These questions are about calculus, I would greatly appreciate your help on both questions! .
asap , please !
Answers
If the function f(x) =(4x² tan x)/sec x , then f'(x) =4( 2x sin(x) + x² cos x) using product rule of differentiation and f'(5) =103.11
What is product rule for differentiation?Product rule for differentiation states that the differentiation the product of two functions is the product of derivative of first function and second function plus product of derivative of second function and first function.
If we have consider the differentiation of product of two functions u ,v that we can write product rule as
(u*v)' = u' v + u v' , where ' represents first derivative with respect to independent variable
Given f(x) = (4x² tan x)/sec x or we can write it as :
f(x) = (4x² )(sin x) as 1/ sec x is cos x , tan x = sin x / cos x
let u =4x² , v = sin x
Then f(x) =u × v
Using product rule of differentiation:
f'(x) = u' v + u v' = (8x sin x) + (4x² cos x) = 4( 2x sin(x) + x² cos x)
To find value of f'(x) at x= 5
f'(5) = 4(10sin5 + 25 cos5) = 103.10569951 = 103.11(rounding off )
Therefore if f(x) = (4x² tan x)/sec x then f'(x) =4( 2x sin(x) + x² cos x) and f'(5) =103.11
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Related Questions
An ordinary die with numbers 1 through 6. Imagine such a die is rolled twice in session and the face values of the two rolld are added together. The sum is recorded as an outcome of a single trial if a random experiment. Compute the probability if rhe sum is decided by 5
Answers
The probability of getting the sum 5 on the faces of both dice is 1/9.
What is defined as the probability?Probability is a branch of mathematics that deals with numerical descriptions of just how likely an occurrence is to occur or how likely a proposition is to be true.
The probability of an event occurring is a number ranging from zero and 1, where 0 indicates the event's impossibility and 1 indicates certainty.Probability (event) = favourable outcome/ total outcome.
There are 36 possible outcomes when rolling two dice. Keep in mind that now the "sample space" is a set that includes all possible outcomes.
(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
The sample space for getting the sum as 5 on both faces is;
S = {(4,1), (3,2), (2,3), (1,4)}
Thus, the favourable outcome is 4
The total outcome is 36.
P (sum as 5) = favourable outcome for 5/total outcome
P (sum as 5) = 4/36
P (sum as 5) = 1/9
Therefore, the probability that sum is 5 on both the faces of dice is 1/9.
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Solve the system, enter as an ordered triple. Need HELP!!
Answers
This means x = 2, y = 3 and z = 1
========================================================
Work Shown:
Double everything in the second equation to get 4x-2y+4z=6
Add this result to the first equation
[tex]x+2y-4z = 4\\4x-2y+4z = 6\\5x+0y+0z = 10[/tex]
The first two lines of that expression above shows us adding x+2y-4z=4 to the equation 4x-2y+4z = 6
The x terms add to x+4x = 5x
The y terms add to 2y+(-2y) = 0y
The z terms add to -4z+4z = 0z
The terms on the right hand side add to 4+6 = 10
That's how we end up with the new equation 5x+0y+0z = 10
That becomes 5x = 10 which solves to x = 2 when we divide both sides by 5.
------------------------
Use this x value in the third original equation to find z
3x-8z = -2
3(2)-8z = -2
6-8z = -2
-8z = -2-6
-8z = -8
z = -8/(-8)
z = 1
------------------------
Use the x and z values we found to find y
x+2y-4z = 4
2+2y-4(1) = 4
2+2y-4 = 4
2y-2 = 4
2y = 4+2
2y = 6
y = 6/2
y = 3
----------------------
Overall we get the solutions to be x = 2, y = 3 and z = 1
We can say the solution as an ordered triple is (x,y,z) = (2,3,1)
Find the length of each side of an equilateral triangle with perimeter 57
inches.
Answers
Answer:
19
Step-by-step explanation:
57 divided by 3 is 13
Answer:
one side is 19 inches
Step-by-step explanation:
57 / 3 = 19
since it is an equilateral triangle the sides are equal so you can just divide by 3
A 34 oz bottle of a new soda costs $3.63. What is the unit rate, rounded to the nearest tenth of a cent?
Answers
3.63/34= 0.1067647058823...
that means each oz of soda is 10.7 cents
Us
What is the mole fraction of KCl in an
aqueous solution that contains
26.3% KCI (weightweight %)?
Answers
Answer:
0.0794%
Subtract the 26.3 from 100 and get the amount for water giving you 73.7
Divide both from their molar masses
26.3/74.55=0.3528
73.7/18.016=4.0908
Add both answers, 0.3528+4.0908=4.4436
Divde the KCl total from the the total moles which gives you your final amswer
0.3528/4.4436=0.0794
Answer: 0.0794
Step-by-step explanation:
PLEASE HELP FAST ILL MARK AS BRAINLIEST
Answers
Answer:
the last one
Step-by-step explanation:
PLS HELP PUT THE LETTERS NOT NUMBERS 20 POINTS AND BRAINLIEST
Answers
I’m not too sure.
A sample of 40 CDs from a student's collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes. Construct a 95% confidence interval for the population standard deviation. (Round your answers to 4 decimal places.) The 95% confidence interval is from to .
Answers
Answer:
(48.65, 56.83)
Step-by-step explanation:
Given that :
Sample size (n) = 40
Mean (m) = 52.74
Standard deviation (s) = 13.21
α = 95%
Confidence interval around sample mean can be obtained using the relation :
Mean ± Zstatistic * s/√n
Z score for 95% confidence interval = 1.96 (Z probability calculator)
s / √n = 13.21 / √40 = 2.0886843
Lower limit of confidence interval :
52.74 - (1.96 * 2.0886843) = 48.646178772 = 48.65
Upper limit of confidence interval :
52.74 + (1.96 * 2.0886843) = 56.833821228 = 56.83
Are
12/20
and
equivalent fractions?
22/30
Α. No
B. Yes, because both fractions are divisible by 2
C. Yes, because the difference between the denominator and numerator in each fraction is 8.
D. Yes, because they can both be simplified
Answers
I just need to fill up space in this answer
Answer:
Step-by-step explanation:
No because 12/20 is not lower form of 22/30
The monthly rents (in dollars) paid by 9 people are given below.
(Note that these are already ordered from least to greatest.)
851, 935, 980, 985, 1005, 1025, 1050, 1080, 1665
Send data to calculator
Suppose that one of the people moves. Her rent changes from $1665 to $1170.
Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
○ It decreases by $
O It increases by
O It stays the same.
O It decreases by
O It increases by
O It stays the same.
Answers
Answer:
It decreases by $
Step-by-step explanation:
It decreases by $ is the correct answer.
Answer:
A - Mean is decreased by 55$
B - Median stays the same.
12+3/5x−8−7/10x=?
Does anybody know what the answer to this question is?
I am really in a hurry. If the answer is true, please tell me. Thank you very much!
(The person who gets it right is going to be the Smartest.)
Answers
Answer:
−1 /10 x+4
Step-by-step explanation:
Group like terms
=3/5x-7/10x+12-8
add
-10x+12-8
1/10x=x/10
-x/10+12-8
−1 /10 x+4
If you need more help just ask
Susan is buying juice for a party. She wants to buy as many bottles of juice as possible, but she only has $10.00 to spend. If each bottle of juice costs $1.35, how can Susan calculate the number of bottles that she can buy?
A.Divide $10.00 by $1.35, and round the quotient down to the nearest whole number.
B.Divide $10.00 by $1.35, and round the quotient up to the nearest whole number.
C.Divide $1.35 by $10.00, and round the quotient down to the nearest whole number.
D.Subtract $1.35 from $10.00, and round the difference down to the nearest whole number.
GIVING BRAINLIEST
Answers
Answer:
A
Step-by-step explanation:
Answer:
A because $10 needed to be divided by $1.35 and and the rounding is needed to get the answer
Rewrite 14 1/3 as an improper fraction
Answers
Answer:
Step-by-step explanation:
((14×3) + 1 )/3 = (43/3)
14 1/3 can be expressed as 43/3, which is an improper fraction.
To rewrite 14 1/3 as an improper fraction, we need to convert the mixed number into a fraction.
First, we multiply the whole number (14) by the denominator of the fraction (3) and add the numerator (1). This gives us the numerator of the improper fraction. The denominator remains the same.
14 × 3 = 42
Next, we add the numerator (1) to the result we obtained above.
42 + 1 = 43
Therefore, the improper fraction equivalent to 14 1/3 is 43/3.
In the fraction 43/3, the numerator (43) represents the total number of parts we have, and the denominator (3) represents the size of each part. It indicates that we have 43 equal parts of size 1/3.
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Lin's family has completed 60% of a trip.They have traveled 30 Miles. How long is the whole trip?
Answers
Answer:
40 miles
Step-by-step explanation:
100 - 60 = 40. 40%
60 ÷ 30 = 2. 2 miles = 10%
10 * 4 = 40
Solve 4/5x-9=3
Need help.
Answers
Answer:
x = 15
Step-by-step explanation:
4/5x - 9 = 3
add 9 to both sides
4/5x = 12
multiply both sides with 5/4
(4/5x)5/4 = 12(5/4)
x = 15
what is 1(0b+10a) ???????????????????
Answers
Answer:
10b+10a
Step-by-step explanation:
Answer:
The answer is 10a
Step-by-step explanation:
(1)(0b+10a)
=(1)(0b)+(1)(10a)
=0+10a
=10a
Hope this helps :)
I can’t figure out the answer
Answers
Answer:
x=-7
tep-by-step explanation:
the line is on the x axis on -7
What is 18/8 written in simplest form?
2 1/4
Answers
Answer:
Actually I think it would be 2 1/3
Step-by-step explanation:
18 goes into 8 twice right, so whole number 2 with 2 left over so that makes it 2 2/6 then 2/2 and 6/2 is 1 and 3 so 2 1/3.
There are a total of 64 students in the volleyball and basketball varsity team. The
volleyball team has 10 more students than the basketball team. How many students are in
each team?
37 volleyball students and 27 basketball students
O 27 volleyball students and 37 basketball students
42 volleyball students and 22 basketball students
O 22 volleyball students and 42 basketball students
Answers
Which equation represents a line that passes through the two points in the
table?
OA.y-1-(x-1)
B. y-6-(x-5)
OC. y+6=(x+5)
OD. y+1-2/(x+1)
X
1
5
сл
y
1
6
Answers
Answer:
A
Step-by-step explanation:
Plug in both point values into each of the equations and see if the LHS = RHS.
Only eq A satisfies for both points
eq B satisfies for point (5,6) but not for (1,1)
Equations C and D satisfy for neither point
The equation of the straight line passing through the points (1, 1) and (5, 6) is 4y = 5x - 1.
What is the general equation of straight line?The general equation of a straight line is -
y = mx + c
Here {m} is the slope which also denotes the unit rate. Unit rate is the rate at which the value of {y} changes per unit change in the value of {x}.
Given is the table as shown in the figure.
The line passes through the points (1, 1) and (5, 6). We can write the slope of the line as -
m = (6 - 1)/(5 - 1)
m = 5/4
So, we can write the equation as -
y = 5x/4 + c
For the point (1, 1), we can write -
1 = 5/4 + c
c = 1 - 5/4
c = (4 - 5)/4
c = -1/4
So, the equation will be -
y = 5x/4 - 1/4
y = (5x - 1)/4
4y = 5x - 1
Therefore, the equation of the straight line passing through the points (1, 1) and (5, 6) is 4y = 5x - 1.
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a figure is made of to rectangular prisms what is the volume?
Answers
Answer:
why did u delete my comment
Step-by-step explanation:
I need help plzzzzzzzzzzzz. I need you guys to show work too
Answers
Answer:
22
Step-by-step explanation:
—Math√(x+3) –4 = 1
√(x+3) = 1 +4
√(x+3) = 5
x + 3 = 5²
x = 25 –3
x = 22
The main span of Bridge A (2800 feet) is _____ percent shorter than the main span of Bridge B (4500 feet).
Answers
The Bridge A' main span is 60% shorter than the span of the Bridge B.
What is defined as the percentage difference?The percentage is the difference between two parameters divided by the average of those values.
It is used to express the distinction between two related data as a percentage. For instance, you can evaluate the price of a computer this year with the cost of a laptop last year.Now, as per the given question;
Bridge A' span = 2800 feet.
Bridge B' span = 4500 feet.
Percentage difference in span length :
[(difference in span) / span of B] × 100%
Difference in span = 4500 - 2800 = 2700
Now, calculate the percentage difference;
Percentage difference = (2700 / 4500) × 100%
Percentage difference = 0.6 × 100% = 60.0 %
Therefore, the main span of the Bridge B is 60% longer than the main span of bridge A.
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Which expression represents twice the sum of w and 6?
A) 2 +6w
B) 20 + 6
C) 20 + 60
D) 2 (w+6)
QC 261
Answers
Answer all of these and I will give you 35 points!!!!!!!!!!!!!!!!!!!!!
Answers
9. LCM of 9, 12, and 15 is 180
12. LCM of 15, 18, and 30 is 90
15. LCM of 40 and 1 is 40
16: factors of 24 : 1,2,3,4,6,8,12, and 24
17: factors of 63 : 1, 2, 4, 8, 16, 32 and 64.
18: factors of 50 : 1, 2, 5, 10, 25, and 50
19: LCM of : 3 , 2 , 7 is 42
20: LCM of : 15 , 2 is 30
21: LCM of : 45, 30 is 90
the median of 4 numbers is 48
3 of the numbers are:
42, 51, and 52
what is the other number
Answers
When 3 among four numbers are 42,52,52 and their median is 48 then the fourth number is 45.
What is Median?
Median is the middle number when the given numbers are arranged in ascending or descending order, basically it divides the data into two halves the one is higher half another is lower half of the data.
For even numbers of data we find median by first arranging the data in ascending order then we take average of the two middle terms.
Given that among 4 numbers three are 42,51,52
Assume that the fourth no be x and also Assume that it is among the middle two numbers as median is given 48 to find this number?
Then the data arranged in ascending order is
42,x,51,51
Median=
[tex]\frac{x+51}{2} =48\\x+51=96\\x= 45[/tex]
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Please help me this is 7th grade math all you have to do is find the slope for the graph if it is right i will give you brianliest
Answers
Answer:
-10/2 or -5 for the slope
Step-by-step explanation:
rise over run: it's going down 10 and over 2 or
for every 5 down it goes 1 over
Which of the following could be the lengths of the three sides of a triangle?
A.1 cm, 2 cm, 3 cm
B.3 in., 3 in., 7 in.
C.4 ft, 8 ft, 12 ft
D.5 cm, 7 cm, 9 cm
Answers
its b
Step-by-step explanation:
cuz to sides are the exact same then one side is bigger than the others :)
The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−2, 4) and goes to S(3, 4) and continues to T(3, −1). The total length of the walking trail is ____ units. (Input whole numbers only.)
Answers
Answer:
32 cm
Step-by-step explanation:
The typical amount of sleep per night for college students can be assumed to be normally distributed with a mean of 7 hours and a standard deviation
of 1.2 hours. From the Standard Deviation Rule, we know that about 95% of the college students typically sleep between:
A 5.8 and 8.2 hours per night
B 4.6 and 9.4 hours per night
C 6 and 8 hours per night
Dit is impossible to determine the answer from the given information.
Answers
Answer:
B 4.6 and 9.4 hours per night.
Step-by-step explanation: