Consider a particle moving along the x-axis where
x(t)
is the position of the particle at time t,
x ′(t)
is its velocity, and
x ″(t)
is its acceleration
Answers
Regarding the velocity and acceleration functions, it is found that:
b) The particle is moving to right on these following intervals: (0,1) U (3,10).
c) The velocity when the acceleration is of zero is: -1 m/s.
When a particle is moving to right?A particle is moving to right when it's velocity is positive.
In this problem, the velocity function is presented as follows:
v(t) = 3t² - 12t + 9.
The velocity function is a concave up quadratic function, which is positive to left of the smaller root and to the right of the larger root.
The roots of the function are given as follows:
v(t) = 3(t² - 4t + 3)
Then:
3(t² - 4t + 3) = 0
t² - 4t + 3 = 0
(t - 1)(t - 3) = 0.
t - 1 = 0 -> t = 1.t - 3 = 0 -> t = 3.Considering the domain of the function, the intervals in which the car is moving right are:
(0,1) U (3,10).
What is the velocity when the acceleration is of zero?The acceleration is given by the following equation:
a(t) = 6t - 12.
It is of zero when:
6t - 12 = 0
6t = 12
t = 12/6
t = 2.
The velocity at this instant is of:
v(2) = 2² - 4(2) + 3 = -1 m/s.
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Related Questions
Exercise
1. If you have a case where n=25 and P=0.04, what is the probability that x is equal to 4?
Answers
If [tex]n=25[/tex] and [tex]p=0.04[/tex], then the probability of [tex]P(X=4)[/tex] is found to be 0.001374.
What is Binomial Distribution?
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability, [tex]p[/tex]) or failure (with probability, [tex]q=1-p[/tex]).
How to Find the Probability of a Binomial Distribution?
The chance of failure raised to the power of the difference between the number of tries and the number of successes is multiplied by the probability of success raised to the power of the number of successes in order to compute the binomial distribution. Next, multiply the final result by the sum of the number of attempts and the number of successes.The formula for binomial distribution is given as, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]From the given question, we have, [tex]n=25[/tex] and [tex]p=0.04[/tex]
Here, have to find the probability of [tex]P(X=4)[/tex], so [tex]k=4[/tex]
The binomial distribution formula is, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]
Substituting the given values in the above equation, we get
[tex]P(X=4)={25 \choose 4}0.04^{4}(1-0.04)^{25-4}[/tex]
[tex]\implies P(X=4)=12650 \times0.00000256\times0.4243\\\implies P(X=4)=0.001374[/tex]
Therefore, the value of [tex]P(X=4)=0.001374[/tex]
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If you roll a die 75 times. How many 1's should you expect to roll?
Answers
Do this: There are 6 sides on a die, one of the sides is a 1, since you roll it 75 times, do 75 / 6 which is 12.5
Show that the terms of the series ∑n=1log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms exceeds 400
Answers
The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
We have been given that the terms of the series ∑n=1log 5r are in AP.
As per the given question,
∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)
n = 20
∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)
Using the property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))
∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)
∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)
Using property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(Sr)=20·1og(5)+log(1×2×3×...20)
∑log(5r) = 20-log(5)+log(201)
∑log(5r) = 32.365524703598
Rounded to the nearest hundredth decimal,
∑log(5r) = 32.37
Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.
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Which question can be answered by finding the quotient of 5/6 divided by 1/20?
Answers
The question that can be answered by finding the quotient of 5/6 divided by 1/20 is C. Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag. How many bags can he make?
How to illustrate the information?It should be noted that the quotient is the value that is gotten when we divide the numbers given.
In this case, Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag.
The number of bags will be:
= 5/6 ÷ 1/20
= 5/6 × 20
= 100 / 6
= 17 bags
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Answer:
17 bags
Step-by-step explanation:
Suppose the government has a balanced budget and wants to increase spending without changing tax rates. The government enters the loanable funds market to borrow $150 billion for economic stimulus spending. How much money is available for private investment after this action has shifted the demand curve as shown in the figure?
Answers
The money available for private investment is $250 billion dollar
What is demand curve ?
The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.
Refer to the attachment for graph:
Once investments and government borrowing are added together, the total is = $400
if borrowing from the government is= $150
private investment
=( investment and and government borrowing) - (government borrowing )
= $400 - $150 = $250
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Day
(t) No. of Calories
Burned
C(t)
2 314
4 356
6 370
8 386
10 405
12 442
14 516
Amanda goes to the gym every day and cross–trains. Based on a chart at the gym showing the calories expended for various activities, Amanda has kept track of the number of calories she has burned over the last two weeks. She wants to find the rate at which she burned calories on day 8. That is, she needs to find C'(8). Estimate the value.
A.
8.00 calories per day
B.
8.75 calories per day
C.
17.50 calories per day
D.
17.75 calories per day
Answer: In photo below
You're Welcome :)
Answers
If she wants to find the rate at which she burned calories on day 8. C'(8) is: B. 8.75 calories per day
How to find the calories per day?First step is to find the upper and lower values for the burned calories on day 8.
Upper value (C'(8) = 405 - 386 /2
Upper value C'(8) = 19/2
Upper value C'(8) = 9.5
Lower value C'(8) = 386 -370/2
Lower value C'(8) = 16/2
Lower value C'(8) = 8
Now let find C'(8)
C'(8) = 9.5+8/2
C'(8) = 17.5/2
C'(8) = 8.75 calories per day
Therefore the correct option is B.
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A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form. 8 in. 5 in. 5 in.
Answers
The length of the straw fitted in the box is 10.67 inches.
What is cuboid?A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.
Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,
Diagonal of a cuboid = √ l² + w² + h²
Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in
Hence, The length of the straw fitted in the box is 10.67 inches.
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step by step explanation to-4x = -x + 3
Answers
The value of x is -1 for equation -4x = -x + 3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -4x = -x + 3
In the given equation minus four times of x equal to minus x plus three
x is the variable
Plus and minus are operators
-4x = -x + 3
Take the variables to one sides
Add +x on both sides
-4x+x=-x+x+3
-3x=3
Divide both sides by -3
x=-1
Hence, the value of x is -1 for equation -4x = -x + 3
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0°F; drops 15° what’s the new temperature
Answers
The new temperature is given as -15°F.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The present temperature is 0°F.
And, the drop in the temperature is 15°.
The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,
0 - 15°F
= -15°F
Hence, the new temperature after the drop is -15°F.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answers
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
What is Equation of Circle?The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.
The standard equation of a circle with center at
(a, b) and radius is r.
So, the standard equation circle is
(x -a)² + (y- b)² = r²
Given:
As, we know the standard form for equation of a circle is
(x-a)² + (y-b)² = b =r²
where (a, b) is the center of the circle and r is the radius of the circle.
We have
diameter = 12 units
radius = 12/2 = 6 units
So, the center will be at (0, 3)
Thus, the equation of circle
(x-0)² + (y-3)² = 6²
x²+ (y-3)² = 36
Hence, the Equation of Circle is x²+ (y-3)² = 36.
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2 step equation:12. Amy wants to start taking gymnastics. There is a one-time fee of $35 to sign up, then it costs $85 per month. If Amy saves up $225, how many months of gymnastics can she take?
Answers
The number of months Amy can take the Gymnastic = 2 months.
Amy wants to start taking gymnastics.
The fee structure of the gymnastics is divided into two parts.
There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.
So the first month fee of the gymnastics = 35 + 85 = 120$
Savings of Amy = 225$
If Amy pays the 1st month fee ,
then the she will be left with the savings = 225$ - 120$ = 105 $
It means Amy can join the gymnastics for one more month .
Hence the number of months Amy can take the Gymnastic = 2 months .
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Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.
Answers
Total: 499.75
Step-by-step explanation:
4 × 110.5 = 442
3 × 19.25 = 57.75
442 + 57.75 = 499.75
ERROR ANALYSIS Describe and correct the error in finding m/1. X 115° +39° + m/1 = 360° 154° +m1 = 360° m1= 206
Answers
) Nike deposits N5,000.00 in a savings bank account. If she is paid an interest rate of 5% per annum for 2 years, how much is the simple interest? NOO. O
Answers
The simple interest that Nike will receive after 2 years is $500.
The principal amount =$5000
Rate = 5% = 0.05
Time = 2 years
Now simple interest = PRT = 5000 × 0.05 × 2 = 500
Hence the simple interest earned by Nike is $500
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.
Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.
A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.
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Find the values of x and y
Answers
X= 20 & Y= 70 in right-angled triangle .
What is right angle triangle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The longest of the three sides, known as the hypotenuse, is the third side.2X + 140 = 180
2X = 40°
X = 20°
X + Y = 90°
Y = 70°
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The equation for line t can be written as y+3= 1/2(x–7). Line u, which is perpendicular to line t, includes the point (3,3). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answers
The equation of a line u perpendicular to line t and passes through (3, -3) is y = -2x + 3
How to represent the slope of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptLine t has equation as y + 3 = 1 / 2 (x - 7).
Line u is perpendicular to line t and it passes through (3, -3).
The products of the slope of perpendicular lines is equals to negative 1.
Therefore,
m₁ m₂ = -1
1 / 2 m₂ = -1
m₂ = -2
Therefore, the equation of the line have a slope of -2.
let's find the y-intercept using (3, -3)
-3 = -2(3) + b
b = -3 + 6
b = 3
Therefore, the equation in slope intercept form is y = -2x + 3.
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I need help with solving problem.
Answers
Answer:
i can help but first what the questions and where are the options?
Step-by-step explanation:
Which of the following is NOT true about the body mass index? A. uses statistical data of weight and height across the population B. measures the percentage of one's body fat directly C. relies on a correlation between weight and body fat D. does not account for one's body frame size or muscle content Please select the best answer from the choices provided. A B C D Mark this and return
Answers
The statement that is not true about body mass index is B. measures the percentage of one's body fat directly
What is Body mass index?The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.
The majority of the time, total body fat and BMI are correlated.
The Body mass index (BMI) formula
= weight in kilograms / square of height in meters
BMI Categories values are classified below
Underweight ≤ 18.5
Normal weight = 18.5–24.9
Overweight = 25–29.9
Obesity = BMI of 30 or greater
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Answer:B
Step-by-step explanation:
What other congruence is needed to prove that △QRP≅△QFP by ASA?
QR≅QF
∠R≅∠F
∠QPR≅∠QPF
PR≅PF
Answers
To prove that the two triangles are congruent by ASA, you need angles QPR and QPF to be congruent.
Answer = angle QPR congruent to angle QPF
-1/2u+3/5=1/6 What is u?
Answers
_____________________
[tex]\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}[/tex]
[tex]u=\frac{13}{15}[/tex][tex]\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}[/tex]
DefinitionsMultiplication - Multiplication, otherwise known as the inverse of division repeats a certain number's value into what it has been multiplied by. Ex. [tex]4\cdot4=16[/tex]
Fraction - A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.
Algebra - Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all mathematics
Reciprocal - In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by [tex]\frac{1}x[/tex] or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction [tex]\frac{a}b[/tex] is [tex]\frac{b}a[/tex]. For the multiplicative inverse of a real number, divide 1 by the number.
_____________________
Now we can solve this equationStep one - Subtract: [tex]-\frac{1}{2} u=\frac{1}{6}-\frac{3}{5}[/tex]Step two - Simplify: [tex]-\frac{1}{2} u=-\frac{13}{30}[/tex]Step three - Multiply by the reciprocal of [tex]-\frac{1}2[/tex]: [tex]-\frac{1}{2}u\cdot -\frac{2}{1}=-\frac{13}{30}\cdot -\frac{2}{1}[/tex]Step four- Simplify: [tex]u=\frac{13}{15}[/tex]Your answer is [tex]u=\frac{13}{15}[/tex]Solve for x.
-8x+14 ≥ 60 OR - 4x + 50 < 58
Choose 1 answer:
(A
E
x≤-
x≤
-
23
4
23
4
x>-2
or x>-2
There are no solutions
All values of a are solutions
Answers
Answer:
[tex]x\leq -7 or x > -2[/tex]
Step-by-step explanation:
-8x+14 ≥ 60 or - 4x + 50 < 58
-8x ≥ 56 or - 4x < 8
[tex]x \leq -7[/tex] or [tex]x > -2[/tex]
Apples cost 1.85 per kilogram
Work out the cost of 1.6 kilogram of apples
for 20 points
Answers
Answer:
1.6 kg = $2.96
Step-by-step explanation:
The given statement is,
→ 1 kg of apple = $1.85
→ a = 1.85
Now the cost of 1.6 kg of apple is,
→ 1.6 × a
→ 1.6 × 1.85
→ $2.96
Hence, 1.6 kg of apple is $2.96.
11 subtracted from the sum of 7y and 2y is -38.
Answers
Answer: 7y = 38.11111111111 2y = 10.8888888889 the sum of these two equals to 49 so 11-49=-38 Hopefully you understood. But I didn't know what you wanted to know from this?
Step-by-step explanation: 11-(7y+2y)=-38
7y+2y=9y (basic math)
11-9y=-38 then you want to move -38 to the other side, and when you move it to the other side it changes its value then from -38 it becomes 38. Same for the -9y, we move it to the other side and it changes its value so now from -9y its 9y. So now are equation should look like this 11+38=9y. 11+38=49 => y=49÷9 y=5.44444444444 (49÷9) x 7 = 38.1111111111 and (49÷9) x 2 = 10.8888888889
Please help asap!! Please please please
Answers
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
What is the similarity test of two triangles?
If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.
In the given figures, the length of side AB is equal to the length of side DE.
Side AB = Side DE ----------(I)
Similarly, the length of side BC is equal to the length of side EF.
Side BC = Side EF ----------(II)
And the measure of angle ABC is equal to the measure of angle DEF.
∠ ABC = ∠ DEF -------(III)
From (I), (II), and (III), and by using the SAS test we can say that
ΔABC ~ ΔDEF ----------- SAS test
Hence,
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
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126=2×3×3×k
Solve for k
Answers
[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:-
[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 18 \times k}}[/tex]
[tex]{ \sf{126 = 18k}}[/tex]
Divide both the sides by 18 in order to find the value of k. Then,
[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]
[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]
On an architect's blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line 1 inches long on the blueprint
Answers
The length of wall in real life is 4 feet.
Given that on an architect's blueprint, 1 inch corresponds to 4 feet.
In this architect's plan, a wall represented by a line 1 inches long on the blue print.
So, the length of wall in real life is = 4 feet.
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Answer:
4ft
Step-by-step explanation:
If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.
2. Write each of the following as a power function in the form f(x) = kx^p.
f(x) = -3/2x^5
Answers
The simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
What is power function ?
A function having a single term that is the sum of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. Consider functions for area or volume as examples (a number that multiplies a variable raised to an exponent is known as a coefficient). A power function is a function where y = x n, where n is any real constant number. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here ,
a) f(x) = [tex]\frac{-3}{2x^5}[/tex]
To write in the form of f(x)= [tex]kx^p[/tex]
=> f(x) = [tex]\frac{-3}{2}* \frac{1}{x^5}[/tex]
=> f(x) = [tex]\frac{-3}{2} x^-5[/tex]
b) g(x) = 5[tex]\sqrt[3]{x}[/tex]
Here we know that [tex]\sqrt[n]{a} = a^\frac{1}{n}[/tex] , then
=>g(x)=5[tex]x^\frac{1}{3}[/tex]
Hence the simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
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Rebecca wants to buy a new phone. She has already saved $110 and received a gift of $50 from her grandmother that she added to her savings. She plans to earn the rest by selling necklaces for $5 each. The phone she wants to purchase costs $485. Write an equation that represents how many necklaces Rebecca will need to sell in order to have enough money to get her phone.
Answers
Answer:
Step-by-step explanation:
She needs to sell 65 necklaces.
-353.92 - (-283.56) -131.29
Answers
-353.92-(-283.56)-131.29= -20,165
Drag each tile to the correct box. Not all tiles will be used.
Find the equations with unit rates greater than the unit rate of the graph. Then arrange these equations in order from least to greatest unit rate.
Answers
The equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x
How to determine the equations with unit rates greater than the unit rate of the graph?
On a graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:
Slope = y2-y1 / x2-x1
Thus, we can any two convenient points on the graph and use it calculate the slope:
Let's pick points (5, 10) and (12, 25)
This implies x1 = 5, y1 = 10 and x2 = 12, y2 = 25
Slope = y2-y1 / x2-x1
Slope = 25-10 / 12-5 = 15/7
Thus, the unit rate of the graph is 15/7 = 2.143
Find the equations with unit rates greater than the unit rate of the graph:
y = 19/8x: unit rate = 19/8 = 2.375
y = 27/13x: unit rate = 27/13 = 2.077
y = 21/9x: unit rate = 21/9 = 2.333
y = 11/5x: unit rate = 11/5 = 2.200
y = 15/17x: unit rate = 15/17 = 0.882
y = 31/15x: unit rate = 31/15 = 2.067
y = 13/6x: unit rate = 13/6 = 2.167
The equations with unit rates greater than the unit rate of the graph are y = 19/8x, y = 21/9x, y = 11/5x and y = 13/6x
Therefore, the equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x. Drag each tile to the correct box accordingly
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