Potential energy required is 4,018 kg m² /s²
What is Potential Energy ?
Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy. Potential energy always measures if we know the height of the object and the mass of the object on which energy is applied as well.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
g= -9.8m/s² , h = 10 m , m = 41kg
as, U = mgh
= (41 )(9.8)(10)
= 4,018 kg m² /s²
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If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).
Answer:
g(f(x)) = 4x^2 + 8x + 4
Step-by-step explanation:
If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).
You are asked to find g of f of x.
This means your x value for the equation g(x) is f(x), hence g(f(x)).
g(2x+1)=(2x+1)^2 + 2(2x+1) +1
g(2x+1) = 4x^2 + 4x + 1 +4x + 2 + 1
Combine like terms.
g(2x+1) = 4x^2 + 8x + 4
g(f(x)) = 4x^2 + 8x + 4
A computer is rendering two scenes. The computer has already rendered 540540540 thousand pixels (\text{kpx}kpxstart text, k, p, x, end text) of a kitchen scene and renders another 90\,\text{kpx}90kpx90, start text, k, p, x, end text each minute. The computer has rendered 960\,\text{kpx}960kpx960, start text, k, p, x, end text of a garden scene and renders 60\,\text{kpx}60kpx60, start text, k, p, x, end text more pixels each minute.
Answer: 14 min
Step-by-step explanation:
After 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90kpx each.
Let after t minutes the scene will have the same amounts rendered.
The linear equation in one variable can be framed as:
540 + 90t = 960 + 60t
After solving the above linear equation in one variable:
90t - 60t = 960 - 540
30t = 420
t = 14 minutes
Thus, after 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
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the dum of twice a number and 15
23
−
1/9
= ?????
I really need help please help me...
Answer: 22.8888888889 but rounded 22.9
Step-by-step explanation: This is so because when you turn 23 to ninths you get 207/9 - 1/9 then put into decimal form, 22.8888888889 or 2.9
Find the coordinate of the midpoint of the segment with the given endpoints. - 16 and - 4 The midpoint is (Simplify your answer.)
Answer:
Step-by-step explanation:
The coordinate of the midpoint of the segment is -10
We have been given,
The coordinate of the endpoints of the segment are , -16 and -4
We need to find the coordinate of the midpoint of the segment.
Using the midpoint formula,
m = (-16-4)/2
= -20/2
= -10
Therefore, the coordinate of the midpoint of the segment is -10
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Factor the expression. 25-40 x+16 x²
Factor the expression 25-40 x+16 x² is [tex](4x-5)^2[/tex]
In mathematics, factorization is defined as breaking down or decomposing an entity (such as a number, matrix, or polynomial) into another entity or product of coefficients. Splitting the mean term means that the mean term of the quadratic must be rewritten as the sum or difference of two terms. The middle term should be split into two parts in terms of the sum or difference of the terms. The general form of the quadratic equation is [tex]ax^2+ bx +c=0[/tex]On rearranging the equation , we get
[tex]16x^2-40x+25=0[/tex] ...(1)
To split the middle term of the quadratic equation, we need to look at the middle term of the quadratic equation under consideration.
Midterm is 40 x , to split the middle term, use the sum-and-product form which is
" The sum-product form is the product of intermediate terms after splitting and must equal a × c and the sum must equal b "
[tex]f(x)=16x^2-40x+25[/tex]
here a = 16 , b = -40 and c = 25
We need to divide into 40x in two parts
40x = 20x + 20x
The product of the terms is [tex]16\times25=400[/tex]
Now we can rewrite 40x as 20x + 20x
Putting in equation (1) , we get
[tex]16x^2-(20+20)x+25=0\\\\(16x^2-20x)-(20x-25)=0\\\\4x(4x-5)-5(4x-5)=0\\\\(4x-5)(4x-5)=0[/tex]
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Sandy is training for a triathlon. Between running and bicycling, she covers a
distance of 200 miles every week. Her average speed on a bicycle ride is 20
mph. Her average speed running is 8 mph. If she spends 16 hours per week
training, how many hours does she spend on each sport?
Answer:
Step-by-step explanation:
Use natural logarithms to solve each equation.
ex/₄-8=6
39.16 approx. is the value of x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 solved by using natural logarithm
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to find x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 using natural logarithm
⇒ [tex]e^{\frac{x}{4} -8}[/tex] = 6
⇒ [tex]\frac{x}{4} - 8[/tex] = ㏑6
⇒ [tex]\frac{x}{4}[/tex] = ㏑6 + 8
⇒ x = ln(1296) + 32
= 39.16 approx.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^{\frac{x}{4} -8}[/tex] = 6
A line passing through point (-6, 1) and has a slope of -3
Write an equation in Ax+By=C
Use integers A, B and C
Answer:
y=-3x-17
Step-by-step explanation:
y=mx+b (slope-intercept form) b=y-intercept= (0,?) m=slope
y=-3x+b substitute values
y+3x=b isolate b to find b
1+3(-6)=b substitute given ordered pair
-17=b
y=-3x-17
The ratio of Richard and Ben's speed is 4:5. The ratio of Richard and Kim's speed is 3:2. If it takes Ben 8 minutes to get to a location, it's going to take Kim _____ minute(s) for the same distance. (FILL IN THE BLANK)
The time it would take Kim running the same distance is 15 minutes.
How long would it take Kim?
Ratio is used to show the relationship between two or more numbers. It shows the frequency that one value is contained within other value(s). The sign that is used to represent ratio is :.
Speed = distance / time
The first step is to determine the time spent by Richard running:
(4 x 1/8) / 5 = 1/10 or 10 minutes
The second step is to determine the time spent by Kim running:
(2 x 1/10) / 3 = 1/15 = 15 minutes
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What values of x and y satisfy the system {y=−2x+3y=5x−4?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the given system of equations is x = 1, y = 1. That is, (1, 1)
From the question, we are to solve the given system of equations.
The given system of equations is
y = -2x + 3y ------------- (1)
y = 5x - 4 ------------- (2)
Substitute equation (2) into equation (1)
y = -2x + 3y
5x - 4 = -2x + 3(5x - 4)
5x - 4 = -2x + 15x - `12
Collect like terms
-4 + 12 = -2x + 15x - 5x
Simplify
8 = 8x
∴ x = 8/8
x = 1
Substitute the value of x into equation (2)
y = 5x - 4
y = 5(1) - 4
y = 5 - 4
y = 1
Hence, the solution to the given system of equations is x = 1, y = 1. That is, (1, 1)
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HELP ASAP I DONT WANT TO FAIL
Answer:
16.3p + (-10)
Step-by-step explanation:
what is the equation for this graph in slope intercept form?
Write each logarithmic expression as a single logarithm.
1/4 log₃2+ 1/4 log₃x
For the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.
We are given the logarithm expression as:
1 / 4 log₃ 2 + 1 / 4 log₃ x
Now, take 1 / 4 common from the expression:
1 / 4 ( log₃ 2 + log₃ x)
Now, we know that log₃ a + log₃ b = log₃ ( a b)
So, we get that:
1 / 4 ( log₃ ( 2 x) )
1 / 4 log₃ 2 x
Therefore, for the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.
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-40 -2 (3m + 1/2) = 7m -2
Answer:
m = -3
Step-by-step explanation:
Which of the following points lie on the line whose equation is y + 4= 3/5 ( x- 2)?
The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)
What points do belong to a given linear equation?
In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.
Now we proceed to check the expression for each case:
(x, y) = (1, - 5)
- 5 + 4 = (3 / 5) · (1 - 2)
- 1 = (3 / 5) · (- 1)
- 1 = - 3 / 5 (FALSE)
(x, y) = (- 8, - 12)
- 12 + 4 = (3 / 5) · (- 8 - 2)
- 8 = (3 / 5) · (- 10)
- 8 = - 30 / 5
- 8 = - 6 (FALSE)
(x, y) = (- 3, - 8)
- 8 + 4 = (3 / 5) · (- 3 - 2)
- 4 = (3 / 5) · (- 5)
- 4 = - 3 (FALSE)
(x, y) = (12, 10)
10 + 4 = (3 / 5) · (12 - 2)
14 = (3 / 5) · 10
14 = 30 / 5
14 = 6 (FALSE)
(x, y) = (7, - 1)
- 1 + 4 = (3 / 5) · (7 - 2)
3 = (3 / 5) · (5)
3 = 3 (TRUE)
The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).
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Evaluate each logarithm.
log₁/₂ 1/2
The answer to the given logarithm expression is log₁/₂ 1/2 = 1
Another technique to clarify exponents in mathematics is through logarithms. A base number's logarithm equals another number.
For instance, log10 100 = 2 if 102 = 100. A logarithm is defined as an influence by which variety must be raised to receive another value. this is often the foremost convenient thanks to represent large numbers. Logarithms have several important properties that prove that logarithmic multiplication and division is written because the logarithm of addition and subtraction. The log is named the logarithm of base e. The logarithm is represented by ln or loge. where 'e' represents Euler's constant, approximately capable 2.71828. as an example, the log of 76 is written as ln 76. The log defines what percentage times 'e' must be multiplied to induce the required output.
Using log property logₐ a = 1log₁/₂ 1/2 = 1
Hence , we evaluated the logarithm which is log₁/₂ 1/2 = 1
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(a +11)(11a +1)
Simplify
Answer:
11a^2 + 122a + 11
Step-by-step explanation:
First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.
You are given that f(x)=x²+4 and g(x)=3 x-1 .
b. Find f(x)+g(x) .
The summation of f (x) and g (x) = x ² + 3 x + 3
Given,
f (x) = x ² + 4
g (x) = 3 x - 1
The question states to find the summation of the function f, that is, f (x) = x ² + 4, and function g, that is, g (x) = 3 x - 1
Performing the addition operation on these functions is just like simple addition.
This implies, adding the two functions f (x) and g (x), we get
f (x) + g (x) = x ² + 4 + 3 x - 1
=> f (x) + g (x) = x ² + 3 x + 3
This assumes that the summation or addition of the two functions f (x) and g (x) gives x ² + 3 x + 3
Therefore, we get the summation of f (x) and g (x) as x ² + 3 x + 3
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Solve each equation. If necessary, round to the nearest ten-thousandth. logB(2 x-1)=1/3
The solution of the given equation by rounding off it to the nearest ten-thousandth is 0.0872.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation log 8(2x - 1) = 1/3
We are given a logarithmic expression: log 8(2x - 1) = 1/3
We know that e^(log b) = b
a log b = (log b)^a
log a + log b = log (ab)
Using exponential on both sides, we have
e^(log 8(2x - 1)) = e^(⅓)
8(2x - 1) = 1.3956
(2x - 1) = 1.3956 / 8
2x = 0.17445
x = 0.0872
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 0.0872.
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3. Noemi's team is working together to write a quadratic equation to model the path of the golf ball question in graphing form.
She calculated the value of `a=-\frac{1}{90}` is she correct?
Include detailed work that supports your answer on the left.
Begin with your equation for this golf ball situation from the previous slide.
The value of a calculated by Noemi is not correct as the correct value is
a = -1/45
We know that the general form of the quadratic equation is given as
y = ax² + bx + c
where, a and b are coefficients of the variable x and c is the constant term.
Now according to the question the path of the golf ball is parabola whose coordinates will be
(0,0) = origin where it starts
(60,80) = vertex or the maximum point
(120,0) = end point
Now putting the value of (x,y) in the above formula to find the value of a,b and c
when (x,y) = (0,0)
0 = a0² + b0 +c
c = 0
when (x,y) = (60,80)
80 = a60² + b60 +c
80 = 3600a + 60b + 0 (1)
when (x,y) = (120,0)
0 = a120² + b120 +c
0 = 14400a + 120b + 0
120b = -14400a
b = -120a
Putting the value of a in equation (1) we get
80 = 3600a + 60(-120a)
80 = 3600a - 7200a
80 = -3600a
a = - 1/45
⇒ b = 8/3
Hence the equation will be y = -1/45x² + 8/3x
and the value of a calculated by Noemi is not correct as the correct value is a = -1/45
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Help for A Brainlist!!! geometry question!!! In the right triangle XYZ, angle X and angle Z are complementary angles. Given ( please see image attached below thank you for the help:) take care)
In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85
In the right triangle XYZ, angle X and angle Y are complementary angles.
The complementary angle is either of two angles whose sum is 90 degrees
Therefore,
Angle X + Angle Z = 90 degrees
In trigonometry,
sinθ = Opposite side / Hypotenuse
sin z= 36/85
z= [tex]sin^{-1}(\frac{36}{85} )[/tex]
z= 25.06
Then the value of cos z is
cos 25.06 = 77/85
Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85
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A common race is a 5K race, where runners travel 5 kilometers. Is it more appropriate to report the distance as 5 kilometers or 5×10^6 millimeters?
This version is much shorter, and more simpler, compared to 5 x 10^6 millimeters. It's more appropriate to use millimeters with very small objects or distances.
Note: 5 x 10^6 = 5,000,000 = 5 million
Incorrect Work/Solution
-7x-3y + x + 2y
-7x-3y + 1/2x+y
-5-x-2y
Identify and explain the error (2 points)
Jack bought 8 drill bits for aed11.22 each, 10 washers for aed10.11 each and 2 hammers for aed 545.59 each. a. calculate the total cost? b. later he bought a box to keep all the items. he paid aed 1500 altogether including box and received aed 12 as balance. find the cost of the box?
Jack spent first a total of AED 1282.04 and when he bought the box it cost AED 205.96
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
No. drill bits = 8 drill bitscost of drill bits = AED 11.22/ drill bitsNo. washers = 10 washers cost of washers = AED 10.11 / washers No. hammers = 2 hammers cost of hammers = AED 545.59 / hammersPaid = AED 1500Balance = AED 12Total cost = ?Box cost = ?Calculating the total cost Jack spend before bought the box:
Total cost = (No. drill bits*cost of drill bits) + (No. washers *cost of washers ) + (No. hammers *cost of hammers)
Total cost = (8 drill bits * AED 11.22/ drill bits) + (10 washers * AED 10.11 / washers) + (2 hammers * AED 545.59 / hammers)
Total cost = AED 89.76 + AED 101.1 + AED 1091.18
Total cost = AED 1282.04
Calculating the box cost:
Balance = Paid - (Total cost + box cost)
Balance = Paid - Total cost - box cost
box cost = Paid - Total cost - Balance
box cost = AED 1500 - AED 1282.04 - AED 12
box cost = AED 205.96
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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1) what is the answer to this
Answer:
Slope: 2/1
equation: y=2/1x+2
Multiply. Write your answer in scientific notation.
8.8 (1 x 10^3
)
Answer:
8.8 x 10^3
Step-by-step explanation:
8.8 * 1 x 10^3 = 8.8 x 10^3 <===== done
Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F.
The expression that represents the temperature of the water after Raul added the ice cubes is 72.3°F + (72.3°F)
Writing an expressionFrom the question, we are to write an expression that represents the temperature of the water after Raul added ice.
From the given information,
The initial temperature is 72.3°F
and
The change in temperature was -39.1°F
Thus,
The expression that represents the temperature of the water after Raul added the ice cubes is
72.3°F + (72.3°F)
Hence, the expression written as the sum of two numbers is 72.3°F + (72.3°F)
Here is the complete question:
Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F. Write an expression that represents the temp of the water after Raul added the ice cubes. Write the expression as the sum of two numbers.
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I need help on number 2
The value of the x means hypotenuse according to the Pythagoras is 12.8.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
From the given information:
The perpendicular length is 12.
And The base is a 4.5
And we have to find that the hypotenuse value.
Then
According to the theorem
Perpendicular^2 + base^2 = Hypotenuse^2
And substitute the value then
12^2 + 4.5^2 = Hypotenuse^2
144 + 20.25 = Hypotenuse^2
Then
Hypotenuse^2 = 144 + 20.25
Hypotenuse^2 = 164.25
Hypotenuse = 12.8.
So, The value of the x means hypotenuse according to the Pythagoras is 12.8.
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Solve each equation.
3⁻²x⁺²=81
After solving the equation, x = -1 is the value of x in [tex]3^{(-2x)+2} = 81[/tex]
⇒ [tex]3^{(-2x)+2} = 81[/tex]
⇒ [tex]3^{(-2x)+2} = 3^4[/tex]
⇒ -2x + 2 = 4
⇒ -2x = 2
⇒ x = 2/(-2)
⇒ x = -1
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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