f’’(x)=cos(x), f’(pi)=2, f(pi)=-1
f(x)=?
PLS URGENT
Answers
The required function f(x) is represented by -1 + F(x + sin(x)).
To find the function f(x), you can use the formula for integration by substitution:
f(x) = F(g(x)) + C
where F is an antiderivative of f, g is a function such that g'(x) = f(x), and C is a constant.
In this case, we can take g(x) = x + sin(x). Then g'(x) = cos(x), so f(x) = F(g(x)) + C = F(x + sin(x)) + C.
We are given that f'(π) = 2 and f(π) = -1, so we can use these values to find the constants C and F.
First, we can find F by taking the derivative of F(x + sin(x)). This gives us:
F'(x + sin(x)) = f(x) = cos(x)
Substituting x = π and using the fact that F'(x + sin(x)) = f'(π) = 2, we get:
F'(π + sin(π)) = 2
Since sin(π) = 0, this simplifies to:
F'(π) = 2
Then, using the fact that F(x + sin(x)) = f(π) = -1 when x = π, we can find the value of F(π):
F(π) = -1
Now that we have found the values of F and F', we can use these to find the value of C.
Since F(x + sin(x)) = F(x) + F'(x) sin(x), we can substitute x = π to get:
F(π + sin(π)) = F(π) + F'(π) * sin(π)
Substituting the values we found above, this becomes:
F(π + 0) = -1 + 2 x 0
Which simplifies to:
F(π) = -1
Since F(π) = -1, we can conclude that C = -1.
Therefore, the function f(x) is given by:
f(x) = F(x + sin(x)) + C = F(x + sin(x)) - 1
= -1 + F(x + sin(x))
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Related Questions
What Is the first step in solving this quadratic equation
X^2+5x=6
A. Combine like terms
B. Set each factor equal to 0
C. Subtract from both sides to set the equation equal to 0
D. Factor
Answers
Answer:
Step-by-step explanation:
We need to move the 6 so that all three terms are on the left and only 0 is present on the right side: To do this, we (C) subtract 6 from both sides to set the equation equal to 0.
x^2 + 5x - 6 = 0
CCSS Math 7
Unit 7. Agles, Triangles, ad Prisms
Find the measure of all the missing anges.
PLEASE HELP WITH ALL THE ANSWERS ITS DUE TOMORROW !!!
Answers
Answer:
1.
a = 112
b = 68
c = 68
2.
a = 127
3.
a=35
b=40
c=35
d=70
4.
a= 30
b=70
c = 30
d=70
e = 130
I'll help you with the rest later
Step-by-step explanation:
a = 112 because of allied angles rule
b and c = 68 because of angles at a point
360-112-112 ÷2
2. a = 127 because of angles on a straight line rule.
180-38-15
3. d= 70, vertically opposite angle
using angles on a straight line, 180 - 70 - 40 ÷ 2
we now have the two angles and because they are vertically opposite a and c = 35
b = 40 because of vertically opposite angles
4. a=30 because 90-70
since a=30, take 90 - 30 to get b, 70
d= 70, vertically opposite angles
e = 130 because a+b+c, vertically opposite angles
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1210 1331
Option 2 (amount in dollars) 1100 1200 1300
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
Answers
A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.
B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;
Option 1; f(n) = n + 100
Option 2; f(n) = n + 100x
C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900
How to solve Linear functions?A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.
For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.
B) For option 1, the function is;
f(n) = n + 100
For option 2, the function is;
f(n) = n + 100x
C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.
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Given the side lengths, determine whether the triangle is acute, right, obtuse, or not a triangle.
15, 16, 21
Answers
The triangle of sides 15, 16, and 21 is Acute.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
We can define a "form factor" for a triangle as ;
f = a² +b² -c²
Here, c is the longest side length. It will be interpreted as :
negative -- obtuse triangle
zero -- right triangle
positive -- acute triangle
For this triangle, our "form factor" is ...
f = 15² +16² -21²
f = 225 +256 -441
f= 40 . . . . a positive number
Hence, the triangle is Acute.
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6/7- 8/9 /- means fraction symbols
Answers
Juan has 5 boxes of pencils with x pencils in each. What expression would you use to represent the
total number of pencils that Juan has? Help plz
Answers
Answer:
5x
Step-by-step explanation:
If Juan has the same x amount of pencils in each of his five boxes then you would multiply 5 times x to find the total number of pencils he has.
7.
Mr. Mones showed his class three figures as shown below
Which of the figures that Mr. Mones showed his class show a proportional relationship between x and y?
Figure I and II
Figure II only
Figure II and III
Figure III only
Answers
Answer:
i got c
Step-by-step explanation:
Sketch the region enclosed by the given curves.
y = 4/x
y = 16x
y = (1/16)x
x > 0
Find its Area.
Answers
Area enclosed by the given curves
y = 4/x, y = 16x, y = (1/16)x, x > 0 is 4log16 = 16log2
Describe the simple curve with an example?Closed curves include, but are not limited to, triangles, quadrilaterals, circles, etc. A simple closed curve is one that begins and ends at the same location without crossing itself. An easy closed curve is a circle.
What kinds of curves are there?Straight Curve a curve that reverses direction but does not cross over itself.
Complex Curve. Open Curve is a particular kind of non-simple curve that crosses its course.
Concealed Curve.
curving upward.
Curve to the left.
Images of curved lines.
We need to break the area into two regions, because the two top curves intersect at x = 1/2
So, the area is
∫[0,1/2] 16x - x/16 dx + ∫[1/2,8] 4/x - x/16 dx
= (8x^2-x^2/32)[0,1/2] + (4logx-x^2/32)[1/2,8]
= 255/128 + (4log16 - 255/128)
= 4log16 = 16log2
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The annual profits of a company are modeled by the function f(x) =x4 – 87x2 – 26x + 2680,where f(x) represents an amount in thousands of dollars, and x is years, starting in 1950. During what years has the company had profits of one million dollars or more?
Answers
Answer:
1950 to 1955, and 1958 to the present
Step-by-step explanation:
did the assignment
Answer:
D. 1950 to 1955, and 1958 to the present
Step-by-step explanation:
edge 2020
Solve there Systems of equations. 2x + y = 15
3x - y = 5
Answers
Answer:
your answer would be (4, 7)
Step-by-step explanation:
Decompose the relations to BCNF : i. R=(ABCD)F={AB→C,B→D;C→A} ii. R=(A,B,C,D,E),F={AB→CE,AC→D,BE→CD,C→D,E→AB}
Answers
Decomposed relations are i. R = R1 ∪ R2 ∪ R3, where R1 = (ABC), R2 = (BD), and R3 = (CA) , ii. R = R1 ∪ R2 ∪ R3 ∪ R4 ∪ R5, where R1 = (ABCE), R2 = (ACD), R3 = (BEDC), R4 = (CD), and R5 = (EAB).
To decompose the given relations into Boyce-Codd Normal Form (BCNF), we need to analyze the functional dependencies and ensure that each functional dependency is fully satisfied.
i. R = (ABCD), F = {AB→C, B→D, C→A}
We observe that the functional dependencies in F are:
1. AB→C
2. B→D
3. C→A
To achieve BCNF, we need to decompose R based on these dependencies. Let's analyze each dependency:
1. AB→C: Since AB is a candidate key (a minimal superkey), we create a new relation, R1 = (ABC), and remove AB→C from F.
2. B→D: As B is not a candidate key, we create another relation, R2 = (BD), and remove B→D from F.
3. C→A: C is not a candidate key, so we create a third relation, R3 = (CA), and remove C→A from F.
The final decomposition is R = R1 ∪ R2 ∪ R3, where R1 = (ABC), R2 = (BD), and R3 = (CA). All functional dependencies are now fully satisfied in BCNF.
ii. R = (A, B, C, D, E), F = {AB→CE, AC→D, BE→CD, C→D, E→AB}
We analyze the functional dependencies in F:
1. AB→CE
2. AC→D
3. BE→CD
4. C→D
5. E→AB
To achieve BCNF, we decompose R based on these dependencies:
1. AB→CE: We create a new relation, R1 = (ABCE), and remove AB→CE from F.
2. AC→D: We create R2 = (ACD), and remove AC→D from F.
3. BE→CD: We create R3 = (BEDC), and remove BE→CD from F.
4. C→D: We create R4 = (CD), and remove C→D from F.
5. E→AB: We create R5 = (EAB), and remove E→AB from F.
The final decomposition is R = R1 ∪ R2 ∪ R3 ∪ R4 ∪ R5, where R1 = (ABCE), R2 = (ACD), R3 = (BEDC), R4 = (CD), and R5 = (EAB). All functional dependencies are now fully satisfied in BCNF.
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Triangle rst has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. what is the area of triangle rst? round to the nearest square inch.
Answers
The area of the triangle is 94.9 square inches
For given question,
We have been given triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches.
Let x be the third side of ΔRST
⇒ 22 + 13 + x = 50
⇒ x = 50 - 35
⇒ x = 15
Let s = sum of three sides of the triangle / 2
s = (22 + 13 + 15)/2
s = 25
Now using the formula for the area of the triangle,
A = √[s × (s-a) × (s-b) × (s-c)]
Let a = 22 inches, b = 13 inches, c = 15 inches
Substituting the values,
⇒ A = √[25 × (25 - 22) × (25 - 13) × (25 - 15)]
⇒ A = √(25 × 3 × 12 × 10)
⇒ A = √9000
⇒ A = 94.9 square inches
Therefore, the area of the triangle is 94.9 square inches
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The area of triangle rst which have sides 22 inches and 13 inches with perimeter 50 inches is 95 square inches.
We are given that the two sides of the triangle rst are 22 inches and 13 inches respectively. Also perimeter of the triangle rst is 50 inches.
We have to find the area of triangle to the nearest square inches.
Let the third side of the triangle rst be x.
Hence,
22 + 13 + x = 50 inch
35 + x = 50 inch
x = 50 - 35
x = 15 inches
Hence, the third side of the triangle is 15 inches.
We will use the Heron's formula here to find the area of the triangle.
Heron's formula = \(\sqrt{s(s-a)(s-b)(s-c)}\)
Here,
s = Semi- perimeter
a, b, and c are sides of the triangle.
Hence,
\(s=\frac{50}{2} \\\\s=25 inches\)
a = 22 inches
b = 13 inches
c = 15 inches
Hence,
Area of the triangle rst = \(\sqrt{25(25-22)(25-13)(25-15)}\\\\ \sqrt{25(3)(12)(10)} =\sqrt{5*5*3*3*2*2*5*2}=5*3*2\sqrt{5*2}=30\sqrt{10}\)
We know that,
\(\sqrt{10}\) ≈ 3.162277
Hence,
\(\sqrt{10} * 30\) ≈ 94.86831 ≈ 95 square inches.
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the length=2.3m and breath=90cm find the perimeter and area of rectangle
Answers
Answer:
the length=2.3m and breath=90cm find the perimeter and area of rectangle
Step-by-step explanation:
length ( l ) = 2.3m breadth ( b ) = 0.9mperimeter = 2( l + b ) = 2 (2.3 + 0.9) = 2 × 3.2 = 6.4marea = l × b = 2.3 × 0.9 = 2.07m²MARK ME BRAINLISTWhich of the following terms correctly describe the object below?
Check all that apply.
a. polyhedron
b. pyramid
c. prism
d. solid
e. cube
f. polygon
*will mark brainliest :))
Answers
Answer:
The given figure is:
a. Polyhedron
c. prism
d. solid
Step-by-step explanation:
First of all, let us consider the given image.
It is a 3 dimensional figure.
It has 2 equal bases which are pentagonal.
Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces.
The faces can be of 'n' number of edges (Polygonal faces).
Its edges are straight, has sharp corners which are also known as vertices.
The given image is a polyhedron as per above definition.
b. Pyramid:
It is also a 3D shape which can have a polygonal base and its faces are triangular which converge on the top to one point.
The given image does not converge to a point on the top, so not a pyramid.
c. Prism:
It is a 3D shape which has it two bases as polygonal structure.
The two bases are equal in shape and size.
There are faces on the body of prism which are formed by joining the edges of the bases.
The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height.
So, the given image is a Solid.
e. Cube:
Cube is a 3D figure, which has all its faces in square shape.
All the sides are equal for a cube.
The given image is not a cube.
f. Polygon:
A polygon is a closed figure in 2 dimensions which has n number of sides.
The given image is not a polygon.
Answer: The given figure is:
a. Polyhedron
c. prism
d. solid
The given figure is a Polyhedron, prism and solid.
What is a polyhedron?A polyhedron is a three-dimensional geometry having plane surfaces connected together with sharp edges and pointed vertices.
First of all, let us consider the given image. It is a 3-dimensional figure. It has 2 equal bases which are pentagonal. Its faces are made along the sides of the bases and are rectangular in shape.
Now, let us classify the given image in the following:
a. Polyhedron:
A polyhedron is a 3-D (three dimensional) shape in which there are flat faces. The faces can be of 'n' number of edges (Polygonal faces). Its edges are straight, has sharp corners which are also known as vertices. The given image is a polyhedron as per the above definition.
c. Prism:
It is a 3D shape which has it two bases as a polygonal structure.The two bases are equal in shape and size. There are faces on the body of prism which are formed by joining the edges of the bases. The given image is a prism with pentagonal bases.
d. Solid:
Any 3D image is called a solid and has a length, width and height. So, the given image is a Solid.
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The cheeseburgers and metoder ofres contain a total of 1150 Gories. The there and two morders offres com a total of 2200 calories. Find the core content of each item burger calores canes
Answers
After the calculations we came to a conclusion that Cb = 500 calories and Mo = 150 calories.
To determine the calorie content of each item, we can set up a system of equations based on the given information.
From the given information, we know that the total calorie content of the cheeseburgers and milkshakes is 1150 calories. This can be expressed as Cb + Mo = 1150.
Additionally, we are told that three cheeseburgers and two milkshakes have a total calorie content of 2200 calories. This can be expressed as 3Cb + 2Mo = 2200.
Solving this system of equations, we can find the values of Cb and Mo, which represent the calorie content of a cheeseburger and a milkshake, respectively.
Further calculation reveals that Cb = 500 calories and Mo = 150 calories.
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What are the domain restrictions of q^2−7q−8 divided by q^2+3q−4 ?
o q≠1 and q≠−8
o q≠−1 and q≠8
o q≠−1 and q≠4
o q≠1 and q≠−4
Answers
The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)
The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:
q² + 3q - 4 = 0
Now, we can factorize the quadratic equation:
(q + 4)(q - 1) = 0
To find the values of q, we set each factor equal to zero and solve for q:
q + 4 = 0 or q - 1 = 0
Solving these equations, we get:
q = -4 or q = 1
So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.
Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.
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Complete Question:
What are the domain restrictions of q²−7q−8/q²+3q−4?
a) q≠1 and q≠−8
b) q≠−1 and q≠4
c) q≠1 and q≠−4
d) q≠−1 and q≠8
1/5÷3/5=
in simplest form
Answers
Answer:
1/5 + 3/5 = 45 = 0.8
Step-by-step explanation:
Spelled result in words is four fifths.
Which of the equations are linear equations? Explain reasoning.
5x − 4y = 3
3x + 3y = 2
2x2−4y2=11
Answers
Answer:
5x - 4y = 3 and 3x + 3y = 2 are linear equations.
Step-by-step explanation:
Linear equations:
Linear equations are algebraic equations with highest power of the variable 1.
So, 5x - 4y = 3 and 3x + 3y = 2 are linear equations.
In a survey of teens, 19% like to volunteer at animal shelters. About how many teens out of 995 would say they like to volunteer at animal shelters?
Answers
Answer: 189 teens
Step-by-step explanation:
Given
- There are 19% of teens who like to volunteer at animal shelters
- There are in total 995 teens
Solve
19% × 995= 189.05
189.05≈189 (Since people must be in whole numbers, we need to round)
Hope this helps!! :)
Please let me know if you have any questions
Help me please
Brainliest if correct THX!!!
Answers
Answer:
1. irrational number
2. rational number
3. terminating decimal
4. repeating decimal
Step-by-step explanation:
1. If x isn't rational, it must be an IRRATIONAL NUMBER(the root I usually means not, hence the opposite of rational)
2. RATIONAL NUMBER
3. TERMINATING DECIMAL
4. 0.77777...= REPEATING DECIMAL(7 is repeating)
4
A, B & C lie on a straight line.
BD = CD.
∠
BDC = 50° and
∠
ADB = 10°.
Work out
x
,
Answers
Answer:
x = 55degrees
Step-by-step explanation:
Find the diagram attached
Since triangle DBC is isosceles, the bse angles are equal. Let the base angles be y, hence;
y + y + <BDC = 180
2y + 50 = 180
2y - 180 - 50
2y = 130
y = 65
From triangle ADC;
x + < ADB + <BDC + <DCB = 180
x + 10 + 50 + 65 = 180
x+ 125 = 180
x = 180 - 125
x = 55degrees
Answer:
55
Step-by-step explanation:
=55
Terry pays £434.71 a year on his car insurance.
The insurance company increases the price by 5.7%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.
Answers
Answer:£459.49
Step-by-step explanation:
(£434.71)*(1.057) = £459.49
For argument ((j→c∧h)∧(¬h))⇒(¬j), either show it is valid via logical equivalence and inference rules, or show it is invalid through a counterexample with truth value assignments of j,c,h.
Answers
The argument ((j→c∧h)∧(¬h))⇒(¬j) is valid using logical equivalence and inference rules.
To prove the argument is valid, follow these steps:
The following logical equivalences hold: j → c ∧ hj ≡ ¬h ∨ ¬cj → ¬h ≡ ¬c ∨ ¬h. Using the logical equivalences, we can then rewrite it as follows:¬h ∨ ¬c ∨ ¬j ≡ ¬(¬h ∨ ¬c ∨ ¬j)Inference rules: To prove the validity of the argument, we will make use of the modus tollens inference rule. The modus tollens rule states that if we have a conditional statement of the form p → q, and we know that q is false, then we can infer that p is false as well. So, (¬j).¬j can be rewritten as j → ⊥, where ⊥ represents a contradiction or falsehood. Hence, we can apply the modus tollens rule to the conditional statement (j → c ∧ h) ∧ ¬h → (¬j), as follows: ¬(j → c ∧ h) ∧ ¬h¬(j → c ∧ h). Using the logical equivalences, we can then further simplify the expression as follows: ¬(¬h ∨ ¬c ∨ ¬j)∧ ¬h¬(¬h ∨ ¬c ∨ ¬j)¬(j → c ∧ h) ∧ ¬h ≡ ¬(¬h ∨ ¬c ∨ ¬j) ∧ ¬h ≡ ¬(j → c ∧ h) ∧ ¬hTherefore, the argument ((j→c∧h)∧(¬h))⇒(¬j) is valid through logical equivalence and inference rules.
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what is slope if -3
Answers
Answer:
yep
Step-by-step explanation:
one angle of a triangle mesures 24 more than the smallest angle in the triangle. the third angle measures twice the measure of the smallest angle
What is the measure of the smallest angle?
24
39
52
54
Answers
The answer, the measure of the smallest angle is 39° in the triangle.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
Let x be the smalletst angle
2nd angle will be x+24
and 3rd angle will be 2x
So sum of all angles x+2x+x+24=180
4x=180-24
x=156/4
x=39
Hence the measure of the smallest angle will be 39°
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Bethany wants to build a wooden deck on her patio, which is in the shape of a parallelogram. The area of the patio is 580 ft2. Find the base. Round your answer to the nearest foot.
Answers
The base of the parallelogram is 18. 3 feet
How to determine the base of the parallelogramFrom the information given, we have that;
Area = 280ft^2
height = 5x
Base = 6x
Note that he formula that is used for calculating the area of the parallelogram is represented with the equation;
Area = bh
Given that the parameters are;
b is the base of the parallelogramh is the height of the parallelogramSubstituting the values of area, base and height.
280 = 5x × 6x
280 = 30x^2
Divide both sides by 30
x^2 = 280/30
Find the square root of both sides
x = √(280/30)
We have that the base = 6x
Substitute the value of x, we get;
Base = 6x = 6(√(280/30))
Base = 18.3ft
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What is 43.0 divided by 0.8
Answers
Answer:
53.75
Step-by-step explanation:
Weirdly it is quite a big number. Just either use a calculator to get the answer, and to double check multiply the answer (A.K.A 0.8 * 53.75) and it should show up as your total, which is 43.0. So answer is 53.75. Hope this helps. Have a great day. :)
Como expresar este ejercisio por cada 6 cuadrados hay 3 círculos.
Answers
The ways that the exercise can be expressed such that for every 6 squares there are 3 circles include:
Ratio FormProportional statement Equation form How to express the exercise ?This question is asked in Spanish on an English site so the answer will be provided in English for better learning by other students.
The ratio of squares to circles is 6:3 or simplified, 2:1. This means for every 2 squares, there is 1 circle.
You could also use a proportional statement such that the number of squares is twice the number of circles. For every 6 squares, there are 3 circles.
There is also equation form where we can say, if S is the number of squares and C is the number of circles, the relationship could be expressed as S = 2C. This means the number of squares is twice the number of circles.
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The translated question is:
How to express this exercise for every 6 squares there are 3 circles.
SOMEONE HELP ME PLEASE!!!!
Answers
Answer:
2 < X < 77 is the right answer.
solution,
5x - 10 < 25
5x < 25 + 10
5x < 35
X < 35/5
X < 7
Hope this helps...
Good luck on your assignment..
please help quickly thank you
Answers
Answer:
d is the answer
Step-by-step explanation:
D is the answer.