and subtract it by 94.50 and you get 175.50.

So your answer would be $175.50.

Hope this helps!
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