Answers
Einstein's mass energy relation, and the formula for finding the percentage error gives;
7) a) 9.0 × 10¹⁶ Joules
b) The bulb could be powered for approximately 47533146.96 years
8) 16.46%
9) The possible values are;
61.093 Joules and 96.77 Joules
What is a percentage error?Percentage error is the ratio of the difference between estimated value and the actual value to the actual value expressed as a percentage.
7) a) The Einstein mass energy relation is presented as follows;
E = m•c²
The speed of light, c = 3×10⁸ m/s
The mass, m = 1 kg, gives;
E = 1 kg × (3×10⁸ m/s)² = 9.0 × 10¹⁶ Joules
The energy present in 1 kg. mass is; 9.0 × 10¹⁶ Joulesb) Energy consumption of the light bulb = 60 J/sec
The duration, t, the light bulb will remain lit is therefore;
t = (9.0 × 10¹⁶)/(60) = 1.5 × 10¹⁵ s ≈ 47533146.96 years8) Percentage error, %error, is found as follows;
%error = ((Approximate value - Actual value)/(Actual value)) × 100
Appreciate value = 46,620 km
Actual value = 40,030.2 km
Which gives;
%error = ((46,620 - 40,030.2)/(40,030.2))×100 ≈ 16.46%
The percentage error of Eratosthenes estimate of the circumference of the Earth is approximately 16.46%9) The calculated value of the kinetic energy = 74.9 J
The observed error in the calculation = 22.6%
Required; The two possibilities for the correct kinetic energy
Solution;
E% = ((Approximate value - Actual value)/(Actual value)) × 100
Taking the calculated value as the approximate value, and the correct value as the actual value, we have;
22.6% = ((74.9 - Actual value)/(Actual value)) × 100
(22.6/100)×Actual value = 74.9 - Actual value
Actual value + 0.226×Actual value = 74.9
1.226 × Actual value = 74.9
Which gives;
Actual value = 74.9 J/1.226 ≈ 61.093 JThe actual value can also be given as follows;
22.6% = ((Actual value - 74.9)/(Actual value)) × 100
Actual value - 0.226×Actual value = ,74.9
Actual value = 74.9 J/(1-0.226) ≈ 96.77 J
The possible values for the kinetic energy are approximately; 61.093 J and 96.77 JLearn more about calculating percentage error in measurements here;
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Related Questions
Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake. How many meters to the nearest tenth did Alexi's sister save by swimming?
Answers
Alexi’s sister saved about 18.4 meters by swimming across the river.
In this question,
Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake.
The south and east directions are perpendicular.
The distance across the south, east and across the river form a right triangle, with the distance across the river as hypotenuse of right triangle.
Let x be the distance across the river.
Using Pythagoras theorem,
27² + 38² = x²
729 + 1444 = x²
2173 = x²
x = 46.6
The distance saved would be the difference between the sum of the two legs of the triangle and the hypotenuse (distance across the river).
distance saved = (27+38) - 46.6
= 18.4
Therefore, Alexi’s sister saved about 18.4 meters by swimming across the river.
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1, Find the difference
63-93
2, Find the difference
-4-5
3, Find the difference
-156-(-45)
Answers
Answer:
63-93=-30
-4-5=-9
-156-(-45)=-111
Step-by-step explanation:
63-93=-30
-4-5=-9
-156-(-45)=-156+45=-111
Hope this helps!
Please mark as brainliest if correct!
Have a great day!
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 25,50,75,100, ........
Answers
The sequence is an arithmetic sequence with d = 25 and the next two terms are 125, 150.
Suppose we are given a sequence: a1, a2, a3, a4, ...
To determine whether the sequence is an arithmetic, geometric, or uncategorized one, we need to check the relation between its consecutive terms.
Arithmetic sequence.
If:
a2 - a1 = a3 - a2 = a4 - a3 = constant
then the given sequence is an arithmetic sequence. Furthermore, the constant d = a2 - a1 is usually called the common difference.
Geometric sequence.
If:
a2/a1 = a3/a2 = a4/a3 = constant
then the given sequence is a geometric sequence. Furthermore, the constant r = a2/a1 is usually called the common ratio.
The given sequence is:
25,50,75,100, ........
Let us check the difference:
50 - 25 = 75 - 50 = 100 - 75 = 25.
We can, then, conclude that the sequence is an arithmetic sequence with d = 25.
To find the next two terms, add 25 to every last terms.
100 + 25 = 125
125 + 25 = 150
Hence the next two terms are: 125, 150.
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100%
Tia left at 4:30 p.m. to drive to school. It took her 25 minutes to drive there.
What time did Tia get to school? Move numbers to the clock to show the time.
Answers
60 POINTS AND BRAINLIE$T
Is this table linear? I need help!
Given from the table below, Is the table linear or nonlinear?
Answers
Answer:
The table is linear because as x increases by 1, y changes by an average rate of |2|. You can also notice the tables both end in |+1|, which shows that the table has a constant rate of change between the two points at the end. Thus, the table is linear. If the table was nonlinear, there would be no constant rate of change between the 2 sets of data.
Name the property of real numbers illustrated by the equation. -(a-b) = (-1)(a-b)
Answers
The equation -(a-b) = (-1)(a-b) has used the property of real numbers is Distributive Property.
Property of Real numbers:
A real number is a value that represents a quantity along a continuous number line. Real numbers can be ordered.
The properties of real numbers are,
Commutative propertyAssociative propertyDistributive propertyIdentity propertyGiven,
The equation is
-(a-b) = (-1)(a-b)
Now we have to find the property used here.
Based on the properties of real number,
The one that exactly matches the equation is Distributive property.
Because the definition of Distributive property is explained through the following,
For three numbers m, n, and r, which are real in nature, the distributive property is represented as:
m (n + r) = mn + mr
The same will be applied in the given equation also.
Therefore, the Distributive property is used in the equation.
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3. If the ratio of yellow pigment to blue pigment in a shade of green paint is 2:3, how many
drops of yellow pigment will be needed if 12 drops of blue are used?
Answers
Drops of yellow pigment is 8.
A ratio is a comparison of two identical values that makes it simple to compare them. This is how a fraction with a numerator and denominator comparison is expressed. Depending on the ratio formula employed in various parts of mathematical computation, the definitions of the numerator and denominator may change.
For a certain shade of green, y = yellow and b = blue, where y/b = 2/3.
How many yellow drips are needed if there are 12 drops of blue,
y/b = 2/3 = x/12
= 2 × 12 = 3 × x
= 24 = 3x
= 24/3 = x
= x = 8
If you have 12 droplets of blue, you will need 8 drops of yellow.
y/b = 2/3
y = 2/3 × b
Substituting the value b = 12
y = 2/3 × 12
y = 24/3 = 8
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The equations of four lines are given. Identify which lines are parallel.
Line 1: y=1/2x−6
Line 2: x−2y=−1
Line 3: y=4x+6
Line 4: y+3=1/4(x−6)
Answers
Answer:
Line 1 and Line 2 are parallel.
Find each measure.
m∠ JLK
Answers
The measure of the major arc JLK will be 206°. Then the correct option is B.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of the minor arc JK will be 154°.
Then the sum of the major arc and minor arc in a circle is 360°.
Then the major arc JLK will be given as,
JLK + JK = 360°
JLK + 154° = 360°
JLK = 206°
The measure of the major arc JLK will be 206°. Then the correct option is B.
Your question was incomplete, but the complete question was attached below.
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How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 4.33%? Show formulas used
Answers
Answer:
Step-by
You have to determine how much more would $10,000 earn in 3 years compounded daily at 1.33% than compounded semiannually at 4.33%.
The first step is to calculate the final amount for both options. To do so, you have to use the following formula:
Where
A is the accrued amount
P is the principal amount
r is the interest rate expressed as a decimal value
t is the time in years
n is the number of compounding periods per year.
→ First, find the accrued amount for P=$10,000, R=1.33%, and t=3 years.
The account compounds daily,
K
A woman traveled 2436.5 miles in 18 hours 15 minutes. Find the average speed of her flight in miles per hour. (Change
18 hours 15 minutes into hours and use the formula d=rt.)
The average speed of the woman's flight was mph.
(Do not round until the final answer. Then round to the nearest tenth of a mile per hour as needed?
Answers
Answer:
133.5
This is because transfer it to hours nd then divide and this is what you get
what is 345x65 how do you should it
Answers
Answer: 22425
Step-by-step explanation: hope this helps!!
Answer:
22425
Step-by-step explanation:
1/16 x cubed root of 2
Answers
Answer:
0.07874506561 or 0.07875
Step-by-step explanation:
cubed root of 2 = 1.25992104989
or 1.260
What is the average rate of change, please simplify your answer (PICTURE BELOW)
Answers
Answer:
[tex]{ \tt{average \: \triangle = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]
x1 is -1; y1 is -3 [from graph (-1, -3)]x2 is 3; y2 is 5 [from graph (3, 5)][tex]{ \tt{ = \frac{5 - ( - 3)}{3 - ( - 1)} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = 2[/tex]
For each function, find the y -intercept
y=-3(x+2)²-4 .
Answers
Answer:
-16
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=-3(0+2)^2-4 \\ \\ =-3(4)-4 \\ \\ =-16[/tex]
Type the missing number in this sequence:
-1, -3, -9, ___,
-81
Answers
Answer:
-27
there is a pattern of x3 every time :)
Write the first four terms of an arithmetic sequence with a common difference of 3 and a third term of 10 . Then write both a recursive definition and an explicit formula for this sequence.
Answers
The first fur terms of an arithmetic sequence are 4, 7, 10, 13
What is a arithmetic sequence?
It is a series of numbers where the gap between succeeding phrases is always the same. for instance, 5, 7, 9, 11, 13, and 15. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
Given, common difference = 3
third term = 10
formula of arithmetic sequence is an = a + (n-1)d
a3 = a + (3-1)3
10 = a + 6
a = 4
a1 = 4
a2 = a + (n-1)d
a2 = 4 + (1)3
a2 = 7
a4 = a + 3d
a4 = 4 + 3.3
a4 = 13
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Currently, you have $80 and your sister has $145. You decide to save six dollars per week of your allowance. Your sister decides to spend her whole allowance plus seven dollars each week. How many weeks will it take for you to have as much money as your sister? Please include an equation.
Answers
Answer:
It will take you nearly 11 weeks
Step-by-step explanation:
80+6x = 145
6x = 145-80
6x = 65
x = 65/6 (weeks)
Determine whether y varies directly with x. if so, find the constant of variation k. 6y = 2x
Answers
Given the equation 6y = 2x, y varies directly with x and the constant of variation k has a value of 1/3.
There are two kinds of variations: direct and inverse.
Direct variation is a linear function defined by an equation of the form y = kx where variable y varies directly as x. On the other hand, inverse variation is a nonlinear function defined by an equation in the form y = k/x where variable y varies inversely as x.
Transforming 6y = 2x into a function of y,
y = 2/6 x
y = 1/3 x
where k = 1/3
Notice that it resembles the form y = kx which describes a direct variation between x and y.
Hence, the equation 6y = 2x shows that y varies directly with x and k = 1/3.
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What is the vertex of the following function?
y=4|x|+1
(4,-1)
(0,1)
(4,1)
(-4,1)
Answers
Answer:
(0,1)
Step-by-step explanation:
|x| is minimized when x=0, meaning the vertex is at (0,1).
What is the equation of the line that passes through the point (4,-3) and has slope 1/2 ?
F. y= (1/2)x+3
G. y= (1/2)x-1
H. y= (1/2)x-5
I. y=x-(1/2)
Answers
The equation of the line passing through the point (4 , -3) and has a slope of 1/2 is H. y = (1/2)x - 5.
The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Given the slope of 1/2 and a point (4 , -3), use the point-slope form to generate the equation of the line by plugging in the values in the equation.
(y - y1) = m(x - x1)
y - -3 = 1/2(x - 4)
y + 3 = (1/2)x - 2
Isolating the variable y in the left side,
y + 3 = (1/2)x - 2
y = (1/2)x - 2 - 3
y = (1/2)x - 5
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A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?
Answers
Answer:
1/30 of a ton of the rock was left at the construction site
Hope this helps :)
Explanation below.
Step-by-step explanation:
1. Make the same denominators to add them which is 6 (LCM).
1/3 + 1/2
2/3 + 3/6 = 5/6
2. Make the same denominator to subtract them since had to take back 4/5 of a ton. 30 would be the Least Common Multiple of 6 and 5.
5/6 - 4/5
25/30 - 24/30 = 1/30
I am 3 units less than -3
Answers
Hi!
your answer is 0
hope this helps!
Find the length of a segment with endpoint coordinates (2,3) and (8,11)
Answers
Answer:
The length is 10.
Step-by-step explanation:
[tex] \sqrt{ {(8 - 2)}^{2} + {(11 - 3)}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {8}^{2} } = \sqrt{100} = 10[/tex]
Write each equation in slope-intercept form. x-2 y+3=1
Answers
The slope - intercept form of the equation x-2 y+3=1 is y = x/2 + 1 .
What is slope - intercept form?Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
The slope - intercept form is y = mx + c
The given equation is
x-2 y+3=1
Subtract 3 from both sides,
x - 2y = -2
Divide the whole equation by 2
x/2 - y = -1
Rearrange the equation -
y = x/2 + 1
So the equation in slope-intercept form is y = x/2 + 1 , where slope is 1/2 and c = 1.
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A car gets miles per gallon of gas. It travels for 45 minutes at miles per hour. How many gallons of gas does the car use during that time? Show your work using units and Giant Ones.
Answers
Answer:
A car gets 25 miles per gallon of gas. It travels for.45 minutes at 65 miles per hour. How many gallons of gas does the car use during that time?
Answer:
25 miles per gallon of gas
travels 45 minutes and 65 miles per hour
Step-by-step explanation:
Simplify by combining like terms.
5+10 s-8 s
Answers
By combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5
Given,
The algebraic expression = 5+10s-8s
Combine the like terms
5+10s-8s = 5+2s
Simplified form is 2s+5
Hence, by combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5
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a certain book has 396 pages the student has already read 3/8 of the pages and now picks up the book again at time x=0 minutes write the equation that describes the total number of pages of the book read as a function of the number of minutes of further reading. Approximately how much time,in mintues,Will it take to finish reading the book?
Answers
The equation that describes the total number of pages of the book read as a function of the number of minutes of further reading is; 2.67x minutes.
The time it will take to finish the whole 396 pages is; 113.3 minutes
How to solve Algebra Word Problems?We are told that the book has 396 pages. Now, the student has read 3/8 of this book.
Thus, number of pages the student has read so far = 3/8 * 396 = 148.5 pages
Now, let the time spent reading these 148.5 pages be x minutes. Thus;
Number of pages read per minute = 148.5/x pages per minute
Number of pages left to finish book = 396 - 148.5 = 247.5 pages
Thus, time to finish remaining pages = 247.5/(149.8/x ) = 1.67x
Thus, time it will take to finish the whole 396 pages = 1.67x + x = 2.67x minutes
The table showing the amount of pages that can be read for specific minutes is attached.
We see that 7 pages are read in two minutes. Thus;
x = (148.5 * 2)/7 = 42.42857 minutes
Thus, time to finish whole book = 2.67 * 42.42857 ≈ 113.3 minutes
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The red snake is 12 inches long. It is 3 times as long as the green snake. Let n represent the green snake. Which number sentence below will solve for n?
A 3x6 inches = 18 inches
B 12 inches x 3 = 36 inches
C 12 inches divided 3= 4 inches
D 12 inches divided 4 = 3 inches
Answers
Answer: Your answer would be C.
Step-by-step explanation:
4 x 3 is 12 so, if you divide the 12 by 3 you will get 4 making C your answer.
(25 points) Please help me I'm stuck on these 3 questions.
Answers
[tex] \bf\bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow \bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( - \frac{4 \times 3 + 1}{4} d + \frac{3}{5} \bigg ) - \bigg(\frac{8 \times 2 + 7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 13}{4}d + \frac{3}{5} \bigg) - \bigg( \frac{23}{8}d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \frac{ - 13}{4}d + \frac{3}{5} + \frac{ - 23}{8} d + \frac{ - 7}{10} [/tex]
[tex] \bf \longrightarrow \bigg( \frac{ - 13}{4}d + \frac{ - 23}{8}d \bigg) + \bigg( \frac{3}{5} + \frac{ - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{(2 \times - 13) + (1 \times - 23) }{8}d \bigg) + \bigg( \frac{(2 \times 3) + (1 \times - 7)}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{ (- 26) + ( - 23)}{8}d \bigg) + \bigg( \frac{(6) + ( - 7)}{10} \bigg) [/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 26 - 23}{8} d\bigg) + \bigg( \frac{6 - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\frac{ - 49}{8}d + \frac{ - 1}{10} [/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
4) Which expression is equal to[tex] \bf\bigg( - 2 \frac{1}{2} n + \frac{1}{4} \bigg) + \bigg(3 \frac{3}{4} n - \frac{5}{8} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{\frac{5}{4}n - \frac{3}{8} } \: {\underline{\underline{ans}}}[/tex]
5) Which expression is equal to[tex] \bf\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:[tex] \bf\longrightarrow\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{1}{5}(3x) + \frac{1}{5}(10) + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{3}{5}x + 2 + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\bigg(\frac{3}{5}x + \frac{-11}{15}x\bigg) + 2[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
