Describe all numbers x that are at a distance of 1 from the number 8 . Express this using absolute value notation. The answer field below uses the symbol mode option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then = , the symbol mode will automatically convert that to ≤ . In the same way, if you type in > and then = , the symbol mode will automatically convert that to ≥ .
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To solve this, let's think about what are the numbers that are at a distance of 1 from 8. We can take 8 and:
[tex]\begin{gathered} 8+1=9 \\ . \\ 8-1=7 \end{gathered}[/tex]Those are the only two numbers that verify the asked. Now we need to express it using absolute value notation. If two numbers are at a certain 'distance', this means that their difference is that 'distance'. Since we want the distance between a number x and 8 to be 1, we can write:
[tex]\begin{gathered} x-8=\pm1 \\ \\ \end{gathered}[/tex]Because:
[tex]\begin{gathered} 7-8=-1 \\ . \\ 9-8=1 \end{gathered}[/tex]And we can write this plus-minus sign using absolute value:
[tex]|x-8|=1[/tex]Thus, the answer is:
[tex]|x-8|=1[/tex]Related Questions
this has two parts to the question I will take a picture of the question please find the sum of the sequence afterwards
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-5, -12, -19, ... , -278
The sum is -5660
22.) In the figure, point P is the circumcenter of triangle JKL.Which of the following statements must be true?I. PX = PYII. PJ = PKIII. PK = PLF I onlyG II onlyH III onlyJ II and III only
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It's important to knwo taht
PX=PY statements must be true, So statement I is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In the figure, point P is the circumcenter of triangle JKL
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect.
The circumcenter is formed by drawing the perpendicular bisectors of all the sides of the triangle using a compass. Extending all the perpendicular bisectors to meet at a point.
The intersection point is the circumcenter.
As the angles are same at X and Y are ninety degrees and has line through the circumcenter.
The lines PX and PY are equal.
Hence PX=PY statements must be true, So statement I is correct.
To learn more on Triangles click:
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(52) BAILANL Lilith gives birth wit... R Rea The graph below represents the total cost of limes at a grocery store. 12 Dollars " 10 8 6 4 6 8 10 12 What is the constant of proportionality? You may use exact answers or ound to the nearest hundredth.
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the constant of proportionality is
[tex]\frac{1}{5}=0.2[/tex]find arc eahaving trouble with this, hope you can help
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From the figure, we can see that the angles ∠CRB and ∠ERA are vertical angles. This means that they are congruent:
[tex]\begin{gathered} ∠CRB\cong∠ERA \\ \\ \Rightarrow m∠ERA=50\degree \end{gathered}[/tex]Finally, since this is a central angle, we conclude that:
[tex]EA=50\degree[/tex]If 3 is one of the factors of the product 177, what is the other factor?
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We can write 177 as the product of 2 factors:
[tex]3\cdot x=177[/tex]We can find the other factor by dividing 177 by 3:
The result is 59, that is a prime number.
So the 2 factors of 177 are 3 and 59.
The division is done by:
1. Dwight is a construction worker who will be employed for 8 months this year on a contract job, and he needs to calculate his projected yearly earnings in order to fill out a loan application. His contract states that he will make $35 an hour and that he will work 45 hours per week for the duration of the contract. (4 points: Part I - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point)Part I: How much will Dwight make per week?Part II: If Dwight worked for the whole year instead of for only 8 months, what would his yearly earnings be?Part IV: Considering that Dwight will only work for 8 months and not for the whole year, what are his projected yearly earnings?
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So it is stated that he will make $35 an hour and that he will work 45 hours per week for the duration of the contract:
Part I: How much will Dwight make per week?
35*45= $1575
Part II: If Dwight worked for the whole year instead of for only 8 months, what would his yearly earnings be?
we have: 1575 per week, 4 weeks per month, 12 months:
1575*4*12 = $75,600
Part III: What fraction of 1 year is 8 months?
A year has 12 months, so:
8/12 = 2/3 of a year
Part IV: Considering that Dwight will only work for 8 months and not for the whole year, what are his projected yearly earnings?
1575 per week, 4 weeks per month, 8 months:
1575*4*8 = $50,400
1/3 1/2 3/4 from smallest to largest
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In order to compare the fractions, we need to put them in the same denominator.
Calculating the least common multiple between the denominators, we have 12, so we have:
[tex]\begin{gathered} \frac{1}{3}=\frac{4}{12} \\ \\ \frac{1}{2}=\frac{6}{12} \\ \\ \frac{3}{4}=\frac{9}{12} \end{gathered}[/tex]Now, comparing the fractions, we have:
[tex]\begin{gathered} \frac{4}{12}<\frac{6}{12}<\frac{9}{12} \\ \\ \frac{1}{3}<\frac{1}{2}<\frac{3}{4} \end{gathered}[/tex]So the correct order is:
1/3, 1/2, 3/4
Find the sale price when the original price is $64.00 and the discount rate is 12%.
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SOLUTION:
Step 1:
In this question, we are given the following:
Find the sale price when the original price is $64.00
and the discount rate is 12%.
Step 2:
Recall that the discount rate is 12% and the original price is $ 64.00
Then, we have that:
[tex]\begin{gathered} 12\text{ \% of \$ 64.00} \\ =\frac{12}{100}X\text{ \$ 64.00} \\ =\frac{768}{100} \\ Discount=\text{ \$ 7.68} \end{gathered}[/tex]Next,
We need to find the sale price =
[tex]\begin{gathered} \text{Original price - Discount price} \\ =\text{ \$ 64.00 - \$ 7. 68} \\ =\text{ \$ 56.32} \end{gathered}[/tex]the slope, m, of the line is the same as the coefficient of the x variable when the equation is in the form y equals MX plus b. what is the slope of the line whose equation is 2x + y equals 10
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Slope m of 2x + y = 10
Then slope m = 2
For a standard normal distribution, find Find P(z
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It is given that,
[tex]P(zHere 'z' is the standard normal variate.CASE-1 Assuming that 'c' lies on right side of z=0 line.
Simplify the expression as,
[tex]P(z<0)+P(0We know that the probability of z being less than zero, is 0.5,[tex]0.5+P(0Observe that the probability comes out to be negative, which is not possible.CASE-2 Assuming that 'c' lies on the left side of z=0 line.
Then,
[tex]\begin{gathered} P(zFrom the Standard Normal Distribution Table, we see that the probability 0.1316 corresponds to the score close to 0.34 i.e.[tex]\varnothing(0.34)=0.1331[/tex]Thus, the value of the variable 'c' is 0.34 approximately.
A student researches the average cost of electricity, in cents per kilowatt-hour, in the United States since 2000 and creates the scatter plot below.
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Given: A scatter plot as shown in the image
To Determine: The image that best represent the model function fitted for the given
Solution
The 'line of best fit' is a line that goes roughly through the middle of all the scatter points on a graph.
Let us examine each of the options
From the above the best model function fitted for the given data is
Please help:Rylan is calculating the standard deviation of a data set that has 9 values. He determines that the sum of the squared deviations is 316.What is the standard deviation of the data set? Round the answer to the nearest tenth.Enter your answer in the box. ___
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Given
Number of values = 9
sum of squared deviations = 316
The sum of squared deviations is related to the standard deviation s by the formula
[tex]\begin{gathered} s\text{ = }\sqrt{\frac{SS}{n-1}} \\ Where\text{ SS is the sum of squared deviations} \\ and\text{ n is the number of sample} \end{gathered}[/tex]Applying the formula to the problem:
[tex]\begin{gathered} s\text{ = }\sqrt{\frac{316}{9-1}} \\ =\text{ }\sqrt{39.5} \\ =\text{ 6.2849025} \\ \approx\text{ 6.3 \lparen nearest tenth\rparen} \end{gathered}[/tex]Answer:
standard deviation = 6.3
Choose all of the equations that have exactly one solution.A. 2(x - 4) = 0B. 7 + 3x = 11+xC. 5x - 8 = 7x + 4 - 2xD. 3 (2x - 1) = -3 + 6xE. 8x - 5 + 4x = 7x - 5-9
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Solve each one for x:
A. 2(x - 4) = 0
Apply distributive property:
2(x)+2(-4)=0
2x-8=0
2x=8
x=8/2
x=4
A has one solution.
B.
7 + 3x = 11+x
3x-x =11-7
2x=4
x=4/2
x=2
B has one solution
C.
5x - 8 = 7x + 4 - 2x
5x-7x+2x = 4+8
0 = 12
C has no solution
D.
3 (2x - 1) = -3 + 6x
6x-3=-3+6x
6x-3 = 6x-3
D has infinite solutions
E.
8x - 5 + 4x = 7x - 5-9
8x+4x-7x=-5-9+5
5x = -9
x= -9/5
x=-1.8
E has one solution.
So, the equations that have only one solution are:
A,B, and E.
Find dy/dx (the derivative ) of f(x) = 4x^2 using limits definition of the derivitive (of limit of the DQ when h> 0Formulas neededa) Equation of a line in slopeyintercept form y = f(x) = mx + bb) Equation of a line slopepoint y y1 = m (x x1)
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Given
[tex]f(x)=4x^2[/tex]Find
derivative of the function
Explanation
By limit definition ,
[tex]\frac{dy}{dx}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]so, we have
[tex]\begin{gathered} \frac{dy}{dx}=\lim_{h\to0}\frac{\lbrace4\left(x+h\right)^2-4x^2\rbrace}{h} \\ \frac{dy}{dx}=\lim_{h\to0}\frac{\lbrace4(x^2+h^2+2xh)^-4x^2\rbrace}{h} \\ \frac{dy}{dx}=\lim_{h\to0}\frac{\lbrace4x^2+4h^2+8xh-4x^2\rbrace}{h} \\ \frac{dy}{dx}=\lim_{h\to0}\frac{8xh+4h^2}{h} \\ \frac{dy}{dx}=\lim_{h\to0}8x+4h \\ \frac{dy}{dx}=8x \end{gathered}[/tex]Final Answer
The derivative of the function is 8x
Help in the Accompanying diagram of the circle O chord CD ….
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Answer:
The length of ED is;
[tex]ED=8[/tex]Explanation:
Given the figure in the attached image.
Chord CD bisects chord AB at E.
So;
[tex]AE=EB=\frac{AB}{2}[/tex]Also applying the Bisecting chord formula;
[tex]AE\cdot EB=CE\cdot ED[/tex]Given;
[tex]\begin{gathered} CE=2 \\ AB=8 \\ AE=EB=\frac{AB}{2}=\frac{8}{2}=4 \\ AE=4 \\ EB=4 \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} AE\cdot EB=CE\cdot ED \\ 4\cdot4=2\cdot ED \\ 16=2\cdot ED \\ ED=\frac{16}{2} \\ ED=8 \end{gathered}[/tex]Therefore, the length of ED is;
[tex]ED=8[/tex]Construct the matrix A=(ij) of type 5x5,
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Solution:
The matrix of the type 5x5 is a matrix with 5 rows and 5 columns.
Then, the matrix is:
The matrix above is of type 5x5.
State the postulate of the theorem that justifies the answer
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From the given information, we can note that angle1 and angle2 are corresponding angles with respect to line u. Angle2 and angle9 are alternate exterior angles with respect to the right vertical line and angle5 and angle7 are alternate interior angles with respect to line v.
Therefore, the theorems which justify the answer are, respectively: Corresponding angles theorem, Alternater exterior angles theorem and Alternate Interior angles theorem.
Tran painted pieces for a model she is building. She painted one cone-shaped piece with a diameter of 3 inches and a slant height of 2 inches using silver paint.What is the approximate area Tran painted silver?
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Answer:
[tex]16.5in^2[/tex]Explanation:
From the question,we are given that the shape is a cone
Thus,we will need to use the formula for the surface area of a cone
Mathematically, we have the area as:
[tex]A\text{ = }\pi r(r\text{ + l)}[/tex]r is the base radius which is the diamter length divided by 2. We have that as 3/2 =1.5 inches
We have the slant height l as 2 inches
We will substitute these values into the formula shown above
[tex]A\text{ = 3.142}\times1.5\text{ (1.5 + 2) = 16.5 sq. inches}[/tex]1. Alexis needs to save at least $1,100 to buy a new laptop. So far she has saved $400. She makes $12 an hour babysitting.inequality_____________
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Let:
x = number of hours babysitting
So far she has saved $400, and she needs to save at least $1100
Therefore, the inequality which represents this situation is:
[tex]400+12x\ge1100[/tex]In case you need to solve for x:
[tex]\begin{gathered} \text{Subtract 400 from both sides:} \\ 12x\ge1100-400 \\ 12x\ge700 \\ \text{Divide both sides by 12:} \\ x\ge\frac{700}{12}=58.33 \\ x\ge58.33 \end{gathered}[/tex]Therefore, Alexis needs to work at least 58.33 hours in order to buy her new laptop
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
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Solution
Given that
[tex]\begin{gathered} \cos A=\frac{8}{17}\text{ and } \\ \sin B=\frac{5}{13} \end{gathered}[/tex]Let's draw the two diagrams for angles A and B
Hence,
[tex]\begin{gathered} \sin A=\frac{15}{17} \\ \cos B=\frac{12}{13} \\ \tan A=\frac{15}{8} \\ \tan B=\frac{5}{12} \end{gathered}[/tex]Therefore,
[tex]\sin (A+B)=\sin A\cos B+\sin B\cos A=\frac{15}{17}\times\frac{12}{13}+\frac{5}{13}\times\frac{8}{17}=\frac{220}{221}[/tex][tex]\sin (A-B)=\sin A\cos B-\sin B\cos A=\frac{15}{17}\times\frac{12}{13}-\frac{5}{13}\times\frac{8}{17}=\frac{140}{221}[/tex][tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}=\frac{\frac{15}{8}+\frac{5}{12}}{1-\frac{15}{8}\times\frac{5}{12}}=\frac{220}{21}[/tex][tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}=\frac{\frac{15}{8}-\frac{5}{12}}{1+\frac{15}{8}\times\frac{5}{12}}=\frac{140}{171}[/tex]If a rock is thrown upward on the planet Mars with a velocity 12 m/s, its height in meterst seconds later is given by y = 12t - 1.86t2. (Round your answers to two decimal places.)(a) Find the average velocity (in m/s) over the given time intervals.() [1, 2]m/s
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Derivate the equation:
[tex]\frac{d}{dt}\left(12t-1.86t^2\right)[/tex][tex]=\frac{d}{dt}\left(12t\right)-\frac{d}{dt}\left(1.86t^2\right)[/tex][tex]=12-3.72t[/tex]Now replace the numbers of the intervals:
1:
8.28
2:
4.56
Find the average:
[tex]\frac{8.28+4.56}{2}=6.42\text{ m/s}[/tex]a car travels for 7 hours at 55 miles per hour use the formula D equals R times T where D equals distance R equals right in SQL time to find a distance the car traveled
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We have the next information
d=r*t
where
t=time=7 hours
r=rate=55 miles/hr
we substitute the values
[tex]undefined[/tex]Calculate 400- 640 divide by 8 + 70 divide by 5
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Solution:
According to the hierarchy of algebraic operations and applying the associative property, we get that:
[tex]400-640\div8+70\div5\text{ = 400-(640}\div8\text{)+(70}\div5\text{)}[/tex]this is equivalent to:
[tex]\text{ 400-(640}\div8\text{)+(70}\div5\text{)}=400-80+14\text{ =334}[/tex]So that, we can conclude that the correct answer is:
[tex]334[/tex]1) Use the proportional relationships to solve for the missing value이6m1.IⅡ1824Om=8Om - 10.6Om = 18Om = 28.
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Answer
Option A is correct.
m = 8
Explanation
[tex]undefined[/tex]John is buying t-shirts for his team at the Hooley plunge. Shirts-4-U charges $5 per shirt and a set up free. John got 30 shirts for $175. Write an equation in slope intercept form to model this situation.M=___ Given point is (__,__)Equation: y=__ x + __
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we are given that the cost of t-shirts follows a linear relationship. If "x" is the number of t-shirts then the total cost must be equal to:
[tex]y=5x+b[/tex]Since the cost of 30 shirts is $175, that means that we have the following point:
[tex](x,y)=(30,175)[/tex]Replacing the point in the equation we get:
[tex]175=5(30)+b[/tex]Solving the operations:
[tex]175=150+b[/tex]Solving for "b" by subtracting 150 to both sides:
[tex]\begin{gathered} 175-150=150-150+b \\ 25=b \end{gathered}[/tex]Replacing we get:
[tex]y=5x+25[/tex]How do I solve? So far no one could be of help. It’s asking for the area of this regular polygon.
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We can notice the triangle on the square, hypotenuse is 8m and the base is half of the lengt of the square we will name it x
then
we can use pythagoras to solve
[tex]a^2+b^2=h^2[/tex]where a and b aer sides of the triangle and h the hypotenuse
replacing
[tex]\begin{gathered} x^2+x^2=8^2 \\ 2x^2=64 \\ x^2=\frac{64}{2} \\ \\ x=\sqrt[]{32}=4\sqrt[]{2} \end{gathered}[/tex]the length of x is half of the side of the square then the side of the square is
[tex]4\sqrt[]{2}\times2=8\sqrt[]{2}[/tex]each side of the square is 8v2 meters
Area
we use formula of the area
[tex]\begin{gathered} A=l\times l \\ A=8\sqrt[]{2}\times8\sqrt[]{2} \\ \\ A=128 \end{gathered}[/tex]area of the square is 128 square meters
Perimeter
we use formula of the perimeter
[tex]\begin{gathered} P=4l \\ P=4\times8\sqrt[]{2} \\ P=32\sqrt[]{2} \end{gathered}[/tex]perimeter of the square is 32v2 meters
I need to know where to graph the system of linear equations. -1/2y = 1/2x + 5 and y=2x + 2 The solution to the system is( , )
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the given expression is
-1/2y = 1/2x +5
multiply the above equation by -2
-2(-1/2y) = -2(1/2x +5)
y = - x - 10 .....(1)
and the other equation is y = 2x + 2 .......(2)
in equation (1) we will put x = 0 , 1 , 2 and find the value of y
when x = 0 then y = -0 - 10 = -10 so point is (0,-10)
x =1 , y = -1 - 10 = -11 so point is (1, -11)
x = 2 , y = -2 - 10 = -12 , so point is (2, -12)
now you will draw the point graph and draw the line by joining them.
in equation (2) put x = 0 , 1 , 2
when x = 0 , y = 2(0) + 2 = 0 + 2 = 2 so point is (0, 2)
x = 1, y = 2(1) + 2 = 4, so the point is (1, 4)
x =2 , y = 2(2) +2 = 6 so the point is (2, 6)
now you will draw the point graph and draw the line by joining them.
Now you will get two lines
after drawing of these lines you will get the intersection point of these lines.
and the intersection point will be (-4, - 6)
Solve the following using substitution: 3X = 6Y -44X + 3Y = -1
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x = -6/11 and y = 13/33
1) Let's solve this by the Substitution Method:
3x =6y -4
4x +3y =-1
Rewriting the 1st equation we have:
[tex]\begin{gathered} x=\frac{6y}{3}-\frac{4}{3} \\ x=2y-\frac{4}{3} \end{gathered}[/tex]2) Let's now plug into the 2nd equation the value of x:
[tex]\begin{gathered} 4x+3y=-1 \\ 4(\frac{6y}{3}-\frac{4}{3})+3y=-1 \\ 8y-\frac{16}{3}+3y=-1 \\ 11y=-1+\frac{16}{3} \\ 11y=\frac{13}{3} \\ y=\frac{13}{3}\cdot\frac{1}{11} \\ y=\frac{13}{33} \end{gathered}[/tex]2.2) Now, let's plug the quantity of y we've just found into the 1st Equation:
[tex]\begin{gathered} 3x=6(\frac{13}{33})-4 \\ 3x=\frac{78}{33}-4 \\ 3x=-\frac{18}{11}\text{ }\times\frac{1}{3} \\ x=-\frac{6}{11} \end{gathered}[/tex]Note that we've simplified the final result.
3) Hence, the answer is:
x = -6/11 and y = 13/33
____ is used to express the solution set of an inequality. It use brackets and a vertical bar to indicate the solution
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Solution
- A Set-builder notation is used to express the solution set of an inequality. It uses brackets and a vertical bar to indicate the solutions.
- For example, the set of even numbers between 1 and 10 exclusive, is:
[tex]\lbrace x|x:2,4,6,8\rbrace[/tex]- As we can see the set above has a bracket and it also has a vertical bar as well.
The height of an object dropped from the top of a 20-meter building is given byh(t)= -5t^2 +20. How long will it take the object to hit the ground?
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It will take the object 2 seconds to hit the ground
Here, we want to get the time it will take the object to hit the ground
To get this, we know that the height at this point is zero
Thus, we have it that h is 0 at this point
Mathematically, we have it that;
[tex]\begin{gathered} 0=-5t^2\text{ + 20} \\ 5t^2\text{ = 20} \\ \text{divide through by 5} \\ \frac{5t^2}{5}\text{ = }\frac{20}{5} \\ \\ t^2\text{ = 4} \\ t\text{ = }\sqrt[]{4} \\ t\text{ = }\pm\text{ 2} \end{gathered}[/tex]But, since time cannot be negative, we have it that t = 2 seconds