I need help question
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We want to find the derivative of
\(f(x)=11\sin x+4\cos x\)To solve that we must remember the derivative of sin and cos
\(\begin{gathered} \frac{d}{dx}(\sin x)=\cos x \\ \\ \frac{d}{dx}(\cos x)=-\sin x \end{gathered}\)Therefore, let's use it to find f'(x)
\(\begin{gathered} f^{\prime}(x)=[11\sin(x)+4\cos(x)\rbrack^{\prime} \\ \\ f^{\prime}(x)=[11\sin(x)\rbrack^{\prime}+\lbrack4\cos(x)\rbrack^{\prime} \\ \\ f^{\prime}(x)=11\cdot[\sin(x)\rbrack^{\prime}+4\cdot\lbrack\cos(x)\rbrack^{\prime} \\ \\ f^{\prime}(x)=11\cdot\cos x-4\sin x \end{gathered}\)Therefore
\(f^{\prime}(x)=11\cos x-4\sin x\)Now let's evaluate the derivative at the point 3π/4
\(\begin{gathered} f^{\prime}(3\pi/4)=11\cos\frac{3\pi}{4}-4\sin\frac{3\pi}{4} \\ \\ f^{\prime}(3\pi/4)=11(-\sqrt{2}/2)-4\sqrt{2}/2 \\ \\ f^{\prime}(3\pi/4)=-\frac{11\sqrt{2}}{2}-\frac{4\sqrt{2}}{2} \\ \\ f^{\prime}(3\pi/4)=-\frac{1}{2}(11\sqrt{2}+4\sqrt{2}) \\ \\ f^{\prime}(3\pi/4)=-\frac{1}{2}(15\sqrt{2}) \\ \\ f^{\prime}(3\pi/4)=-\frac{15\sqrt{2}}{2} \end{gathered}\)Hence
\(f^{\prime}(3\pi/4)=-\frac{15\sqrt{2}}{2}\)Related Questions
Shivani and Kathleen are collecting clothes for a clothing drive. Kathleen collected 1/4 asmany clothes as Shivani did. If Shivani collected 4 1/4 bags of clothes, how many bags ofclothes did Kathleen collect?
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Answer:
Kathleen collected 1 1/16 clothes
Explanation:
Given that Kathleen collected 1/4 as many clothes as Shivani did.
Let the number of clothes Shivani collected be represented by x
Then Kathleen collected
\(\frac{1}{4}x\)Since Shivani collected 4 1/4 bags
It means he collected 17/4 bags.
Kathleen collected
1/4 of 17/4
\(\begin{gathered} =\frac{1}{4}\times\frac{17}{4} \\ \\ =\frac{17}{16} \end{gathered}\)Kathleen collected 17/16 clothes , this is the same as 1 1/16 clothes
Select all numbers that have an absolute value of 6.3.
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Answer:
-6.3
Step-by-step explanation:
Its the only thing I can think of. |-6.3| |6.3|
Solve for A = s=a+b+c/2
Answers
Answer:
Step-by-step explanation:
a + b + c/2 = s
a = -c/2 - b + s
Please HELP!!! I am on a BIG TIME CRUNCH!!! This is due RIGHT NOW!!!
Answers
Answer:
y=x+4
Step-by-step explanation:
PLZ give brainlest
Hi, I am having hard time figuring this out. I need to understand the "how to" really well, so as much detail in the solving would be ideal.
Word problem: Tuition fees for California State University were $5,131 during the 2010-2011 academic year. Historically, tuition has increased at an 8% per year rate. Use the formula from Problem 83 to find what the tuition was 20 years ago and 30 years ago. Hint: First solve for P, then substitute the given value for F. Round to the nearest dollar. (equation in #83 to use here is F=P(1+r)² where F is the future price of an item priced at P dollars, r is the inflation rate expressed as a decimal, and t is the time in years)
The given answers for this problem are: 20 years ago, tuition was $1,101 and 30 years ago tuition was $510.
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Answer:
For this problem we have:
Initial value P = $5131Increase rate r = 8% or 0.08Time 20 years ago t = -20 30 years ago t = -30Find the value of F using the formula and substitute the values:
F(t) = P(1 + r)^tF(-20) = 5131(1 + 0.08)^(-20) = 1100.84685219 ≈ $1101and
F(-30) = 5131(1 + 0.08)^(-30) = 509.905093313 ≈ $510In analyzing hits by certain bombs in a war, an area was partitioned into regions, each with an area of km2. A total of bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly hits. In applying the Poisson probability distribution formula, P(x) , identify the values of , x, and . Also, briefly describe what each of those symbols represents.
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Answer:
The answer is "\(\bold{ \mu =0.967, x=3, \ and \ e= 2.718}\)".
Step-by-step explanation:
A distribution of poulet applies because it deals through events (bomb hits) over even a sample space (the region with \(0.95 \ km^2\) area).
Its average hit number per area is:
\(\to \mu = \frac{\text{Number of hits of bomb}}{ \text{number of regions number}}\)
\(=\frac{535}{553} \\\\= 0.967 \\\\\)
\(\to x = 3\\\\\to e = 2.718\)
n×50=5,000 explain solution.
Answers
Answer:
100 is your answer
Step-by-step explanation:
I simply switched around the equation the answered it that way
Example: n×50=5,000
5000/50=n
500/50=100
HELP AS FAST AS HUMANLY POSSIBLE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! NO LINKS I WILL REPORT IF THERE ARE LINKS!!!!!!!!!
Answers
Answer:
C
Step-by-step explanation:
C
Answer:
its appears to be c
Step-by-step explanation:
to mark brainliest
Help please !!!!!!!!!!
Answers
Answer:
$ 50,000
Step-by-step explanation:
Let her salary = x
\(8\dfrac{3}{4} *x=4375\\\\\dfrac{35}{400}*x=4375\\\\x=4375*\dfrac{400}{35}\\\\x = 125*400\)
Salary = $ 50,000
40 POINTS IM BEING TIMED
Layla and Cayden are racing at the playground. The playground is rectangular and has a length of 82 meters and a width of 50 meters. Cayden will run around the entire perimeter of the rectangular playground while Layla will run diagonally across the playground twice. (She will end where she started). Cayden runs 3 meters per second and Layla runs 2 meters per second.
A: Who will finish first?
B: How much faster will that person's finish time be?
HELP PLEASEEEEEEEEEEEEEEEEEEEEEEE
FOR THE FIFTH TIME I ASKED THIS QUESTION ;-;
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Answer:
(A.)Cayden will win
(B.) He'll win by 9 seconds
Step-by-step explanation:
Need help with proofs, anyone know how?
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Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.
Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;
MS ≅ QSNS ≅ RSMN ≅ QN ∠NMS and ∠NQSΔMNS ≅ ΔQNSRead more on perpendicular bisectors here: brainly.com/question/19154899
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Complete Question:
The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS
We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.
NS and NS
NS and RS
MS and RS
MS and QS
HALP PLAS NEED HALP PLESAAA
Answers
Answer:
the answer is 32
Step-by-step explanation:
ywwwww
Answer:
the answer is 32..... 32
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 95% confidence; n = 349, x = 42
Answers
Answer:
0.5705Step-by-step explanation:
Margin of error is expressed as M.E = \(z * \sqrt{\frac{\sigma}{n} }\) where;
z is the z score at 95% confidence
\(\sigma\) is the standard deviation
n is the sample size
Given n = 349, \(\sigma = 42\) and z score at 95% confidence = 1.645
Substituting this values into the formula above we will have;
M.E = \(1.645*\sqrt{\frac{42}{349} }\)
\(M.E = 1.645*\sqrt{0.1203} \\\\M.E = 1.645*0.3468\\\\M.E = 0.5705 (to\ four\ dp)\)
is 10/12 and 40/64 a proportion
Answers
Answer:
No, it is not a proportion
Step-by-step explanation:
10/12 and 40/64 is not a proportion since although the numerator is constant because when multiplied by 4, it gives us 40, however, when you multiply 4 by 12, you get 48, therefore, it is not a proportion since the changes in the value of a proportion must be constant in both the numerator and denominator.
Hope this helped! :D
please fast if could
Answers
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A/60
B/45
C/105
The measurement of angle A is
The measurement of angle B is
The measurement of angle Cis
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The second pair of points representing the solution set of the system of equations is (-6, 29).
To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.
Given the system of equations:
y = x^2 - 2x - 19
y + 4x = 5
Substituting the x-coordinate of the second point (-6) into equation 2:
y + 4(-6) = 5
y - 24 = 5
y = 5 + 24
y = 29
Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).
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Question
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
y = x2 − 2x − 19
y + 4x = 5
The pair of points representing the solution set of this system of equations is (-6, 29) and
_________.
Subtract 10x^2– 10x + 2 from - 8x^2 + 7x–7
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here is your answer...
2x^2-3x-5
Select all the expressions that have a value of 180 when b=4
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Can you tell me if there are a word bank of answers and I can tell there are more then one answer so ima need more information
Please look at photo. Thank you!
Polynomial and rational functions:
A) Find all x and y intercepts. Check all that apply:
X intercepts: 4, 0, 1, and/or none.
Y intercepts: 1, 4, 0 and/or none.
B) write the equations for all vertical and horizontal asymptotes. Enter the equations by writing “and” or “none” when necessary.
C) find the domain and range of f. Write each answer as an interval or union of intervals.
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A) All x- and y-intercepts include the following:
x-intercepts: none.
y-intercept: 1.
B) The equation for vertical asymptote is x = 4 and the equation for horizontal asymptote is y = 0.
C) The domain and range of f are:
Domain = [-∞, 4) U [4, ∞]
Range = [0, ∞]
What is the x-intercept?In Mathematics, the x-intercept is the point at which the graph of a function crosses or touches the x-coordinate and the y-value or value of "y" is equal to zero (0).
Part A.
Based on the graph of this rational function, the x-intercept and y-intercept include the following:
x-intercept: none.
y-intercept: 1.
Part B.
An equation that represents the vertical asymptote is x = 4 while the equation represents the horizontal asymptote is y = 0 because the line does not cross those points.
Part C.
By critically observing the graph of this rational function, we can logically deduce the following domain and range:
Domain = [-∞, 4) U [4, ∞] or {x|x ≠ 4}.
Range = [0, ∞] or {y|y ≥ 0}.
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is this graph a minimum or a maximum pls help
Answers
The vertex of the graph is a maximum at (-2, 4)
Calculating if the vertex of the graph a maximum or a minimum?From the question, we have the following parameters that can be used in our computation:
The graph
The graph is a quadratic function
From the graph, we can see that the graph has a maximum value
This maximum value represents the vertex of the graph
And it is located at (-2, 4)
So, we have
Maximum = (-2, 4)
Hence, the maximum value of the function is (-2, 4)
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5^2 i want to know what that is.
Answers
Answer:
25
Step-by-step explanation:
Only answer question 2
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to find out how much $ she earned per day, all you have to do is divide $2,100 by 70, which is $30.
i hope this helps!!
70x=$2100
70 days and “x” being the amount of money made for each of those 70 days.
7x3 is 21 so 70x30 equals 2100
Answer is B $30
Answer the questions below to find the total surface area of the can.
Answers
Answer:
\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)
Step-by-step explanation:
We can find the Surface Area of the can by adding the areas of each of its parts:
\(SA = 2( A_{\text{base}}) + A_\text{side}\)
First, we can calculate the area of the circular base:
\(A_{\text{circle}} = \pi r^2\)
\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)
\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)
Next, we can calculate the area of the rectangular side:
\(A_\text{rect} = l \cdot w\)
\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)
Since the width of the side is the circumference of the base, we need to calculate that first.
\(C_\text{circle} = 2 \pi r\)
\(C_\text{base} = 2 \pi (0.75 \text{ in})\)
\(C_\text{base} = 1.5 \pi \text{ in}\)
Now, we can plug that back into the equation for the area of the side:
\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)
\(A_\text{side} = 6\pi \text{ in}^2\)
Finally, we can solve for the surface area of the can by adding the area of each of its parts.
\(SA = 2( A_{\text{base}}) + A_\text{side}\)
\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)
\(\boxed{SA = 7.125\pi \text{ in}^2}\)
\(\boxed{SA \approx 22.4 \text{ in}^2}\)
Please can anyone help me
Answers
Answer:
I believe that is it -19.
Step-by-step explanation:
f(8) = -2x - 3
-2 times 8 equals to -16 minus 3 equals to -19.
Help me with geometry that's due tonight!
Answers
2. Since it’s the particular bisector you just equal them to each other so 5x = 4x + 3 which equals x=3 then you plug it back in for line AC which equals 15
One leg of a triangle has a length of 3m. The other sides have lengths that are consecutive integers find these lengths
Answers
The length of the other two sides are 4m and 5m
How to determine the lengthsUsing the Pythagorean theorem, we have that the square of the hypotenuse sides is equal to the sum of the squares of the other two sides of the triangle
This is represented as;
x² = y² + z²
From the information given, we have that;
z = 3m
x = x + 1
y = x
Substitute the values, we get
(x + 1)² = x² + 3²
Find the squares
(x + 1) ² = 9 + x²
expand the bracket
(x + 1) ( x + 1) - x² = 9
x² + x + x + 1 - x² = 9
collect like terms
2x = 8
x = 4
Then,
x + 1 = 5
x = 4
Hence, the values are 4m and 5m
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Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
m - 4 = -7m - 8
-8 - 3m = 4 - m
-3m - 8 = 4 - m
-15m = -4m
-7m - 8 = m - 4
-8 - 7m = -4 + m
You can have multiple answers
Answers
The equation equivalent to -2m - 5m - 8 = 3 + (-7) + m is
-7m - 8 = m - 4. Option E
This is further explained below.
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?Generally, the equations equivalence is mathematically given as
-2m - 5m - 8 = 3 + (-7) + m
Therefore
-7m - 8 = 3 + (-7) + m
When we write the equation such that the variable appears on the right-hand side first, we get the following:
-7m - 8 = m - 4
In conclusion, The equation equivalent to -2m - 5m - 8 = 3 + (-7) + m is
-7m - 8 = m - 4.
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Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.
Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag
Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.
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The system of equations where the combination of the candies gives you a total of 22 points are:
x + y = 9
2x + 3y = 22
How can we create system of equations?To create the equations, we shall first define the variables:
x = the number of purple candies
y = the number of yellow candies
Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.
Then, we would make sure that the total number of candies selected is 9.
The first equation represents the total number of candies selected:
x + y = 9
The second equation represents the total number of points obtained:
2x + 3y = 22
Therefore, the system of equations is:
x + y = 9
2x + 3y = 22
This is a system of linear equations.
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is this right, be fr please
Answers
Answer:
1. yes
2.yes
Step-by-step explanation: you did the math right good
2.Yess
Good jobbb
4. What is the circumference of a circle whose area is 81π cm squared?
Answers
Circumference = 2pi*r
Step 1: find the radius from area
81pi=pi*r^2
81=r^2
9=r
Step 2: plug in radius to the circumference equation
Circumference = 2pi*r
18pi is the answer, otherwise know as 56.52 as well.
Step-by-step explanation:
Let us assume R be the radius of circle We know that, area of circle = πR2 81πr2 = πR2 R = √81 r R = 9r Circumference = 2 πr = 2 π (9r) = 18πr