At time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.
What are coordinates?Coordinates are two numbers (Cartesian coordinates) or a letter and a number that point to a specific point on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical).To find the position:
The derivative of x with respect to t is zero when the velocity is zero. That is to say,
x' = 1.5t² - 6t + 3 = 0 or t² - 4t + 2 = 0Use the quadratic formula to solve.
t = (1/2) [ 4 +/- √(16 - 8)] = 3.4142 or 0.5858 sWhen t =0.5858 s, the position is:
x = 0.5(0.5858³) - 3(0.5858²) + 3(0.5858) + 2 = 2.828 mWhen t=3.4142 s, the position is:
x = 0.5(3.4142³) - 3(3.4142²) + 3(3.4142) + 2 = -2.828 mReject the negative answer.
So, when t = 0.586 s, the velocity is zero and the distance is 2.83 m.
The second derivative of x with respect to t is zero when the acceleration is zero.
That is to say,
3t - 6 = 0t = 2The distance traveled is:
x = 0.5(2³) - 3(2²) + 3(2) + 2 = 0So, when the acceleration is zero, t = 2 s, and the distance traveled is zero.
Therefore, at time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.
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The correct question is given below:
A girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the XY coordinate axes, and the surface of the parking lot lies in the XY plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t + 2 where x and t are expressed in meters and seconds, respectively. determine when the velocity is 0 m/s, and the position and the total distance traveled when the acceleration is zero.
A is the Midpoint of line RT. Find line RT if line RA= 3x and line AT= 5x-12
A. 6
B. 36
C.18
D. 30
[tex]\stackrel{3x}{R\rule[0.35em]{10em}{0.25pt}} A\stackrel{5x-12}{\rule[0.35em]{10em}{0.25pt}T} \\\\\\ 3x~~ = ~~5x-12\implies 3x+12=5x\implies 12=2x\implies \cfrac{12}{2}=x\implies \boxed{6=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE RT}}{3(6)~~ + ~~5(6)-12\implies 18+18\implies \text{\LARGE 36}}[/tex]
RADICALS PLEASE HELP
(3√3 - 5√2) (2√3 + 5√2)
Answer: -32+5√6
Step-by-step explanation:
(3√3 - 5√2) (2√3 + 5√2)=
(3√3 * 2√3) + (3√3 * 5√2) - (5√2 * 2√3) - (5√2 * 5√2) =
(3*2*√3*√3) + (3*5*√3*√2) - (5*2*√2*√3) - (5*5*√2*√2)=
6*3 + 15*√(3*2) - 10*√(2*3) - 25*2=
18+15√6-10√6-50=
18-50+(15-10)*√6=-32+5√6
How to do this exercise step by step?
A group of workers can plant at a rate of 34 acres per day.
How many acres can they plant in 2 days?
Answer:
68 acres per day
Step-by-step explanation:
34 acres per day × 2 days = x
34 × 2 = x
x = 68 acres per day
Hope this helps!
Answer:
68 acres
Step-by-step explanation:
34 acres= 1 day
x=2 days
x=68 acres
they can plant 68 in 2 days
What is 2/3n plus 3/2n equals negative 13/4
Answer:
n=-2/3
Step-by-step explanation:
2/3n + 3/2n = -13/4
Make 2/3n and 3/2n into 4/6n and 9/6n so you can add them together.
13/6n = -13/4
Divide both sides by 13/6
n=-2/3
^ i hope thats what you were asking for :)
Given f(x) = 2x - 1, g(x) = 3x^2 + 5, and h(x) = 4x+ 6 find h(g(f(x))).
Answer:
48x^2 - 48x + 38
Step-by-step explanation:
To get the composite function first understand the process of which a function inside another operates.
First solve one step at a time by trying to evaluate the inside before evaluating the outside using substitution.
For instance, h(g(f(x))) is the h function of g function of f.
Since f(x) is the inner component of the composite function, replace the x of g with the value of f(x).
Such that g(x) = 3x^2 + 5 → 3(f(x))^2 + 5 →
3(2x - 1)^2 + 5 → 3(2x - 1)(2x - 1) + 5 [foil] → 3(4x^2 - 4x + 1) + 5 → 12x^2 - 12x + 3 + 5 →
12x^2 - 12x + 8
Thus g(f(x)) = 3(f(x))^2 + 5 = 12x^2 - 12x + 8.
Finally to compute h(g(f(x))), using the process from the first composite function, same can be applied here:
Since h(x) = 4x + 6 →
h(g(f(x))) =
h(12x^2 - 12x + 8) =
4(12x^2 - 12x + 8) + 6 [distribute] →
48x^2 - 48x + 32 + 6 [combine like terms] →
48x^2 - 48x + 38
solve
3*2^x+1-4^x=8
help me as soon as possible
Answer: 3.5
Step-by-step explanation:
If your trying to solve for X the answer would be 3.5 because you calculate 2 to the power of 1 and get 2 which then by now your equation should look along the lines of 3×2X+1−4^1 X=8
Calculate 4 to the power of 1 and get 4 then you Subtract 1 from both sides.
and then Subtract 1 from 8 to get 7. Combine all terms containing X which would make the equation come down to a standard form which then means you would have to divide both sides by 2, by dividing by 2 undoes the multiplication by 2. You should get 7/2 which then = 3 and 1/2 converted into 3.5
Write the expression of a polynomial given the roots:
x = √6
The expression is [tex](x - \sqrt{6} )^{n}[/tex] , n = 1, 2, 3....
Polynomial expression:
A polynomial expression is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
It is given that
x = √6
x - √6 = 0
[tex](x - \sqrt{6} )^{n}[/tex] where n = 1,2,3.....
Therefore the expression of the polynomial given roots is [tex](x - \sqrt{6} )^{n}[/tex] .
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a body’s weight varies inversely with the square of its distance from the center of the earth; if a chicken weighs 12 pounds when it is 5,000 miles from the earth’s center, how much will the chicken weigh when it is 10,000 miles from the earth’s center ?
The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
There are two types of proportions.
1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.
2) Inverse Proportion - describes the indirect relationship between two quantities. It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.
According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.
y = k/x
let y = a body's weight
x = square of its distance from the center of the earth
Solving for the proportionality constant, k.
y = k/x
12 = k / (5000^2)
k = 12 x 25, 000, 000
k = 300, 000, 000
The equation for the relationship in the problem can now be represented by:
y = 300,000,000/x
where
y = a body's weight
x = square of its distance from the center of the earth
Evaluating the new equation where x = square of 10,000:
y = 300,000,000/x
y = 300,000,00/(100,000,000)
y = 3
Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
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reflection about common monomial factor plss pa hel po
Answer:
Step-by-step explanation:
A common monomial factor is a single-term polynomial that divides into each term of a given polynomial evenly.
the mean time that a certain model of light bulb will last is hours, with a standard deviation equal to hours.
The mean time that a certain model of light bulb will last is hours is 900 hours and the required percentage of bulbs is 2.5%
Here,
x is the time that a certain bulb will last.
(in houses.
μ=900 hours;
σ=1200 hours.
The standardized value for a light bulbs lasts 1100 hours, is,
z=x-μ/σ
z=1100-900/100=2
We know, for a bell-shaped distance, Approximately,
68% of the data falls within M-uσ;
By rule (ii), here,
95% of the data falls within (μ-2σ,u+2σ)
(900-2x100,900+2x100)
(700,1100)
So (100-95=5%) falls outside of (700,1100)
Since, the distance is symmetric (i.e. bell-shaped); we find the percentage of bulbs that is expected lo lase longer than 1100 hours, is
5/2% =2.5%
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.What does the standard deviation means?Image result for standard deviationA standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.To learn more about standard deviation visit:
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Here's a box plot that summarizes the average monthly rainfall of several cities.
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 8, in increments of 0.5, labeled Monthly rainfall (centimeters). A left whisker extends from 3.5 to 5.5. The box extends from 5.5 to 7 and is divided into 2 parts by a vertical line segment at 6. The right whisker extends from 7 to 7.5. All values estimated.
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 8, in increments of 0.5, labeled Monthly rainfall (centimeters). A left whisker extends from 3.5 to 5.5. The box extends from 5.5 to 7 and is divided into 2 parts by a vertical line segment at 6. The right whisker extends from 7 to 7.5. All values estimated.
Find the range of the data.
The range of the data provided in the boxplot given the minimum number and the maximum number is 2.
What is the range of the data?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines known as the whiskers and a box. The left whisker represents the lowest number in the dataset. The right whisker represents the highest number in the dataset. The difference between these numbers is the range.
The box can be used to determine the first quartile, median and the third quartile. These values can be determined using the lines on the box.
The range of a data set is the difference between the highest number and the lowest number. Range is used to measure the variance of a dataset.
Range = highest number - lowest number
7.5 - 5.5 = 2
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shift the graph right by 2 units and up by 3 units what cube root equation is it?
James sold simi rare Pokemon cards for 11$ each after he paid 200 for a booster box. The equation y = 11x - 200 shows the profit James will make from selling Pokemon cards, where x is the number of Pokemon cards and y is the profit he makes. If James sales more than 17 cards but less than 26 cards, what would the range of the situation be
the range of possible profits, in dollars, is given by the inequality:
-13 < y < 86
what would the range of the situation be?We know that the linear equation:
y = 11*x - 200
Shows the profit for selling x pokemon cards.
We know that he sells more than 17 and less than 26, then:
17 < x < 26
Then the minimum profit is:
y = 11*17 - 200 = -13
The maximum profit is:
y = 11*26 - 200 = 86
We conclude that the range of possible profits, in dollars, is:
-13 < y < 86
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a sequence is defined by f (n) =-4+2n for n is greater than or equal to 1. which of the following statements is the recursive definition of f?
a. f(1)=-2, f(n)=f(n-1) +2
b. f(1)=-4, f(n)=f(n-1) +2n
c. f(1)=-2, f(n)=f(n-1) + (-4)
d.f(1)=-4, f(n)=f(n-1) +2
EXPLAIN WHY
The recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2. (Correct choice: A)
What is the recursive definition of an arithmetic sequence?A recursive formula is a formula to find the value of an element in terms of previous elements of the same series. According to the statement, a sequence is defined by f(n) = - 4 + 2 · n. To derive the recursive definition, we must use algebra properties on the following difference:
Δf = - 4 + 2 · (n + 1) - (- 4 + 2 · n)
Δf = 2
n = 1
f(1) = - 4 + 2 · 1
f(1) = - 2
Then, the recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2.
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Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 3 : 2 She needs to make 40 litres of punch for a party. How much of each ingredient does she need?
Fruit juice = litres
Lemonade = litres [4]
Answer:
Fruit Juice = 24 litres
Lemonade = 16 litres
Step-by-step explanation:
So, the ratio: [tex]3:2[/tex] really just means: "for every every 3 litres of fruit punch, there is 2 litres of lemonade.
Or in other words, every 3 litres of fruit punch, the entire mixture of both fruit punch and lemonade will be 5 litres, since there is 3 litres and 2 litres.
So dividing the 40 litres, by this 5 litres, we get 8. So we know there will be "8" of 3 litres of fruit punch, and "8" of 2 litres of lemonade.
Thus there will be 24 litres of fruit punch, and 16 litres of lemonade.
Use the words factor and quotient to describe related multiplication and.division facts
A quotient is an answer in the division. The divisor (denominator) and the quotient are the factors. The dividend (numerator) is the amount being divided — it doesn’t matter whether the dividend is larger or smaller than the divisor.
In elementary school, we refer to this process only in terms of fractions, so many people don’t realize that fractions are just division. If your fraction is proper, you will get a decimal number or simplified equivalent fraction. If the numerator (multiple) is the larger number, then the quotient will represent the other factor after dividing.
For example, in the equation x + 5 = 10, x is the unknown variable, and you want to find some number, which when added to 5 would result in 10.
Quotients are answers to a division problem.
For example, the quotient of 8÷2 would be 4.
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Where is making a frame to display a drawing she made. The frame 11 1/5 wide the frame has a rectangular shape and area of 560cm2
The Height of the frame having area of 560cm² is 50cm.
What is the area of the rectangle?By splitting a rectangle into two equal-sized right triangles, the formula for calculating the area of a rectangle may be obtained. For instance, a diagonal is drawn from vertex A to vertex C in the rectangle ABCD that is supplied.
The rectangle is split into two identical right-angled triangles by the diagonal AC.
(ABCD) Area = b × h
Given,
The area of the frame = 560cm²
Width of the frame = 11 1/5
Length = ?
Area of the rectangle = Length × Breadth
560 = 11 1/5 × L
⇒ L = 560 × 5/56
⇒ L = 50cm
The frame is 50cm tall.
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Correct question -
Claire is making a frame to display a drawing she made. The frame is 11 1/5 cm wide. The frame has a rectangular shape and an area of 560cm². How tall is the frame?
One safe investment pays 10% per year, and a more risky investment pays 13% per year.
a. How much must be invested in each account if an investor of $100,000 would like a return of $10,780 per year?
b. Why might the investor use two accounts rather than put all the money in the 13% investment?
is invested in the 10% account.
is invested in the 13% account.
4
b. Why might the investor use two accounts?
a. S
OA. Although the 13% account earns more interest, the 10% account has no hidden fees.
B. The 13% investment is riskier than the 10% investment. There is a greater chance the investor will lose money if it is all placed in the 13% account.
C. Investing in two accounts always yields more money than investing in just one account.
Answer:
0.10x + 0.13y = 10780
x + y = 100000
x = 74000 --------------10%
y = 26000 --------------13% (more risky)
9. What is the domain of this function: ((0, 1), (2, 3), (-1, 3), (4, 5)}?
a. (0, 2, -1, 4)
b.
(0, 2)
c. (3)
d.
(1,3,5)
e. None of the above
Check the picture below.
Answer:
g
Step-by-step explanation:
Solve.
-2x+3y-z = -2
3x+y=4
-2y + 2z = 4
Answer:
(x,y,z) = (1,1,4)
Step-by-step explanation:
[tex]A: -2x + 3y - z = -2\\B: 3x+y=4\\C: -2y+2z=4\\[/tex]
[tex]Solve\ B\ for\ y: y = 4-3x\\Solve\ C\ for\ z: 2z=4+2y\ \ z=2+y\\Substitute\ B_y\ into\ C_z: z = 2+4-3x\ \ z=6-3x\\Substitute\ B_{y\ in\ terms\ of\ x}\ and C_{z\ in\ terms\ of\ x} into A: \\-2x + 3(4-3x) - (6-3x) = -2\\Distribute: -2x + 12-9x-6+3x=-2\\Combine\ Like\ Terms\ on\ either\ side: -2x-9x+3x=-2-12+6\\Factor\ out\ x\ and\ perform\ arithmetic\ on\ right: x(-2-9+3) = -8\\Perform\ Arithmetic: x(-8)=-8\\Divide:x=1[/tex]
[tex]Plug\ x\ into\ B_y: y=4-3(1)\\Perform\ Arithmetic: y=1\\Plug\ y\ into\ C_z: z=2+2(1)\\Perform\ Arithmetic: z=4[/tex]
If m ∠ F L G = 14 x + 5 ° and m ∠ H L G = 17 x − 1 ° , find m ∠ F L H .
The measure of angle FLH is 31x + 4
How to determine the measure of FLH?See attachment for the image that completes the question
The given parameters are
m∠FLG = 14x + 5°
m∠HLG = 17x − 1 °
The measure of FLH is calculated as
FLH = m∠FLG + m∠HLG
This gives
FLH = 14x + 5 + 17x - 1
Collect the like terms
FLH = 14x + 17x + 5 - 1
Evaluate the like terms
FLH = 31x + 4
Hence, the measure of FLH is 31x + 4
See attachment for the image that completes the question
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A gopher has dug holes in opposite corners of a rectangular yard. one length of the yard is 7.3 meters and the distance between the gopher's holes is 9.8 meters. how wide is the yard?
The yard is 6 meters wide by use of Pythagoras crossing the diagonal to create a rectangular triangle.
What is Pythagoras?The formula for the Pythagoras theorem is written as c2 = a2 + b2, where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, to generate a Pythagoras triangle, the Pythagoras equation can be used to any triangle with one angle that is precisely 90 degrees.
d² = l² + w²
d = 10
l = 8
Solving for w, the width is
w² = d² - l²
So, we can replace the values with d = 10 and l = 8, to get
w² = 10² - 8²
w² = 100 - 64
w² = 36
w = 6
Hence the width of the yard is 6.
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Tamara is a chef at a restaurant. She buys rice in bags
that weigh 20 pounds.
Each night, Tamara uses 0,4 pounds of rice. She needs to
order another bag when there are 1.6 pounds of rice left
in her bag.
Question: On Day 1 there are 20 pounds
of rice in her bag. On what day will
Tamara need to order a new bag of rice?
Using a linear function, it is found that Tamara will need to order a new bag after 46 days.
What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis(x = 0).The slope and the intercept in the context of this problem are given as follows:
Slope of -0.4, as she uses 0.4 pounds a day.Intercept of 20, as the bag initially has 20 pounds.Hence the weight of the bag after d days is given by:
W(d) = 20 - 0.4d.
He needs to order a new bag when W(d) = 1.6, hence:
1.6 = 20 - 0.4d.
0.4d = 18.4
d = 18.4/0.4
d = 46 days.
Hence she needs to order the new bag in 46 days.
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what the zero functions? f(x)=x^4-3x^3-4x^2
The zeroes of the function f(x) = x⁴ - 3x³ - 4x² are x = -1 , 0 , 4.
What are zeroes of a function f(x)?
The zeroes of a function are the x - intercepts (the points where the graph cuts the x - axis) of the graph of the function f(x).
Given is a function f(x) as → f(x) = x⁴ - 3x³ - 4x²
In order to find the zeroes of the function → f(x) = x⁴ - 3x³ - 4x², we will plot the graph of the function. The graph is attached at the last. We can see that the graph cuts the x - axis at three coordinates → (- 1, 0) , (0, 0) , (4, 0). The x - intercepts will be → -1, 0, 4.
Therefore, the zeroes of the function f(x) = x⁴ - 3x³ - 4x² are x = -1 , 0 , 4.
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A chef uses a recipe with the following ingredients then the chef decides to make more than 1 batch of recipe. if a total of 30 cups of mangoes and blueberries are used, how many batches of the recipe did the chef make? 3 cups used for 1 mango and 2 cups used for blueberries, 5 cups for apples and 1 cup used for blackberries
Answer:11 cups
Step-by-step explanation:
Srry if im wrong :)
You are solving a measurement problem where the numbers 4.5160 x 10−3, 2.09 x 107, and 5.8 x 103 are multiplied. how many significant digits should the product have?
The product should have a 1 significant digit.
Scientific notationsWhen multiplying Scientific notations, the significant figure of the final result must be approximated to the scientific notation that has the least decimal place.
From the question given, if we 4.5160 x 10^3, 2.09 x 107, and 5.8 x 10^3 are multiplied, the product should have 1 significant digits since the least decimal value that occur in question is 1dp
Hence the product should have a 1 significant digit.
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Number 4, please help
Hi there!
From the given conditions:
[tex]1→1 ⟹1 \times 1 = 1[/tex]
[tex]5→7⟹ 5 \times 7 = 35[/tex]
[tex]8→11 ⟹8 \times 11 = 88[/tex]
[tex]9→4 ⟹9 \times 4 = 36[/tex]
[tex]10 →2 ⟹10 \times 2 = 20[/tex]
Sum = 180, no. of customers = 25
[tex]average = \frac{sum}{no.ofcustomers} [/tex]
[tex] ⟹ \frac{180}{25} = 7.2[/tex]
Therefore, on average, the satisfaction rating of the landscape company was 7.2
On Saturday, the bookstore sold x books. On Sunday, the bookstore sold 3 more books than on Saturday. The expression 2x + 3 represents the total number of books sold over the weekend.
What does the "2" represent in the expression 2x + 3?
A.the number of books sold on Saturday
B.how much more books were sold on Saturday
C.the total number of books sold
D.the number of days
When you answer these, can you number them?