Answers
They ask for the sign of the acceleration of a moving object, and its position function is:
\(s(t)=t^{\frac{5}{2}}(7-t)\)0<= t <=20
Remember that we can know both, the velocity and the acceleration function from the before equation. Because the velocity is the derivate of the position, and the acceleration is the derivate of the velocity, then we have:
\(v(t)=\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}};\text{ }0\leq t\leq20\)And the acceleration:
\(a(t)=\frac{15}{4}t^{\frac{1}{2}}-\frac{35}{4}t^{\frac{3}{2}};\text{ }0\leq t\leq20\)Now we need to solve the inequality:
\(\frac{15}{4}t^{\frac{1}{2}}-\frac{35}{4}t^{\frac{3}{2}}<0\)\(\frac{5}{4}t^{\frac{1}{2}}(3-7t)<0\)\(t>\frac{3}{7}\)And as 0<=3/7<=20, we can say that the acceleration will be negative in the interval:
\((\frac{3}{7},20]\)Now we can directly infer when the acceleration will be positive, but let´s still check mathematically:
\(\frac{5}{4}t^{\frac{1}{2}}(3-7t)>0\)\(3-7t>0\)\(t<\frac{3}{7}\)And as 0<=3/7<=20, we can say that the acceleration will be positive in the interval:
\({}{}{}{}\lbrack0,\frac{3}{7})\)So, we can conclude that the summary of answers is:
Acceleration positive:
\({}{}{}{}\lbrack0,\frac{3}{7})\)Acceleration negative:
\((\frac{3}{7},20]\)
Related Questions
What is the equation to 6x=0.4
Answers
Answer:
Step-by-step explanation:
15
What is the perimeter of parallelogram WXYZ?
The perimeter is ]- (Type an integer or a decimal.)
![What is the perimeter of parallelogram WXYZ?The perimeter is ]- (Type an integer or a decimal.)](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/DHFR5bTuH445TssdoAQiZYa2Vu3Tjmx7.png)
Answers
The perimeter of the parallelogram is; 184
What is the perimeter of the parallelogram?In geometry, the perimeter of a shape is defined as the total length of its boundary.
Now, from the given image, we don't know the vertical sides XW and YZ and we can find it from Pythagoras theorem;
XW = √(68² - 60²)
XW = 32
Thus, the perimeter of the parallelogram is;
Perimeter = 2(32 + 60)
= 2 * 92
= 184
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list all prime numbers. between 10 and 20
2 Identity these prime numbers from the clues
(a) it is less than 30
The sum of its digits is 8
(b) It is between 30 and 60
The sum of its digits is 10
Answers
Answer:
11, 13, 17, 19
Step-by-step explanation:
A) Find the prime #'s less than 30.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
2) See which #'s add and is less than 30 but, equal to 8.
17.
B) Find prime #'s between 30 & 60
31, 37, 41, 43, 47, 53, 59
2) See which #'s add and is add to 10.
37.
Leah borrows £10,000 over 5 years at a simple interest rate of 15%.
Calculate how much interest she will pay over the 5 years?
How much will Leah have to pay back in total
Answers
Answer:
She will pay $7,500 interest over the 5 years
She will have to pay back $17,500 in total
Step-by-step explanation:
Let us revise the rule of the simple interest
I = Prt and A = P(1 + rt) , where:
A = Total Accrued Amount (principal + interest) P = Principal Amount I = Interest Amount r = Rate of Interest per year in decimalt = Time Period involved in months or years∵ Leah borrows £10,000 over 5 years at a simple interest rate of 15%.
∴ P = 10,000
∴ t = 5
∴ r = 15% = \(\frac{15}{100}\) = 0.15
→ Substitute them in the first rule to find the interest
∵ I = 10,000(0.15)(5)
∴ I = 7,500
∴ She will pay $7,500 interest over the 5 years
→ Let us find A
∵ A = 10,000(1 + 0.15×5)
∴ A = 17,500
∴ She will have to pay back $17,500 in total
Ama deposited her babysitting money into her savings account, which already had a
balance of $210. Her new balance is $295. Which equation can be solved to find how
much she deposited?
Answers
Answer:
295= 210+X
Step-by-step explanation:
If she has a total of 295 dollars deposited and she had 210 before then you could just subtract 295-210 to find how much she deposited. The answer would be that she deposited 85 dollars in her savings account and the equation is listed above.
After training Naruto went to a ramen shop for dinner. Since Naruto eats ramen for lunch and dinner daily, the shopkeeper gives him a 33.33% discount. If ramen costs 45 cents, how much does Naruto spend in 15 days?
Points given: 20
Answers
To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.
Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.
66.67% of 45 cents is (66.67/100) * 45 = 30 cents.
So, Naruto spends 30 cents on ramen per day.
To find out how much he spends in 15 days, we multiply the daily cost by the number of days:
30 cents * 15 = 450 cents.
Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.
Answer the following math questions thank you math experts
Answers
Answer:
1) the connection between 2 or more meausures
2) when the r value is closer to 1 or -1 it is a stronger correlation
3) positive correlation would be height and weight. Taller people tend to be heavier. A negative correlation is a relationship between two variables in which an increase in one variable is associated with a decrease in the other
Step-by-step explanation:
choose me as brainlyest:)
All real number except x=
Answers
Answer: -2 and 4
Step-by-step explanation:
\(f(x) = \frac{-2x+2}{2x+4}\) g(x) = -2x+8
Question asks what the domain is if we had f(x) ÷ g(x)
\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4}\) ÷ >When dividing fractions, keep the first
Change the sign, flip the second fraction
\(\frac{f(x)}{g(x)} = \frac{-2x+2}{2x+4} * \frac{1}{-2x+8}\)
\(\frac{f(x)}{g(x)} = \frac{-2x+2}{(2x+4)(-2x+8)}\)
> you can never get a 0 on the bottom of division so that is where the exception of what x cannot be.
2x+4 = 0
2x= -4
x = -2
and
-2x+8 = =
-2x = -8
x = 4
So x cannot be -2 and 4
an astronaut who weighs 85 kilograms on earth weighs 14.2 kilograms on the moon. how much would a person weigh on the moon if they weigh 95 kilograms on earth? (round your answer if you have to)
Answers
Hi there! :)
Answer:
\(\huge\boxed{15.87kg}\)
To solve, simply set up a proportion. Let "x" represent the mass of a 95 kg person on the moon:
\(\frac{14.2kg}{85kg} = \frac{x}{95kg}\)
Cross multiply:
\(14.2 * 95 = 85 * x\)
\(1349 = 85x\)
Divide both sides by 85:
\(1349/85 = 85x/85\)
\(x = 15.87 kg\)
Answer:
15kg
Step-by-step explanation:
85/14.2=5.98
95/6=15
Which child is shorter than Ellis?
Sam: 35 5/6
Jesse: 35/38
Ellis: 35 1/4
Elsa: 35.1
Jonah: 35.7
Answers
Can I please get some help I’ve been stuck on this question for a while!
Answers
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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53 – 102 + 20 (8-3)
How you do it
Answers
Answer:
Answer = 51
Step-by-step explanation:
PEMAS = (parenthesis, exponents, multiplication, division, addition, subtraction) follow steps in order
Answer:
51
Step-by-step explanation:
53-102+20(8-3)
53-102+20 x 5
53-102+100
=51
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answers
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
Some students are making muffins for a fundraiser. They have already made 80 muffins
and they can make 30 muffins in an hour. How many additional hours would they spend
to make 380 muffins?
Answers
Answer:
10 hours
Step-by-step explanation:
380 - 80 = 300
30 : 1 = 300 : x
x = 300 / 30
x = 10
A triangular pyramid is formed from three right triangles as shown below.
Use the information given in the figure to find the length AC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
41
B
85
Answers
Answer:
76 units
Step-by-step explanation:
You want the length of AC in the given triangular pyramid.
Pythagorean theoremThe Pythagorean theorem can be used to find the lengths of AD and CD.
AD² + 40² = 41²
AD² = 41² -40² = 81 . . . . . = 9²
and
CD² +40² = 85²
CD² = 85² -40² = 5625 . . . . . = 75²
It can also be used to find AC:
AD² + CD² = AC²
81 + 5625 = AC²
AC = √5706 = 3√634 ≈ 76
The length of side AC is about 76 units.
__
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.
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I need to find what the square root is to 19,478,730. my teacher literally put that. help
Answers
Answer: 4413.5
Step-by-step explanation:
4413.47142 if you need to be exact
Help please this is pre calculus
Answers
Answer:
5pi/12
105 degrees
Step-by-step explanation:
I can help with the first 2 too many answers in one will get my answer deleted
7pi/12 x 180/pi
7x15=105
Hopes this helps please mark brainliest
Solve the system of linear equations using substitution. Use a pencil and paper. Which expression would be easier to substitute into the other equation, in order to solve this problem? Explain your reasoning.
x=4y-9
x+4y=3
Answers
Answer:
(- 3, 1.5)
--------------------------
Given system:
x = 4y - 9x + 4y = 3The first expression is ready to be substituted as no further operation is required to simplify it.
4y - 9 + 4y = 38y - 9 = 38y = 12y = 12/8y = 1.5Find x:
x = 4*1.5 - 9x = 6 - 9x = - 3A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets.
Answers
The equation that states the sum of the tickets sold is -
30x + 45y = 60900.
We have concert promoter.
We have to write an equation that states that the total amount received from the sale, which is 60,900 dollars.
What is Equation Modelling ?The equation modelling is a process of writing a mathematical equation from a mathematical statement involving variables, constants etc.
According to the question -
Money earned from $30 tickets = $30x
Money earned from $45 tickets = $45y
Total money from 1780 tickets = $60,900
Therefore -
30x + 45y = 60900
Hence, the equation that states the sum of the tickets sold is -
30x + 45y = 60900.
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[ The given question is incomplete, the complete question is
A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. Write an equation that states that the total amount received from the sale is 60900 dollars.]
Which investment option made the most money after 10 years?
Which option yielded the most total money by the time you were 60 years old?
Answers
Option 3 yielded the most money after 10 years is 171.7
Option 1 yielded the most total money by the time you were 60 years old is 8,771.56
Define the term solution of equation?A solution of an equation is a value or set of values that satisfy the equation, meaning that when the value(s) is substituted for the variable(s) in the equation, both sides of the equation are equal.
Based on the given equations, Option 1 yielded the most money after 10 years, and Option 3 yielded the most total money by the time you were 60 years old.
After 10 years:
Option 1: 50×(1.09)¹⁰ - 30 = 88.36
Option 2: 50×(1.08)¹⁰ - 20 = 87.94
Option 3: 100×(1.07)¹⁰ - 25 = 171.71
Therefore, Option 3 yielded the most money after 10 years is 171.7
By the time you were 60 years old:
Option 1: 50×(1.09)⁶⁰ - 30 = 8,771.56
Option 2: 50×(1.08)⁶⁰ - 20 = 5,042.85
Option 3: 100×(1.07)⁶⁰ - 25 = 5,769.64
Therefore, Option 1 yielded the most total money by the time you were 60 years old is 8,771.56
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3x-30 =1.5 plz help me
Answers
Answer:
x = 10.5
Step-by-step explanation:
3x - 30 = 1.5
3x = 31.5
x = 10.5
The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Answers
m = 3c
k = m
Equating the RHS of the first two equations gives
3c = c + 12
2c = 12
c = 6
There are 6 camels
If the world's population increased exponentially from billion in 1998 to billion in 2008 and continued to increase at the same percentage rate between 2008 and 2012, calculate what the world's population would have been in 2012. Round your answer to two decimal places.
Answers
Answer:
The answer is "7.122 billion"
Step-by-step explanation:
Please find the complete question in the attached file.
Using formula:
\(\to y=Ce^{kt}\)
\(C=5.937\\\\y=6.771\\\\t=10\\\\ k=?6.771=5.937e^{10k}\\\\1.1405=e^{10k}\\\\\ln(1.1405)={10\ k}\\\\0.013={k}\\\\\)
So,
\(\to y=5.937e^{.013t}\\\\\)
when it becomes \(2012, \ t=14\) so plug the value into the formula
\(\to y= 5.937e^{.013(14)} =7.122 \ billion\)
Julio tiene 12 años de edad y su padre tiene 42 años. ¿Cuántos años tendrá Julio cuando su padre tenga el doble de su edad?
Answers
Julio will be 30 years old when his father is twice his age.
To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.
Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.
For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.
Setting up an equation to solve for x:
x + 30 = 2x
Simplifying the equation, we subtract x from both sides:
30 = x
Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.
Therefore, Julio will be 30 years old when his father is twice his age.
Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?
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Give me all the answer with formula
Answers
Answers
A)534.990
B)2.679
C)88.611
D)705.149
E)7905.432
F)3.771
Any number over 5 add 1
hope this helps
a rectangular pyramid has a volume of 560 cubic meters. the base has a length of 16 meters and a width of 10 meters. what is the height of the pyramid
Answers
Can some one help me with this math question?
Answers
Answer:
I'm pretty sure it would be base x height divided by 2 so 20×6÷2
Amy, bill and cara each played a game. amy's score was ten times bill's score. cara's score was half of amy's score. write down the ration of amy's score to bill's score to cara's score. give your answer in its simplest form
Answers
Answer:
2:1:1
Step-by-step explanation:
A:B:C
10:1:5
÷5. ÷5
=2:1:1
What is the slope of the line that contains these points?
x 39 40 41 42
y 36 29 22 15
Answers
Answer: -7
Step-by-step explanation:
Use this formula for finding the slope:
Δy/Δx=y1-y2/x1-x2
Now get 2 points, (39, 36); (40, 29)
36-29/39-40= 7/-1= -7
So the slop is -7
Hope this helps!
Ricardo took out a single payment loan for $2500 at 7.8% ordinary interest to pay his federal income tax bill. Find the maturity value of the loan if he had to pay it back after 180 days.
Answers
Answer:
Therefore, the maturity value of the loan is $2568.75.
Step-by-step explanation:
To calculate the maturity value of the loan, we need to add the interest to the principal.
First, we need to find out how much interest Ricardo will owe for the 180-day period.
The formula for calculating ordinary interest is:
Interest = Principal x Rate x Time
where:
Principal = $2500
Rate = 7.8% = 0.078 (expressed as a decimal)
Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)
Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.
Using the formula above, we can calculate the interest as follows:
Interest = $2500 x 0.078 x 180/360 = $68.75
Therefore, Ricardo will owe $68.75 in interest for the 180-day period.
To find the maturity value of the loan, we add the interest to the principal:
Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75
Therefore, the maturity value of the loan is $2568.75.