A craft store is having a big sale. Sticker sheets are on sale for $0.50 per sheet. Regularly, they cost $1.25 per sheet.
What is the percent of decrease in the price of stickers per sheet?
Enter your answer in the box.
Answer: 60% decrease
Work Shown:
Difference = Large - Small = 1.25 - 0.50 = 0.75
Percent decrease = (difference/original)*100%
Percent decrease = (0.75/1.25)*100%
Percent decrease = (0.60)*100%
Percent decrease = 60%
The customer is getting a 60% discount.
Answer: 60%
Step-by-step explanation:
The person above is correct.
Particle P moves along the y-axis so that its position at time t is given by y(t)=4t−23 for all times t. A second particle, particle Q, moves along the x-axis so that its position at time t is given by x(t)=sin(πt)2−t for all times t≠2.
As time t approaches 2, what is the limit of the position of particle Q ? Show the work that leads to your answer.
Show that the velocity of particle Q is given by vQ(t)=2πcos(πt)−πtcos(πt)+sin(πt)(2−t)2 for all times t≠2.
Find the rate of change of the distance between particle P and particle Q at time t=12. Show the work that leads to your answer.
a) The limit of the position of particle [tex]Q[/tex] when time approaches 2 is [tex]-\pi[/tex].
b) The velocity of particle [tex]Q[/tex] is [tex]v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t -\sin \pi t}{(2-t)^{2}}[/tex] for all [tex]t \ne 2[/tex].
c) The rate of change of the distance between particle [tex]P[/tex] and particle [tex]Q[/tex] at time [tex]t = \frac{1}{2}[/tex] is [tex]\frac{4\sqrt{82}}{9}[/tex].
How to apply limits and derivatives to the study of particle motiona) To determine the limit for [tex]t = 2[/tex], we need to apply the following two algebraic substitutions:
[tex]u = \pi t[/tex] (1)
[tex]k = 2\pi - u[/tex] (2)
Then, the limit is written as follows:
[tex]x(t) = \lim_{t \to 2} \frac{\sin \pi t}{2-t}[/tex]
[tex]x(t) = \lim_{t \to 2} \frac{\pi\cdot \sin \pi t}{2\pi - \pi t}[/tex]
[tex]x(u) = \lim_{u \to 2\pi} \frac{\pi\cdot \sin u}{2\pi - u}[/tex]
[tex]x(k) = \lim_{k \to 0} \frac{\pi\cdot \sin (2\pi-k)}{k}[/tex]
[tex]x(k) = -\pi\cdot \lim_{k \to 0} \frac{\sin k}{k}[/tex]
[tex]x(k) = -\pi[/tex]
The limit of the position of particle [tex]Q[/tex] when time approaches 2 is [tex]-\pi[/tex]. [tex]\blacksquare[/tex]
b) The function velocity of particle [tex]Q[/tex] is determined by the derivative formula for the division between two functions, that is:
[tex]v_{Q}(t) = \frac{f'(t)\cdot g(t)-f(t)\cdot g'(t)}{g(t)^{2}}[/tex] (3)
Where:
[tex]f(t)[/tex] - Function numerator.[tex]g(t)[/tex] - Function denominator.[tex]f'(t)[/tex] - First derivative of the function numerator.[tex]g'(x)[/tex] - First derivative of the function denominator.If we know that [tex]f(t) = \sin \pi t[/tex], [tex]g(t) = 2 - t[/tex], [tex]f'(t) = \pi \cdot \cos \pi t[/tex] and [tex]g'(x) = -1[/tex], then the function velocity of the particle is:
[tex]v_{Q}(t) = \frac{\pi \cdot \cos \pi t \cdot (2-t)-\sin \pi t}{(2-t)^{2}}[/tex]
[tex]v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t -\sin \pi t}{(2-t)^{2}}[/tex]
The velocity of particle [tex]Q[/tex] is [tex]v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t -\sin \pi t}{(2-t)^{2}}[/tex] for all [tex]t \ne 2[/tex]. [tex]\blacksquare[/tex]
c) The vector rate of change of the distance between particle P and particle Q ([tex]\dot r_{Q/P} (t)[/tex]) is equal to the vectorial difference between respective vectors velocity:
[tex]\dot r_{Q/P}(t) = \vec v_{Q}(t) - \vec v_{P}(t)[/tex] (4)
Where [tex]\vec v_{P}(t)[/tex] is the vector velocity of particle P.
If we know that [tex]\vec v_{P}(t) = (0, 4)[/tex], [tex]\vec v_{Q}(t) = \left(\frac{2\pi\cdot \cos \pi t - \pi\cdot t \cdot \cos \pi t + \sin \pi t}{(2-t)^{2}}, 0 \right)[/tex] and [tex]t = \frac{1}{2}[/tex], then the vector rate of change of the distance between the two particles:
[tex]\dot r_{P/Q}(t) = \left(\frac{2\pi \cdot \cos \pi t - \pi\cdot t \cdot \cos \pi t + \sin \pi t}{(2-t)^{2}}, -4 \right)[/tex]
[tex]\dot r_{Q/P}\left(\frac{1}{2} \right) = \left(\frac{2\pi\cdot \cos \frac{\pi}{2}-\frac{\pi}{2}\cdot \cos \frac{\pi}{2} +\sin \frac{\pi}{2}}{\frac{3}{2} ^{2}}, -4 \right)[/tex]
[tex]\dot r_{Q/P} \left(\frac{1}{2} \right) = \left(\frac{4}{9}, -4 \right)[/tex]
The magnitude of the vector rate of change is determined by Pythagorean theorem:
[tex]|\dot r_{Q/P}| = \sqrt{\left(\frac{4}{9} \right)^{2}+(-4)^{2}}[/tex]
[tex]|\dot r_{Q/P}| = \frac{4\sqrt{82}}{9}[/tex]
The rate of change of the distance between particle [tex]P[/tex] and particle [tex]Q[/tex] at time [tex]t = \frac{1}{2}[/tex] is [tex]\frac{4\sqrt{82}}{9}[/tex]. [tex]\blacksquare[/tex]
Remark
The statement is incomplete and poorly formatted. Correct form is shown below:
Particle [tex]P[/tex] moves along the y-axis so that its position at time [tex]t[/tex] is given by [tex]y(t) = 4\cdot t - 23[/tex] for all times [tex]t[/tex]. A second particle, [tex]Q[/tex], moves along the x-axis so that its position at time [tex]t[/tex] is given by [tex]x(t) = \frac{\sin \pi t}{2-t}[/tex] for all times [tex]t \ne 2[/tex].
a) As times approaches 2, what is the limit of the position of particle [tex]Q?[/tex] Show the work that leads to your answer.
b) Show that the velocity of particle [tex]Q[/tex] is given by [tex]v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t +\sin \pi t}{(2-t)^{2}}[/tex].
c) Find the rate of change of the distance between particle [tex]P[/tex] and particle [tex]Q[/tex] at time [tex]t = \frac{1}{2}[/tex]. Show the work that leads to your answer.
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I NEED HELP ASAP (the image is attached)
divide -2^3-5x^2+4x+2 by x+2
Answer:
−5x+14−34/x+2
Step-by-step explanation:
Pls, choose me as brainliest!
What was the median number of posts made?
Answer: The median number of posts made is 8.5
Which function is
graphed below?
Answer:
f(x) = cos x
cos 0= 1
cos pi = -1
cos pi/2 = 0
Will someone help me with this problem please.
Answer:-5 10 ,13
Step-by-step explanation:
20men working 8hours a day took 18days to complete a work . How long will 24 men working 5 hours a day take to complete the some work
Step-by-step explanation:
20 men work 8 hours a day for 18 days.
that are
20×8×18 = 2880 work hours to complete that work.
if 24 men work 5 hours a day, that are
24×5 = 120 work hours per day.
we still need to do the total 2880 work hours.
so, they will need
2880 / 120 = 24 days to complete the work.
What is the solution to 2.8x + 6 > 20?
Answer:
5
Step-by-step explanation:
From the expression 2.8x + 6 > 20
we have,
2.8x + 6 = 20,
2.8x + 6 - (20) = 0 ( Moving all terms to the left)
We then add the numbers and variables together,
to get 2.8x + (6-20) = 0
2.8x + (-14) = 0
2.8x - 14 = 0
2.8x = 14 ( Divide both terms by 2.8x)
2.8x/2.8 = 14 /2.8
x = 14 / 2.8
x = 5
Write an expression equivalent to
- 3+ y - 4 - 12/31
Nate’s classroom has three tables of different lengths. Of 4
Answer:
Step-by-step explanation:
I think you need to multiply 4 1/2x3 and 2 1/2x4 and then when you get the answers for both you add them together hopefully this works
if 9x^2-6x+5 is rewritten as p^2-2p+5, what is p in terms of x
Answer:
p = 3x
Step-by-step explanation:
p² = 9x² = 3² *x²
p² = (3x)²
p = 3x
Please help due today
Answer:
Step-by-step explanation:
Literary devices Drag and drop.
Click on the literary device and place the correct example METAPHOR ONOMATOPOEIA OSIMILE SIMILE SIMILE METAPHOR SIMILE PERSONIFICATION SIMILE HYPERBOLE ONOMATOPOEIA HYPERBOLE ALLITERATIO
1. Books are the keys to your imagination. 2. Gahl Her voice sounds like nails on a chalkboard! 3. He is a walking dictionary. 4. Her tears were a river flowing down her cheeks. old as these hills! 5. I think my grandfather is as 6. In our eighth grade concert, we shone like stars. 7. Bark-Bark! Bark! The dog woke me up. 8. I ate a ton of food for dinner. 9. Buzz-The bee buzzed in my ear. 10. It seems to have been raining for 40 days and 40 nights. 11. He runs like a horse. 12. Sally sells seashells by the sea shore. 13. That child is a bear when he is sleepy.. 14. That little girl is as sweet as sugar. 15. The curtains danced in the breeze.
Answer:
Step-by-step explanation:
This Is not mathematics btw but here we go
1. Metaphor
2. Simile
3. Metaphor
4. Metaphor
5. Simile
6. Simile
7. Onomatopoeia
8. Hyperbole
9. Onomatopoeia
10. Hyperbole
11. Simile
12. Alliteration
13. Metaphor
14. Simile
15. Personification
Answer:
Step-by-step explanation:
METAPHOR 1. Books are the keys to your imagination., 6. In our eighth grade concert, we shone like stars., 14. That little girl is as sweet as sugar. He is a walking dictionary., 11. He runs like a horse.
ONOMATOPOEIA 7. Bark-Bark! Bark! The dog woke me up.
SIMILE Gahl Her voice sounds like nails on a chalkboard!
PERSONIFICATION 4. Her tears were a river flowing down her cheeks. old as these hills!, 13. That child is a bear when he is sleepy.., 15. The curtains danced in the breeze.
HYPERBOLE 8. I ate a ton of food for dinner.
ONOMATOPOEIA 9. Buzz-The bee buzzed in my ear.
HYPERBOLE 10. It seems to have been raining for 40 days and 40 nights.
ALLITERATION 12. Sally sells seashells by the sea shore.
Is
−
204
in the sequence below?
22
,
18
,
14
,
10
,
6
,
.
.
.
Answer:123
67
Step-by-step explanation:
2by2
Tatiana wants to give friendship bracelets to her 32 classmates. She already has 5 bracelets, and she can buy
more bracelets in packages of 4.
Write an inequality to determine the number of packages, p, Tatiana could buy to have enough bracelets.
4p+5=32 or 7 packages
I got this because there are 4 bracelets in one package and she doesn't know how many packages she needs so we put p for packages next to the 4 and you already have 5 so you add the 5 to it, all of that should come out to 32. If the equation wasn't what you were looking for you subtract 5 from 32 and get 27, then you divide 4 by 27 and you get 6.75, then you round it up and you get 7. The number of packages she needs is 7.
Sally has a bunch of pennies in her piggy bank. She gives 1/3 of her pennies to her older brother. Then, she gives 2/5 of her remaining pennies to her younger sister. After all this, Sally has 24 pennies remaining. How many pennies did Sally start with?
She started with 60 pennies
Ratios and propotionsLet the number of a bunch of pennies she has to be "x"
If she gives 1/3 of her pennies to her older brother, she will have 2/3 x remaining
If she gives 2/5 of her remaining pennies to her younger sister, she will have 2/3x- (2/5 of 2/3x) = x remainijg
If Sally has 24 pennies remaining, then;
2/3x - 4/15x = 24
10x-4x/15 = 24
6x/15 = 24
6x = 15 * 24
x = 60
This means that she started with 60 pennies
Learn more on ratios here:
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Suhana left at 11:45 to a trip to Dubai Expo 2020 and arrived at her destination 4 hours and 25 minutes later. What time did she reach
Answer:
4:10
Step-by-step explanation:
let's start by adding 4 hours to 11:45
12:45
1:45
2:45
3:45
now let's add 25 minutes
3:70
that is 4:10
a yacht that travels 1.375 km in 165 minutes expressed in km/h
The speed of a yacht traveling a distance of 1.357 km in 165 minutes is 0.5 km/h
What is Speed?The speed of an object is the distance covered by the object in respect to time.
Mathematically:
[tex]\mathbf{Speed = \dfrac{distance}{time}}[/tex]
[tex]\mathbf{Speed = \dfrac{1.375 \ km}{165 minutes }}[/tex]
We know that 60 minutes = 1 hour165 minutes = 2.75 hours[tex]\mathbf{Speed = \dfrac{1.375 \ km}{2.75 \ hours}}[/tex]
Speed = 0.5 km/hour
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6. A right triangle has one vertex on the graph of
y = 9 – x2
, x > 0, at (x, y), another at the origin, and the
third on the positive x-axis at (x,0). Express the area A of
the triangle as a function of x.
Which side of triangle should be known?
Answer:
the included side or the shortest side
Can Any One help me please
Answer:
its 71
Step-by-step explanation:
i used the calc
Which quadrilateral has one pair of parallel sides, but is not a parallelogram?.
Only the trapezoid has one pair of parallel side while all the other quadrilateral( in this question) square, rhombus and rectangle has two pair of parallel sides.
What value of b will make the expressions −12.8x+b and −3.2(4x−2.1)+2.4 equivalent?
Enter your answer in the box.
Step-by-step explanation:
-12.8x + b = -3.2(4x - 2.1) + 2.4 =
= -12.8x + 6.72 + 2.4
b = 6.72 + 2.4 = 9.12
how many centermetres are there in a metre
Answer:
100 Centermeters in one meter
Step-by-step explanation:
Hope This Helps
Have A Great Day
Which of these algebraic expressions matches the verbal description "k cubed plus 7"? a. k3 +7 b. (k + 7) C. k + 73 d. 3k + 7 e 30k + 7)
Answer:
A
Step-by-step explanation:
Just as squared has an exponent of 2, cubed has an exponent of 3.
Therefore, k is seen as [tex]K^{3}[/tex] (or K^3 if that is too small to see)
Another keyword is "plus" as this indicates addition which has a symbol of +
So in this case, your answer would be A) K^3 + 7
Find each angle measure
Answer:
I have attached a photo. That might help you out.
if anything remains unclear, feel free to let me know in the comments.
Which us the simplified form of
[tex] {p}^{0} [/tex]
21. Amanda invests $5,000 in a CD at an annual interest rate of 2%. What will her investment be worth at the end of three years?
(From Unit 4, Lesson 1.)
5. Clare and Han are discussing how to find the missing lengths. Clare says she is using
similarity. Han says he is using the Pythagorean Theorem.
a. Do you agree with either of them? Show or explain your reasoning.
b. Find the missing sides.
The values of the missing sides is DE = 12 and AC = 6.5
Similar triangles
Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion. Also all the corresponding angles are congruent.
Using Pythagoras:
AC² = AB² + BC²
AC² = 2.5² + 6²
AC = 6.5
Using similar triangles:
BC / DE = AB / EF
6/DE = 2.5/5
DE = 12
The values of the missing sides is DE = 12 and AC = 6.5
Find out more on Similar triangles at: https://brainly.com/question/14285697
