Answers
The numeric value of f(x) at x = π/5 is given as follows:
f(π/5) = - 2π/5 - 2
How to obtain the function?We are given the second derivative of the function, as follows:
f''(x) = -25sin(5x).
As we have the second derivative of the function, the function itself is obtaining integrating the second derivative twice.
Using integral by substitution, the first derivative is given as follows:
f'(x) = 5cos(5x) + K1
In which K1 is the constant.
When x = 0, f'(0) = 3, hence the value of K1 is obtained as follows:
3 = 5 + K1
K1 = -2.
Hence:
f'(x) = 5cos(5x) - 2.
Integrating again, the function is given as follows:
f(x) = 5sin(5x) - 2x + K2.
When x = 0, y = -2, hence the constant K2 is obtained as follows:
K2 = -2.
Thus the function is:
f(x) = 5sin(5x) - 2x - 2.
The numeric value of the function at x = π/5 is obtained as follows:
f(π/5) = 5sin(5(π/5)) - 2(π/5) - 2.
f(π/5) = 5sin(π) - 2π/5 - 2
f(π/5) = - 2π/5 - 2 -> as sin(π) = 0.
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Related Questions
PLSSSSSSSSSSSSSSS HELP ME I WILL GIVE BRAINIEST
Answers
Absolute value numbers will always be positive numbers
Answer:
The answer is A
Step-by-step explanation:
Use a calculator to see what would happen if you used a credit card to pay the minimum monthly payment. Calculate using the following information: Cost of computer (balance): $600 Annual percentage rate (APR): 12.9% Total duration of payments: 2 years Use the simple interest formula: A = (P)(r)(t) If you make only the minimum payment each month, what will the total cost of the computer be?
Answers
Answer:
C. $755 i got it right
Step-by-step explanation:
If you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To calculate the total cost of the computer if you make only the minimum payment each month, we need to use the simple interest formula:
A = P(1 + rt)
where A is the total amount paid, P is the principal or balance, r is the annual interest rate expressed as a decimal, and t is the time in years.
P = $600
r = 12.9% or 0.129 (annual interest rate)
t = 2 years
To find the monthly interest rate, we divide the annual interest rate by 12 (the number of months in a year):
Monthly interest rate = 0.129 / 12 = 0.01075
Now, we can use this monthly interest rate to calculate the minimum monthly payment:
Minimum monthly payment = 1% x P = 0.01 x $600 = $6
Therefore, the minimum monthly payment is $6.
To find the total cost of the computer over the 2-year period, we need to calculate the total amount paid (A) by making the minimum monthly payment each month:
A = P(1 + rt)
A = $600(1 + 0.01075 x 2 x 12)
A = $600(1 + 0.258)
A = $755.00
Therefore, if you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).
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Damian reads 21 pages in 1 hour. How many pages can he read in 3 hours? StartFraction 21 pages Over 1 hour EndFraction = StartFraction question mark pages Over 3 hours EndFraction To go from 1 hour to 3 hours, you _______ . Damian can read _________ pages in 3 hours.
Answers
Answer: (Multiply by 3)
63 pages in 3 hours
Step-by-step explanation:
Answer:
To go from 1 hour to 3 hours, you
✔ multiply by 3
.
Damian can read
✔ 63
pages in 3 hours.
Step-by-step explanation:
Find the area of the shape shown below.
Answers
Answer:
The answer is 32
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
((base 1 + base 2)/ 2 )* h
Now all you have to do is substitute the numbers in.
Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.
Answer:
32 square units
Step-by-step explanation:
\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)
Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.
Ashley and her brother combined to read a total of 33 books over the summer. Ashley read three more than four times as many books as her brother . How many books did each person read?
Answers
Answer:
Ashley read 27 books and her brother read 6 books.
Step-by-step explanation:
Let the number of books her brother read be x.
No. of books her brother reads = x
No. of books Ashley reads = 4x + 3
No. of books her brother reads + No. of books Ashley reads = 33
x + 4x + 3 = 33
Evaluate.
5x + 3 = 33
Isolate 5x.
5x = 33-3
= 30
Find x.
x = 30 ÷ 5
x = 6
Amount of books her brother reads = 6
Amount of books Ashley reads = 4(6) + 3
= 24 + 3
= 27
Nolan was given a box of assorted chocolates for his birthday. Each night, Nolan treated himself to some chocolates. There were originally 30 chocolates in the box and after 8 nights, there were 6 chocolates remaining in the box. Write an equation for
C
,
C, in terms of
t
,
t, representing the number of chocolates remaining in the box
t
t days after Nolan's birthday.
Answers
The equation of remaining chocolate C in terms of t is C = 30 - 3t.
What is an equation?A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.
Given that,
Initial number of chocolates in box = 30
Also given that after 8 nights, number of remaining chocolates = 6
Implies that,
In 8 nights, 24 chocolates were treated.
In 1 night, 3 chocolates were treated.
The equation of remaining chocolate C in terms of t can be written as
C = 30 - 3t.
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Determine the domain of each relation, and determine whether each relation describes y as a function of b, x = b
Answers
The Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.
Explain about the domain of the function?X is equal to why's absolute value, and we're looking for the domain. Remember that the domain is simply the set of all conceivable X values. As a result, when we look at the this equation, an absolute value sign just on y axis makes all negative numbers positive and all positive numbers, just that one number, positive.For the stated question:
Relation : x = b
Its absolute value of a negative is equal to the absolute amount of a positive alone.
Since zero's absolute value was only zero, all of the X values has to be positive or zero. Because if an exit value had a negative value, the absolute value sign could be in contravention of its rule.Therefore, the domain includes only positive numbers plus zero, and we can use any value for X to check whether or not it is a function. Let's assume that X is 20. 20 equals are available. the reason in its entirety Since we just observed that absolute value of the a negative number up above, y in this case may either equal only positive 20 and y can equal negative 20. This case's negative 20 is only 20, after all.Thus, the Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.
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\(\frac{2}{3} + \frac{4}{6}\)
Answers
Answer:
\(\huge\boxed{\sf 1 \frac{1}{3}}\)
Step-by-step explanation:
Given expression:\(\displaystyle =\frac{2}{3} + \frac{4}{6} \\\\Equalize \ the \ denominator \\\\= \frac{2 \times 2}{3 \times 2} + \frac{4}{6} \\\\= \frac{4}{6} + \frac{4}{6} \\\\Add \\\\=\frac{4+4}{6} \\\\= \frac{8}{6} \\\\Simplify\\\\= \frac{4}{3} \\\\Convert \ into \ mixed \ fraction\\\\= 1 \frac{1}{3} \\\\\rule[225]{225}{2}\)
Mom baked a Dutch apple pie in a 9-inch pie pan. She cut the pie into 6 equal pies so that
everyone gets the same sized piece.
a. Determine the central angle created by two pieces of pie.
b. Determine the area covered by each piece of pie to the nearest tenth of a square inch.
c. Determine the circumference of the original pie to the nearest tenth of an inch.
9
d. If a piece of pie had an arc length of g7, determine the area of the piece of pie to the
nearest tenth of a square inch. What would be the central angle of this piece of pie?
Answers
The area and arc length of each piece can be found using the
relationship between a circle and a sector of the circle.
Responses (b, c, and d are approximated):
a. 120°
b. 10.6 square inch
c. 28.3 in.
d. Area: 15.8 in.², Central angle: 89.1°
How can the pie pieces dimensions be evaluated?Given:
Diameter of the pan, d = 9-inch
Number pie pieces cut from the apple pie = 6
The pie pieces are sectors of a circular pie.
a. The central angle of one pie pieces = \(\dfrac{360^{\circ}}{6}\) = 60°
Therefore;
The central angle of two pie pieces = 2 × 60° = 120°b. Area of circular pie = π·r²
Where;
\(r = \mathbf{\dfrac{d}{2}}\)
Therefore;
\(r = \dfrac{9}{2} = \mathbf{ 4.5}\)
\(The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}\)
The area covered by each pie piece is approximately 10.6 square inchc. The circumference of a circle = 2·π·r
The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.
d. Let the arc length of the pie piece = 7 inches
\(\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8\)
The area of the pie piece is approximately 15.8 in.²\(The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}\)
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0.66666666666 in 3 significant figures
Answers
Answer:We round a number to three significant figures in the same way that we would round to three decimal places. We count from the first non-zero digit for three digits. We then round the last digit. We fill in any remaining places to the right of the decimal point with zeros
Step-by-step explanation:
JKL and CDE are congruent. If JKL = 137, what is CDE
Answers
<CDE = 137°
When two triangles are congruent:
The corresponding angles are equalThe sizes and shapes are equalThe areas are equalThe perimeters are equalSince △JKL and △CDE are congruent, all the corresponding angles are equal.
Therefore, <JKL = <CDE = 137°
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What is the pattern for the sequence 1.3, 8.3, 27.3, 64.3,…?
Answers
The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3
Calculating the pattern for the sequenceThe pattern in the question is given as
1.3, 8.3, 27.3, 64.3,…
In the above expressions and pattern, we can see that
The decimal part remain unchangedThe digit before the decimal is the cube of its positionFrom the above, we have the following
Current term = (n)³.3
Note that the decimal does not represent product
And also the pattern is a geometric sequence
Hence, the pattern for the sequence is f(n) = (n)³.3
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The ratio of 25minutes to one hour is
?
12:5
5:12
1:12
Answers
given that - 1 hour = 60 min
then, 25 60
then, we cut it from the table of 5 !!
therefore, 5:12
Answer:
5:12
Step-by-step explanation:
Ratio of 25mins to one hour
step 1: there are 60 mins in one hour so we can say
one hour = 60 mins.
step 2:
we find the ratio.
25 : 60 ( find the lowest term that can divide both terms without a remainder which is 5).
25 : 60 .. = 5 : 12.
Simplify the expression. √686x¹y7 OA. 7xy √2xy OB. 7zy 2xy Oc 7xy √xy² OD. 7x²y √2xy?
Answers
The correct simplified answer is \(49\sqrt{2xy}\)
According to the question, the expression can be simplified as:
Given expression: \(\sqrt{686 xy7 } = \sqrt{7 X 7 X 7 X 2 X7xy}= 49\sqrt{2xy}\)
Hence, the correct answer is \(49\sqrt{2xy}\)
What is simplification?
The word simplification makes the complicated expression into simpler expression. Simplification method uses basic mathematics properties for the complicated expression. After simplification, the calculation become easy.
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On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
Answers
The statement that is true about the function is:
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).What is the function of a graph?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
The minimum value of the curve = (1.9, -5.7),
The maximum value = (0, 2)
The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)
The point the function crosses the y-axis (the y-intercept) = (0, 2)
The given points can be plotted using MS Excel, from which we have:
F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.
Hence, the correct option is A.
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The Wright family is driving from Dallas, Texas to Portland, Maine: a distance of about
1,875 miles. If they take 15 days to make the trip, how many miles will they drive per
day?
Answers
Answer: 125 miles a day
Step-by-step explanation: Divide 1875 by 15 to get 125 miles a day.
Mr. Marshal spent his salary of $8 400 in the following manner: Rental .....1/5 Food.......1/10 Bank ......1/4 Miscellaneous ......... the remainder. what fraction of the money was spent on miscellaneous. how much did he spend on rental. if marshal spent 4/9 of miscellaneous on a trip what fraction of his entire salary was spent on the trip ?
Answers
Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.
To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.
Rental: 1/5
Food: 1/10
Bank: 1/4
To find the fraction spent on miscellaneous:
Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)
Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40
Fraction spent on miscellaneous = 1 - 17/40 = 23/40
So, Mr. Marshal spent 23/40 of his salary on miscellaneous.
To find the amount spent on rental, we multiply the fraction spent on rental by his salary:
Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680
Therefore, Mr. Marshal spent $1,680 on rental.
If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.
Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90
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What are the zeros of the function below? Check all that apply.A.-5B.2C.-3D.3E.-2F.0
Answers
Given
\(f(x)=\frac{x(x-2)}{(x+3)(x-5)}\)Solution
Set f(x) = 0
\(\begin{gathered} 0=\frac{x(x-2)}{(x+3)(x-5)} \\ Rewrite \\ \frac{x(x-2)}{(x+3)(x-5)}=0 \\ cross\text{ multiply} \\ We\text{ have} \\ x(x-2)=0 \\ x=0 \\ x=2 \end{gathered}\)The final answer
Which expression is equivalent to the given expression
Answers
Answer:
i think the answer is A. 2x^3y^2
HELP!!!! Write an exponential function to describe the given sequence of numbers.
Answers
Answer:
y = 5^(x+1)
Step-by-step explanation:
y = 5^(x+1)
x = 1 for the initial step
Write and equivalent expression for the following expression: ab
Answers
Answer:
ab = a(b)
Step-by-step explanation:
cuz u can just add parentheses
Complete the table below to find solutions to the linear equation 9x+y=−18. A
Answers
Answer:
y=-9x-18
Step-by-step explanation:
u just bring 9x to other side
Answer:
X Y
0 -18
2 -36
-2 0
Step-by-step explanation:
Help pleaseee!! I will give brainlist
Answers
The length FE in the circle is 6 units
The arc AE has a measure of 64 degrees
Calculating the length FEFrom the question, we have the following parameters that can be used in our computation:
The circle
Given that the lengths from the center to either chords are equal
This means that
FE = 6 units
Calculating the measure of arc AEFor the other circle, we have
BC = 58 degrees
AB = ED
The arc AE is calculated as
AE = 180 - BC - ED
Where
AB = ED = BC = 58 degrees
So, we have
AE = 180 - 58 - 58
Evaluate
AE = 64
Hence, the arc AE is 64 degrees
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Perform the indicated operation.
1) f(x) = 4x + 5
Find f(f(-1))
Answers
Answer:
Step-by-step explanation:
f(-1)= 4(-1) + 5 = -4 + 5 = 1
f(1)= 4(1) + 5 = 9
Solve each single-step equation. Show your work. -15+n=-9
Answers
Answer:
6
Step-by-step explanation:
-15+6 means it goes minus basically its 15-6(-15+6)=-9
Answer:
n=24
Step-by-step explanation:
First add 15 to the right side equaling 24. Therefore n=24
there are 50 people in a coffee shop fourteen are tourist.what percent of people in the shop are tourist and non tourist
Answers
Answer:
tourist: 28%
non-tourist: 72%
Step-by-step explanation:
total: 50
tourists: 14
non-tourists:50 - 14 = 36
tourist percentage: 14/50 × 100% = 28%
non-tourist percentage: 36/50 × 100 = 72%
Lin has two small baking pans, each shaped like a rectangular prism.explain or show your reasoning.b. Lin's second pan has a length of 83 inches, a width of 154 inches, and the height of 32 inches. What is the volume of the second pan?
Answers
b)
volume = l x w x h
where
l=length
w=width
h=height
volume = 83 x 154 x 32
=409024 in³
The volume of the second pan is; 409024 in³
Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. Find the weight per carton.
Answers
Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.
Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.
How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.
Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.
The weight per carton is 55 pounds.
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if x²+X+1=0 then what is the value of x²⁰¹⁵ + x²⁰¹³ + x
Answers
Since \(x^2 + x + 1 = 0\) means \(x^2+x = -1\), we have for any \(n\) the recursive relation
\(x^n (x^2 + x) = x^{n+2} + x^{n+1} = -x^n \implies x^{n+2} = -x^{n+1} - x^n\)
Let \(f(x)=x^{2015}+x^{2013}+x\). Substitution using the recursive rule generates an alternating power-reduction pattern:
\(f(x) = \left(-x^{2014} - x^{2013}\right) + x^{2013} + x = -x^{2014} + x\)
\(f(x) = -\left(-x^{2013} - x^{2012}\right) + x = x^{2013} + x^{2012} + x\)
\(f(x) = \left(-x^{2012} - x^{2011}\right) + x^{2012} + x = -x^{2011} + x\)
\(f(x) = -\left(-x^{2010} - x^{2009}\right) + x = x^{2010} + x^{2009} + x\)
\(f(x) = \left(-x^{2009} - x^{2008}\right) + x^{2009} + x = -x^{2008} + x\)
\(f(x) = -\left(-x^{2007} - x^{2006}\right) + x = x^{2007} + x^{2006} + x\)
and so on.
Notice that in the equivalent forms of \(f(x)\) involving 3 terms, the largest power of \(x\) is a multiple of 3, and the next largest power is 1 less. This means after so many iterations of substitutions, we would end up with
\(f(x) = x^3 + x^2 + x\)
Then by factorizing, the expression of interest reduces to
\(f(x) = x (x^2 + x + 1) = x \times 0 = \boxed{0}\)
Write as the opposite of a square root. -3√5
Answers
The value of -3√5 as the opposite of the square root is -75.
What in mathematics is a square root?
The factor we can multiply by itself to obtain a given number is the number's square root.
Square root is represented by the symbol sqrt, which stands for square root of, end square root. Squaring an integer is the reverse of finding its square root.
-3√5
The opposite of the square root is the square, so,
-3√5 = -3 × 5²
-3√5 = - 3 × 25
-3√5 = - 75
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