the velocity of the object at time `t₀ = 5` is `-5` (option D).
The object moves along a coordinate line, its position at each time t ≥ 0 is given by `x(t) = -t² + 5t + 1`. We need to find the velocity at time `t₀ = 5`.
The velocity `v(t)` is the derivative of position `x(t)` with respect to time `t`, so we need to differentiate the given position function to find velocity.
`x(t) = -t² + 5t + 1
`Differentiating `x(t)` with respect to `t` using the power rule of differentiation:
`v(t) = d(x(t))/dt = d(-t² + 5t + 1)/dt = -2t + 5`
We need to find the velocity at `t₀ = 5`.
Substituting `t = 5` into the velocity function `v(t) = -2t + 5`, we get:v(5) = -2(5) + 5= -10 + 5= -5
Therefore, the velocity of the object at time `t₀ = 5` is `-5` (option D).
Answer: option D) `-5`
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Need help with this ASAP! Thank You
Step-by-step explanation:
Statements
Reasons
1. PQ || MN
1. Given
2. O is the midpoint of NP
2. Given
3. NO = OP
3. Definition of midpoint
4. ∠ZMO = ∠QOP
4. Alternate interior angles are congruent (corresponding angles of parallel lines)
5. ∠LNMO = ∠LPQO
5. Alternate interior angles are congruent (corresponding angles of parallel lines)
6. ΔMNO ≅ ΔPRO
6. Angle-side-angle (ASA) congruence theorem
7. AMNO ≅ AQPO
7. Corresponding parts of congruent triangles are congruent (CPCTC)
Which expression is equivalent to 8x + 5x?
Answer:
13x
Step-by-step explanation:
8x + 5x
Combine like terms
13x
Answer:
X(8+5)
Step-by-step explanation:
Distribute the X to each number you get 8x+5x. Therefore the two are equivalent.
The direct distance between city A and city B is 200 miles. The direct distance between city B and city C is 300 miles. Which could be the direct distance between city C and city A?
Answer:
Hey welcome and the answer would be 500 miles
gwen earns 716.01 in 29 hours. how much will she earn in 23 hours to the nearest cent?
Answer:
She will earn $567.87 in 23 hours
Step-by-step explanation:
Because I found out that for every 1 hour she earns $24.69 ($716.01÷29=$24.69). So, then I multiplied $24.69 by 23 and got $567.87. So, Gwen earns $567.87 in 23 hours
Answer:
567.87$
Step-by-step explanation:
This is the answer because, first you must find how much Gwen makes in an hour, you must find it by dividing 716.01 by 29 to get $24.69. Now in order to find how much Gwen makes, we will multiply 24.69 by 23 to get $567.87
six more than two times a number u have to write an algebraic equation
Answer: 2x+6
Step-by-step explanation: two times a number plus six in other words
Answer: 2a+6
Step-by-step explanation:
solve the equation
3x+7y=29
x-3y=-17
Answer:
the answet is x=-2 and y=5
find the coefficient of
a^3
Answer:
1
Step-by-step explanation:
1 is answer.it may help you to understand.
b) Write 25x10^6 in standard form.
Answer:
25x10^6 = 25,000,000
[tex] [/tex]
help me apappp dkneosk
Answer:
C: perpendicular lines
Step-by-step explanation:
A theater manager predicts that 1000 tickets to a play will be sold if each
ticket costs $60. The manager predicts that 20 less tickets will be sold for every $1
increase in price. For what prices p can the manager predict that at least 800 tickets
will be sold?
Answer:
[tex]p\leq\$70.[/tex]
Step-by-step explanation:
The 1000 tickets will be sold when each ticket costs $60.
The manager wants to sell at least 800 tickets which is maximum
1000-800=200 tickets less than 1000.
Given that for 20 less tickets will be sold for every $1 increase in price.
So, 20x2=40 less tickets will be sold for $1x2=$2 increase in price.
Proceeding in a similar way, for any natural number n:
20 x n less tickets will be sold for $1 x n=$n increase in price.
Here, 200=20x10, so n=10
So, 20x10 less tickets will be sold for $1x10=$10 increase in price.
Hence, the manager can increase the price of each ticket up to $10.
So, to sell at least 800 tickets, the maximum price of each ticket can be $60+$10=$70.
Hence, the value of [tex]p[/tex] is
[tex]p\leq\$70.[/tex]
The volume of a sphere is 26667 cm³.
Calculate the diameter of the sphere.
Volume of sphere = πr³
cm
Given the volume of the sphere as 26667 cm³, we calculated the radius to be approximately 17.7 cm using the formula for the volume of a sphere. By multiplying the radius by 2, we found that the diameter of the sphere is approximately 35.4 cm.
To calculate the diameter of a sphere when given its volume, we can use the formula for the volume of a sphere:
V = (4/3) * π * r³
Where V is the volume and r is the radius of the sphere. Since we are given the volume, we can rearrange the formula to solve for the radius:
r = ([tex]\sqrt[3]{(3V / (4\pi )}[/tex]))
Substituting the given volume V = 26667 cm³ into the formula, we have:
r = ([tex]\sqrt[3]{(3 * 26667 / (4\pi )))}[/tex]
Calculating this expression, we find:
r ≈ ([tex]\sqrt[3]{80001 / \pi ))}[/tex] ≈ 17.7 cm
Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:
d = 2 * r ≈ 2 * 17.7 ≈ 35.4 cm
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Let f(x) = - 3x + 5 and simplify f(x + 2).
Step-by-step explanation:
it may help you to understand.
.An open box is to be formed out of a rectangular piece of cardboard whose length is 12cm longer than its width. to form the box, a square of side 5cm will be removes from each corner od the cardboard. then the edges of the remaining cardboard will be turned up. if the box is to hold at most 1900cm³ what mathematical statement would represent the given situation
a. x² - 12x ⩽ 360
b. x² - 12x ⩽ 380
c. x² - 8x ⩽ 400
d. x² + 8x ⩽ 400
The maximum value of x = 18.8 approx. Hence the mathematical statement that represents the given situation is x² - 12x ⩽ 380. The correct option is b.
Given that an open box is to be formed out of a rectangular piece of cardboard whose length is 12cm longer than its width.
To form the box, a square of side 5cm will be removed from each corner of the cardboard. Then the edges of the remaining cardboard will be turned up.
If the box is to hold at most 1900 cm³ then the mathematical statement that represents the given situation is:
x² - 12x ⩽ 380. Hence, option (b) is the correct.
Consider the width of the rectangular cardboard be x cm.
Then its length would be x + 12 cm.
Now the square of 5cm is removed from each corner.
The height of the box would be 5 cm, as given.
Then, the length and width of the box would be (x + 12 - 10) cm and (x - 10) cm respectively.
Hence the base of the box would be x² - 20x + 100 cm².
Now we need to determine the maximum value of x so that the box can hold a maximum of 1900 cm³.
The volume of the box is given by length × width × height
x(x + 2) (5) ⩽ 1900x² + 10x - 1900
⩽ 0x² - 190x + 190 ⩽ 0(x - 10) (x - 19)
⩽ 0x ⩽ 19
[Since x > 0]
Therefore, x lies between 0 and 19.
When we plot the graph for the given expression, the curve intersects x-axis at x = 10 and x = 19.
Hence the value of x should be between 10 and 19.
Now let's determine the maximum value of x. For that, substitute x = 19 in the volume of the box.
We get the volume of the box to be 1901 cm³ which is greater than 1900 cm³.
The correct option is b.
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Determine the (a) Characteristic Polynomial, (b) Characteristic Equation, (c) Eigenvalues (d) Eigenvectors of C (e) Eigenspace (f) Inverse of Matrix & (g) Diagonalized Matrix of A
[ 2 -1 0 ]
A= [ 1 0 -2 ]
[ 2 1 4 ]
(a) The characteristic polynomial of matrix A is[tex]λ^3 - 6λ^2 - 4λ + 24[/tex]. (b) The characteristic equation is[tex]λ^3 - 6λ^2 - 4λ + 24 = 0.[/tex] (c) The eigenvalues of matrix A are λ = 4, λ = -2, and λ = 3. (d) The corresponding eigenvectors can be found by solving the system of equations (A - λI)v = 0, where I is the identity matrix. (e) The eigenspace is the span of the eigenvectors associated with each eigenvalue. (f) The inverse of matrix A is [-0.0833 -0.2917 0.125], [-0.3333 -0.5417 0.25], and [-0.1667 -0.2083 0.125]. (g) The diagonalized matrix of A is [4 0 0], [0 -2 0], and [0 0 3].
(a) To find the characteristic polynomial, we compute the determinant of (A - λI), where A is the given matrix and I is the identity matrix. The characteristic polynomial is obtained by expanding the determinant.
(b) The characteristic equation is formed by setting the characteristic polynomial equal to zero.
(c) The eigenvalues are the roots of the characteristic equation.
(d) To find the eigenvectors, we solve the system of equations (A - λI)v = 0, where v is the eigenvector and λ is the eigenvalue.
(e) The eigenspace is the set of all vectors that can be obtained by scaling the eigenvector associated with a specific eigenvalue.
(f) The inverse of matrix A is found by using the formula A^(-1) = (1/det(A)) * adj(A), where det(A) is the determinant of A and adj(A) is the adjugate matrix of A.
(g) The diagonalized matrix is obtained by using the eigenvectors as columns of the matrix, with the eigenvalues on the diagonal.
In summary, the characteristic polynomial of matrix A is [tex]λ^3 - 6λ^2 - 4λ +[/tex]24, the eigenvalues are λ = 4, λ = -2, and λ = 3, the eigenvectors can be obtained by solving the system of equations, the eigenspace is the span of the eigenvectors, the inverse of A is determined using the formula and the diagonalized matrix is formed using the eigenvectors and eigenvalues.
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A man takes a renovation loan of $28 800 for 4 years at 3.75% per annum. (a) Find the simple interest payable. (b) Find the monthly repayment.
To find the simple interest payable, we can use the formula:
Simple Interest = Principal × Rate × Time
where:
Principal = $28,800
Rate = 3.75% per annum (expressed as a decimal, so 3.75% = 0.0375)
Time = 4 years
(a) The simple interest payable is $4,320.
Simple Interest payable:
Simple Interest = $28,800 × 0.0375 × 4
Simple Interest = $4,320
Therefore, the simple interest payable is $4,320.
(b) The monthly repayment amount is approximately $690.
To find the monthly repayment, we need to calculate the total amount to be repaid and then divide it by the number of months in the loan term.
Total amount to be repaid = Principal + Simple Interest
Total amount to be repaid = $28,800 + $4,320
Total amount to be repaid = $33,120
The loan term is 4 years, which is equivalent to 4 × 12 = 48 months.
Monthly repayment = Total amount to be repaid / Number of months
Monthly repayment = $33,120 / 48
Monthly repayment ≈ $690
Therefore, the monthly repayment amount is approximately $690.
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a landscape photographer observes that the peaks of the histogram are on the left side. what can the photographer deduce from the histogram?
A histogram is a graphical representation of the tonal range of an image. It shows how many pixels are found in an image for each tonal value.
Tonal values run from black on the left side of the histogram to white on the right side. In this case, if the peaks of the histogram are on the left side, then the photographer can deduce that the image is underexposed. This implies that the camera's exposure settings were not correctly calibrated or that there was a lack of light in the environment. When the peaks of the histogram are located on the left side, the image will have a lack of brightness and detail in the shadows.
A landscape photographer should be familiar with histograms and how they function to capture the ideal shot. A histogram is a graphical representation of the tonal range of an image. It shows how many pixels are found in an image for each tonal value. Tonal values run from black on the left side of the histogram to white on the right side. An ideal histogram should have tonal values distributed uniformly across the tonal range. However, if the peaks of the histogram are on the left side, then the image is underexposed. This implies that the camera's exposure settings were not correctly calibrated or that there was a lack of light in the environment.The underexposed image appears darker and lacking in detail in the shadows, which are important for landscape photography. To correct this issue, the photographer should adjust the camera's exposure settings or add more light to the scene, or both. The photographer could increase the ISO value, use a larger aperture, or slow down the shutter speed to fix the exposure. The goal is to reposition the peaks to the center of the histogram or as close as possible to the center of the histogram. Correcting the exposure settings will result in a well-balanced histogram that includes detail in the highlights and shadows.
If the histogram's peaks are on the left side, the image is underexposed. Adjusting the camera's exposure settings or increasing the amount of light in the scene will help the photographer obtain a properly exposed image with a balanced histogram.
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A box has three cards numbered 1, 2, and 3 A bag has three balls labeled A, B, and C Felipe will randomly pick a card from the box and record the number chosen. Then he will randomly pick a ball from the bag and record the letter chosen. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the letter chosen is A.
The total number of possible outcomes for the event in which the letter chosen is A is 3.
A sample space is a set of all the possible outcomes that can be generated by performing a random experiment. Felipe chooses one card from the box, numbered 1, 2, or 3, and then he chooses a ball from the bag, labeled A, B, or C.
Hence, the number of possible outcomes is 3 x 3, or 9.
Below is the sample space describing all the possible outcomes:
{1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Now, we must find all the possible outcomes for the event in which the letter chosen is A.
Felipe picks a card from the box, numbered 1, 2, or 3.
If he selects card 1, he can then choose ball A, B, or C, resulting in three possible outcomes.
If he selects card 2, he can also select ball A, B, or C, resulting in another three possible outcomes.
If he chooses card 3, he can also choose ball A, B, or C, resulting in another three possible outcomes.
Hence, the total number of possible outcomes for the event in which the letter chosen is A is 3.
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Davis earned $3,000 at the bookstore. If he worked for 50 weeks and earned the same amount of money each week, how much did he earn per week?
Answer:
60
Step-by-step explanation
Answer:
$60
Step-by-step explanation:
3000 / 50 =60
the value of 10 divided by - 5 is equal to
Answer:
-2
Step-by-step explanation:
10 divide -5 = -2
Help me solve this problem please
Answer:
a
Step-by-step explanation:
Answer:
2d - 16
Step-by-step explanation:
16 less than twice d
first of all we know were subtracting
-16
and we know were multiplying
2d
now put it together
2d - 16
this problem can be switched
-16 + 2d
6. Four friends play a game. At the end the game, each player counts the number of
points they earned and rolls a die. The bonus score is equal to the number rolled
multiplied by the square root of the number of points earned. The table below shows
each friend's bonus score.
Friend
Bonus Score
Jackie
2 x V 82
Philip
3 x V 51
Cassidy
6 V 19
Antonio
2 v 56
Which of the following lists the friends from highest to lowest bonus score?
No
Answer:
ill help
Step-by-step explanation:
Answer:
Cassidy
6 V 19=26
Philip
3 x V 51=21
Jackie
2 x V 82=18
Antonio
2 v 56=14
I hope this is good enough:
At a football stadium, 25% of the fans in attendance were teenagers. If there were 130 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
Total number of people in the stadium = 520
Step-by-step explanation:
Let the total number of people in the stadium = x
Since, 25% of the fans are teenagers, number of teenagers in the stadium
= 25% of x
= [tex]\frac{25}{100}\times x[/tex]
= 0,25x
If the number of teenagers in the stadium = 130
0.25x = 130
x = [tex]\frac{130}{0.25}[/tex]
x = 520
Therefore, total number of fans in the stadium = 520.
help me please and thank you
Answer:
Option 1
Step-by-step explanation:
If you multiply all the numbers, you get
7.5= 7500
5.6=5600
2.5=2500
Answer:
The answer would be Option C
Step-by-step explanation:
Descending is GREATEST TO LEAST therefore it would be C.
I hope this helped! :)
25 points and brainiest
What is a fraction and how do you use it?
Answer:
Step-by-step explanation:
A fraction is literally a division question in one number. You can use it to determine parts of something (parts of a whole)
Which expression is equivalent to 2x-2(20-3x)+12
Answer:
-7x-48
Step-by-step explanation:
2x-3(20-3x)+12
2x-60-9x+12 (distribute)
-7x-48
hope this helps
brainliest?
how is this scientific notation: 12,050,000 = 1.25×107 wrong
Answer:
1.205 x 10⁷
Step-by-step explanation:
“一二一1
What is x plus 7 equals -1 what does x equal
Answer:
x = -8
Step-by-step explanation:
You'll want to do -1 minus 7 to get your answer, -8.
help me pls
a s a p!
Answer:
45:30:100
Step-by-step explanation:
the answer would be 9:6:20
I will give brainliest
Answer:
NO
Step-by-step explanation:
Because pi goes on forever so you can but if multiplying ;The estimate of pi which is 3.14 you get 9.42
Description What are some of (s i x) columns that should be part of a communication matrix? In addition, what are the three types of project communications timing schedules?
Here are six columns that should be part of a communication matrix: Stakeholder Name, Communication Objective, Information Needs, Communication Channel, Frequency, Responsible Party.
Regarding project communications timing schedules, here are three common types: Regular Scheduled Communications, Ad Hoc Communications, Milestone-Based Communications,
Stakeholder Name: List the names or roles of the project stakeholders who need to receive or provide information.
Communication Objective: Define the purpose or objective of the communication with each stakeholder. This could include sharing project updates, seeking feedback, or discussing specific deliverables.
Information Needs: Specify the type of information required by each stakeholder. This could include progress reports, budget updates, status of deliverables, or any other relevant details.
Communication Channel: Identify the most effective communication channel for each stakeholder. This could be face-to-face meetings, emails, phone calls, video conferences, project management software, or any other medium that suits the stakeholders' preferences and requirements.
Frequency: Determine how frequently you should communicate with each stakeholder. This could be daily, weekly, monthly, or at specific project milestones.
Responsible Party: Assign responsibility for initiating and managing communication with each stakeholder. This ensures accountability and helps avoid miscommunication or missed interactions.
Regarding project communications timing schedules, here are three common types: Regular Scheduled Communications, Ad Hoc Communications, Milestone-Based Communications,
Regular Scheduled Communications: These communications occur on a predetermined schedule, such as weekly or monthly meetings, status updates, or progress reports. They help keep stakeholders informed about the project's overall status and provide an opportunity for discussion and feedback.
Ad Hoc Communications: Ad hoc communications happen as needed or in response to specific events or circumstances. They are not pre-scheduled but are triggered by certain situations. For example, when an issue arises that requires immediate attention or when a milestone is achieved, ad hoc communications may be necessary.
Milestone-Based Communications: Milestone-based communications are tied to specific project milestones or significant events. These communications occur when a particular phase is completed, a major deliverable is achieved, or an important decision needs to be made. They help ensure that stakeholders are informed about important project progress and decisions.
By incorporating these types of project communication timing schedules into your overall communication plan, you can establish effective and timely communication with stakeholders throughout the project lifecycle.
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