Answers
Answer:
[tex]\begin{aligned} \textsf{a)} \quad & \textsf{Position function}: \quad s(t) = -16t^2+1362 \\ & \textsf{Velocity function}: \quad v(t) = -32t\end{aligned}[/tex]
[tex]\textsf{b)} \quad \overline{v}=-48\:\: \sf ft/s[/tex]
[tex]\begin{aligned}\textsf{c)} \quad v(1) & = -32\:\: \sf ft/s\\ v(2) & = -64\:\: \sf ft/s\end{aligned}[/tex]
[tex]\textsf{d)} \quad t = 9.226\:\: \sf s \:\: (3\: d.p.)[/tex]
[tex]\textsf{e)} \quad v = -292.242\:\: \sf ft/s \:\: (3\: d.p.)[/tex]
Step-by-step explanation:
Given:
[tex]s(t)=-16t^2+v_0t+s_0[/tex]
Part (a)If v₀ is the initial velocity, and s₀ is the initial position:
[tex]\implies v_0=0[/tex]
[tex]\implies s_0=1362[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Position function}: \quad s(t) & =-16t^2+0+1362\\ \implies s(t) & = -16t^2+1362 \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Velocity function}: \quad v(t)&=s\:'(t)\\ \implies v(t) &=-32t\end{aligned}[/tex]
Part (b)Average velocity is the change in displacement divided by the change in time:
[tex]\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]
Given interval: 1 ≤ t ≤ 2
[tex]\implies t_1=1[/tex]
[tex]\implies t_2=2[/tex]
Find the values of s(t) at t = 1 and t = 2:
[tex]\implies s(1)=-16(1)^2+1362=1346[/tex]
[tex]\implies s(2)=-16(2)^2+1362=1298[/tex]
Substitute the values into the formula:
[tex]\overline{v}=\dfrac{s(2)-s(1)}{2-1}=\dfrac{1298-1346}{2-1}=-48\:\: \sf ft/s[/tex]
Part (c)To find the velocity at t = 1 and t = 2, substitute these values into the velocity function found in part (a):
[tex]\implies v(1)=-32(1)=-32\:\: \sf ft/s[/tex]
[tex]\implies v(2)=-32(2)=-64\:\: \sf ft/s[/tex]
Part (d)The time required for the coin to reach ground level is when s(t) = 0:
[tex]\begin{aligned}s(t) & = 0\\-16t^2+1362 & = 0\\16t^2 & = 1362\\t^2 & = 85.125\\t & = \sqrt{85.125}\\t & = 9.226\: \sf s\:\:(3\:d.p.)\end{aligned}[/tex]
Part (e)To find the velocity of the coin at impact with the ground, substitute the found value of t from part (d) into the equation for velocity found in part (a):
[tex]\begin{aligned}v(t) & = -32t\\\implies v(\sqrt{85.125}) & = -32(\sqrt{85.125})\\ v & =-295.242\:\: \sf ft/s\:\:(3\:d.p.)\end{aligned}[/tex]
Note: I have used the non-rounded value of t from part (d) for accuracy.
Related Questions
6000 was rounded to 1 significant figure.
What is the lower bound?
Answers
To lowest bound 5999.5
Vote me brainliest
Ryan wants to buy two video games. One costs $35.89 and the other costs $43.65. He estimates the total cost of the two games to be about $80. Is his estimate higher or lower than the actual cost? Explain.
Answers
Answer:
Actual cost = 35.89 + 43.65 = 79.54 so it is some what lower than estimated cost.
Step-by-step explanation:
quadrilateral A'B'C'D. Describe a sequence F. Quadrilateral ABCD is congruent to of rigid motions that takes A to A, B to B, C to C, and D to D. (Lesson 1-17) A' B' C' A D C B
Answers
The sequence of transformations that take quadrilateral ABCD to quadrilateral A'B'C'D' is given by:
Rotation 90º clockwise.Translation left.What are examples of transformations in the graph of a function?Examples of transformations are given as follows, along with explanations on the changes caused by the transformations.
Translation: Can be either left/right or down/up, changing the position of the figure.Reflections: Can be over one of the axes or over a line, changing the orientation of the figure.Rotations: Happens over a degree measure, changing the inclination, along with the orientation, of the figure.Dilation: Happens when the coordinates of the vertices of the original figure are multiplied by the scale factor, changing the side lengths of the figure.As a dilation changes the side lengths the figure, a dilated figure is not congruent to the original figure, hence a dilation does not happen for this problem.
The first change was in the inclination and orientation of the figure, hence it underwent a rotation. From the movement of the vertices, for example, A to the bottom to the top, B from right to left, the rotation was of 90º clockwise.
Then, the function had the base at the same position, however it moved left, hence the second transformation was a translation left.
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Four friends are on vacation in Hawaii.
Leilani is hiking in Oahu at 952 m in elevation.
Keanu is snorkeling at -2 m in elevation.
Kiah is scuba diving at 608 m in elevation.
Kanoa is enjoying a picnic at 4 m in elevation.
Which friend is closest to sea level?
Answers
Sea level on a number line is referred to as 0, because it’s the regulation point. That being said, we can list how far each person is above or below sea level:
Leilani’s elevation is +952 meters.
Keanu’s elevation is -2 meters.
Kiah’s elevation is -608 meters (scuba diving takes place in the sea).
Kanoa’s elevation is +4 meters.
With this information, it’s easy to deduce that Keanu is only 2 meters from sea level, and that is the least distance out of all the given information.
Answer Recap: Keanu is closest to sea level.
1. Find the sum of the measures of all the angles in all of the triangles shown in
this diagram.
Answers
The sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.
We need to find the sum of the measures of all the angles in all of the triangles shown in this diagram.
What is the triangle?A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.
The sum of all the angles of the triangle is equal to 180°.
From the figure, by counting, we get there are 20 triangles.
As we know, the sum of all the interior angles of a triangle is 180°.
So, the sum of the measures of all the angles in all of the triangles = The number of triangles × 180°
= 20 × 180°
= 3,600°
Therefore, the sum of the measures of all the angles in all of the triangles shown in the given diagram is 3,600°.
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Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer. need answers ASAP
Answers
Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.
Are all rational numbers also whole numbers:#Every Rational number is not a whole number because A whole number is a component set of zero and all positive numbers such as 0, 1, 2, 3, 10, 15,… include only positive integers. It excludes negative integer, decimal, and fractional values .
Rational Number includes all the fractions, integers as well as decimal numbers.
Here set of whole number like 3, 4, 5 we can write this number as a fraction of 1 like 3/1, 4/1, 5/1… in ratio of two integers. Therefore every whole number is a rational number but every rational number is not a whole number.
Are all whole numbers is a rational number :#Whole numbers are that starts from 0 to infinity. Whole numbers can be written in the form of 0/1, 1/1, 2/1, … Thus, every whole number is a rational number but every rational number is not a whole number.
Simplify each number. (-343)¹/₃
Answers
The result of simplifying each number (-343)¹/₃ using the properties of exponents is -7
To solve this exercise we have to resolve algebraic operations following the exponent properties.
(-343)¹/₃
Base= - 343
Exponent= 1/3
The base number -343 is the same as: -7³, then we get:
(-7³)¹/₃
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(-7)⁽³*¹/₃⁾
(-7)⁽³/₃⁾
(-7)⁽¹⁾
-7
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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On a map 2cm represents 30 mi. The actual distance between two towns is 75mi. What is the distance between the towns on the map
Answers
On the map, the separation between the two towns would be 5 cm.
Detailed explanation:
First, consider 2 cm and 30 miles as a ratio, which means that wherever you measure 2 cm with a ruler on a map, 30 miles will be scaled to that location.
Then, using some logic, we can state that if 2 cm = 30 mi, then 4 cm = 60 mi (double the 2 cm will result in doubling the 30 cm), and 1 cm = 15 mi (if you divide the 2cm by 2, 30mi will also be divided by 2). Because of this, 5cm (4cm + 4cm + 1cm) on the map equals 75mi (which is 30mi + 30mi + 15mi).
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A triangle has side lengths of (8w + 8x) centimeters, (3w+10y) centimeters, and
(4y + 8x) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
Answers
Answer:
(8w+8x)(8w+8x)+(3w+10y)(3w+10y)+(4y+8x)(4y+8x)
Step-by-step explanation:
Solve each equation. If necessary, round to the nearest ten-thousandth. log₇3 x=3
Answers
The solution of the given equation by rounding off it to the nearest ten-thousandth is 7.8295.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: log₇3x = 3
We are given a logarithmic expression: log₇3x = 3 —- 1
We know that log₇3 = log 3 / log 7 and log (ab) = log a + log b
Using in equation 1, we have,
log₇3x = 3
log 3x / log 7 = 3
(log 3 + log x) / log 7 = 3
log 3 + log x = 3 × log 7
log 3 + log x = 2.535
log x = 2.535 - 0.4771
log x = 2.0579
x = 7.8295
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 7.8295.
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if the test scores of a class of 35 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 65.6, then the mean of the combined group is
Answers
The mean of the combined group of classes is 69.35
Mean is given by by dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).
It is given that,
The mean of test scores of a class having 35 students = 73.1
And,
The mean of test scores of a class having 26 students = 65.6
We need to find,
The mean of the combined group of classes = mean of both classes
Mean of both classes = [tex]\frac{73.1 + 65.6}{2}[/tex]
= [tex]\frac{138.7}{2}[/tex]
= 69.35
Hence, 69.35 is the mean of the combined group of classes
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What is the quotient of 1. 843\times 10^71. 843×10 7 and 4. 85 \times 10^44. 85×10 4 expressed in scientific notation?
Answers
The quotient of 1.843 × 10^7 and 4.85 × 10^4, expressed in scientific notation, is 3.8 × 10^2.
Scientific notation is a way of expressing a very large or a very small number that are too much to be written in decimal form. The scientific notation is represented as:
a × 10^b
where a is between 1 and 10 and b is an integer representing the number of zeros
To divide numbers in scientific notation,
1. Divide the decimal numbers.
1.843 ÷ 4.85 = 0.38
2. Subtract the exponents of your power of 10.
7 - 4 = 3
3. Place the new power of 10 with the decimal in scientific notation form.
0.38 × 10^3 = 3.8 × 10^2
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What’s the algebraic expression of:
Six times the sum of a and b squared minus four times the product of a and b squared
Answers
Answer:
6(a+b)^2 + 4ab^2
Step-by-step explanation:
sum is addition (a+b)
product is multiplication (ab)
6(a+b)^2 + 4ab^2
2 You hang two strands of Decorative light strand one change color every 30 seconds straight to change every 45 seconds both strands just change color how many seconds will the strands change color at the same time
Answers
The two strands of Decorative light will shine at same time after every 15 seconds.
What is defined as the Highest common factor?The greatest of all their common factors is the Highest Common Factor (HCF) of more than one number. As a result, it is also known as the greatest common factor (GCF).There isn't an exact formula for determining the greatest common factor of two numbers. However, when considering prime factorization, we can write a statement that aids in evaluating the greatest common factor of more than one number.The stated condition are-
The light strand one change color every 30 seconds.
The light strand second change color every 45 seconds.
Prime factorization of both number are;
30 = 2×3×5
45 = 3×3×5
The numbers with highest power are;
HCF(30, 45) = 3×5 = 15.
Thus, the time after which both the light strands will change colour at the same time is 15 seconds.
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2. A clothing company buys 458 of a
new style of blouse. Each blouse costs
the company $24. What was the total
spent on the blouses?
Answers
Answer:
6,192
Step-by-step explanation:
Name the property illustrated by the statement " (7a * 2b) + 3c = 3c + ( 7a * 2b)" Group of answer choices Associative Property of Multiplication Associative Property of Addition Commutative property of Multiplication Commutative Property of Addition
Answers
The property illustrated by the statement where the equation is given as (7a * 2b) + 3c = 3c + (7a * 2b) is the Commutative Property of Addition
How to name the property illustrated by the statement?The equation is given as
(7a * 2b) + 3c = 3c + (7a * 2b)
The Commutative Property of Addition states that
a + b = b + a
In this case
a = (7a * 2b) and b = 3c
When the Commutative Property of Addition is applied using the above variables, we have
(7a * 2b) + 3c = 3c + (7a * 2b)
Hence, the property illustrated by the statement where the equation is given as (7a * 2b) + 3c = 3c + (7a * 2b) is the Commutative Property of Addition
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3. ASSESS REASONABLENESS Two moving truck companies offer the same
vehicle at different rates. At Haul-n-Save, the truck can be rented for $30,
plus $0.79 per mile. At Rent It Trucks, the truck can be rented for $75,
plus $0.55 per mile.
a. Write equations for the total cost of renting a truck from each company.
b. Graph the equations on the same coordinate plane. Examine the graph
to estimate after how many miles of driving the total rental cost will be
the same from each company.
c. Check your estimate. How reasonable is your estimation?
Justify your reasoning.
Answers
Using linear functions, it is found that:
a. The equations are given by: H(x) = 30 + 0.79x, R(x) = 75 + 0.55x.
b. The costs will be the same after 187.5 miles.
c. The estimate from the graph is reasonable, as it is the value of x for which both equations are equal.
What is the definition of a linear function?A linear function is defined according to the following rule:
y = mx + b
In which:
m is the slope of the function, also called the rate of change of the function, given by the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For each function in the context of this problem, we have that:
The slope is the cost per mile.The intercept is the rent cost.Hence the equations for each company are given as follows:
H(x) = 30 + 0.79x.R(x) = 75 + 0.55x.The graph is given at the end of the answer, and from the intersection point, we have that the costs will be the same after 187.5 miles.
Numerically, this value is given as follows:
H(x) = R(x)
30 + 0.79x = 75 + 0.55x
0.24x = 45
x = 45/0.24
x = 187.5.
Hence the estimate from the graph is reasonable.
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Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₉3.3
Answers
Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 3.3}{log \\9}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c (a) +log_c (b) = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
[tex]log_9{3.3}[/tex]
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
[tex]log_9{3.3}[/tex] = [tex]\frac{log \ 3.3}{log \ 9}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 3.3}{log \\9}[/tex]
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Determine if the sequence below is it arithmetic or geometric in determine the common difference/ratio in the simplest form 125,25,5
Answers
The sequence given by the terms 125,25,5 is a geometric sequence with common ratio 1/5.
In a geometric sequence, each term following the first is found by multiplying the preceding one by a constant, non-zero quantity known as the common ratio.
The nth term of a geometric series with first term a and common ratio r is given by [tex]a_n=ar^{n-1}[/tex] .
In the given sequence, the first term denoted by a is 125. The second term is 25 and the third term is 5.
Ratio of the second term to first term = 25/125 = 1/5
And the ratio of third term to second term is = 5/25 =1/5
Hence since the ratios are equal therefore the sequence is geometric, and the common ratio is 1/5 .
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A student states that a triangle can be formed with side lengths 2 in, 3 in, and 6 in. is the student correct? why, or why not? yes, because 2 3 < 6 yes, because 6 2 > 3 no, because 2 3 < 6 no, because 6 2 > 3
Answers
A student is not correct when he stated that a triangle can be formed with side lengths 2 in, 3 in, and 6 in because 2 + 3 < 6.
A triangle is a polygon with three sides and three vertices.
To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
Let a = 2, b = 3 , c = 6
a + b > c : 2 + 3 > 6 5 > 6 False
a + c > b : 2 + 6 > 3 8 > 3 True
b + c > a : 3 + 6 > 2 9 > 2 True
If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.
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Find the exact value of cos (-315)° .
Answers
Answer:
[tex]\frac{1}{\sqrt{2}}[/tex]
Step-by-step explanation:
cos(-315)° = cos 315°
The cosine function is an even function.cos 315° = cos 45°
cos(360°-x)=cos(x)This is equal to
[tex]\frac{1}{\sqrt{2}}[/tex]
Review the graph. A student spends 16.5 hours studying and receives a mark of 61.4%. Which statement describes this result?
Answers
Using the line of best fit, the correct statement that describes this result is given by:
D. The result is an outlier and there is no gap in the data.
What is the missing information?The statements are missing, and are given as follows:
A. The result is not an outlier and there is a gap in the data.
B. The result is not an outlier and there is no gap in the data.
C. The result is an outlier and there is a gap in the data.
D. The result is an outlier and there is no gap in the data.
What does the line of best fit mean?The line of best fit gives the expected exam score for a student that studies x hours. For example, for a student that studies 16 hours, the expected score is of 90.
The actual score is 61.4%, which is significantly less than the expected score, meaning that there is an outlier. However, there are no gaps in the data-set, as as the line considers students between 0 and 20 hours, and 16 is in this interval.
This means that option D is correct.
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please help im giving 60 points on my most recent question earn another 10 here :D
Find the midpoint given the endpoints:
(___),(___)
Answers
Note: 1.5 = 3/2
=======================================================
Explanation:
The two points shown on the graph are located at (-3, -2) and (1, 5)
Let's focus on the x coordinates for now.
To find the midpoint of -3 and 1, we do two things in the order shown
Add up the values: -3+1 = -2Divide in half: -2/2 = -1Therefore, -1 is the midpoint of -3 and 1 on the number line.
It is also the x coordinate of the midpoint.
------------
Repeat these steps for the y coordinates of the given points.
Add: -2+5 = 3Divide in half: 3/2 = 1.5This is the y coordinate of the midpoint.
-------------
The midpoint overall is located at (-1, 1.5)
I used GeoGebra to confirm the answer as correct.
WILL GIVE BRAINLIST TO BEST ANSWER
Julia drove a car 10 miles in 30 minutes. Jasmine drove a motorcycle 3 miles in 12 minutes. who drove faster? show work!
Answers
Julia drove 0.33333333 miles per minute since 10/30=.33333333, 0.33333333 miles per minute
Jasmine drove .25miles per minute. 3/12=.25miles per minute
HELP..........................
Answers
Answer: D
Step-by-step explanation:
? 4 cm Area = 20 cm² 6 cm
Answers
The height of the triangle whose base is 4 cm and area is 20 cm² is 10 cm .
The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane. The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × b × h.It is given that base is 4 cm and area is 20 cm² .
Putting above values in area formula , we get
Area = 1 / 2 × base × height
20 = 1 / 2 × 4 × height
20 = 2 × height
10 cm = height
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The complete question is given below :
Find the height of the triangle whose base is 4cm and area is 20 cm².
Simplify each number. (-32)⁶/₅
Answers
Simplify by expressing 32 as a product of its prime factors. Write it in index form and apply the power rule: (a^m)^n = a^mn
32 =2x2x2x2x2 = 2^5
(-2^5)^6/5 = -2 ^ 5x6/5 = -2^6
= -64
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The result of simplifying each number (-32)⁶/₅ using the exponent rules is 64
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(-32)⁶/₅
Base= -32
Exponent = 6/5
The base number -32 is the same as: -2⁵, then we get:
(-2⁵)⁶/₅
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(-2)⁵*⁶/₅
(-2)⁶
64
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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Anybody know the answer to this question?
Answers
Answer:
slope 1/3
y = -2
x=1/3-2
Step-by-step explanation:
slope 1/3
y = -2
x=1/3-2
What percent of 40 is 70
Answers
Answer:
think its 175%
Step-by-step explanation:
Convert the fraction to a decimal, then multiply by 100 =175%
Look at the image.
Please help
Answers
Answer:
well, best i can do for you : F
Step-by-step explanation:
Calculator soup
I forgot how to do this stuff, sorry