A particle travels along the x-axis such that its position at time t is given by the function x(t) = 2t2 + t. What is the average speed of this particle over the interval 2 ≤ t ≤ 10?
4
25
32
200
Answers
Answer:
25.
Step-by-step explanation:
At time 2, x(t) = 2(2)^2 + 2 = 10
At time 10, x(t) = 2(10)^2 + 10 = 210.
Average speed for this interval
distance / time
= (210 - 10) / (10 - 2)
= 200/8
= 25.
Related Questions
Which table represents a linear function?
x y
1 3
2 7
3 11
4 15
x y
1 3
2 8
3 15
4 21
x y
1 3
2 9
3 3
4 9
x y
1 3
2 9
3 27
4 81
Answers
The first table represents a linear function.
What is a linear function?A linear function is one that changes at a constant rate. Any linear function has an increase or decrease that is constant. The slope of the line, denoted by the letter m in the equation y = mx + b, is this constant rate of change.
Given are the tables with values of x and y.
In a table of linear functions, the ratio of the difference in y values to the difference in x values is consistently constant.
The first table is given as:
x y
1 3
2 7
3 11
4 15
Only table 1 in the provided tables represents a linear function.
This is because the equivalent values of y change by 4 when the value of x changes by 1.
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Theatre tickets cost either $30 or $42. One evening twice as many $30 tickets are sold as $42 tickets and the total money taken is $18564. Find the total number of tickets that are sold.
Answers
1 + 2 = 3
18564 / 3 = 6188
6188 x 2 = 12376
Ratio = 6188:12376
6188 / 42 = 148 tickets
12376 / 30 = 413 tickets
413 + 148 = 561 tickets
What is the measure of m?n20m5= [?]?]Vm =Give your answer in simplest form.Enter
Answers
To answer this question, we need to remember the next theorem:The
We have that the hypotenuse is the largest side of a right triangle. In this case, it is equal to (5 + 20) = 25 units.
The leg of the right triangle we need to find is m, and we know that the projection of m on the hypotenuse is 5 units.
Theref
What is the range for -|x+3|
Answers
The function is -|x+3|. The range is (-∞,0].
Given that,
The function is -|x+3|
We must determine the function's range.
A function's domain and range are its constituent parts. The domain of a function is the set of all possible input values, whereas the range of a function is its potential output. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B.
The function is -|x+3|
The domain is (-∞,∞)
The range is (-∞,0]
Therefore, the range is (-∞,0].
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please help this worth half ny grade
Answers
Answer:
see image
Step-by-step explanation:
See attached image
Guys i need helps is this right?
Answers
determine whether the function has a minimum or maximum f(x)=-2/3x+5 if x<0 -x if 0 4 -x^2+4x+4 if x>4
Answers
The function has no minimum or maximum
How to determine the minimum or the maximum of the functionThe function is given as
f(x) = -2/3x + 5 if x < 0
f(x) = -x^2 + 4x + 5 if x > 4
The above function is a piecewise function
And the type of functions in the piecewise function are
Linear functionQuadratic functionA linear function does not have a minimum or a maximum
This means that the function would have no minimum or maximum
Hence, the minimum or the maximum value of the function does not exist
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3
1
1. How many groups of 1/8 are in 3?
8
2. Evaluate.
5
groups
|||
Answers
Answer:
answer to question 1: 24
Explanation: (btw sorry i couldn't answer question 2) multiply 8 times 3 and you get the answer
The required group of number is 24 of 1/8 in 3.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given numbers are 1/8 and 3.
Let there are n number of groups of 1/8 in 3.
To find the value of number of groups n,
Use equation form,
1/8 n = 3
n = 3 x 8
n = 24.
There are 24 groups of 1/8 in 3.
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I need help on this question
Answers
F(x) = -(x-4)^2 +9
(Negative slope, and vertex is point (4,9))
30 points asap
The equation y = –117.5 x + 31,379.9 gives the population y of a city x years after 1975. What is the real-world meaning of the rate of change and the y-intercept?
Rate of Change: The city’s population decreases by about 118 people each year. Y-intercept: In 1975, the city’s population was about 31,380 people.
Rate of Change: The city’s population decreases by about 31,380 people each year. Y-intercept: In 1975, the city’s population was about 118 people.
Rate of Change: The city’s population decreases by about 1975 people each year. Y-intercept: In year 0, the city's population was about 118 people.
Answers
The equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,
Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means In 1975, the city’s population was about 31,380 people.
In the question ,
the equation that gives the population y of a city in x years is
y = –117.5 x + 31,379.9
let us find the population for 1976
So , x = 1 ,
we get , y = –117.5(1) + 31,379.9
y = –117.5 + 31,379.9
y = 31262.4
So, the population in the year 1976 is 31262.4
change in population = population in 1976 - population in 1975
= 31262.4 - 31,379.9
= -117.5
≈ -118
to find the population in the year 1977
x = 2 ,
we get , y = –117.5(2) + 31,379.9
= –235 + 31,379.9
= 31144.9
change in population = population in 1977 - population in 1976
= 31144.9 - 31262.4
= -117.5
≈ -118
From above , we can see that the population is decreasing in the year 1976 and 1977 , by 118 people,
hence , we can say that , the city’s population decreases by about 118 people each year
For population in 1975 , we put x=0 ,
So , y = –117.5(0) + 31,379.9
= 31379.9
≈ 31380
Therefore , the equation y = –117.5 x + 31,379.9 gives the population y of a city in x years after 1975 , in real world ,
Rate of Change means The city’s population decreases by about 118 people each year , and Y-intercept means In 1975, the city’s population was about 31,380 people .
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What is the answer to the problem for sin, sec, tan. I don’t really need a detailed explanation just the answer. Thank you.
Answers
Answer:
[tex]\begin{gathered} \sin(\theta)=-0.35 \\ \\ sec(\theta)=-1.07 \\ \\ \tan(\theta)=0.38 \end{gathered}[/tex]Step-by-step explanation:
Remember that for a given terminal point of an angle, we define those trigonometric functions as following:
[tex]\begin{gathered} \sin(\theta)=\frac{y}{\sqrt{x^2+y^2}} \\ \\ sec(\theta)=\frac{\sqrt{x^2+y^2}}{x} \\ \\ \tan(\theta)=\frac{y}{x} \end{gathered}[/tex]This way, we'll have that:
[tex]\begin{gathered} \sin(\theta)=-0.35 \\ \\ sec(\theta)=-1.07 \\ \\ \tan(\theta)=0.38 \end{gathered}[/tex]Standard Form & Scientific Notation• 3 examples of converting from standard form to scientific notation• 3 examples of converting from scientific notation to standard form
Answers
Required:
We need to convert from standard form to scientific notation and also scientific notation to standard form.
Explanation:
a) Convert from standard form to scientific notation:
1) Consider the number 4,520,000.
The given number can be written as follows.
[tex]4,520,000=452\times10000[/tex][tex]=452\times10^4[/tex][tex]=452\times10^4\times\frac{10^2}{10^2}[/tex][tex]=452\times\frac{10^4\times10^2}{10^2}[/tex][tex]=\frac{452}{100}\times10^6[/tex][tex]=4.52\times10^6[/tex]The scientific notation of s
[tex]4.52\times10^6[/tex]2) Consider the number
[tex]35.98\times10^3[/tex]Multiply and divide by 10.
[tex]35.98\times10^3=35.98\times10^3\times\frac{10}{10}[/tex][tex]=\frac{35.98}{10}\times10^3\times10[/tex][tex]=3.598\times10^4[/tex]The scientific notation is
[tex]3.598\times10^4[/tex]3) Consider the number.
[tex]600.89\times10^{-8}[/tex]Multiply and divide by 100.
[tex]600.89\times10^{-8}=600.89\times10^{-8}\times\frac{100}{100}[/tex][tex]=\frac{600.89}{100}\times10^{-8}\times10^2[/tex][tex]=6.0089\times10^{-6}[/tex]The scientific notation is
[tex]6.0089\times10^{-6}[/tex]b) convert from scientific notation to standard form:
1)
Consider the notation:
[tex]6.285\times10^{-5}[/tex][tex]Use\text{ }10^{-5}=\frac{1}{100000}.[/tex][tex]6.285\times10^{-5}=\frac{6.285}{100000}[/tex][tex]=0.00006285[/tex]The standard form is 0.00006285.
2) Consider the notation.
[tex]7.9\times10^4[/tex][tex]Use\text{ }10^4=10000.[/tex][tex]7.9\times10^4=7.9\times10000[/tex][tex]=79000[/tex]The standard form is 79,000.
3) Consider the notation.
[tex]9.008\times10^5[/tex][tex]Use\text{ }10^5=100000.[/tex][tex]9.008\times10^5=9.008\times100000[/tex][tex]9.008\times10^5=900800[/tex]The standard form is 900,800.
The half-life of a radioactive kind of uranium is 2 years. How much will be left after 4 years, if you start with 776 grams of it?
Answers
ANSWER
194 grams
EXPLANATION
We have that the half life of the uranium is 2 years.
This means that it will take 2 years for the uranium to decay to half of its original value.
The formula for exponential decay is:
[tex]y=ab^t[/tex]where y = the value after the decay
a = initial value
b = rate of decay.
t = number of years
First, we have to find b.
We have that 776 grams of uranium will decay to half its amount (388 grams) in 2 years. This means that:
[tex]\begin{gathered} 388\text{ = 776 }\cdot b^2 \\ \Rightarrow b^2\text{ = 388 / 776} \\ b^2\text{ = 0.5} \\ b\text{ = }\sqrt[]{0.5} \\ b\text{ = 0.707} \end{gathered}[/tex]Therefore, after 4 years (t = 4), the amount of uranium left will be:
[tex]\begin{gathered} y\text{ = 776 }\cdot(0.707)^4 \\ y\text{ = 776 }\cdot\text{ 0.25} \\ y\text{ = 194 grams} \end{gathered}[/tex]That is the amount of uranium that will be left after 4 years.
Walter Slater sells appliances and earns 2.5% commission in addition to his salary. Last month he sold
$63,000 in appliances. How much was his commission check?
Answers
Answer:
1575
Step-by-step explanation:
Comment
You are just asked to figure out the commission. The rule is to place 100 underneath what is given as the %. In effect, % = x / 100 in decimal form. In this case x = 2.5
So the % is 2.5/100 = 0.025 as a decimal
So commission is 63000 * 0.025 = $1575 commission
Calculate the volume of liquid that would fill the bowl of the glass. SHOW ALL WORK!!
Answers
Answer:
49.7 cm³Step-by-step explanation:
We need to find the volume of the cone with:
Diameter = 5 cm andSlant height = 8 cmFirst, find the height, using Pythagorean, where hypotenuse of the triangle is 8 cm and base is the radius = 5 cm/2 = 2.5 cm:
[tex]h = \sqrt{8^2-2.5^2} =\sqrt{57.75} =7.6[/tex] (rounded)Find the volume of the cone:
[tex]V=\pi r^2h/3=3.14*2.5^2*7.6/3 = 49.7[/tex] (rounded)What’s the answer plss I need help asp
Answers
Answer:
I am 80% positive that it is DE but there is still that other 20% so keep in mind I am not entirely sure
Please help me asap (20 points)
Answers
Answer:
1.7^28/1.6^21 the second option.
Step-by-step explanation:
I need help finding the measurements of the numbered angles Question 1 and 2
Answers
In figure one the value of ∠2 = 65 ° ∠1 = 115° .
In figure two the value of ∠2 = 74° ∠1 = 106°.
What are corresponding angles in parallels lines?In the case of parallel lines, corresponding angles are congruent. Corresponding pairs are all angles that are situated in the same location with respect to the parallel and transversal lines. According to the definition of corresponding angles, when three parallel lines intersect two of them, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles. Alternate angles, co-Interior angles, and matching angles are three facts regarding angles in parallel lines that we use to do this. When a transversal crosses two parallel lines, alternate and matching angle pairs coincide. Only when a transversal crosses two parallel lines perpendicularly are consecutive angles congruent. When a transversal intersects two parallel lines, however, subsequent angles are not necessary.
Figure 1
Given angle = 65°
= ∠2
Cause they are corresponding angles.
∠1 + ∠2 = 180°
∠1 = 115
Figure 2
Given angle = 74 °
= ∠ 2
Cause they are corresponding angles.
∠1 + ∠2 = 180°
∠1 = 106°
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The northern hemisphere of planet earth has an inner core that is made up of iron and nickel. This iron nickel core is 30% of the volume of the northern hemisphere. If the diameter of the earth is 8,000 miles, what is the volume of iron-nickel core?
Answers
It turns out that the dynamo effect depends on the presence of up to 20% nickel in the Earth's core, a metal that behaves very differently from iron under extreme temperatures. Unlike the northern hemisphere mineral-rich crust and mantle, the core is made almost entirely of metal—specifically, iron and nickel. The shorthand used for the core's iron-nickel alloys is simply the elements' chemical symbols—NiFe. Elements that dissolve in iron, called siderophiles, are also found in the core.
Explain about the volume of iron nickel core?The core is almost entirely comprised of metal, notably iron and nickel, in contrast to the crust and mantle, which are rich in minerals. Iron-nickel alloys found in the core are denoted by their chemical symbols, NiFe. The core also contains siderophiles, or substances that dissolve in iron.volume calculation for the earth. Since the Earth is nearly spherical, its volume (V) may be determined using the formula V = 4/3 pi x r3, where r is its radius.The core of the earth is made up of iron, nickel, and other heavy metals like gold since they are the heaviest of all the metals and gravitated into the center of the planet.To learn more about iron nickel core refer to:
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Adam's school is 12 miles from his house. It takes his older brother
20 minutes to drive him to school.
If Adam's brother drives s mph faster than usual, how fast will
they reach the school?
Answers
I have a question about exponential functions I will submit a photo
Answers
The values are given as:
(a) Approximate the value of e^6 to 4 decimal places:
The value of
[tex]e^6=403.42879[/tex]The approximate value to 4 decimal places is 403.4288.
(b) Approximate the value of e^(-0.66) to 4 decimal places:
[tex]\text{The value of e}^{-0.66}=0.5168513344916[/tex]Approximated value to 4 decimal places is 0.5168..
Sid burrowed a single payment loan at $10,000 at an interest rate of 5.5%. The term of the loan is 120 days. What is the maturity value of his loan at exact interest?
Answers
For this case
P = 10 000
i=0.055
t=120
After you compute the formula you would get
A = 6 170 141
NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?
Answers
Answer:
Total moving cost = $2,053.84
Step-by-step explanation:
Let's write down Jay's requirements and costs associated
9 hours of loading/unloading at $95 per hour = 95 x 9 = $855
7 hours of packing/unpacking at $80 per hour = 80 x 7 = $560
200 miles of transportation at $2.50 per mile = 2.50 x 200 = $500
Total before-tax cost of moving = $855 + $560 + $500 = $1, 915
Sales Tax is additional at 7.25%
Sales Tax amount = 1915 x 7.25%
= 1915 x 7.25/100 = 138.8375 = $138.84
Total cost including sales tax = 1915.00 + 138.84 = $2,053.84
If you leave $2500 in an
account earning 9% interest, compounded daily, how
much money will be in the account after 4 years?
Answers
The amount of money that will be in the account after 4 years is $3,583.16
How many times is interest compounded annually?
The fact that the interest rate of 9% in this scenario is compounded daily means that the interest is compounded every day of the year, 365 days in a year, hence, our future value formula needs an adjustment for daily compounding as shown below:
FV=PV*(1+r/m)^(n*m)
FV=the accumulated balance in the account after 4 years=unknown
PV=amount invested or deposited initially=$2500
r=annual interest=9%
m=number of times in a year that interest is compounded=365
n=number of years=4
FV=$2500*(1+9%/365)^(4*365)
FV=$3,583.16
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Did anybody see my question for 24 I really need help
Answers
Answer:
48
hope its right sorryyyy
In the diagram, ABC is a straight line.
Work out the size of the angle marked x.
Answers
Answer:
See below
Step-by-step explanation:
1 note the other angle at d = 62 ( isosceles triangle)
2 x = 180 - 62 - 62 -25
Answer:
x = 31°
Step-by-step explanation:
since AB = BD then Δ ABD is isosceles with base angles congruent, so
∠ ADB = ∠ BAD = 62°
the sum of the 3 angle in Δ ABD = 180° , so
∠ ABD = 180° - 62° - 62° = 180° - 124° = 56°
∠ ABD and ∠ CBD are a linear pair and sum to 180° , so
56° + ∠ CBD = 180° ( subtract 56° from both sides )
∠ CBD = 124°
the 3 angles in Δ CBD sum to 180° , then
x + 124° + 25° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to-end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. IS THE RELATIONSHIP PROPORTIONAL
THIS IS DUE TODAY
Answers
Reason is because a rectangle has 4 sides at here for he can only put 4 chairs per table
Help!! Which of the following is a true statement of the figure ?
Answers
Answer:
3rd option
Step-by-step explanation:
In the 3rd option, two sides from each triangle in the large triangle are compared.
In the space provided below, solve the inequality x/8 - 13 > -6 for x algebraically. Show all work.
Answers
Answer:
x > 56
Step-by-step explanation:
x/8 - 13 > -6
x/8 > 7
x > 56
What is the length of side BC to one decimal place?
Answers
Answer:
BC ≈ 9.0
Step-by-step explanation:
using the tangent ratio in the right triangle
tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{10}[/tex] ( multiply both sides by 10 )
10 × tan42° = BC , then
BC ≈ 9.0 ( to 1 dec. place )
