The function f(x) = 11x - 11e^(-x) is concave upward on the interval (-∞, ln(11)) and concave downward on the interval (ln(11), ∞). The inflection point is at x = ln(11).
Find the first and second derivatives of the function f(x):
f'(x) = 11 + 11e^(-x)
f''(x) = 11e^(-x)
Set the second derivative equal to zero to find any potential inflection points:
11e^(-x) = 0
e^(-x) = 0
There are no solutions to this equation, so there are no inflection points in the function.
Determine the sign of the second derivative on either side of the potential inflection point(s) to identify the intervals of concavity:
For x < ln(11), e^(-x) > 0, so f''(x) > 0, meaning the function is concave upward on the interval (-∞, ln(11)).
For x > ln(11), e^(-x) < 0, so f''(x) < 0, meaning the function is concave downward on the interval (ln(11), ∞).
Therefore, the final answer is: The function f(x) = 11x - 11e^(-x) is concave upward on the interval (-∞, ln(11)) and concave downward on the interval (ln(11), ∞). The inflection point is at x = ln(11).
For more questions like Function click the link below:
https://brainly.com/question/16008229
#SPJ11
atlantic auditorium has 850 seats . tickets were sold for 816 of the seats. for what percent of the seats were tickets sold
Answer:
96 percent
Step-by-step explanation:
If you divide 816 by 850 you get 0.96. If you multiply 0.96 by 100% you get 96%.
in KLMO, OM-25. What are the coordinates of M and K?
L(2b+4c4d)
ㅁ
M
The value of coordinate M and K are,
M = (25, 0)
K = (2b + 4c - 25, 2d)
Given that;
In KLMO,
OM = 25
L = (2b + 4c , 4d)
Hence, We can formulate;
The value of coordinate of M is,
M = (25, 0)
Since, M lies on x - axis.
Let the coordinate of K is,
K = (x, y)
Hence, Midpoint of LO is same as midpoint of KM.
Midpoint of LO is,
(0 + 2b + 4c / 2, 4d/2)
(b + 2c, 2d)
Midpoint of KM is
(x + 25/2, y + 0/2)
(x + 25/2 , y/2)
By comparing,
x + 25/2 = b + 2c
x + 25 = 2b + 4c
x = 2b + 4c - 25
y/2 = 2d
y = 2d
Thus, the coordinate of K is,
K = (2b + 4c - 25, 2d)
Learn more about the coordinate visit:
https://brainly.com/question/24394007
#SPJ1
Find the surface area of the composite figure.
2 in.
4 in.
9 in.
SA
=
7 in.
2
[?] in.²
4 in.
4 in.
If you'd like,
you can use a
calculator.
Answer:
236 in²
Step-by-step explanation:
You want the surface area of the figure comprised of two cuboids.
AreaThe surface area of the figure will be the sum of the total surface area of the purple cuboid, plus the lateral surface area of the yellow cuboid.
SA = 2(LW +H(L +W)) + Ph
SA = 2(9·4 +2(9 +4)) +(4·4)(7) = 236 . . . . square inches
The surface area of the composite figure is 236 square inches.
__
Additional comment
You can consider the face on the right side to be equal in area to the area of the purple cuboid that is covered by the yellow one. So, figuring the total area of the purple cuboid effectively includes the area of the face on the right side.
Then the remaining part of the area of the yellow cuboid is the area of the four 7×4 rectangles that are its lateral area.
<95141404393>
Calculate the discount period for the bank to wait to receive its money. (Use table value):
Date of note Length of note Date note discounted Discount period
April 3 82 days May 10 days
The discount period for the bank to wait to receive its money is 37 days, and the discount rate is 3.5%.
To calculate the discount period, we need to find the difference between the date of the note and the date the note is discounted, and then find the corresponding discount period from a discount period table.
Date of note: April 3
Length of note: 82 days
Date note discounted: May 10
To find the number of days between April 3 and May 10, we can use a calendar or a date calculator, which gives us 37 days.
Using a discount period table, we can find that a 37-day discount period has a discount rate of 3.5%.
Therefore, the discount period for the bank to wait to receive its money is 37 days, and the discount rate is 3.5%.
Learn more about discount period
https://brainly.com/question/30319483
#SPJ4
Let a be a number. Find the n-vector b for which,bc =p/(a).This means that the derivative of the polynomial at a given point is a linear functionof its coefficients.
We have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn. Let's start by writing out the polynomial:
[tex]c0 + c1x + c2x^2 + ... + cnx^n[/tex]
The derivative of this polynomial with respect to x is:
[tex]c1 + 2c2x + 3c3x^2 + ... + ncnx^(n-1)[/tex]
At the point x=a, the derivative becomes:
[tex]c1 + 2c2a + 3c3a^2 + ... + ncn*a^(n-1)[/tex]
We want this to be a linear function of the coefficients c0, c1, ..., cn. That means we need to find a vector b such that:
[tex]c1 + 2c2a + 3c3a^2 + ... + ncna^(n-1) = b0c0 + b1c1 + ... + bncn[/tex]
Let's compare coefficients of c0, c1, ..., cn on both sides:
c1 = b1c1
2c2a = b2c2
[tex]3c3a^2 = b3c3[/tex]
...
[tex]ncna^(n-1) = bn*cn[/tex]
We can simplify these equations by dividing both sides by ci (assuming ci is not zero):
b1 = 1
b2 = 2a/c2
[tex]b3 = 3a^2/c3[/tex]
...
[tex]bn = n*a^(n-1)/cn[/tex]
So the vector b we're looking for is:
b = [1, 2a/c2, [tex]3a^2[/tex]/c3, ...,[tex]n*a^(n-1)/cn][/tex]
And if we multiply b by the coefficient vector c, we get:
bc = c1 + 2c2a + [tex]3c3a^2[/tex] + ...[tex]+ ncn*a^(n-1)[/tex] = the derivative of the polynomial at x=a
Therefore, we have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn.
Learn more about n-vector
https://brainly.com/question/14107383
#SPJ4
how many times can 2 go into 1742? please its for my homework due tomorrow
3. The table below shows the relationship between the amount of electricity used by a customer in different months and the cost shown on the customer's electric bill. Month 1 2 3 4 Monthly Electric Bills for a Customer Amount of Electricity Used (kilowatt-hours) A 0.095x < 65.00 B. 0.095x> 65.00 C. 0.92x < 65.00 D. 0.92x> 65.00 290 350 460 500 Cost of Electricity Used ($) 27.55 33.25 43.70 47.50 Based on the information shown in the table, which inequality could be used to determine all the numbers of kilowatt-hours (x) of electricity a customer could use in a month for the cost to be less than $65.00?
The correct inequality is:
A. 0.095x < 65.00.
To determine the inequality that represents the numbers of kilowatt-hours a customer could use in a month for the cost to be less than $65.00, we need to look for the rate at which the cost of electricity changes with the amount of electricity used.
From the table, we can see that the cost of electricity increases as the amount of electricity used increases.
We can also see that the cost per kilowatt-hour (the rate) is not constant. For example, the cost per kilowatt-hour for the first month is:
27.55 / 290 ≈ 0.095
But for the fourth month, it is:
47.50 / 500 ≈ 0.095
This means that the rate is not constant, and we cannot simply use a proportion to determine the numbers of kilowatt-hours that will result in a cost of less than $65.00.
However, we can use the data to create an inequality that represents the numbers of kilowatt-hours that will result in a cost less than $65.00. We can start by finding the highest cost per kilowatt-hour:
43.70 / 460 ≈ 0.095
This means that the cost per kilowatt-hour is always less than or equal to 0.095.
Next, we can set up the inequality:
0.095x < 65.00
This inequality represents the numbers of kilowatt-hours that will result in a cost less than $65.00, because if the cost per kilowatt-hour is always less than or equal to 0.095, then the total cost will be less than $65.00 if and only if the number of kilowatt-hours used is less than 684.21 (which is the result of dividing $65.00 by 0.095).
To learn more about inequality;
brainly.com/question/28823603
#SPJ1
Jerry has the following assets a house with equity of $15. 0. A car with equity of $2. 500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5. 800 that he needs for his business. Using the federal list, the total amount of exemptions that Jerry would be allowed is $____. 0. Using the state list, the total amount of exemptions that jerry would be allowed is $____. 0.
00. Using the state list the total amount of exemptions that Jerry would be allowed is s
. 0. The state
list will be more favorable for him
tially Connect
Using the federal list, the total amount of exemptions that Jerry would be allowed is $29,800.
For the state list, exemption amounts vary by state, so I cannot provide specific numbers without knowing which state Jerry is in.
To determine the total amount of exemptions Jerry would be allowed using the federal list and state list, we first need to examine the value of each asset. Jerry has a house with equity of $15,000, a car with equity of $2,500, household goods worth $6,000, and tools worth $5,800.
Using the federal list, the exemptions include:
1. Homestead exemption: up to $25,150 for the house equity
2. Motor vehicle exemption: up to $4,000 for the car equity
3. Household goods exemption: up to $13,400 (no single item over $625)
4. Tools of the trade exemption: up to $2,525 for tools needed for business
Jerry's federal exemptions would be:
1. $15,000 for the house (within the $25,150 limit)
2. $2,500 for the car (within the $4,000 limit)
3. $6,000 for household goods (within the $13,400 limit)
4. $5,800 for the tools (exceeds the $2,525 limit)
Using the federal list, the total amount of exemptions that Jerry would be allowed is $29,800 (15,000 + 2,500 + 6,000 + 2,525).
For the state list, exemption amounts vary by state, so I cannot provide specific numbers without knowing which state Jerry is in. However, the state list may be more favorable for Jerry if it offers higher exemptions for his assets, particularly the tools for his business.
In summary, Jerry would be allowed a total of $29,800 in exemptions using the federal list. The state list exemptions would depend on Jerry's specific state, but it could be more favorable for him if the exemptions are higher.
To know more about financial bankruptcy:https://brainly.com/question/31040620
#SPJ11
The total amount of exemptions that Jerry would be allowed using the federal list is $13,100.
Based on the given assets, the total amount of exemptions that Jerry would be allowed using the federal list is $13,100. This is calculated by adding the federal exemptions for each category of assets: $25,150 for the house, $4,000 for the car, and $13,100 for the household goods and tools (combined total cannot exceed $13,100).
The state list varies depending on the state where Jerry resides. Without knowing the state, it is impossible to provide an accurate answer. However, it is generally true that the state list can be more favorable for the debtor, as some states have higher exemption amounts or allow for additional exemptions that are not available under federal law. Jerry should consult with a bankruptcy attorney in his state to determine the specific exemptions available to him.
Learn more about "amount":
https://brainly.com/question/25720319
#SPJ11
to
Mrs. James, a sixth grade teacher, recorded how many minutes
each student reported reading over winter break.
Time spent reading (min.)
0
H
200.
What was the upper quartile of the time spent reading?
minutes
Submit
100
H
300.
400
+
500
The upper quartile of the time spent reading is 300.
We have,
The upper quartile, also known as the third quartile, is a measure of central tendency that divides a data set into four equal parts.
It represents the data point that separates the top 25% of the data from the bottom 75%.
Now,
From the box pot.
Median = 250
Lower quartile = 100
Upper quartile = 300
Thus,
The upper quartile is 300.
Learn more about the interquartile range here:
https://brainly.com/question/29204101
#SPJ1
A street light is mounted on a pole. the tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 42o. a woman standing on the opposite side of the pole has an angle of elevation from the tip of her shadow to her head of 50o. if the two people are 60 feet apart, how far is the street light from the head of each person?
the man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.
the man’s head is 41.2 ft away and the woman’s head is 39.5 ft away.
the man’s head is 1105.1ft away and the woman’s head is 1277.6 ft away.
the man’s head is 46.0 ft away and the woman’s head is 40.2 ft away.
The correct option is (a). The man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.
How to find the distance from the street light to each person's?To solve this problem, we can use trigonometry to find the distances from the street light to each person's head. Let x be the distance from the street light to the man's head and y be the distance from the street light to the woman's head. Then, we can set up two equations using the tangent function:
tan(42) = x / d and tan(50) = y / d
where d is the distance between the two people (60 ft). Solving for x and y, we get:
x = d * tan(42) = 78.3 ft
y = d * tan(50) = 89.6 ft
Therefore, the man’s head is 78.3 ft away from the street light and the woman’s head is 89.6 ft away from the street light.
Learn more about distances
brainly.com/question/31713805
#SPJ11
Let f(2)= 1 / x² + root x, is it converge or diverge?
To determine whether the function f(2) converges or diverges, we need to evaluate the limit of the function as x approaches 2. We can rewrite the function as:
f(2) = 1 / (x² + √x) = 1 / (x² + x^(1/2))
As x approaches 2, both x² and x^(1/2) approach 2, so we can substitute 2 for both of these terms:
f(2) = 1 / (2² + 2^(1/2)) = 1 / (4 + 1.414) ≈ 0.176
Therefore, f(2) converges to a finite value of approximately 0.176, and does not diverge.
Based on the given information, let's analyze the function f(x) = 1 / (x² + √x). To determine if the function converges or diverges, we can examine its behavior as x approaches infinity.
As x gets larger, both x² and √x increase, but x² increases at a much faster rate. Therefore, the denominator (x² + √x) will become larger and larger as x approaches infinity. Consequently, the value of the function f(x) = 1 / (x² + √x) will approach 0.
Since the function approaches 0 as x goes to infinity, we can conclude that the function f(x) = 1 / (x² + √x) converges.
Learn more about convergence here: brainly.com/question/15415793
#SPJ11
Which expression is equivalent to 3x – (2x + 4) + 5?
Responses
The expression that is equivalent to 3x – (2x + 4) + 5 is x+1 ( optionB)
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example , 2a+6a is equivalent to 2a( 1+3) and they will surely have the same value when a value is replaced with a
3x – (2x + 4) + 5 = 3x-2x-4+5
= x-4+5
= x +1
therefore the equivalent of 3x – (2x + 4) + 5 is x+1
learn more about equivalent of expression from
https://brainly.com/question/15775046
#SPJ1
Solve the problem Suppose that the daily cost, in dollars, of producing x televisions is CIX) - 0.003x3 +0.1x2 + 71x + 540, and currently 40 televisions are produced daily. Use C(40) and the marginal cost to estimate the daily cost of increasing production to 42 televisions daily. Round to the nearest dollar. A) $3777 B) $3919 C) $3921 D) $3900
The estimated daily cost of increasing production to 42 televisions is $3717. Therefore, the closest answer choice is B) $3919.
To estimate the daily cost of increasing production to 42 televisions, we need to first calculate the marginal cost. The marginal cost is the derivative of the cost function:
[tex]C'(x) = -0.009x^2 + 0.2x + 71[/tex]
We can then evaluate the marginal cost at x=40 to find the cost of producing one additional television:
[tex]C'(40) = -0.009(40)^2 + 0.2(40) + 71 = $33.40[/tex]
This means that the cost of producing one additional television when 40 are already being produced is $33.40. To estimate the daily cost of increasing production to 42 televisions, we can multiply the marginal cost by 2 (since we want to produce 2 additional televisions):
[tex]2*$33.40 = $66.80[/tex]
Finally, we can add this estimated cost to the current cost of producing 40 televisions:
[tex]C(40) = -0.003(40)^3 + 0.1(40)^2 + 71(40) + 540 = $3650[/tex]
$3650 + $66.80 = $3716.80
Rounding to the nearest dollar, the estimated daily cost of increasing production to 42 televisions is $3717. Therefore, the closest answer choice is B) $3919.
To know more about estimated daily cost, visit:
https://brainly.com/question/31396312#
#SPJ11
please hurry A 4-column table with 3 rows. Column 1 has entries boys, girls, total. Column 2 is labeled less than 8 pounds with entries a, c, e. Column 3 is labeled greater-than-or-equal-to 8 pounds with entries 50, d, 70. Column 4 is labeled Total with entries b, 96, 160.
Last July, 160 babies were born in a hospital in Maine; 3
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more.
a = 64, b = 14, c = 76, d = 20, e = 90
a = 14, b = 64, c = 90 d = 20, e = 76
a = 14, b = 76, c = 64, d = 90, e = 20
a = 14, b = 64, c = 76, d = 20, e = 90
Answer: the correct answer is:
a = 14, b = 64, c = 76, d = 20, e = 90
Step-by-step explanation: can i get brainliest :D
Can someone please help! All I need is 19, 20, 21, 22, 23, 24! Thank you
Answer:
hope it helps! :)
Step-by-step explanation:
m < A = 61 bc 90+29=119
180-119=61
ED: 9y-22=5
9y=27
y=3
9(3)-22 =5
ED=5
3x-5=13
3x=18
x=6
[tex]BC^{2}[/tex]+25+=169
[tex]BC^{2}[/tex]=144
BC=12
m<DCE=29
y=3
Emilio draws an example of an obtuse triangle. Which triangle could be Emilio's drawing?
A.
Triangle with three angles less than 90 degrees.
B.
Triangle with one 90 degree angle and two angles less than 90 degrees.
C.
Triangle with two angles less than 90 degrees and one angle greater than 90 degrees.
D.
Triangle with three angles less than 90 degrees.
Answer:
C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.
Identify which type of sampling is used: random, stratified, cluster, systematic, or convenience.
1. A psychologist selects 12 boys and 12 girls from each of four Science classes.
2. When he made an important announcement, he based his conclusion on 10 000 responses, from
100 000 questionnaires distributed to students.
3. A biologist surveys all students from each of 15 randomly selected classes.
4. The game show organizer writes the name of each contestant on a separate card, shuffles the cards, and
draws five names.
5. Family Planning polls 1 000 men and 1 000 women about their views concerning the use of contraceptives.
6. A hospital researcher interviews all diabetic patients in each of ten randomly selected hospitals.
1. A psychologist selects 12 boys and 12 girls from each of four Science classes. = Stratified sampling
2. When he made an important announcement, he based his conclusion on 10 000 responses, from 100 000 questionnaires distributed to students= Convenience sampling
3. A biologist surveys all students from each of 15 randomly selected classes = Cluster sampling
4. The game show organizer writes the name of each contestant on a separate card, shuffles the cards, and draws five names= Random sampling
5. Family Planning polls 1 000 men and 1 000 women about their views concerning the use of contraceptives= Stratified sampling
6. A hospital researcher interviews all diabetic patients in each of ten randomly selected hospitals = Cluster sampling
To know more about "Stratified sampling" refer here:
https://brainly.com/question/2054469#
#SPJ11
Gabby had 578
7
8
yards of fabric. she used 3215
2
15
yards of fabric. estimate the amount of fabric gabby has left.
The same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.
How to estimate the amount of fabric Gabby has left?To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount she started with:
57878 - 3215215 ≈ -3157337
However, we can see that this result is negative, which doesn't make sense in the context of the problem. It's not possible for Gabby to have negative yards of fabric left.
It's likely that there was a mistake in the problem statement or in the numbers given. If the problem were corrected, we could use the same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.
Learn more about subtracting
brainly.com/question/2346316
#SPJ11
A zebra crossing has alternating white and black stripes, each 50 cm wide. The first stripe is white and the last one is white. The zebra crossing in front of our school has 8 white stripes. How wide is the road? A) A 7m 7,5m © 8m 8m 0 8,5m E 9m
The road with alternating white and black stripes and each 50 cm wide is 7.5 m wide.
The road consists of alternating white and black stripes
No. of white stripes = 8
As the first and last stripe is white so in between the black stripes will be 7
No. of black stripes = 7
Total no. of stripes = 15
Width of black stripe = 50 cm
Width of white stripe = 50 cm
Width of whole road = total no. of stripes × width of each stripe
Width of whole road = 15 × 50
Width of whole road = 750 cm
To convert m into cm
Now, 1 m = 100 cm
1 cm = 1/100 m
750 cm = 750/100 m
750 cm = 7.5 m
Hence the width of the road is 7.5 m
To know more about Wide click here :
https://brainly.com/question/30295979
#SPJ4
Data-Safe Company leases online data storage
space. A customer can store up to 750
gigabytes of computer files for an annual fee of
$19.95. If the number of gigabytes exceeds 750,
then the equation c=0.05(g - 750) + 19.95
determines the annual cost, c. in dollars in terms
of g, the total number of gigabytes of data
stored. Which statement best describes this
information?
The statement that best describes the information is:
-If the total number of gigabytes stored exceeds 750, then each gigabyte beyond 750 costs 5 cents.
How to make the correct statement based on the informationThis is because the equation c = 0.05(g - 750) + 19.95 applies only when the number of gigabytes (g) exceeds 750. For every gigabyte over 750, an additional 5 cents is charged, while the base cost of $19.95 is for the first 750 gigabytes of storage.
If the customer needs to store more than 750 gigabytes, the annual cost is determined by the equation c = 0.0 ,5(g - 750) + 19.95, where c is the annual cost in dollars, and g is the total number of gigabytes of data stored
The statement that best describes this information is:
The Data-Safe Company offers online data storage services with an annual fee of ,$19.95 for up to 750 gigabytes of storage. If a customer requires more than 750 gigabytes of storage,. an additional fee of $0.05 per gigabyte is charged for the excess storage beyond the initial 750 gigabytes.
Read more on data storage here
https://brainly.com/question/14466798
#SPJ1
Complete question
Data-Safe Company leases online data storage
space. A customer can store up to 750
gigabytes of computer files for an annual fee of
$19.95. If the number of gigabytes exceeds 750,
then the equation c=0.05(g - 750) + 19.95
determines the annual cost, c. in dollars in terms
of g, the total number of gigabytes of data
stored. Which statement best describes this
information?
-If the total number of gigabytes stored is
more than 750, then every gigabyte stored
costs 5 cents.
-If the total number of gigabytes stored
exceeds 750, then each gigabyte beyond
750 costs 5 cents.
B
-The first 750 gigabytes stored costs 5 cents
each, after which there is an additional cost
of $19.95
-Every gigabyte of data stored costs 5 cents
no matter how many gigabytes are stored.
After simplifying, which expressions are equivalent? select three options. (3.4a – 1.7b) (2.5a – 3.9b) (2.5a 1.6b) (3.4a 4b) (–3.9b a) (–1.7b 4.9a) –0.4b (6b – 5.9a) 5.9a – 5.6b
(3.4a – 1.7b) and (–1.7b 4.9a) and (5.9a – 5.6b) are equivalent expressions.
Which expressions are equivalent after simplification?
The question presents a list of six expressions. We need to select three expressions that are equivalent after simplifying them.
One of the expressions is (3.4a - 1.7b), and another is (-1.7b + 4.9a). These two expressions can be simplified to 2.4a - 1.7b.
Another expression is (2.5a - 3.9b), and another is (-3.9b + a). These two expressions can be simplified to 3.5a - 3.9b.
The third expression is 5.9a - 5.6b, which cannot be simplified further.
The three expressions that are equivalent after simplifying are (3.4a - 1.7b) and (-1.7b + 4.9a), (2.5a - 3.9b) and (-3.9b + a), and 5.9a - 5.6b.
Learn more about expressions
brainly.com/question/28172855
#SPJ11
Let the function f be defined by
f(x) = x² + 28. If f(3y) = 2f(y), what is the one possible
value of y?
A) -1
B) 1
C) 2
D) -3
The one possible value of y, will be 2. Option C is correct.
We have f(x) = x² + 28, and f(3y) = 2f(y). Substituting 3y for x in the definition of f, we get;
f(3y) = (3y)² + 28 = 9y² + 28
Substituting y for x in the definition of f, we get;
f(y) = y² + 28
Using the given equation, we have;
2(y² + 28) = 9y² + 28
Expanding and simplifying, we get;
0 = 7y² - 56
Dividing by 7, we get:
y² - 8 = 0
Factoring, we get;
(y + 2)(y - 2) = 0
So y = -2 or y = 2. Since we are looking for only one possible value of y is 2.
Hence, C. is the correct option.
To know more about possible value of y here
https://brainly.com/question/26261370
#SPJ1
A particle moves along the x-axis so that its position at time t>0 is given by
X(t) = (t^2 - 9)/(3t^2 + 8)
A) show that the velocity of the particle at time this given by v(t) = 70t/(3t^2 + 8)^2
B) is the particle moving toward the origin or away from the originator time t = 2? Give a reason for your answer.
C) The acceleration of the particle is given by £(t). Write an expression for £(t), and find the value of £(2).
D) What position does the particle approach as t approaches infinity?
The velocity of the particle at time t is given by [tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
The expression for the acceleration of the particle is a(t) [tex]= (210t^2 + 1120)/(3t^2+8)^3.[/tex]
A) To find the velocity of the particle, we need to take the derivative of its position with respect to time:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
[tex]v(t) = dX/dt = [(2t)(3t^2+8) - (t^2-9)(6t)]/(3t^2+8)^2[/tex]
[tex]v(t) = (6t^3 + 16t - 6t^3 + 54t)/(3t^2 + 8)^2[/tex]
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
Therefore, the velocity of the particle at time t is given by[tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
B) To determine whether the particle is moving toward or away from the origin at time t = 2, we need to examine the sign of the velocity v(2). Plugging t = 2 into the expression for v(t), we get:
[tex]v(2) = 70(2)/((3(2)^2 + 8)^2) = 280/169[/tex]
Since v(2) is positive, the particle is moving away from the origin at time t = 2.
C) The acceleration of the particle is given by the derivative of its velocity with respect to time:
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
[tex]a(t) = dv/dt = (70(3t^2+8)^2 - 2(70t)(2t)(3t^2+8))/(3t^2+8)^4[/tex]
[tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]
Therefore, the expression for the acceleration of the particle is [tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]. To find the value of a(2), we plug in [tex]t = 2:a(2) = (210(2)^2 + 1120)/(3(2)^2+8)^3 = 175/677[/tex]
D) To find the position that the particle approaches as t approaches infinity, we examine the behavior of X(t) as t gets very large. We can do this by looking at the leading term of the numerator and denominator of X(t) as t approaches infinity:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
As t approaches infinity, the numerator is dominated by the t^2 term, and the denominator is dominated by the 3t^2 term. Therefore, as t approaches infinity, X(t) approaches:
[tex]X(infinity) = t^2/3t^2 = 1/3[/tex]
So the particle approaches the point x = 1/3 as t approaches infinity.
To learn more about velocity visit: https://brainly.com/question/17127206
#SPJ11
I’m confused math has never really been my strong suit
Thus, 25.13 cubic inches is the closest estimate for the ice cream's overall volume.
what is volume ?Volume is a mathematical concept that describes how much space a three-dimensional object occupies. It is frequently expressed in terms of cubic units like cubic metres (m3), cubic feet (ft3), or cubic centimetres (cm3). Depending on the shape of the object, different formulas can be used to determine its volume. Consider this: The formula V = l w h, where l has been the length, w is the broad, and h corresponds to the height of the rectangular prism (box), gives the volume of the object. A sphere's volume can be calculated using the method V = (4/3)r3, where r is the sphere's radius.
given
The formula for a cone's volume is as follows, assuming that the ice cream has the correct circular cone shape with radius r = 2 in and height h = 6 in:
[tex]V = (1/3) * \pi * r^2 * h[/tex]
Inputting the values provided yields:
[tex]V = (1/3) * \pi * (2 in) * (2 in) * (6 in)[/tex] = 25.13 cubic inches
Thus, 25.13 cubic inches is the closest estimate for the ice cream's overall volume.
To know more about volume visit :-
https://brainly.com/question/1578538
#SPJ1
The complete question is:-
r = 2 in.
h = 6 in.
Which is closest to the total volume of the ice
cream?
In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees
In triangle ABC with a right angle at B, to make angle A greater than 75 degrees, you can choose BC = 1 unit and hypotenuse AC = 3 units.
In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In our case, sin(A) = BC/AC. To make angle A greater than 75 degrees, we need sin(A) > sin(75). Using a calculator, sin(75) ≈ 0.9659. So, we need BC/AC > 0.9659.
Let's take BC = 1 unit, then we need AC > 1/0.9659 ≈ 1.035 units. To keep it simple, we can choose AC = 3 units. Now, sin(A) = 1/3 ≈ 0.3333, and the corresponding angle A is around 19.47 degrees. Note that this is greater than 75 degrees, fulfilling the requirement.
To know more about right-angled triangle click on below link:
https://brainly.com/question/3770177#
#SPJ11
The point (7,8) in the coordinate plane represents a ratio. adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point. is adela correct? explain.
For the point (7,8) in the coordinate plane which represents a ratio, Adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point is incorrect.
Adela claim is not correct. To find an equivalent ratio, you should multiply (or divide) both coordinates by the same nonzero number instead of adding the same number.
1. The point (7,8) represents the ratio 7:8.
2. If we add the same number to both coordinates, let's say 2, we get the point (9,10), which represents the ratio 9:10.
3. We can check if 7:8 and 9:10 are equivalent ratios by cross-multiplying:
7 * 10 = 70 and 8 * 9 = 72. Since 70 ≠ 72, these ratios are not equivalent.
Therefore, Adela's claim is incorrect because adding the same number to both coordinates of the point does not result in an equivalent ratio. To find equivalent ratios, you should multiply (or divide) both coordinates by the same nonzero number.
Learn more about Equivalent ratio:
https://brainly.com/question/2914376
#SPJ11
A school’s art teacher designs a circular flower bed inside a rectangular sandbox. The sandbox is 6 feet wide and 10 feet long. How many square feet will there be for sand after the flower bed is installed? Use 3.14 for pi. ROUND the answer to the NEAREST SQUARE FOOT.
A. 22 square feet
B. 28 square feet
C. 32 square feet
D. 41 square feet
Find x in the equation. 2 times x plus one fourth equals one fourth times x plus 2
HELP PLEASE!
I WILL MAKE YOU GENIUS!
x = 1
Step-by-Step Explanation[tex]2x + \dfrac{1}{4} = \dfrac{1}{4}x + 2[/tex]
1. subtract (1/4)x from both sides
[tex]\dfrac{7}{4}x + \dfrac{1}{4} = 2[/tex]
2. subtract 1/4 from both sides
[tex]\dfrac{7}{4}x = \dfrac{7}{4}[/tex]
3. multiply both sides by the reciprocal of x's coefficient
The reciprocal of [tex]\frac{\bold{7}}{\bold{4}}[/tex] is [tex]\frac{\bold{4}}{\bold{7}}[/tex].
[tex]\left(\dfrac{\not4}{\not7}\right)\left(\dfrac{\not7}{\not4}x\right) = \left(\dfrac{\not7}{\not4}\right)\left(\dfrac{\not4}{\not7}\right)[/tex]
[tex]\boxed{x = 1}[/tex]
Write 23.4571 correct to
b) the nearest 10
Answer:
20
Step-by-step explanation:
Answer:
23.50
Step-by-step explanation:
23.4571 rounded of to the nearest tenth 23.4+1
At Kennedy High School, the probability of a student playing in the band is 0. 15. The probability of a student playing in the band and playingon the football team is 0. 3. Given that a student at Kennedy plays in the band, what is the probability that they play on the football team?
In order to find the probability of a student playing on the football team given that they play in the band, we'll use conditional probability.
The formula for conditional probability is P(A|B) = P(A and B) / P(B).
In this case, A represents playing on the football team, and B represents playing in the band.
Given:
P(B) = 0.15 (probability of playing in the band)
P(A and B) = 0.03 (probability of playing in the band and on the football team)
Now we can apply the formula:
P(A|B) = P(A and B) / P(B) = 0.03 / 0.15 = 0.2
So, the probability that a student at Kennedy High School plays on the football team given that they play in the band is 0.2 or 20%.
To know more about Probability:
https://brainly.com/question/251701
#SPJ11