Answer:
[tex]\dfrac{137}{3}\approx 45.7\; \sf m[/tex]
Step-by-step explanation:
To find the velocity function, integrate the acceleration function (and add a constant of integration).
[tex]\begin{aligned}\displaystyle v(t)=\int a(t) &= \int (2t + 2)\; \text{d}t\\\\&=\int 2t \; \text{d}t+\int 2\; \text{d}t\\\\&=\dfrac{1}{2} \cdot 2t^{(1+1)}+2t+\text{C}\\\\&=t^2+2t+\text{C}\end{aligned}[/tex]
To find the constant of integration, C, substitute v(0) = -15 into the velocity function and solve for C:
[tex]\begin{aligned}v(0)=(0)^2+2(0)+\text{C}&=-15\\0+0+\text{C}&=-15\\\text{C}&=-15\end{aligned}[/tex]
Therefore, the velocity function (in m/s) is:
[tex]v(t)=t^2+2t-15[/tex]
As we want to find the distance travelled during the given time interval 0 ≤ t ≤ 5, we first need to determine if the particle momentarily stops at any point in the given interval (and therefore changes direction). The particle will stop when its velocity is zero, so when v(t) = 0:
[tex]\begin{aligned}v(t)&=0\\\implies t^2+2t-15&=0\\t^2+5t-3t-15&=0\\t(t+5)-3(t+5)&=0\\(t-3)(t+5)&=0\\\\\implies t&=3, -5\end{aligned}[/tex]
As time is positive only, the velocity is zero at t = 3 seconds.
Therefore, at t = 3, the particle changes direction and begins to move in the opposite direction. Therefore, the displacement between 0 ≤ t ≤ 5 consists of two parts: 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5.
To find the distance travelled, first find the displacement function by integrating the velocity function:
[tex]\begin{aligned}\displaystyle s(t)=\int v(t) &= \int (t^2+2t-15)\; \text{d}t\\\\&= \int t^2\; \text{d}t+\int 2t\; \text{d}t-\int 15\; \text{d}t\\\\&=\dfrac{1}{3}t^3+t^2-15t\left(+\text{C}\right) \end{aligned}[/tex]
Distance is the absolute value of displacement.
As we want to find the distance travelled for the intervals 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5, we need to add the absolute values of displacement for these intervals. So, the absolute values of the definite integrals for these intervals:
[tex]\begin{aligned}\textsf{Distance}&=\left|\int^3_0 v(t)\right|+\left|\int^5_3 v(t)\right|\\\\&=\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^3_0\right|+\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^5_3\right|\\\\&=\left|\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)-\left(\dfrac{1}{3}(0)^3+(0)^2-15(0)\right)\right|+\\&\left|\left(\dfrac{1}{3}(5)^3+(5)^2-15(5)\right)-\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)\right|\\\\&=\left|(-27-0)\right|+\left|\left(-\dfrac{25}{3}-(-27)\right)\right|\end{aligned}[/tex]
[tex]\begin{aligned}&=27+\dfrac{56}{3}\\\\&=\dfrac{137}{3}\end{aligned}[/tex]
Therefore, the total distance travelled during the given time interval is 137/3 ≈ 45.7 meters.
A drawer is filled with 2 white shirts, 5 black shirts, and 3 gray shirts. One shirt is
chosen at random from the drawer. Find the probability that it is not a white shirt.
Okay, let's break this down step-by-step:
* There are 2 white shirts, 5 black shirts, and 3 gray shirts in the drawer.
* That's a total of 2 + 5 + 3 = 10 shirts.
* We want to find the probability that the chosen shirt is NOT white.
* So there are 5 + 3 = 8 shirts that are NOT white.
* Probability = (Number of favorable outcomes) / (Total possible outcomes)
* So in this case, Probability = 8/10 = 4/5
Therefore, the probability that the chosen shirt is NOT white is 4/5.
Calculate how far the village is north of O
Step-by-step explanation:
See image
Find a rational number halfway in between the two numbers.
8/10 and 1/8
A rational number between 8/10 and 1/8 is 37/80.
We know that a rational number between two rational numbers can be given by finding the average of the two given numbers:
The numbers are 8/10 and 1/8.
Let's simplify the fractions first:
8/10 = 4/5 (dividing both numerator and denominator by 2)
1/8 = 1/8 (already in simplest form)
Average = [tex](\frac{4}{5} + \frac{1}{8})/2[/tex]
= [tex](\frac{(4*8) + (5*1)}{40} )/2[/tex]
= [tex](\frac{37}{40}) /2[/tex]
= [tex]\frac{37}{80}[/tex]
So, the rational number halfway between 8/10 and 1/8 is 37/80.
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What is the equation of the line that represents the horizontal asymptote of the function
f(x) = 3000 (1 +0.09)^x-2 +4?
Answer: y=4
Step-by-step explanation:
The Parent function [tex]y=a^{x}[/tex] has a horizontal asymtote at y=0
because the function approaches 0 but never touches it no matter how small the number you input. See image. Asymtotes are like a boundary that is not passed
Your curve has been shifted up 4 so y=4
See image
Extra info: y-intercept = 3000
shifted right 2
It’s probability and I need your help pls
The theoretical probabilities are: 0.15, 0.15, and 0.05 respectively
What is probability?Probability is a branch of mathematics concerned with the analysis of random phenomena
The given parameters that will help us to get the probabilities are
25% are stakeholders
20% have dark hair
The probability of being stakeholders 20%/25%
= 0.20/0.25 = 0.
b) 1-0.8 * 1.0.25
0.2 * 0.75 = 0.15
c. 0.2 * 0.75 = 0.15
d. Has light hair and is a stakeholder
0.20 * 0.25
= 0.05
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The scale drawing car length is 3cm. If the scale is 1cm:4ft, what is the actual car length?
Answer: The actual car length is 12ft.
Step-by-step explanation:
Actual car length = 3cm x 4ft/cm = 12ft
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
To the nearest whole dollar, the antique dresser was purchased by Danielle as follows: A. purchase price: $120, advertised price: $300.
How the purchase price is determined?The purchase price of the antique dresser can be determined by reversing the solution from the discounted price.
The discounted price is divided by the discount factor to calculate the advertised or marked price.
Let the purchase price of the antique dresser = x
Markup = 250%
Discount = 15%
Discounted price = $255
Discount factor = 0.85 (1 - 0.15)
Marked up or advertised price = $300 ($255 ÷ 0.85)
Purchase price = $120 ($300 ÷ 2.5)
Thus, the correct option is Option A.
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What is the area of a sector when 0=pi/2 radians and r=8/3
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59[/tex]
Suppose that 7 green balls and 9 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?
Answer: 0.2461
Step-by-step explanation:
There are 16 balls in total, and 9 of them are purple. If the first ball drawn is replaced before the second is drawn, then the number of purple balls and the number of total balls in the urn remain the same for the second draw.
The probability of drawing a purple ball on the first draw is 9/16. Since the ball is replaced, the probability of drawing a purple ball on the second draw is also 9/16.
The probability that the second ball drawn is a purple ball, given that the first ball drawn was replaced and was a green ball:
(7/16) * (9/16) = 63/256 ≈ 0.2461
please help me, i need it :)
Chloe can travel 4.4 miles less than Jin on one gallon of gas.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
Chloe travels 93 miles on 5 gallons of gas, hence the constant is given as follows:
k = 93/5
k = 18.6 miles per gallon.
Jin's ratio is of 23 miles per gallon, hence he can travel more and the difference is given as follows:
23 - 18.6 = 4.4 miles per gallon.
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I need help with questions 2 and 3 please.
Answer:
1.x=7 or x=-7
2.x=root of 65 or x=-root of 65
Step-by-step explanation:
I have put what I mean by root 65
5.8.PS-20
Question Help
Todd plans to run at least 3 miles each week for his health. Todd has a circular route in the neighborhood to run. Once
around that route is 420 yards. If Todd runs that route 10 times during the week, will he cover at least 3 miles? Explain.
Click the icon to view the customary units.
Select the correct answer, and fill in the answer boxes to complete the explanation.
(Type integers, fractions, or mixed numbers.)
OA. No, because 3 miles is
•B. Yes, because 3 miles is
yards, and 10 times around the route is
yards, and 10 times around the route is
yards, which is less than 3 miles.
yards, which is the greater than 3 miles.
Answer:
No
Step-by-step explanation:
No, because 10 times around the route is 4200 yards, which is less than 3 miles
Find all possible zeros
The possible zeros from the function would be zero.
How to find the possible zeros ?To find all possible zeros of the polynomial f(x) = 2x³ + 3x² - 10x + 7, we can use the Rational Root Theorem.
We can test these possible zeros by plugging them into the polynomial:
f(1) = 2(1)³ + 3(1)² - 10(1) + 7 = 2
f(-1) = 2(-1)³ + 3(-1)² - 10(-1) + 7 = 12
f(7) = 2(7)³ + 3(7)² - 10(7) + 7 = 776
f(-7) = 2(-7)³ + 3(-7)² - 10(-7) + 7 = -732
f(1/2) = 2(1/2)³ + 3(1/2)² - 10(1/2) + 7 = -0.5
f(-1/2) = 2(-1/2)³ + 3(-1/2)² - 10(-1/2) + 7 = 8.5
f(7/2) = 2(7/2)³ + 3(7/2)² - 10(7/2) + 7 = 89.75
f(-7/2) = 2(-7/2)³ + 3(-7/2)² - 10(-7/2) + 7 = -83.75
None of the possible rational zeros are actual zeros of the polynomial f(x) = 2x³ + 3x² - 10x + 7.
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The full question is:
Find all possible zeros. (Enter your answers as a comma-separated list.) f(x) = 2x3 + 3x2 − 10x + 7
IF YOU CAN ANSWER THIS CORRECT WITH A Good explanation I'll give 5 stars, a thanks and brainly (also your very smart)
Rebecca is x years old.Mary is 8 years older than rebecca. Jill is three times older than mary. The sum of their ages is 67.
A) form an expression in terms of x
Answer:
A) 5x+32=67
Rebecca is 7, Mary is 15, and Jill is 45
Step-by-step explanation:
Rebecca is x years old.
If Mary is 8 years older than Rebecca, Mary's age is 8 more than x.
We can write Mary's age as:
x+8
Jill is three times older than Mary.
This means that Jill's age is equal to three times x+8.
We can write Jill's age as:
3(x+8)
Use the distributive property.
3(x+8)=
3x+24
So, Jill's age (in terms of x) is 3x+24.
The sum of their ages is 67, so if we add all of their ages, we will get 67.
x+(x+8)+(3x+24)=67=
5x+32=67
Not sure if you want this solved, but here it is:
5x+32=67=
5x=35=
x=7
Let's find Mary's age.
x+8=
7+8=
15.
Now, let's find Jill's age.
3x+24=
3(7)+24=
21+24=
45.
So, Rebecca is 7, Mary is 15, and Jill is 45.
you roll a 6 sided die; what is P(4 or less than 3)
Answer:
1/2
Step-by-step explanation:
The probablility of any number on a die is 1/6.
So the numbers 4, 2, and 1 each have a probability of 1/6 meaning that each have a total probability of: 1/2. 3 is not accounted for due to our restriction.
Angles in a Triangle
Answer:
a = 40°
Step-by-step explanation:
An isosceles triangle has two sides that are the same size. The angles opposite from those sides are equal (they are called base angles.) And, the three angles in a triangle add up to 180°
So,
100 + a + a = 180
combine like terms
100 + 2a = 180
subtract 100
2a = 80
divide by 2
a = 40
HELP ASAP (I chose 34 as random number) (please good explanation because I want to know how to do this well)
The table shows the grading scale for Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Pick a number between 28 and 39. This number will represent how many points you earned. If you have a pop quiz worth a total of 40 points, using the number you selected, calculate the percentage you earned on the test. Show each step of your work. (8 points)
Part B: Based on the percentage found in Part A, would you earn a grade of A, B, or C using the grading scale provided? Explain your answer. (4 points)
Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40 points.
What is a percentage?A percentage is a means to represent a piece of 100 as a ratio or percentage. The sign for it is % (percent), which stands for "per hundred." If you state, for instance, that 50 out of 100 people like chocolate, then means that 50 out of 100 people, or 0.5 (50/100), like chocolate overall. In several disciplines, including finance, business, mathematics, and statistics, percentages are frequently used.
Part A:
Say we decide to set the number of points gained on the quiz at 40. The following formula is used to determine your percentage score if the quiz was worth a total of 40 points and you received 34 of them:
(Points earned / Total Points) x 100% is the percentage score.
Score in percentage: (34 / 40) x 100%
Score in percentages: 85%
Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40.
Part B:
You would receive a B on the specified grading scale based on the percentage score of 85%. The percentage score gained in section A falls within the range required for a B grade on the grading scale, which is awarded for percentage scores between 80% and 89%.
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Find the measure of 3x-46+14=90
Answer:
Step-by-step explanation:
3x = 90 + 46 - 14
3x = 122
x=[tex]\frac{122}{3}[/tex]≈40,7
Answer: 40.6 repeated
Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated
Adeline has a box full of notebooks. If she gives 13 notebooks to each of her children, she will have 8. notebooks left. if she gives 15 notebooks to each childish will have zero notebooks left.how many notebooks and how many children does Adeline have
Answer:
Adeline has 60 notebooks and 4 children.
Step-by-step explanation:
Let's assume that Adeline has 'x' notebooks and 'y' children.
According to the given information, if Adeline gives 13 notebooks to each child, she will have 8 notebooks left. This can be represented by the equation:
x - 13y = 8 ...(1)
Similarly, if she gives 15 notebooks to each child, they will have zero notebooks left, which can be represented by the equation:
x - 15y = 0 ...(2)
We now have two equations with two variables. To solve for 'x' and 'y', we can use the method of elimination. Multiplying equation (1) by 15 and equation (2) by 13, we get:
15x - 195y = 120 ...(3)
13x - 195y = 0 ...(4)
Subtracting equation (4) from equation (3), we get:
2x = 120
x = 60
Substituting the value of 'x' in equation (2), we get:
60 - 15y = 0
y = 4
Therefore, Adeline has 60 notebooks and 4 children.
to graph -5,5 start at 0,0 and then go?
Answer:
No
Step-by-step explanation:
to grap (-5,5) do not start at (0,0)
-5 is at the x axis so start it at (-0) then for 5 its juts (0) so (-0,0)
In 1852, a person sold a house to a lady for $30. If the lady had put the $30 into a bank account paying 6% interest, how much would the investment have been worth in the year 2012 if interest were compounded in the following ways?
9. Maria is twice the age of Jonas, who is
twice the age of Franklin. Franklin is 2. yr
less than half Maria's age. How old are
Maria, Jonas, and Franklin?
Answer: Maria is 12 years old, Jonas is 6 years old, and Franklin is 3 years old.
Step-by-step explanation: Let's start by assigning variables to represent the ages of Maria, Jonas, and Franklin.
Let's use the variable "M" to represent Maria's age.
Let's use the variable "J" to represent Jonas's age.
Let's use the variable "F" to represent Franklin's age.
From the problem statement, we know that:
Maria is twice the age of Jonas: M = 2J
Jonas is twice the age of Franklin: J = 2F
Franklin is 2 years less than half of Maria's age: F = 0.5M - 2
We can use these equations to solve for the ages of Maria, Jonas, and Franklin.
First, we can substitute J = 2F into the equation M = 2J to get M = 2(2F) = 4F.
Next, we can substitute this expression for M into the equation F = 0.5M - 2 to get F = 0.5(4F) - 2, which simplifies to 2F = 6 and therefore F = 3.
Now that we know Franklin's age, we can use the equation J = 2F to find Jonas's age: J = 2(3) = 6.
Finally, we can use the equation M = 2J to find Maria's age: M = 2(6) = 12.
Therefore, Maria is 12 years old, Jonas is 6 years old, and Franklin is 3 years old.
Please help don't know how to do
Answer:
Step-by-step explanation:
Step 1: FOIL
Step 2: Simplification
Step 3: Getting ready to combine like terms
A lunch box is 24 cm long, 15 cm wide and 5 cm thick. What is
the volume of the lunch box?
Answer:
( Use this formula below to help you find the volume of all equations using volume)
Volume formal = L × W × H
Volume formal = 24 × 15 × 5
Answer = 24 × 15 × 5 = 1,800
Cylinder 1 contains a 1.25 M stock solution of Cu(NO3)2. What volume of stock is needed to prepare 20.0 mL of 0.0750 M Cu(NO3)2 solution shown in Cylinder 2?
The Volume of stock solution needed = 1 mL
How to solveMolarity of stock solution (M1) = 1.50 M
The volume of stock solution needed (V1) = to be calculated
Molarity of diluted solution (M2) = 0.0750 M
The volume of diluted solution (V2) = 20 mL
M1V1 = M2V2
Volume of stock solution (V1) = M2V2 / M1 = (0.075 M x 20 mL) / (1.5 M) = 1 mL
So; the Volume of stock solution needed = 1 mL
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Find the area of the shapes below. Make sure to label your answers with units.
You must show all of your work to receive credit.
Find the area for a
a) The area of the triangle is 13.3 square units.
b) The area of the rectangle is 57.4 square units.
Let's start with the triangle. The area of a triangle can be calculated by multiplying its base and height and then dividing the result by 2. In your case, the base of the triangle is 7 units and the height is 3.8 units. Therefore, the area of the triangle can be calculated as:
Area of triangle = (Base × Height) ÷ 2
= (7 × 3.8) ÷ 2
= 13.3 square units
Now, let's move on to the rectangle. The area of a rectangle can be calculated by multiplying its length and width. In your case, the width of the rectangle is 7 units and the height is 8.2 units. Therefore, the area of the rectangle can be calculated as:
Area of rectangle = Length × Width
= 8.2 × 7
= 57.4 square units
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help me in 8th grade mathhh
Answer:
C
Step-by-step explanation:
input y=x+3 into the second equation and solve for x
-2x+y=1
so -2x +x+3 =1
solve for x
x = 2
y= 5
Select the statement that shows equivalent measurements.
4.5 meters = 0.0045 kilometers
4.5 meters = 0.045 centimeters
4.5 meters = 0.45 decimeters
4.5 meters = 45 decameters
The statement that shows equivalent measurements is "4.5 meters = 0.0045 kilometers".
How to solve the problem?
To convert meters to kilometers, we need to divide by 1000, since there are 1000 meters in a kilometer. Therefore, 4.5 meters is equal to 4.5/1000 = 0.0045 kilometers.
The other statements are incorrect:
4.5 meters is not equal to 0.045 centimeters, since there are 100 centimeters in a meter, so 4.5 meters is equal to 450 centimeters.
4.5 meters is not equal to 0.45 decimeters, since there are 10 decimeters in a meter, so 4.5 meters is equal to 45 decimeters.
4.5 meters is not equal to 45 decameters, since there are 10 meters in a decameter, so 4.5 meters is equal to 0.45 decameters.
It is important to be able to convert between different units of measurement in order to make accurate comparisons and calculations. In this case, the correct conversion factor was used to convert meters to kilometers, resulting in an equivalent measurement.
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=
Suppose that you decide to borrow $14,000 for a new car. You can select one of the following loans, each requiring
regular monthly payments.
Installment Loan A: three-year loan at 5.1%
Installment Loan B: five-year loan at 4.8%
PA
[1-(1-+-:)]
Use PMT=
to complete parts (a) through (c) below.
a. Find the monthly payments and the total interest for Loan A.
The monthly payment for Loan A is S
(Do not round until the final answer. Then round to the nearest cent as needed.)
mlm
*****
H
√
V
1,
(0,0)
More
Answer:
$2,602.44
Step-by-step explanation:
To find the monthly payments and the total interest for Loan A, we can use the formula for the present value of an installment loan:
PV = PMT x [1 - (1 + r/n)^(-nt)] x (n/r)
where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years of the loan.
For Loan A, we have:
PV = $14,000
r = 0.051 (5.1% as a decimal)
n = 12 (monthly payments)
t = 3
Substituting these values into the formula and solving for PMT, we get:
PMT = PV / ([1 - (1 + r/n)^(-nt)] x (n/r))
= 14000 / ([1 - (1 + 0.051/12)^(-12*3)] x (12/0.051))
= $417.79
So the monthly payment for Loan A is $417.79.
To find the total interest paid over the life of the loan, we can simply multiply the monthly payment by the total number of payments and subtract the original loan amount:
Total interest = PMT x (nt) - PV
= 417.79 x (3 x 12) - 14000
= $2,602.44
Therefore, the total interest paid for Loan A is $2,602.44.
The function h(t)=-4t^2+14t+8 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked. How long does it take for the football to hit the ground?
Answer:
t = 4
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function, when h(t) equals 0 that means the ball is touching the ground, giving the maximum time it took for the ball to hit the ground.
[tex]\frac{-b\frac{+}{-} \sqrt{b^2-4*a*c} }{2*a} \\\frac{-14\frac{+}{-} \sqrt{14^2-4*-4*8} }{2*-4} \\t = -0.5,4[/tex]
It takes 4 seconds, since time can not be negative