An object moves according to a law of motion, where, its position is described by the following function, s = f(t) = t^4 - 4t + 1. The time t is measured in seconds and s in meter.a. Sketch the velocity graph and determine when is the object moving in the positivedirection.b. Draw a diagram of the motion of the object and determine the total distancetraveled during the first 6 seconds.
Answers
SOLUTION
(a) The function given is the distance graph. The velocity fuction is the derivative of the distance function. This becomes
[tex]\begin{gathered} f(t)=t^4-4t+1 \\ f^{\prime}(t)=4t^3-4 \\ v=4t^3-4 \end{gathered}[/tex]the graph is shown below
From the velocity graph above, the function is moving in a positive direction from 1 second and beyond
(b) The diagram of motion of the object is shown in the distance graph below
The total distance travelled is the integral of the velocity function from 0 to 6 as shown below
[tex]\begin{gathered} \int_0^64x^3-4 \\ =[\frac{4x^4}{4}-4x]_0^6 \\ =[x^4-4x]_0^6=6^4-4(6)-(0^4-4(0)) \\ =1296-24-0 \\ =1272 \end{gathered}[/tex]Hence the answer is 1272 m
Related Questions
The quotient of 1 and the square of a number. Write it as an expression
Answers
Answer:
1 ÷ [tex]\sqrt{n\\}[/tex] = x
Step-by-step explanation:
For the given, "the quotient of 1 and the square of a number", the expression is 1+√n
What is a mathematical expression?
A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.
The phrase "The quotient of 1 and the square of an integer" is presented.
The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.
If n is the number the expression can be written as,
=1+√n
Thus, for the given expression the expression is 1+√n.
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Write and equation for each of the following problems and solve. (40 points each)3. The length of a rectangle is 5 cm more than three times the width. If the width is 12, what is thelength of the rectangle?
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It is given that,
The length of a rectangle is 5 cm more than three times the width.
That is, l=3w+5
Put width, w=12.
Therefore, the length becomes,
l=3(12)+5
l=36+5
l=41 cm.
Hence, the length of the rectangle is 41 cm.
Please explain and help me get the correct answer. Thank you. Practice work that is not graded.
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First, from the formula given we solve the equation for D:
[tex]\begin{gathered} 4PD=D^2LN\pi, \\ \frac{4PD}{LN\pi}=D^2, \\ \sqrt{\frac{4PD}{LN\pi}}=D^{}. \end{gathered}[/tex]Now, substituting the given data:
(a) PD=405 cu in, L=4.7 in, and N=7,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times405}{4.7\times7\times\pi}}in=\sqrt[]{15.6736175}in\approx3.96\text{ in}[/tex](b) PD=399.4 cu in, L=2 in, and N=6,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times399.4}{2\times6\times\pi}}in=\sqrt[]{42.37765618}in\approx6.51\text{ in}[/tex]Answer:
(a) 3.96 in.
(b) 6.51 in.
Drop down options for 1 2 and 4 are Forest A or Forest B
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Given :
[tex]A(t)=107(1.015)^t[/tex][tex]B(t)=88(1.025)^t[/tex]1)
Set t=1 we get
[tex]A(t)=107(1.015)^t[/tex]Pick a number 1 through 20. Now do it again.Now do it a third time. I am going to writedown my prediction of what numbers youpicked. Assuming no magic was used, what isthe probability I guessed right? Put youranswer in fraction form. (Note: Numbers CANbe used more than once.)
Answers
There are 20 numbers to choose from. Thus, the total sample space is 20.
If you choose one number, the probability of choosing that number is:
[tex]\frac{1}{20}[/tex]Now, if after choosing one number in the first round, you proceed to choose another number in the second round.
The probability of choosing a number for this second round will be:
[tex]\frac{1}{20}[/tex]Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.
For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:
[tex]\frac{1}{20}[/tex]The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.
Thus the final answer:
[tex]\frac{1}{20}\times\frac{1}{20}\times\frac{1}{20}=\frac{1}{8000}[/tex]Therefore, the final answer is:
[tex]\frac{1}{8000}[/tex]Help solve this problem it's 8th grade math identifying coordinates on a graph
Answers
Answer:
C -9, -4
E -8, 4
G-4, 0
I-6, -8
B0, 0
D-16, 4
F-2, 9
H0, 7
J9,-2
A combined total of 598 hamburgers and cheeseburgers were sold. There were 52 fewer cheeseburgers sold in hamburgers. How many hamburgers were sold
Answers
explanation:
598-52 = 546
A crate of medicine with a density of 2,200 kilograms per cubic meter will be shipped from England to the U.S. What is the crate's density in pounds per cubic foot?
Answers
The crate's density in pounds per cubic foot = 137.28 lb/ft³
What is density?Density is defined as the quantity that shows the relationship between the mass and volume of an object which is measured in kilograms per cubic meter or in pounds per cubic foot.
The density of the given crate of medicine = 2,200 kg / m³
To convert to pounds per cubic foot;
1 kg/m³ = 0.0624 lb/ft³
2,200 kg/m³ = X
Make X the subject of formula;
X = 2,200 × 0.0624/1
X = 137.28 lb/ft³
Therefore, when converter to pounds per cubic foot the density of the crate of the medicine= 137.28 lb/ft³.
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Which graph best represents 16≤x²+y²≤25
Answers
The most appropriate choice for annular region will be given by
This graph represents an annular region shown in the figure
What is annular region?
Annular region represents the space between two concentric circles of different radii.
Equation of annular region centered at (0, 0) is
[tex]a^2 \leq x^2+y^2\leq b^2[/tex]
Here,
[tex]x^2 + y^2\geq 16\\x^2 + y^2 \geq 4^2\\[/tex]
It denotes the outside of a circle of radius 4 centered at (0, 0)
[tex]x^2 + y^2\leq 25\\x^2 + y^2 \leq 5^2\\[/tex]
It denotes the inside of a circle of radius 5 centered at (0, 0)
So the complete graph is being attached here.
This region is known as annular region
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ABC is shown . D is a point on AB,AC =7, AD=6, and , BC=18.
Answers
ok
AC = 7
AD = 6
BC = 18
It must be 12, because the sum of two sides of a triangle is higher than the other side.
And 6 + 5 = 11
AB + AC = 11 + 7 = 18
in the figure shown Line O is parallel to line P and line M is Parallel to linea N
Answers
we have that
In this problem angle x and angle of 62 degrees are supplementary angles
that means
x+62=180
solve for x
x=180-62
x=118 degreesBill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the compound amount in 6 years
Answers
Given:
Initial deposit = $8500
rate of interest = 5% compounded annuallly
time (t) = 6 years
If Ao is invested at an annual interest rate r and compounded semiannually, the amount At after t years is given by the formula:
[tex]A_t\text{ = }A_0(1\text{ + }\frac{r}{2})^{2t}[/tex]The compound amount in 6 years:
[tex]A_t\text{ = 8500 }\times\text{ (1 + }\frac{0.05}{2})^{2\times6}[/tex]Simplifying we have:
[tex]\begin{gathered} A_t\text{ = 8500 }\times1.025^{12} \\ =\text{ 11431.56} \end{gathered}[/tex]Answer:
$11431.56
This figure shows a circle with a radius of 3.
A circle with its radius labeled as 3.
What is the circumference of the circle?
Answers
The circumference of the circle has a value of 18.86 units
How to determine the circumference of the circle?From the question, we have the following parameters:
Radius, r = 3 units
The circumference of the circle can be calculated using the following circumference formula
C = 2πr
Where
π = 22/7 (a constant)
r = 3
Substitute the known values in the above equation
So, we have the following equation
C = 2 * 22/7 * 3
Evaluate the products
So, we have the following equation
C = 18.86
Hence, the circumference is 18.86 units
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Elijah and his brother ran a race. Elijah reached the finish line in 60.26 seconds and his brother reached the finish line 6 seconds later. How long did it take Elijah's brother to run the race?
Answers
For each relation, decide whether or not it is a function.
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Relation 1 and Relation 3 are functions while Relation 2 and Relation 4 are not functions.
Function is a relation which maps a set to another set with some criteria.
It includes a property that one element of the domain set should only be related to exactly one element in the range set. That is, same element from the domain cannot be related to different elements in the range. Also all elements in the domain should have images in the range also.
Now we will check all the relations given one-by-one.
In relation 1, the relations are:
Chair ---------> 0
Pencil --------> 0
Paper ---------> 4
Star ------------> 1
Here All the domain elements are mapped only once to one element from the range. So it is a function.
In relation 2, the relations are:
4 ----------------> 5
4 ----------------> 9
0 ----------------> -9
1 -----------------> 4
8 -----------------> -4
Here 4 is mapped to both 5 and 9. So it does not satisfy the definition of a function and hence is not an function.
In relation 3, the relations are:
z -----------------> c
k -----------------> a
a -----------------> k
c ------------------> c
Here also all elements in the domain are mapped only once to an element from the range. So it is a function.
In relation 4, the relations are:
-4 -----------------> m
-4 -----------------> d
-4 -----------------> c
9 -----------------> s
Here, -4 is mapped to m, d and s. So it cannot be a function as it has more than one images.
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A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is not yellow
P(not yellow)
Answers
The probability that it is not yellow candies will be 119/139.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A bag contains;
Number of red candies = 42
Number of green candies = 45
Number of yellow candies = 20
Number of purple candies = 32
Now,
Total number of candies in a bag = 42 + 45 + 20 + 32
= 139
And, The number of candies in a bag not contain yellow candy
= 139 - 20
= 119
Thus, The probability that it is not yellow candies will be;
Probability = Number of not yellow candies / Total candies
= 109 / 139
Therefore, The probability that it is not yellow candies will be 119/139.
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A sequence is defined by the recursive formula f(n + 1) = 1.56(0). Which sequence could be generated using the formula? 0 -12 -18, -27 ! EE 0 -20, 30, -45, -18, -16.5, -15, ... 0-16, -17.5, -19, ...
Answers
f(n+1) is
[tex]f(n+1)=\frac{3}{2}^nf(n-(n-1)[/tex]Therefore, substitutig, we get, option c.
Find the solution of the system of equations.6x – 3y = -303x – 6y = 12
Answers
6x - 3y = -30 -------------------------------(1)
3x - 6y = 12 ---------------------------------(2)
Multiply through equation(1) by 3 and then multiply through equation (2) by 6
18x - 9y = - 90 ---------------------------------(3)
18x - 36y = 72 ----------------------------------(4)
subtract equation (4) from equation (3)
micrometers, T is measured in seconds, and D accounts for the weakening of the earthquake due to the distance from the epicenter.
If an earthquake occurred for 4 seconds and D = 2, which graph would model the correct amount on the Richter scale?
Answers
The graph that can be used to model the correct amount on the Richter scale is r = log(a/4) + 2.
How to illustrate the information?It should be noted that the magnitude of an earthquake is gotten by using the equation:
r = log(a / t) + d.
where
r = magnitude of an earthquake
a = amplitude
t = time
d = distance.
In this case, the earthquake occurred for 4 seconds and D = 2. We'll substitute the value into the equation and this will be r = log(a/4) + 2.
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8. Tabitha made 12 out of 23 free throw attempts in the first half of practice and 20 out
of 27 attempts in the second half of practice. What is her free throw average for the
whole practice, written as a decimal?
Answers
Answer: 0.64 ...........
Quadrilatral ABCD has the following vertices
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
Angle a is right angle
is ABCD a rectangle
pls help i will give brainliest
Answers
From the calculations below, we can tell that quadrilateral ABCD is not a rectangle because AB is not parallel to CD
How to Identify a rectangle?
We are given that the quadrilateral is ABCD with the vertices as;
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
We are further told that Angle A is a right angle. Thus;
AB must be perpendicular to AD.
Secondly, for ABCD to be a rectangle, AB must be parallel to CD. Thus;
By slope formula, for AB and CD are gotten from the formula;
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope of CD = (-6 - 1)/(6 - 8)
Slope of CD = -7/-2 = 7/2
Slope of AB = (4 - (-2))/(-4 - (-6))
Slope of AB = 6/2
Slope of AB = 3
Since Slope of AB and AC are not equal then ABCD is not a rectangle.
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After 12 weeks, how much more will he made in sales of buttered popcorn than the sales of caramel popcorn
Answers
We have two functions for the sales of popcorn:
[tex]\begin{gathered} B(w)=8w+9 \\ C(w)=6w-1 \end{gathered}[/tex]being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.
We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.
We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.
Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).
Then, we can calculate the difference in sales as:
[tex]\begin{gathered} D=11\cdot B(12)-11\cdot C(12) \\ D=11\cdot(8\cdot12+9)-11\cdot(6\cdot12-1) \\ D=11\cdot(96+9)-11\cdot(72-1) \\ D=11\cdot105-11\cdot71 \\ D=1155-781 \\ D=374 \end{gathered}[/tex]Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.
IS THIS A FUNCTION YES OR NO?? (ALGEBRA 1)
Answers
Answer: Yes
Step-by-step explanation:
Yes, the numbers in the table are a function. The equation for the equation would be
y = 2x
Convert compressions to simplified faction or integer. If it’s not a real number, enter None
Answers
Given an expression:
[tex](-81)^{\frac{1}{4}}[/tex]We have to simplify the expression, if it does not result in a real number then the answer is NONE.
Let:
[tex]x=(-81)^{\frac{1}{4}}[/tex]Then,
[tex]\begin{gathered} x=(-81)^{\frac{1}{4}} \\ \Rightarrow x^4=((-81)^{\frac{1}{4}})^4 \\ \Rightarrow x^4=-81 \end{gathered}[/tex]There is no real number whose power 4 is a negative number.
Thus, the answer is not a real number. The answer is NONE.
I NEED HELP ON TRIG PROOFS, SOMEONE PLEASE HELP!!!! URGENT!!!!
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Step-by-step explanation:
:)))))))))))))))))))))
Solve for X picture include
Answers
The sum of angles of a triangle is equal to 180 degree.
Determine the value of x, by using angle sum for the triangle.
[tex]\begin{gathered} 2x-4+3x-4+3x-4=180 \\ 8x=180+12 \\ x=\frac{192}{8} \\ =24 \end{gathered}[/tex]The value of x is 24
Evaluate. 43⋅(100÷25)−50 Enter your answer in the box.
Answers
Answer:
122
Step-by-step explanation:
43 * (100/25) - 50
43 * 4 - 50
172 - 50
122
Hope this helps! :)
Write two expressions that represent the volume of the cube, one with exponents and one without. The side of the cube is the fraction 3/5.
Answers
(3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5.
1.) For the first expression with exponents:
(3/5)to the power of 3 can be written as , where the number 3/5 is called the base, and 3 is the power or exponent of the expression. So (3/5) times 3 .
Where, Side of the cube (a) = 3/5
⇒ (3/5)^3
⇒ 0.216 cube.units
2.) For the second expression without exponents:
The formula of volume of the cube is given by volume(side) =a*a*a, where a is the length of its sides or edges.
Cube ⇒ ( 3/5 × 3/5 × 3/5)
Cube ⇒ 0.216 cube.units
Cube of having side (3/5) = 0.216 cube.units
Hence, (3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5 .
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A sequence is defined recursively using the formula f(n+1) =-0.5f(n) . If the first term of the sequence is 120, what is f(5)?
−15
−7.5
7.5
15
Answers
Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:
[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]
Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:
[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]
Then substitute f(3) down to f(1):
[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]
Therefore, f(5) = 7.5
Solve for x:
3(x+1)-22+13=12
Answers
Answer:
x=6
Step-by-step explanation:
3 (x+1) -22 +13=12
3x+3 -22+13=12
3x+3-9=12
3x-6= 12
3x= 12+6
3x= 18
x= 18/3
x= 6