The separation between a 6.8 kg particle and a 3.7 kg particle in order for their gravitational attraction to have a magnitude of 2.9 ✕ 10^−12 N will be 24 m.
m₁ = 6.8 kg
m₂ = 3.7 kg
F = 2.9×10^−12 N
We want to determine the distance r between both particles. The gravitational force on particle 2 due to particle 1 has the same magnitude as the force on particle 1 but in the opposite direction. If a distance r separates two masses, then the magnitude of the gravitational force acting on each due to the presence of the other is given by
F = Gm₁m₂/r² Eqn(1)
Where G is the gravitational constant and equals 6.6×10^−11 N⋅m²/kg².
By solving equation (1) for r, we get
r = √(Gm₁m₂/F)
Now we can plug our values for m₁, m₂ and G into equation (2) to get the separated distance r
r = √(Gm₁m₂/F)
= √{[(6.6×10^−11 N⋅m²/kg²)(6.8 kg)(3.7 kg)]/(2.9×10^−12 N)}
= 24 m
The gravitational force is very small due to the small masses where this force is indistinguishable.
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The um of two number i 50. The larger number i 4 le than 5 time the lower number. Find the number
After solving, the lower number is 9 and the larger number is 41.
The sum of two number is 50.
The larger number is 4 less than 5 times the lower number.
Let the lower number is x.
Five times the lower number = 5x
Larger number 4 less than five times the lower number = 5x - 4
Sum of number = 50
Lower Number + Larger number = 50
x + 5x - 4 = 50
Simplify
6x - 4 = 50
Add 4 on both side, we get
6x = 54
Divide by 6 on both side, we get
x = 9
Now finding the number.
Lower Number = x = 9
Larger Number = 5x - 4
Larger Number = 5(9) - 4
Larger Number = 45 - 4
Larger Number = 41
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The complete question is:
The sum of two number is 50. The larger number is 4 less than 5 times the lower number. Find the number.
I need help on scale factors and dilations
Mira's scale factor of 7 in would not be reasonable because it would make the dimensions of A' too small.
Why the scale factor Mira found would not be reasonable and give the correct scale factor?For example, if A had a width of 8 inches and a length of 5 inches, then using a scale factor of 7 in would result in A' having a width of 56 inches and a length of 35 inches. This would be much smaller than what the client wants. The correct scale factor would be 1.5 in, which would make A' a rectangle with a width of 12 feet and a length of 7.5 feet, which meets the client's request.Jess could use any of the following scale factors: 1.33, 1.5, 1.67, 1.75, 2, 2.25, 2.5, 2.75, 3, and 3.5. All of these scale factors would result in a rug with a width of 12 feet while still increasing the size. This process of finding the scale factor to meet a certain criteria is known as scaling.Mira's scale factor of 7 in would not be reasonable because the dimensions of A and A' are not proportional. A' is larger than A, but its sides are not 7 times larger than A. The correct scale factor would be the ratio of the lengths of A' and A. In this case, A is 8 cm and A' is 15 cm, so the correct scale factor is 15/8, or 1.875.Jess can use any scale factor between 1 (no change) and 1.5 to dilate the rug and meet the customer's request. A scale factor between 1 and 1.5 would increase the length of the rug without making the width exceed 12 feet. This process is called enlargement or scaling up.To learn more about scale factor refer to:
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a food scientist collected data on a sample of organic snacks. they summarized the amount of sugar (in mg) in each snack in the histogram below. which statement best describes the meaning of one of the bars in the histogram?
The sample size is: n=39
Class frequency
120-125 1
125-130 3
130-135 7
135-140 13
140-145 10
145-150 3
150-155 2
Total 39
∵Therefore, The sample size is: n=39
A histogram is a graphical representation of a frequency distribution with continuous classes that has been grouped. It is an area diagram with bases and intervals between class boundaries, and areas proportional to frequencies in the corresponding classes. Because the base spans the intervals between class boundaries, all rectangles in such representations are adjacent.
How Do You Plot a Histogram?
the Indianapolis 500 race takes 200 laps to complete. if 1 lap is 4km, how many kilometers must a competitor drive to complete the race
The competitor drive 804.672 or 800 Km to complete the race.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The Indianapolis 500 race takes 200 laps to complete.
and, 1 lap = 4 Km
Then, for 200 laps the competitor need to drive
= 200 x 4
= 800 Km
also, Indianapolis 500 race is to cover 500 miles in 200 laps then we can write it as
1 miles = 1.60934 Km
and 500 miles= 804.672 Km
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workout the equation of the line whuch has a gradient of 2 and passes through the point (1,4)
Answer:
y = 2x + 2.
Step-by-step explanation:
The equation of a line with gradient "m" can be represented as y = mx + b, where b is the y-intercept. To find the equation of a line that passes through the point (1, 4) and has a gradient of 2, we can use the point-slope form of a line:
y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the gradient.
Plugging in the values for the gradient (m = 2), point (x1 = 1, y1 = 4), we have:
y - 4 = 2(x - 1)
Expanding the right side, we get:
y - 4 = 2x - 2
Adding 4 to both sides, we get:
y = 2x + 2
So the equation of the line that has a gradient of 2 and passes through the point (1, 4) is y = 2x + 2.
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Alicia already pent $10. 25 of her paycheck. If thi wa 20% of her paycheck, how much wa he paid?
Alicia was paid $ 51.25.
A percentage is a rate that means a part of a whole number. A percentage is a number or ratio expressed as a fraction.Percentages are fractions with 100 as the denominator.According to the question,
Let the amount that Alicia was paid by Y.
If she already spent $10.25 of her paycheck and this is 20% of her paycheck, then
20 % of Y = 10.25
⇒ [tex]\frac{20}{100} * Y[/tex] = 10.25
⇒0.2 * Y = 10.25
⇒ Y = [tex]\frac{10.25}{0.2}[/tex] ( by using division)
∴ Y = 51.25
So, Alicia was paid $ 51.25.
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CTIVITY 1 QUESTION 1 The Stanger Child Welfare organisation is planning a fund-raiser and intends selling 200 tickets R150,00 each. The organisers have to choose between the Salt Rock Conference Centre and the Stanger Town Hall as a venue. A musical group has agreed to provide the music for free. 1. 1.1.1. The Stanger Town Hall charges basic fees of R3000 and R90 per person. TABLE 1: The cost of hiring the Stanger Town Hall Number of tickets sold (n) 0 50 100 B Cost(C) in rand 3 000 7 500 12 000 15 600 1.1.2. 200 21 000 a) Write the formula that represents the cost (C) of hiring the Stanger Town Use your formula to determine the value of B b) c) Use TABLE I to draw and label a straight line graph on the answer sheet. The Salt Rock Conference Centre has no basic fee but charges R120 per person. TABLE 2: The cost of hiring the Salt Rock Conference Centre Number of tickets sold (n) 0 50 160 200 100write the formula that represents the cost (c)
Answer:
Step-by-step explanation:
1.1.1. The formula that represents the cost (C) of hiring the Stanger Town Hall is C = B + 90n, where B is the basic fee, n is the number of tickets sold, and 90 is the cost per person.
To determine the value of B, we can use the information given in Table 1. When n = 0, C = 3 000. Plugging this into the formula, we get 3 000 = B + 90(0), so B = 3 000.
Therefore, the formula for the cost of hiring the Stanger Town Hall is C = 3 000 + 90n.
b) To draw a graph of the cost of hiring the Stanger Town Hall, we can use the information from Table 1 and plot points on a coordinate plane with the number of tickets sold on the x-axis and the cost in rand on the y-axis. Then, connect the points with a straight line.
1.1.2. The formula that represents the cost (C) of hiring the Salt Rock Conference Centre is C = 120n, where n is the number of tickets sold, and 120 is the cost per person.
The cost of hiring the Salt Rock Conference Centre will be directly proportional to the number of tickets sold, As we can see from the formula C=120n and as we increase the number of tickets sold the cost will also increase.
c) To draw a graph of the cost of hiring the Salt Rock Conference Centre, we can use the information from Table 2 and plot points on a coordinate plane with the number of tickets sold on the x-axis and the cost in rand on the y-axis. Then, connect the points with a straight line.
Step-by-step explanation:
=> The simplest form of
56
:
98
56:98 is
4
:
7.
4:7.
Step-by-step explanation:
Given ratio -
56
:
98
56:98
We have to reduce it to its simplest form,
For that, we have to find the GCD of the numerator as well as the denominator:
So, the GCD for
56
56 and
98
98 is
14.
14.
Now, divide both the numerator and denominator by the GCD:
=
>
56
÷
14
98
÷
14
=>
98÷14
56÷14
=
>
4
7
=>
7
4
Hence, the simplest form is
4
:
7.
4:7.
Write a function that models the data.
x y
0 250
1 150
2 90
3 54
4 32.4
Answer:250(0.6)
Step-by-step explanation:
The value of the function is f ( x ) = 250 ( 0.6 )ˣ
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The values of x are in set x = { 0 , 1 , 2 , 3 , 4 , }
The values of y are in set y = { 250 , 150 , 90 , 54 , 32.4 }
Now , the equation will be y = 250 ( 0.6 )ˣ
when x = 0
y = 250 ( 0.6 )⁰
y = 250 ( 1 )
y = 250
when x = 1
y = 250 ( 0.6 )¹
y = 250 ( 0.6 )
y = 150
when x = 2
y = 250 ( 0.6 )²
y = 250 ( 0.36 )
y = 90
when x = 3
y = 250 ( 0.6 )³
y = 250 ( 0.216 )
y = 54
when x = 4
y = 250 ( 0.6 )⁴
y = 250 ( 0.1296 )
y = 32.4
Hence , the function is y = 250 ( 0.6 )ˣ
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how many kilometers is 2528.5 cm? calculate and type your answer with correct significant numbers
0.025285 km is 2528.5 cm. 0.02528 km as significant figures.
The given centimeters:
2528.5 cm
To convert kilometers to cm, we first need to convert the given number in centimeters to meters and then to kilometers.
To convert from centimeters to meters:
1 cm = 1/100 m
2528.5 cm = (2528.5 / 100) = 25.285 m
To convert meters to kilometers:
1 m = (1/ 1000) km
25.285 m = (25.285 / 1000) km = 0.025285 km
Since, 2528.5 cm has 5 significant figures, we can write 0.025285 km as 0.02528 km in 5 significant figures.
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Match the following reasons with the statements given.
Prove:
The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
Given:
△RAS is isosceles
AM is median
Prove:
△RAM ≅ △SAM
1. Triangle RAS is isosceles, AM is a median
2. AR = AS
3. AM = AM
4. MR = MS
5. Triangle RAM congruent to Triangle SAM
(SSS, Reflexive, Definition of isosceles triangle, Definition of median, Given)
The required match of the given reasons with the statement is,
1. AR = AS [equal sides of the isosceles triangle]
2. AM = AM [common side]
3. MR = MS [As median bisect the line RS]
△RAM ≅ △SAM (SSS, Reflexive, Definition of isosceles triangle
Definition of the median, Given)
In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
Here,
Triangle RAS is isosceles, AM is a median
Consider triangle RAM and SAM
1. AR = AS [equal sides of the isosceles triangle]
2. AM = AM [common side]
3. MR = MS [As median bisect the line RS]
△RAM ≅ △SAM (SSS, Reflexive, Definition of an isosceles triangle, Definition of the median, Given)
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(c) sin² A(1 + cot² A) = 1
The sine of an angle's complementary angle is equal to the cosine of that angle, and the reverse is true for the other direction.
What is sine and cosine?The cosine of an angle is equal to the sine of its complementary angle, and the opposite is true for the other way around. The functions sine and cosine, sometimes known as sin() and cos(), show the shape of a right triangle. Sin() is the ratio of the opposite side to the hypotenuse when viewed from a vertex with angle, while cos() is the ratio of the adjacent side to the hypotenuse.Sin 180 has exactly zero value. In order to determine the angle or sides of a right-angled triangle, one of the basic trigonometric functions is sine. Trigonometric ratio is another name for it.Identity :
[tex]{cosec}^2 \mathrm{~A}-\cot ^2 \mathrm{~A}=1$[/tex]
LHS [tex]$=\left(1+\cot ^2 \mathrm{~A}\right) \sin ^2 \mathrm{~A}$[/tex]
[tex]{cosec}^2 \mathrm{~A} \times \sin ^2 \mathrm{~A}$[/tex]
[tex]$=\frac{1}{\sin ^2 A} \times \sin ^2 A$[/tex]
= 1
= RHS
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x-intercept of the line 3x+20y=–12.
Answer:x=-4
Step-by-step explanation
1. Set y as 0. Doing so will help you solve for x
3x +20(0)=-12 aka 3x=-12
2. Divide each sides by 3
3x(divided by three) = -12 (divided by three)
x=-4
(your answer would be negative because a negative divided by a postitive is negative.)
Practice proving that a quadrilateral is a parallelogram.
Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. Line segments Z C and C X are congruent. The length of W C is 2 x + 5 and the length of C Y is 3 x + 2.
In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?
x =
Answer:
x = 3
Step-by-step explanation:
2x + 5 = 3x + 2
-5 -5
2x = 3x + 2 - 5
-3x -3x
2x - 3x = 2 - 5
-x = -3
x = 3
Write a quadratic function for the area of the figure. Then, find the area for the given value of x.
x=7
A quadratic function for the area of the figure is A(x)= (Simplify your answer.).
A quadratic function for the area of a figure can be represented as [tex]A(x) = ax^2 + bx + c,[/tex] where a, b, and c are constants and x is the side length of the figure.
Write a quadratic function for the area of the figure?[tex]A(x) = x^2 - 6x + 9\\A(7) = (7^2) - (6\times 7) + 9 \\= 49 - 42 + 9 = 16[/tex]
In this case, the given value of x is 7, so the area of the figure can be found by plugging 7 into the equation. [tex]A(7) = a(7^2) + b(7) + c = 49a + 7b + c.[/tex]
Therefore, the area of the figure for [tex]x = 7 , 49a + 7b + c.[/tex]
The quadratic equation can also be used to calculate the area of the figure for any given value of x.
To do this, simply plug in the desired value of x into the equation and solve for the area.
For example, if we want to find the area of the figure for x = 4, then we would plug 4 into the equation and solve for the area. [tex]A(4) = 16a + 4b + c[/tex].
This shows that the area of the figure for x = 4 is 16a + 4b + c.
In summary, the quadratic equation [tex]A(x) = ax^2 + bx + c[/tex] can be used to calculate the area of a figure for any given value of x.
For the given value of x = 7, the area of the figure is calculated to be [tex]49a + 7b + c.[/tex]
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Complete question -
Write a quadratic function for the area of the figure. Then, find the area for the given value of x.
x=7
A quadratic function for the area of the figure is A(x)= (Simplify your answer.).
on the road between two towns (Bergville and Reddington). The is a sign that shows the distance to each town . The distances given are the nearest kilometres Bergville 12km and Reddington 15km ( a) what are the smallest and largest possible distance between the two towns.
( b ) Two walkers meet at the sign past one sets off towards Bergville and the other to Reddington . what is the possible difference between the distance they walk
Answer:(a) The smallest possible distance between the two towns would be 12km (the distance to Bergville) + 15km (the distance to Reddington) = 27km. The largest possible distance would be 12km + 15km + 1km (the margin of error for each distance being given to the nearest kilometer) = 28km.
(b) The possible difference in the distance the two walkers walk would be the difference in the distances given on the sign, which is 15km - 12km = 3km. However, this difference would also be affected by the margin of error of 1km for each distance given on the sign, so the possible difference in distance could range from 2km to 4km.
PLEASE ANSWER THIS IS DUE MONDAY!!! The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller one. When x is the bigger number, find the numbers.
The numbers are 19 and 71 respectively
How to determine the numbersLet's call the smaller number "y".
The larger number would be 3 times y plus 14,
Which we can write as 3y + 14.
From the problem, we know that the sum of the two numbers is 90, so we can write an equation:
y + (3y + 14) = 90
Remove the brackets
y + 3y + 14 = 90
So, we have
4y + 14 = 90
4y = 76
Divide both sides by 4
y = 19
So the smaller number is 19 and the larger number is 3 times that plus 14, which is 3 * 19 + 14 = 71.
So the two numbers are 19 and 71.
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Monique has 20/40 Bodily Injury Liability Insurance and $25,000 Property Damage
Liability Insurance. She causes an accident while driving. In the other car, one person
has $30,000 in medical expenses and another has $25,000 in medical expenses. The
other car has $12,000 in damage and Monique's car has $6,000 in damages.
How much will the insurance company pay?
$73,000
$45,000
$52,000
$58,000
The insurance firm will pay $45,000, claims the statement .The correct option B.
What does the term "property damage" mean?Damage to personal or real estate is known as property damage. A vehicle accident that results in damage or a chemical release on real estate might serve as examples. To guard it against possibility of property damage, property owners might get property insurance.
Personal Accident Liability Insurance for Monique provides up for $20,000 per person or $40,000 overall in coverage. Therefore, the insurance provider will cover the two passengers in the other car's medical expenditures up to a maximum of $40,000.
For damages to the other automobile, she Damage To property Liability Insurance provides up to $25,000 in coverage.
So in total, the insurance company will pay $40,000 + $25,000 = $65,000.
However, Monique's policy has a per-accident limit, so the insurance company will pay up to the policy limit, which is $45,000.
Thus, the insurance company will pay $45,000.
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The Complete Question :
Monique has 20/40 Bodily Injury Liability Insurance and $25,000 Property Damage
Liability Insurance. She causes an accident while driving. In the other car, one person
has $30,000 in medical expenses and another has $25,000 in medical expenses. The
other car has $12,000 in damage and Monique's car has $6,000 in damages.
How much will the insurance company pay?
a. $73,000
b. $45,000
c. $52,000
d. $58,000
What is the length of a side of rhombus jklm? 4 units 8 units 12 units 16 units
The length of the sides of the rhombus JKLM is 12 units.
A rhombus is one of parallelograms. The opposite sides of a rhombus are parallel, and the opposite angles are equal. Furthermore, all of the sides of a rhombus are the same length, and the diagonals intersect at right angles.
In the problem, the sides of rhombus JKLM are:
JK = 2x + 4
JM = 3x
Since the length all of the sides of a rhombus are the same, then:
JM = JK
3x = 2x + 4
Substract both sides by 2x:
3x - 2x = 2x + 4 - 2x
x = 4
To find the length of a side, substitute x = 4 into:
JM = 3x
JM = 3(4) = 12
Hence, the length of the sides of the given rhombus is 12.
The picture in your question is missing. Most likely it was like on the attached picture.
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Answer:
12
Step-by-step explanation:
JK = JM
2x + 4 = 3x
x = 4
JK = JM = 3 x 4 = 12
Solve the equation below
(2×-9)(×+8)
Answer:
-18x + -144
Step-by-step explanation:
the inside diameter of an open cylindrical tank was measured. the results of four replicate measurements were 5.2, 5.7, 5.3, and 5.5 m. measurements of the height of the tank yielded 7.9, 7.8, and 7.6 m. calculate the volume in liters of the tank and the standard deviation of the result.
The volume of the cylinder tank is 179530L and the standard deviation of the result is 5.869 L.
For the open cylindrical tank, the volume of the cylinder is given by:
V = (πd^2 h)/4
Where d is the diameter of the base and h is the height of the cylinder.
As there are four measurements for the diameter, the mean of the diameter is:
d = (5.2+5.7+5.3+5.5)/4=5.425
As there are three measurements for the heigh, the mean of the height is:
h = (7.9+7.8+7.6)/3=7.767
Hence, the volume of the cylinder is:
V = (π〖5.425〗^2 (7.767))/4 = 179.53 m^3 or 179530 L
In order to calculate the standard deviation of volume, calculate the standard deviation of diameter and height and calculate the volume.
SD = √(∑▒(di-d)^2 )/(N-1)
SD = √(∑▒〖(5.2-5.425)^2+(5.7-5.425)^2+(5.3-5.425)^2+(5.5-5.425)^2 〗)/(4-1) = 0.221
SD = √(∑▒(hi-h)^2 )/(N-1)
SD = √(∑▒〖(7.9-7.767)^2+(7.8-7.767)^2+(7.6-7.767)^2 〗)/(3-1) = 0.153
Hence, the SD of the volume is:
SD = (π(0.221)^2 (0.153))/4 = 0.005869 m^3 or 5.869 L
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Find the circumference and the area of a circle with a diameter 9m.
Use the value 3.14 for pi, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
circumference= 28.26
Area= 63.585
Step-by-step explanation: So, to do this question you have to know the formula for both circumference and the area. So to find the circumference you have to do
2*3.14*4.5 -(9/2)
= 28.26
And to find the area you have to do.
3.14*4.5^2
= 63.585
Therefore, those are the answers. Please let me know if they are wrong.
the perimeter of a rectangle is 24 inches the length and width are positive integers. how many distinct area can the rectangle have?
The 6 distinct possible areas can the rectangle have.
Given the perimeter of a rectangle, we can find the length (l) and width (w) using the formula:
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.
Perimeter of a rectangle = 2(Length + Width) square unitsLet us derive the formula for its perimeter and area
2l + 2w = 24
Solving for l and w, we get:
l + w = 12
l and w can be any combination of positive integers that add up to 12. The possible combinations are:
(1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6)
Therefore, there are 6 distinct possible combinations of length and width for a rectangle with a perimeter of 24 inches, and therefore 6 distinct possible areas.
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A car goes 42 miles in 45 minutes (3/4 of an hour)
a. How fast was the car going?
b. At this rate how long will it take to go 100 miles?
a) The speed of car is, 56 miles per hour.
b) The time to complete 100 miles is, 25/14 hour.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
A car goes 42 miles in 45 minutes (3/4 of an hour).
Now, We know that;
⇒ Speed = Distance / Time
Substitute the given values, we get;
⇒ Speed = 42/(3/4)
⇒ Speed = 42 × 4/3
⇒ Speed = 56 miles per hour
Thus, The speed of car is, 56 miles per hour.
And, At the same rate, the time to complete 100 miles is,
⇒ Speed = Distance / Time
⇒ 56 = 100 / Time
⇒ Time = 100 / 56
⇒ Time = 25/14 hour
Thus, The time to complete 100 miles is, 25/14 hour.
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make an educated guess what is the limit of the sequence an= 5n2 n3 5 . then use the definition of a limit to prove that your guess is correct.
My best guess is that the sequence an= 5n2 n3 5 has an infinite limit. The definition of a limit, which indicates that as n gets closer to infinity, the limit of an= 5n2 n3 5 is also infinite, can be used to demonstrate this.
My best guess is that the sequence an= 5n2 n3 5 has an infinite limit. The definition of a limit, which indicates that as n gets closer to infinity, the limit of an= 5n2 n3 5 is also infinite, can be used to demonstrate this. In other words, when n increases without limit, the value of a will also increase until it reaches infinity. We can examine the value of a for various values of n to illustrate this. The value of a rises sharply as n rises. As an illustration, an equals 12500 when n = 5 and 250000 when n = 10. The value of a rises exponentially as n rises, proving that the sequence's limit, an= 5n2 n3 5, is truly infinite. Additionally, we may provide a formal demonstration for this using the limit definition. The limit of the sequence an= 5n2 n3 5 is in fact infinity when n = is substituted into the expression, yielding a = 523 ,5 = ∞, which proves that the limit of the sequence an= 5n2 n3 5 is indeed infinity.
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if ∫175f(x)dx=2.4 , and ∫1711f(x)dx=15.1, then ∫115f(x)dx=
The sum of the integrals of 175 and 1711 times the function of x is the integral of 115 times the function of x.
Calculate 175f(x)dx in step one.
∫175f(x)dx = 2.4
Calculate 1711f(x)dx in step two.
∫1711f(x)dx = 15.1
The next step is to deduct 175f(x)dx from 1711f(x)dx.
15.1 - 2.4 = 12.7
Step 4 is to add the outcome to 175f(x)dx.
2.4 + 12.7 = 15.1
In step five, take away 175f(x)dx from 115f(x)dx.
∫115f(x)dx = 15.1
By deducting the integral of 175 times the function of x from the integral of 1711 times the function of x, we get at 12.7, which is the answer to the question. The solution is 15.1, which we may obtain by adding this result to the integral of 175 times the function of x. This indicates that 15.1 is the same as the integral of 115 times the function of x.
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gallium-67 has a half-life of 78 hours. if you began with 10.0 g of ga-67, how many grams remain after 6.5 days?
The amount of gallium-67 remain after 6.5 days = 2.5 grams
We know that the half-life of the radioactive isotope is nothing but the time needed for the isotope to be half of its initial value of mass.
This means, with each half-life, the isotope will be halved of its initial value.
The formula for the numbers of half-lives:
numbers of half-lives = total time passed / the half-life of the isotope
Here, total time passed = 6.5 days
= 156 hours
the half-life of the isotope = 98 hours
Let n represents the number of half lives.
Using above formula,
numbers of half-lives n = 156 / 98
numbers of half-lives n = 1.59
numbers of half-lives n ≈ 2
So, the remaining mass would be,
remainig mass m = initial mass / [tex]2^n[/tex]
m = 10 / 2²
m = 2.5 g
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Una compañía de autobuses quiere saber si el número de quejas que recibe está en función del número de autobuses que tiene. La compañía realizó un estudio en el que comparó el número promedio de autobuses por hora en días distintos y el número de quejas que recibieron en esos días. Se ajustó una recta a los datos para modelar la relación.
The line that represent the graph have the equation of y = 4x + 42 .
What is a equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire Different graph equations may be used to express the aforementioned graphs.
We must determine the slope and the y-intercept in order to graph this line. Y=mx+b, where m is the slope and b is the y-intercept, is the equation's slope-intercept form.
From the graph we can 2 points on the graph are
(0, 42) and (6, 18)
The equation of the graph will be
y - 42 = 18 - 42 /(6 - 0) *(x - 0)
⇒ (y -42)*6 = 24x
⇒y-42 = 4x
⇒y = 4x + 42.
The line that represent the graph have the equation of y = 4x + 42 .
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write an equation in slope intercept form for a line that has given slope and passes through the given point: slope = -1/2, (6,-5)
Based on the slope of -1/2, we have:
y = -1/2 x + b
Substitute in (6,-5), we have:
-5 = -1/2 (6) + b
We can solve this for b:
-5 = -3 + b
-2 = b
Now we have the equation:
y = -1/2 x - 2
You start the day with $27 in cash. You spend $14 at the movie theater and $9 on lunch. You end the day by cashing a $30 check. What is the change in the amount of cash you carry throughout the day?
Answer:at the end of the day u have 34 dollars
the amount that u carry around is 4 dollars.
Step-by-step explanation: $27-14=13
13-9=4.
4+30=34.
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A board game uses a bag of 105 lettered tiles. You randomly choose a tile and then return it to the bag. The table shows the number of vowels and the number of consonants after 50 draws. Predict the number of vowels in the bag.
Answer:
Without knowing the exact number of vowels and consonants in the bag, it is not possible to accurately predict the number of vowels. However, if the bag is made up of a certain proportion of vowels and consonants and this proportion remains consistent throughout the draws, we can use the proportion of vowels and consonants in the 50 draws to estimate the proportion in the bag.
For example, if after 50 draws, there are 20 vowels and 30 consonants, we can estimate that the bag contains 40% vowels and 60% consonants. So, we can estimate the number of vowels in the bag as 42(105 x 40%).
Answer:
Step-by-step explanation:
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