Answers
The numeric value of the function f(x) at x = 5 is given as follows:
f(5) = 74.75.
How to obtain the function f(x)?The second derivative of the function f(x) is given as follows:
f''(x) = 2x + 6sin(x).
Integrating the second derivative, the first derivative of the function is given as follows:
f'(x) = x² - 6cos(x) + K.
When x = 0, y' = 2, hence the constant K is given as follows:
2 = -6 + K
K = 8.
Hence:
f'(x) = x² - 6cos(x) + 8.
Integrating the first derivative, the function is given as follows:
f(x) = x³/3 - 6sin(x) + 8x + K.
When x = 0, y = 4, hence the constant K is given as follows:
K = 4.
Then:
f(x) = x³/3 - 6sin(x) + 8x + 4.
The numeric value at x = 5 is given as follows:
f(5) = 5³/5 - 6sin(5) + 8(5) + 4
f(5) = 74.75.
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Related Questions
A design team for an electric car company finds that under some conditions the suspension system of the car performs in a way that produces unsatisfactory bouncing of the car. When they perform measurements of the vertical position of the car y as a function of time t under these conditions, they find that it is described by the relationship: y(t)=y0e−αtcos(ωt) where y0=0.75m, α=0.95s−1, and ω=6.3s−1. In order to find the vertical velocity of the car as a function of time we will need to evaluate the derivative of the vertical position with respect to time, or dydt. For this trajectory, what would the vertical component of acceleration for the module be at time tm=t0−σ=325s? Recall that acceleration is the derivative of velocity with respect to time.
Answers
Answer:
The vertical acceleration when t = 325 s is -2.76 × 10⁻¹³² m/s²
Step-by-step explanation:
The relationship is given as follows;
\(y(t) = y_0 \cdot e^{(-\alpha t)} \times cos (\omega \cdot t)\)
Where:
y₀ = 0.75 m
α = 0.95 s⁻¹
ω = 6.3 s⁻¹
Given that the velocity, v, is found by the following relation;
\(v = \dfrac{dy}{dt} = -\dfrac{\alpha \cdot y_0 \cdot cos(\omega \cdot t) + \omega\cdot y_0 \cdot sin(\omega \cdot t) }{e^{\alpha \cdot t} }\)
The acceleration, a, can be found by differentiating the velocity with respect to time as follows;
\(a = \dfrac{d^2 y}{dt^2} =\dfrac{d\left (-\dfrac{\alpha \cdot y_0 \cdot cos(\omega \cdot t) + \omega\cdot y_0 \cdot sin(\omega \cdot t) }{e^{\alpha \cdot t} } \right )}{dt}\)
\(a = {\dfrac{\left (\alpha ^2 - \omega ^2 \right )\cdot y_0 \cdot cos(\omega \cdot t) + 2 \cdot \omega\cdot \alpha \cdot y_0 \cdot sin(\omega \cdot t) }{e^{\alpha \cdot t} } }\)
Which gives;
\(a = {\dfrac{\left (0.95 ^2 - 6.3 ^2 \right )\times 0.75 \times cos(6.3 \times 325) + 2 \times 6.3\times 0.95 \times 0.75 \times sin(6.3 \times 325) }{e^{0.95 \times 325} } }\)Hence the vertical component of the acceleration is given as follows;
\(a_{vertical} = {\dfrac{ 2 \times 6.3\times 0.95 \times 0.75 \times sin(6.3 \times 325) }{e^{0.95 \times 325} } } = -2.76 \times 10^{-132} m/s^2\)
The vertical acceleration when t = 325 s = -2.76 × 10⁻¹³² m/s².
In this exercise we have to use the knowledge of vertical acceleration to calculate the car's acceleration, so we have to:
\(a= -2.76 * 10^{-132} m/s^2\)
The relationship is given as follows;
\(y(t)=y_0e^{-\alpha t}cos(wt)\)
knowing that the values are:
\(y_0 = 0.75 m\) \(a = 0.95 s^{-1\) \(w = 6.3 s^{-1\)
Knowing that speed can be described by:
\(v= \frac{dy}{dt} = -\frac{\alpha y_0 cos(wt) +wy_0 sin(wt)}{e^{\alpha t}}\)
The acceleration, can be found by differentiating the velocity with respect to time as follows;
\(a = \frac{d^2y}{dt^2}= \frac{(\alpha ^2-w^2) y_0 cos(wt) + 2w\alpha y_0 sin(wt)}{e^{\alpha t}}\)
Replacing the known values, we find that:
\(a= -2.76 * 10^{-132} m/s^2\)
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A researcher wants to know if drinking beer makes a person more attractive to mosquitos. 120 people were recruited to partake in this experiment. Each person was randomly assigned to either drink beer or to ingest water. The subject after drinking their beverage was seated close enough so that odor from the individual would be detectable by the mosquitoes (note that the mosquitoes could not actually touch the humans). The researcher then recorded whether or not the mosquito flew toward the subject (assumed flying toward person meant they were attracted to them). 68 people were assigned to drinking beer, while the other 52 were assigned to drinking water. Out of the 68 who drank beer 43 of them had a mosquito fly toward them, while 26 of those who drank water had a mosquito fly toward them. (This is based loosely off an experiment performed by Lefevre et al. (PLOS ONE, 2010)).
Research Question: Are mosquitos more attracted to people who drink beer than water?
1. Identify the explanatory and response variables. State their type.
2. Fill out the 2x2 table below.
TOTAL TOTAL
3. State the parameter of interest and assign a symbol.
4. Calculate the conditional proportions. What does each stand for? Assign a symbol to each.
5. Are the values in question #4 statistics or parameters? Explain.
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Answer:
No because both of them mosquito got attracted to them
Answer:
Research answer: No because people who drink more water more than beer should NOT have mosquitoes attracted to them
1. i can identify that if you drink more beer you can get mosquito bites
2. 68 26
3. ?
4. they stand for how many people drink beer or water
5. statistics because in my stats, i can see more people drinking water more than beer
Step-by-step explanation:
*BRAINLIEST* What values are equal to the inequality?
Answers
Answer:
A.-9
C.5
D.7
Explanation:
Take every number and put it in the spot of x and multiply every number by themselves like 9x9 or 5x5. Then see if it is equal too or less than 81. If it is equal too or less than 81 then it is correct.
Could I please have BRAINLIEST?
Which of the following sets of interior angle measures can form a triangle?
Select all that apply.
A. 45, 45, 45*
B. 60, 60, 60°
C. 40.50,90°
D. 30.60.90*
E. 90,90°, 45°
F. 90, 90, 90°
pleaseee helppp
Answers
As per the angle sum property, the interior angles that form the triangle is option
B. 60, 60, 60°
C. 40.50,90°
D. 30.60.90*
Angle sum property
Angle sum property states that the sum of all the interior angles of the triangle is equal to 180 degrees.
Given,
Here we have the list of interior angles
A. 45, 45, 45*
B. 60, 60, 60°
C. 40.50,90°
D. 30.60.90*
E. 90,90°, 45°
F. 90, 90, 90°
Now, we have to find in which for these angle will form the tringle.
As per the definition of the angle sum property, the sum of all the interior angle of the triangle is 180°.
Based on these we have to verify each of the given interior angles,
A) 45 + 45 + 45 = 135
B. 60 + 60 + 60 = 180
C. 40 + 50 + 90 = 180
D. 30 + 60 + 90 = 180
E. 90 + 90 + 45 = 225
F. 90 + 90 + 90 = 270
Therefore, based on these values we have identified that the options (B), (C), and (D) forms the triangle.
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HELP ME OUT PLS!!!
What is the measure of Angle z in this figure?
A) 124°
B) 90°
C) 180°
D) 56°
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you roll a six-sided number cube find theprobabilsty of rolling each of the followingP(1 or 6)
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When you roll a six-sided number cube you can get the next set of possible results:
\(\lbrace1,2,3,4,5,6\rbrace\)You have a total of 6 possible results.
From the set of possible results you get the set of presults that are 1 or 6:
\(\lbrace1,6\rbrace\)You have 2 results that are 1 or 6
The probability of rolling (1 or 6) is: The number of results that are 1 or 6 divided in the total number of possible results:
\(P(1or6)=\frac{2}{6}=\frac{1}{3}\)Then, the probability of rolling (1 or 6) is 1/3Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
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developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
I need some help with this problem
Answers
Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))
(a) The number of terms in an arithmetic progression is 40 and the last is -54. Given that the sum of the 15 terms added to the sum of the first 30 terms is zero. Calculate (1) The first term and common difference, (ii) the sum of the progression.
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(i) The first term (a) is 24 and the common difference (d) is -2.
(ii) The sum of the progression is 2520.
i) Finding the first term and common difference:
Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).
The nth term formula is: An = a + (n-1)d
Using the given information, we can substitute the values:
-54 = a + (40-1)d
-54 = a + 39d
We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:
S15 + S30 = 0
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values for S15 and S30:
[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0
Simplifying the equation:
15(2a + 14d) + 30(2a + 29d) = 0
30a + 210d + 60a + 870d = 0
90a + 1080d = 0
a + 12d = 0
a = -12d
Substituting this value into the equation -54 = a + 39d:
-54 = -12d + 39d
-54 = 27d
d = -2
Now we can find the value of a by substituting d = -2 into the equation a = -12d:
a = -12(-2)
a = 24
Therefore, the first term (a) is 24 and the common difference (d) is -2.
ii) Finding the sum of the progression:
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values:
S40 = (40/2)(2(24) + (40-1)(-2))
S40 = 20(48 - 39(-2))
S40 = 20(48 + 78)
S40 = 20(126)
S40 = 2520
Therefore, the sum of the arithmetic progression is 2520.
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Determine if the pairs of expressions below are always equivalent. Prove your answer
A. 4n + 12 and 4 (n +3)
B. m + m 3m and 3m + 2
C. 4x + 8y and 4 (x + 8y)
D. 3 (2t + 2 ) and ( t + 1 ) x 6
E. p + p and p + 7
Answers
9(8d-5)+13=12d-2
No fractions, just a straight number
Answers
Help plz I was stuck on this question for 1 week
Answers
In the diagram, there is a half circle so the circumference would be πr.
Now plug in the radius of 3 to get
Area of circle = 3π or 9.425.
Add 10 to that from the perimeter of the triangle.
Final answer = 19.425
Which expression is equivalent to 7(15 + x)?
Answers
Answer:
7x + 85
Step-by-step explanation:
Distribution
PLEASE HELP!!!!!!!!!!!!!
Answers
Hope this helps!
BRAINLIEST
Find an equation of the line that is perpendicular to 2x-3y=3 that passes through the point (1,2)
Answers
Answer:
The answer is
\(3x + 2y = 7\)Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
From the question the original line is
2x - 3y = 3
Write the equation in the general form above
That's
3y = 2x - 3
y = 2/3x - 1
Comparing with the general equation above
Slope = 2/3
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
Slope of perpendicular line = - 3/2
So the Equation of the line using point
( 1 , 2) and slope - 3/2 is
\(y -2 = - \frac{3}{2} ( x - 1) \\ 2y - 4 = - 3(x - 1) \\ 2y - 4 = - 3x + 3 \\ 3x + 2y - 4 - 3 = 0\)
We have the final answer as
\(3x + 2y = 7\)
Hope this helps you
3. Stu had $50 to buy 5 pair of socks. Please help me.
Answers
Answer:
B. p=(50-25)÷5
Step-by-step explanation:
HELP ASAP AND I KNOW ITS B OR C BUT I DUNNO WHAT ONE
What is the vertical distance between (7, –22) to (7, 12)?
–34 units
–10 units
10 units
34 units
Answers
Answer:
D
Step-by-step explanation:
since the x- coordinates of both points are 7 then the points lie on a vertical line.
the distance is then the absolute value of the difference of the y- coordinates, that is
distance = | - 22 - 12 | = | - 34 | = | 34 | = 34 units
or
distance = | 12 - (- 22) | = | 12 + 22 | = | 34 | = 34 units
Answer:
the vertical distance between (7, –22) to (7, 12) is 10 units
Bill and ross are twins, their brother mark was born on the same day as twins but is three year older. if mark was born in 1990, in what year did the three boys get total age 21
Answers
Step-by-step explanation:
x = age of one of the twin boys
when they had together 21 years of age,
Bill was x years old
Ross was x years old
Mark was x+3 years old
so, we have
x + x + (x + 3) = 21
3x + 3 = 21
3x = 18
x = 6
Bill and Ross were 6 years old.
Mark was 6+3 = 9 years old.
Mark was born in 1990.
1990 + 9 = 1999
so, it was 1999 when they had together 21 years of age.
you roll a single die numbered from 1 to 6 twice. what is the probability of rolling a 6 the first time and an odd number second
Answers
Answer:
1/12
Step-by-step explanation:
Since the two rolls are independent, then the chance of getting a 6 in the first and an odd number in the second is obtained by multiplying the two probabilities.
1/6 is the probability of rolling 6, 1/2 is the probability of rolling an odd number
1/6 times 1/2 is 1/12
hihhhhi someone help please ..
Answers
Answer:
1. 2³
2.2⁵= 2×2×2×2×2= 32
2⁶= 2×2×2×2×2×2= 64
Step-by-step explanation:
hope it helps
Answer:
1. \(2^{3}\)
2. It represents \(2*2*2*2*2\) and \(2*2*2*2*2*2\)
Step-by-step explanation:
1. it would have to be an exponent so 2*2*2 is 8 and 2^3 is also 8
2. it is an exponent so it would basically be multiplying the number times the number/amount of exponents so 2^5= 32 and 2^6=64
hope this helped :)
Point D is the midpoint of what segment?
Answers
Point D is the midpoint of segment GH.
What is midpoint?A point on a line that divides the line into the equal line segments is called midpoint.
In the given diagram,
given lines are GH and CF.
Also given that,
GD = DH
Since, D bisects line GH into two equal parts, therefore by using midpoint property,
D is the midpoint of segment GH.
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I need explanation for example 8.
Thankyou
Answers
There is a probability of 94/315 that the problem will be solved.
We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.
The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.
The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.
The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.
The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.
To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:
2/7 + 4/7 + 4/9 = 94/315
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to make sure you understand the derivation based on the five assumptions (a-e), select the correct order in which the assumptions were used in the derivation above.
Answers
The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.
The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.
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A stainless steel patio heater is a square pyramid. The length of one side of the base is The slant height of the pyramid is What is the height of the pyramid?
The height of the pyramid is about
(Round to one decimal place as needed.)
Answers
Please mark me brainliest !!
Intel estimates that about 12 quintillion transistors are shipped around the globe each year. If that represents 10,000 times the number of ants on the planet, find the number of ants on Earth. (Show all your workings. Final answer MUST standard notation.)
Answers
Answer:
Number on ants on Earth = 1.2 × 10¹⁵
Step-by-step explanation:
1 quintillion = 10¹⁸ or (1000000000000000000)
∴ 12 quintillion = 12 × 10¹⁸
12 quintillion = 10,000 × Number of ants on Earth
Let the number of ants on Earth = n
12 quintillion = 10,000 × n
dividing both sides by 10,000
12 quintillion ÷ 10,000 = n
\(n = \frac{12\ \times\ 10^{18} }{10,000} \\n = \frac{12\ \times\ 10^{18} }{10^{4}}\\n = 12\ \times\ \frac{10^{18}}{10^{4}} \\applying\ the\ second\ law\ of\ indices\ (\frac{x^m}{x^n} = x ^{m-n})\\ n = 12\ \times\ 10^{(18 - 4)\\n = 12\ \times 10^{14}\\in\ standard\ form\\n = 1.2\ \times 10\ \times\ 10^{14}\\\therefore n = 1.2\ \times\ 10^{15}\)
Number on ants on Earth = 1.2 × 10¹⁵
Need help asap. Will mark brainliest.
Answers
Answer:
\(X=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}\)
Step-by-step explanation:
Matrix Equations
Given:
\(A=\begin{bmatrix}-7 &-2 \\9 &7 \\2 &4 \end{bmatrix}\)
\(B=\begin{bmatrix}-4 &-3 \\3 &9 \\9 &-4 \end{bmatrix}\)
Find X such that:
B - X = 3A
Subtracting B:
- X = 3A - B
Multiplying by -1:
X = -3A + B
Find -3A:
\(-3A=-3\begin{bmatrix}-7 &-2 \\9 &7 \\2 &4 \end{bmatrix}=\begin{bmatrix}21 &6 \\-27 &-21 \\-6 &-12 \end{bmatrix}\)
Add to B:
\(X=-3A+B=\begin{bmatrix}21 &6 \\-27 &-21 \\-6 &-12 \end{bmatrix}+\begin{bmatrix}-4 &-3 \\3 &9 \\9 &-4 \end{bmatrix}=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}\)
Thus:
\(X=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}\)
The points D, E, F and G all lie on the same line segment, in that order, such that the ratio of DE:EF:FGDE:EF:FG is equal to 6:5:1.6:5:1. If DG=36,DG=36, find DF.DF.
Answers
Answer:
i
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answers
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
Find the sum of the first 378 counting numbers
WITH SOLUTION
Answers
Step-by-step explanation:
Counting numbers are 1,2,3,4,5........,378
Here it forms an AP with a = 1, d=1, an or l=378, n=378
Sum of 378 numbers = n/2(a+l)
= 378/2(1+378)
= 189(379)
= 71631
MATHH QUESTION HELP. mesasuremtns
Answers
Answer:
Step-by-step explanation:
Answer:
See image
Step-by-step explanation:
Look at the front side of the building. It's a triangle, with the height given. We can see a right triangle here which means we can use the Pythagorean theorem. a^2 + b^2 = c^2 (a and b are the shorter sides called legs and c is the longest side called the hypotenuse)
20^2 + 13^2 = c^2
400 + 169 = c^2
569 = c^2 square root both sides
Sqrt 569 is approximately 23.85 ft. This is the length from the roof peak down the front edge to the bottom front right corner in the image.
Now, if we consider the roof itself. That edge is now a leg (on the front face it was the hypotenuse). The other leg is the 35 ft width given. So we'll use pythagorean theorem again to find the diagonal
23.85^2 + 35^2 = c^2
568.8 + 1225 = c^2
1793.8 = c^2
Square root both sides of the equation.
Sqrt 1793.8 = c
42.35 ft = c
The diagonal of the roof is just over 42 feet, that is 42.35 feet.
