[Calculus] analyze speed from position. Show steps, please!
Answer:
B
Step-by-step explanation:
We are given that the position of a particle is modeled by the function:
[tex]s(t)=2t^3-24t^2+90t+7[/tex]
And we want to find the times for which the speed of our particle is increasing.
In other words, we want to find the times for which our acceleration is positive (a(t)>0).
So first, we will find our acceleration function. We can differentiate twice.
By taking the derivative of both sides with respect to t, we acquire:
[tex]\displaystyle s^\prime(t)=v(t)=\frac{d}{dt}\big[2t^3-24t^2+90t+7\big][/tex]
Differentiate:
[tex]v(t)=6t^2-48t+90[/tex]
This is our velocity function. We can differentiate once more to acquire the acceleration function. Therefore:
[tex]\displaystyle v^\prime(t)=a(t)=\frac{d}{dt}\big[6t^2-48t+90\big][/tex]
Differentiate:
[tex]a(t)=12t-48[/tex]
If our speed is increasing, our acceleration must be positive. So:
[tex]a(t)>0[/tex]
By substitution:
[tex]12t-48>0[/tex]
Now, we can solve for t:
[tex]12t>48\Rightarrow t>4[/tex]
Therefore, the only interval for which the speed of the particle is increasing (i.e. the acceleration is positive) is for all times t>4.
So, our answer is B.
Write an equation, and then solve.
5. Kiesha and Wanda went to the mall for 4.5 hours. While they were there, they went to a movie that lasted 130
minutes and ate dinner for 70 minutes. They spent the rest of the time walking around the mall. How long did
they spend walking around the mall?
Answer:
70 mins
Step-by-step explanation:
Lets first convert the 4.5 hours to minutes. We know that there's 60 mins in an hour, so we can just multiply 4.5 by 60 to get 270 minutes. Now we know the total time spent at the mall.
Then, we can add the times given in the question.
130 mins + 70 mins + walking mins = 270 mins
To solve, simply collect like terms:
200 mins + walking mins = 270 mins
walking mins = 270 mins - 200 mins
walking mins = 70 mins
Need Heeeeeelp please ...
In one class, there are 2 of every 8 students in the class chewing
gum. If there are 32 students in the class, how many students are
chewing gum?
Answer:
8
Step-by-step explanation:
Answer:
8 people are chewing gum
Step-by-step explanation:
32/8=4, meaning there are 4 sets of 8 students.
If 2 students are chewing gum for every 8, and there are 32 students, that would mean that multiplying 4 by 2 to get 8 total kids chewing gum.
You could also say that 6*4=24, and 32-24=8 if you want to double check.
Hope this helps :)
Tyree and four friends go to the movies. Each person buys a movie ticket for $7, a snack for $5, and a drink for $2. Write an expression for the total cost of the trip to the movies. Then find the total cost.
Answer:
Tyree and all of his friends get 1 ticket for $7. Next they all get 1 snack for $5. Then they all get a drink for $2. So:
1=7
1=5
1=2
Then you take each person (which there are five of then) and you times all five people by 7, 5, 2.
5 x 7=35
5 x 5=25
5 x 2=10
After that you add it all together:
35 plus 25=60
60 plus 10=70
Step-by-step explanation:
your welcome
Answer:
Im not sure if it ment, Tyree and four friends go to the movies. Each person buys a movie ticket for $7, a snack for $5 (meaning only one snack), and a drink for $2. (Meaning only one drink) or if it ment Tyree and four friends go to the movies. Each person buys a movie ticket for $7, a snack for $5 (meaning everyone got a snack), and a drink for $2(meaning everyone got a drink). So i did the math for both of them, if they only got 5 tickets, one snack, and one drink, it would be 42 (the math problem is 35 + 2 + 5). if they got 5 tickets, 5 snacks, and 5 drinks, it would be 70(the math problem is 35 + 25 + 10). Hope this helps!
the food pantry distribution 10 oz bags of rice if 3 5 lb bags are donated to the pantry how many 10 ounce bags can be made
Answer:
24 bags can be made from three 5 pounds bags.
Step-by-step explanation:
Given that:
Three 5 pound bags are donated.
Total weight of bags = 3*5 = 15 pounds
We know that:
1 pound = 16 ounces
15 pounds = 16*15 = 240 ounces
A bag weighs 10 ounces.
Number of bags = [tex]\frac{240}{10}[/tex]
Number of bags = 24 bags
Hence,
24 bags can be made from three 5 pounds bags.
102 - Harder brackets
Find an expression without brackets
for the area of each rectangle.
(x + 3)
area =
12)
No
calc
р
(-9)
Total
area =
121
Answer:
For figure 1:
Area of rectangle = 7x + 21
For figure 2:
Area of rectangle = [tex]\mathbf{p^2-9p }[/tex]
Step-by-step explanation:
We need to find area of rectangle
The formula used is: [tex]Area\:of\:rectangle=Length\times Width[/tex]
For figure 1:
Length = 7
Width = x+3
Putting values in formula and finding area of rectangle
[tex]Area\:of\:rectangle=Length\times Width\\Area\:of\:rectangle=7\times (x+3)\\Now,\: multiply\:7\:with\:terms\;inside\:the\:bracket\\Area\:of\:rectangle=7(x)+7(3)\\Area\:of\:rectangle=7x+21\\[/tex]
So, area of rectangle = 7x + 21
For figure 2:
Length = p
Width = p-9
Putting values in formula and finding area of rectangle
[tex]Area\:of\:rectangle=Length\times Width\\Area\:of\:rectangle=p\times (p-9)\\Now,\: multiply\:p\:with\:terms\;inside\:the\:bracket\\Area\:of\:rectangle=p(p)-p(9)\\Area\:of\:rectangle=p^2-9p\\[/tex]
So, area of rectangle = [tex]\mathbf{p^2-9p }[/tex]
The following data is from a simple random sample of 12 students GPAs. 3.12 2.45 4.0 3.76 3.54 2.78 3.39 3.21 1.98 3.43 3.98 2.77 Develop a point estimate of the population mean.
Answer: 3. 2
Step-by-step explanation:
Given the data:
3.12 2.45 4.0 3.76 3.54 2.78 3.39 3.21 1.98 3.43 3.98 2.77
Point estimate of population mean :
Σx / N
(3.12 + 2.45 + 4.0 + 3.76+ 3.54 + 2.78 + 3.39 + 3.21 + 1.98 + 3.43 + 3.98 + 2.77)
= 38.41 / 12
= 3.2008
Tina contributes 9.5% of her monthly salary towards her 401(k) and her employer matches her contribution up to 5.4% of her annual salary. If the interest rate of her 401(k) is 8.1% compounded monthly and her monthly salary is $2,461, determine the amount in her account after 25 years. Round to the nearest cent.
a.
$339,804.33
b.
$354,452.86
c.
$344,941.24
d.
$347,269.59
Please select the best answer from the choices provided
A
B
C
D
Answer:
In 25 years, Tina will have $354,452.86
Step-by-step explanation:
Monthly Contribution - $366.69 (Tina & Employer)
Length of Time in Years - 25
Estimated Interest Rate - 8.1%
Compound Frequency - Monthly
polynomial expression
6x2 + 10x - 56
Answer:
-34
Step-by-step explanation:
Answer:
The answer is 34
Step-by-step explanation:
i was following the order of PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
so i did 6x2 which got me to 12 and then I added 10 which gave me 22, and then lastly i subtracted 56-22 which gave me 34.
~Hope this explanation has helped you, have a great day/ night!~
1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of varnish what quantity of mineral spirits will i need in ml ? 3-Robison's tapestries all measure 1.5m x 1m wide. Express the proportion of the tapestries' heights to width using whole numbers. Give the answer in ration.
Answer:
(1) The required ratio of spirit to varnish is 1:3.
(2) You need 80 ml of mineral spirit.
(3) The ratio of tapestries' heights to width is 3:2.
Step-by-step explanation:
(1) If you need to mix 25% mineral spirit to the varnish, then the solution would contain 25% mineral spirit and 75% varnish.
So, [tex]\frac{spirit}{varnish}=\frac{25}{75}[/tex]
[tex]=\frac{1}{3}[/tex]
Thus, The required ratio of spirit to varnish is 1:3.
(2) If you use 240ml of varnish, then this quantity is 75% of the total solution or ration of varnish to the total solution will be 3:4.
Let [tex]x[/tex] be the quantity of total solution.
Then, [tex]240:x=3:4[/tex].
⇒[tex]\frac{240}{x}=\frac{3}{4}[/tex]
⇒[tex]3x=240*4[/tex]
⇒[tex]x=\frac{240*4}{3}[/tex]
⇒[tex]x=320[/tex]
That is, total solution is 320 ml.
Now, Spirit = Total solution - Varnish
⇒Spirit = 320ml-240ml
⇒Spirit = 80ml
Hence, if you use 240 ml of varnish, you need 80 ml of mineral spirit.
(3) Robison's tapestries all measure 1.5m long and 1m wide. First, we express dimensions in whole numbers by multiplying them by 10.
Then, dimensions are 15m long and 10m wide.
Now, Height : Width = 15:10
⇒[tex]\frac{Height}{Width} =\frac{15}{10}[/tex]
⇒[tex]\frac{Height}{Width} =\frac{3}{2}[/tex]
Hence, the ratio of tapestries' heights to width is 3:2.
I will give you a good amount of points if you answer this correct
Answer:
I think the answer is B. The equation has infinitely many solutions.
Step-by-step explanation:
4(3x + 4) = 15x + 12 - 3x + 4
*group like terms so 4(3x+4) = 15x - 3x + 12 + 4
*add similar elements 15x - 3x = 12x
*add the numbers 12 + 4 = 16
*Expand to 12x + 16 - 16 = 12x + 16 - 16
*You simplify 12x = 12x
*Subtract 12x from both sides
*Then Simplify which is 0
Which means Both sides are equal to 0
True for all X
-4 > x - 3 find x in the equation
Answer:
X= -1
Step-by-step explanation:
market price of a dress is 1500 rupees shop owner give a discount of 20% find the discount and the bill amount paid
Step-by-step explanation:
Marked price (mp) =rs 1500
discount (d) = 20%
discount amount = d% of mp
=20/100 *1500
= Rs. 300
bill amount paid = mp -d
= 1500 - 300
= Rs. 1200
Position vectors u and v have terminal points of (-6, 3) and (4, -2), respectively. Find the resulting terminal point of 2v - u.
(14, -7)
(2, 1)
(14, 1)
(2, -7)
Answer:
(14 , -7)
Step-by-step explanation:
terminal points: A (-6,3) B (4,-2)
u = x₁ + i y₁ u = -6 + i3
v =x₂ + iy₂ = 4 - i2 2v = 8 - i4
2v - u = (8 - i4) - (-6 + i3) = 14 -i7
Resulting terminal point: (14 , -7)
Position vectors u and v have terminal points of (-6, 3) and (4, -2), respectively. Find the resulting terminal point of 2v - u.
(14, -7)(2, 1)
(14, 1)
(2, -7)
Please help ASAP!! 20 points givin
Answer:
d or b
Step-by-step explanation:
quick math
Could somebody pls help me with this question
Answer:
18 minutes is the answer
Step-by-step explanation:
•Time couple rested in 2 hrs = 12 min
•Time couple rested in 1 hr = 12/ 2 min = 6min
•Time couple rested in 3 hrs = 6×3 min = 18 min
HOPE IT HELPS YOU
MARK ME AS BRAINIEST
AND YOU CSN THANK ME IN THE COMMENT
What is the following product?
Answer:
10.25 which is equal to letter c
Step-by-step explanation:
I used a calculator and figured out which equals it
I GIVEEE BRAILILSTTTTTTTT
Answer:
umumumuykik.iu.fg
Step-by-step explanation:
lui;iou;uyfluylfuy;lui;uy;
(15 POINTS) Select the correct answer.
Which equation has infinitely many solutions?
A. -5(x + 2) = -4x - 12 - X + 2
B. 3x – 4 + 2x = 5(x-4)
C. 5(x + 7) = -5(X - 7)
D. 6x + 2 - x = -2x - 2 + 7 x
Find the values of the variables in the parallelogram.
Step-by-step explanation:
We can find x very easily because the left and right sides are parallel,making the diagonal connecting them a transversal therefore x=33°
To find y we know that the sum of interior angles of a triangle is 180°
y+109°+33°=180°
y+142°=180°
y=38°
Now,
x+38°+z=180
33+38+z=180
z=180-71=109°
An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.1 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.
Student 1 2 3 4 5 6 7
Score on first SAT 500 380 560 430 450 360 560
Score on second SAT 540 470 580 450 480 400 600
Required:
a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.
Answer:
Since the calculated value of t = -0.215 falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05.
e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.
Step-by-step explanation:
Student 1 2 3 4 5 6 7
Score on first SAT 500 380 560 430 450 360 560
Score on second SAT 540 470 580 450 480 400 600
Difference d -40 -90 -20 -20 -30 -40 -40 ∑ -280
d² 1600 8100 400 400 900 1600 1600 ∑14600
a. Let the hypotheses be
H0: ud= 0 against the claim Ha: ud ≠0
The degrees of freedom = n-1= 7-1= 6
The significance level is 0.05
The test statistic is
t= d`/sd/√n
The critical region is ║t║≤ t (0.025,6) = ±2.447
d`= ∑di/n= -280/7= -4
Sd²= ∑(di-d`)²/n-1 = 1/n-1 [∑di²- (∑di)²n]
= 1/6[14600-(-4)²/7] = [14600-2.2857/6]= 2432.952
b. Sd= 49.3249= 49.325
Therefore
c. t= d`/ sd/√n
t= -4/ 49.325/√7
t= -4/18.6435 = -0.2145= -0.215
d. Since the calculated value of t = -0.215 falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05
e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.
What do you get when you cross an electric eel and a sponge puzzle time riddle
Answer:
A shock absorber?
Step-by-step explanation:
A local pizza shop has a membership program for frequent buyers. The membership
costs $15 per month and members get a discounted price of $2 per slice of pizza.
Mayerlin purchased a membership to this pizza shop. How much would Mayerlin
have to pay the pizza shop if she bought 11 slices of pizza this month? What would be
the monthly cost for x slices of pizza?
Answer:
cost of slices=2x
cost=monthly fee+cost of slices
15x+2x
Step-by-step explanation:
please solve question in picture branoist to first and correct
Answer:
The correct answer is Option 3: 12y
Step-by-step explanation:
A polynomial term is usually made of a variable and a co-efficient.
Like terms are those terms that have the same variables i.e. x and 44x are like terms.
Given expression is:
[tex]6y-2y+8y[/tex]
All the terms have only y which means that all three terms are alike.
The coefficients of like terms are added or subtracted according to their sign.
[tex]6y-2y+8y[/tex] = 12y
Hence,
The correct answer is Option 3: 12y
Is anyone here good at calculus I’m willing to pay.
Find the missing value in the percent statement using a proportion.
______ is 75% of 4.
Answer: 3
Step-by-step explanation: Hope I helped
Write an expression that represents the number of shells in pile 2.
Answer:
2
Step-by-step explanation:
4/2=2
Question 16 please help me
Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)? (–1 + i) + (21 + 5i) + 0 –1 + (i + 21) + 5i (–1 + 21) + (i + 5i) –(1 – i) + (21 + 5i)
Answer:
i think the answer is C, (-1 + 21) (i + 5i)
Step-by-step explanation:
i just took the test and got a 92% but it didnt tell me which ones were wrong. thats my best guess though. i hope it helps!
The expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression as, (-1 + 21)+(i + 5i). Option C is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is, (–1 + i) + (21 + 5i)
We have to find the expression that demonstrates the use of the commutative property of addition
According to the commutative property of addition, altering the order of addends has no impact on the sum.
Commutative law refers to either of two rules pertaining to the addition and multiplication of numbers that are expressed symbolically as a + b = b + a and ab = ba. These principles imply that rearranging the terms or factors of any finite sum or product has no effect on it.
Thus, the expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression as, (-1 + 21)+(i + 5i). Option C is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ6
