Consider the function f(x) = 4 − 2 sec x. Find the exact coordinates of three points on
the function where f has a horizontal tangent
Answers
The exact coordinates of points where the horizontal tangent exists are:
(0,2)
([tex]\pi[/tex],6)
([tex]-\pi[/tex],6)
What is meant by tangent?
A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.
Given function is f(x)=4-2secx
We can write it as
y=4-2secx
The slope of the tangent to this curve is:
[tex]\frac{dy}{dx} =-2secx*tanx[/tex]
Given that the tangent is horizontal, which means that the slope is zero.
-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].
So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].
When x=0 ⇒ y=4-2sec0
⇒y=2
When x=π ⇒ y=4-2secπ
y=6
When x=-π⇒ y=4-2sec(-π)
y=6
Therefore the exact coordinates of points where the horizontal tangent exists are:
(0,2)
([tex]\pi[/tex],6)
([tex]-\pi[/tex],6)
The graph is attached below.
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Related Questions
Problem 1. Compute the complex norm |z|= √zz for the following complex numbers z:
1. z = −i
2. z = (2 + i)2
3. z = (3 −4i)3
4. z = (3 + 4i)3
Answers
Recall that the complex norm (or modulus) of a complex number z = a + bi is defined as the nonnegative square root of the product of the complex number and its conjugate, i.e., |z| = √(z × z*), where z* is the complex conjugate of z.
Using this definition, we can calculate the complex norm of each of the given complex numbers as follows:
[tex]z = -i\\z* = i (conjugate of -i)\\|z| = √(z z*) = √(-i i) = √1 = 1Therefore, |z| = 1.[/tex][tex]z = (2 + i)^2\\z* = (2 - i)^2 (conjugate of (2 + i)^2)\\|z| = √(z z*) = √((2 + i)^2 (2 - i)^2) = √((2^2 + 2i + i^2) (2^2 - 2i + i^2))= √((4 + 4i - 1) (4 - 4i - 1)) = √(9 * 9) = 9Therefore, |z| = 9.[/tex][tex]z = (3 - 4i)^3\\z* = (3 + 4i)^3 (conjugate of (3 - 4i)^3)\\|z| = √(z z*) = √((3 - 4i)^3 (3 + 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex][tex]z = (3 + 4i)^3\\z* = (3 - 4i)^3 (conjugate of (3 + 4i)^3)\\|z| = √(z z*) = √((3 + 4i)^3 (3 - 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex]What is complex number?A complex number is a number that can be expressed in the form [tex]a + bi[/tex], where a and b are real numbers, and i is the imaginary unit defined by [tex]i^{2} = -1[/tex]. The real part of the complex number is a, and the imaginary part is bi.
Complex numbers can be added, subtracted, multiplied, and divided in a manner similar to real numbers. They can also be graphed on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part.
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Solve for x with the given measures
Answers
Answer: X= -66
Step-by-step explanation:
If m angle UYV=56
Then WYX= -x-10=56
then X=-66
1.2. Identify and explain TWO types of goals in line with Anelisa 'story. 1.3. Discuss the benefits of goal setting on your career choice. 1.4. Discuss any THREE challenges Anelisa experienced that could have been been obstacles in achieving his goals. 1.5. Analyse how Anelisa's personal values contributed to his success. 1.6. Critically discuss how relationships can impact negatively on the achievement of goals TOTAL ACTIVITY 1: [30] Gauteng Department of Education (2+2) (4) (2x2) (4) (3x2) (6) (4x2) (8) (2x3) (6) 2023 Grade 11 Life Orientation Task
Answers
Types of Goals in line with Anelisa's story:
Personal Growth Goals: These goals are related to Anelisa's personal development and could include things like increasing her knowledge, learning new skills, and expanding her experiences.Career Goals: These goals are related to Anelisa's professional development and could include things like advancing in her career, increasing her income, or improving her job performance.Benefits of goal setting on your career choiceGoal setting helps individuals focus their efforts, prioritize their time and resources, and measure their progress towards achieving their goals. In the context of career choice, goal setting can help individuals:
Clarify their career aspirations and identify their strengths, weaknesses, opportunities, and threats.Develop a roadmap for their career journey and align their actions with their career vision.Stay motivated and engaged in their work and avoid feeling overwhelmed or discouraged by the challenges they face.Improve their performance and productivity, and increase their chances of achieving their desired outcomes.Challenges Anelisa experienced:
Lack of resources: Anelisa may have lacked the resources needed to achieve her goals, such as financial support, access to training programs, or sufficient time to complete her tasks.Resistance from others: Anelisa may have encountered resistance from others who opposed her goals, either because they disagreed with her vision or because they felt threatened by her ambition.Self-doubt and fear of failure: Anelisa may have struggled with self-doubt and fear of failure, which could have held her back from pursuing her goals and taking calculated risks to achieve them.Anelisa's personal values, such as determination, resilience, and a strong work ethic, likely played a significant role in her success. These values likely gave her the motivation and drive to pursue her goals, despite the challenges she faced. Additionally, her values may have helped her stay focused on her goals, maintain her sense of purpose, and make decisions that aligned with her vision for her life.
Relationships can impact the achievement of goals in both positive and negative ways. On the positive side, supportive relationships can provide individuals with emotional support, encouragement, and practical resources that can help them achieve their goals. On the negative side, relationships can also be a source of conflict and distraction, especially if they are not aligned with the individual's goals or values.
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Answer:
Step-by-step explanation:
lack of financial stability Nd resoouces
what is the substitution for -3x+5y=21
Answers
Answer:
5
_ y - 7
3
the five is floating for some reason its supposed to be under the line
Samuel took a survey of people entering several random ice cream shops to find out who liked vanilla and who liked chocolate ice cream.
biased or unbiased
Answers
Answer:
ummmm i would say unbiased fam only bc i love ice cream and i always wonder whichwtch one does people like more.
Step-by-step explanation:
What is the solution to the image below?
5
10
-5
10
Answers
Answer: x=10
Step-by-step explanation:
Determine the Domain and Range for the graph below. Write your answer in interval notation and as an inequality.
Domain written in Interval Notation:
Domain written as an Inequality:
Range written in Interval Notation:
Range written as an Inequality:
Points on the graph are:
(0,1) (1,2) (2,3) (3,4) (4,5)
(-1,0) (-2,-1) (-3,-2) (-4,-3)
Answers
The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5] ; (2) Domain [-1,-4], Range =[0,-3]
Domain and Range of a set of Ordered pairsThe domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.
The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.
From the points on the graph given:
(0,1) (1,2) (2,3) (3,4) (4,5)
Domain: (0, 1, 2, 3, 4)
In interval notation: = [0,4]Range: (1, 2, 3, 4, 5)
In interval notation: = [1, 5](-1,0) (-2,-1) (-3,-2) (-4,-3)
Domain: ( -1, -2, -3, -4)
In interval notation: = [-1, -4]Range: (0, -1, -2, -3)
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Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total is made up of Green?
Answers
9.19% of the total is made up of Green.
What is a percentage?The percentage formula is dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of green cars = 120
Number of green planes = 250
Number of green trains = 500
Total = 870
Now,
The total number of all colors of the car, plane, and train.
= 870 + 1250 + 820 + 800 + 990 + 4730
= 9460
Now,
The percentage of green cars, planes, and trains.
= 870/9460 x 100
= 9.19%
Thus,
9.19% of the total is made up of Green.
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Need help with this Question pls
Answers
Step-by-step explanation:
a. £5,37
b.£2,07
c.£15,70
legend has it that Isaac Newton discovered gravity when an apple feel down from a tree and hit him on the head. I a 0.2 kg apple fell 7 meters before hitting Newton, what was its change in PE during the fall?
Answers
The change in potential energy of the apple during the fall was approximately 13.72 joules.
What is the name of potential energy?One of the two types of energy is potential energy, which is the latent energy in an object at rest. Kinetic energy, on the other hand, is the energy that an item in motion expresses.
The formula: can be used to determine the change in potential energy (PE) of a mass m object that falls a distance h from the Earth's surface.
ΔPE = mgh
where g is the acceleration brought on by gravity close to Earth's surface, which is roughly 9.8 m/s^2.
In this instance, the apple weighs 0.2 kg, falls 7 metres, and accelerates by gravity at a rate of 9.8 m/s^2. So, the potential energy change is as follows:
PE is equal to (0.2 kg) times (9.8 m/s^2) times (7 m) Equals 13.72 joules (J)
As a result, the apple's potential energy changed by around 13.72 joules during the fall.
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3. The number of pages
in my book is less
than 96 and greater
than 90.
Who could I be?
2
I have 3 letters in my
'name.
Who am I?
4.
Answers
The number of pages in the book is given by the inequality 90 < A < 96 , where A is the number of pages
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of pages in the book be A
And , it is more than 90 and less than 96
So , the value of A is { 91 , 92 , 93 , 94 , 95 }
On simplifying , we get
90 < A < 96 , where A is the number of pages
Hence , the inequality is 90 < A < 96
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Use the commutative and/or associative properties to simplify (17)(0.25)(4).
Answers
The solution is, (17)(0.25)(4) = 17.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
(17)(0.25)(4)
=(17)*1
=17
at first we have to multiply the last two terms i.e. (0.25) and (4), then, we multiply the result 1 with 17, and get the result 17.
Hence, The solution is, (17)(0.25)(4) = 17.
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[tex] {x}^{\frac{2}{3} }{ } = 64 [/tex]
Solve the following equation
Answers
The value of x in the given equation using laws of exponents is; x = 512
How to use Laws of Exponents?The different laws of exponents include;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
We have the equation as;
x^(2/3) = 64
We can write 64 as (∛512)²
This can be further expressed as;
512^(2/3)
Thus, we have;
x^(2/3) = 512^(2/3)
Thus, by identity rule;
x = 512
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Select the correct answer. Which is a warning sign that someone needs the help of a mental health professional? a. Feeling shy when asked to walk onstage b. Overeating to increase bodily strength c. Inablity to sleep properly for weeks.
Answers
Inability to sleep properly for weeks is a warning sign that someone needs the help of a mental health professional. Correct option is C.
Difficulty sleeping, or insomnia, can be a warning sign that someone needs the help of a mental health professional. Insomnia can be caused by a number of mental health conditions, such as anxiety, depression, or post-traumatic stress disorder (PTSD), as well as other factors such as stress, poor sleep habits, or physical health problems.
Feeling shy when asked to walk onstage and overeating to increase bodily strength may be signs of anxiety or other emotional or psychological issues, but they are not necessarily warning signs that someone needs the help of a mental health professional.
However, if these behaviors are causing significant distress or interfering with daily life, it may be a good idea to seek the help of a mental health professional.
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12x + 7 < −11
OR
5x-8>40
Answers
Answer:
x <-1.5
or
x <9.6
Step-by-step explanation:
12x + 7 < - 11
12x < -11 - 7
12x < - 18
12x/12 < -18/12
x = -1.5
OR.
5x - 8 > 40
5x > 40 + 8
5x > 48
5x/5 > 48/5
x > 9.6.
1. Takis Machine Shop paid a base rate for the state's workers' compensation insurance of $9.40 per $100 paid in wages. Takis has a monthly payroll of $53,896.84. After reevaluating the frequency and severity of accidents at machine shops, the state increased the base rate to $10.40 per $100 paid in wages. Assuming the monthly payroll stays the same, how much more will Takis pay each year for state workers' compensation insurance in dollars. Round to the nearest hundredth of a percent.
2. The Madison County tax assessor determined the market value of a home to be $590,000. The rate of assessment in Madison County is 40% of market value. The tax rate is 42.73 mills. Calculate the real estate tax in dollars. Round to the nearest hundredth of a percent.
3. Vanesa Vasquez contributes $2,500 per year to her Roth IRA, an ordinary annuity, starting at age 35. If she earns 7.4% annual interest compounded annually, what is the fair market value of her Roth IRA at age 65? How much interest will she have earned in dollars? Round to the nearest hundredth of a percent.
4. Marty and Roslyn Seymour purchase a GNMA Mortgage issue bond selling at a premium of 103.7% of its $10,000 face value. The bonds are selling at a premium because they have an annual yield of 8.75%. Find the interest rate as a percent? Round to the nearest hundredth of a percent.
5. Ricardo Ramirez took out a single-payment loan for $2,500 at 7.8% ordinary interest to pay his federal income tax bill. If the maturity value of the loan was $2,548.75, in how many days would Ricardo have to pay back the loan?
Answers
Answer: do you need me to answer all or anthor example.
Step-by-step explanation:
I will answer
Pat deposits $ 600 in a savings account at a simple interest rate of 6% per year for 5
years. how much will pat have earned in interest by the end of 5 years
Answers
Answer:
will earn in interest $ 180
In a particular metal mixture there are:
1 part mercury to 5 parts copper,
3 parts tin to 10 parts copper,
You would need how many parts mercury to how many parts tin?
A) 1:3
B) 2:3
C) 6:13
D) 4:15
Answers
Answer:
B) 2:3
Step-by-step explanation:
If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.
RatioThe ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.
mercury : copper = 1 : 5 = 2 : 10
Then ...
mercury : tin : copper = 2 : 3 : 10
You need 2 parts mercury to 3 parts tin.
mercury : tin = 2:3 . . . . . . choice B
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A(t) = 17t - 1/2 * t ^ 2 power lawn mowers, 10. Suppose that the factory's cost of manufacturing units is C(x) After hours of operation, an assembly line has assembled C(x) = 2772 + 110x (a)Express the factory's cost as a (composite) function of the number of hours of operation of the assembly line )What is the cost of the first 2 hours of operation?
Answers
The function of the number of hours of operation of the assembly line will be 2772 + 110[17t - 1/2t²].
The cost of the first 2 hours of operation will be $6292
How to calculate the functionFrom the information, A(t) = 17t - 1/2t² power lawn mowers, 10 and we suppose that the factory's cost of manufacturing units is C(x) after hours of operation, an assembly line has assembled C(x) = 2772 + 110x.
Therefore, the (composite) function of the number of hours of operation of the assembly line will be:
= 2772 + 110[17t - 1/2t²]
The cost of the first 2 hours of operation will be:
2772 + 110[17t - 1/2t²]
= 2772 + 110[17 × 2 - 1/2 × 2²
= 2772 + 110(34 - 2)
= $6292
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Rewrite in simplest terms: (5x + 5y) - (-x + 10y)
Answers
Answer:
6x - 5y
Step-by-step explanation:
( remove the unnecessary parentheses)
= 5x + 5y + x - 10y
= 6x + 5y - 10y
= 6x + 5y
Written as a simplified polynomial in standard form, what is the result when
(x − 2)² is subtracted from 4x?
Answers
Step-by-step explanation:
(x-2)(x-2)-4x
x²-2x-2x +4-4x
x²-4x-4x +4
x²-8x+4
Answer:
4x - (x - 2)² = 4x - x² + 4 = 3x + 4
Step-by-step explanation:
Write the equation is slope intercept form given
f(0) = -3 and f(1) = 2
Answers
The equation is slope-intercept form is equal to y = 5x - 3.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (-3, 2).At point (0, -3), a linear equation of this line can be calculated in slope-intercept form as follows:
y - (-3) = (2 + 3)/(1 - 0)(x - 0)
y + 3 = 5x
y = 5x - 3.
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Shen is riding in a bike race that goes through a valley and a nearby mountain range.
The table gives the altitude (in feet above sea level) for the five checkpoints in the race.
Use the table to answer the questions.
Checkpoint Altitude
(feet above sea level)
1 3,459
2 1,499
3 668
4 -202
5 -99
(a) The top of a hill rises 66 feet above Checkpoint 4.
What is the altitude of the top of the hill?
(b) How much higher is Checkpoint 1 than Checkpoint 5?
Answers
1) Note that the altitude of the top of the hill is -136 feet above sea level.
2) Note that Checkpoint 1 is 3,558 feet higher than Checkpoint 5.
What is the rationale for the above response?Altitude or height is a distance measurement between a reference datum and a point or object, generally in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.
1) Checkpoint 4 has an altitude of -202 feet above sea level. The top of the hill rises 66 feet above Checkpoint 4. Therefore, the altitude of the top of the hill is:
-202 + 66 = -136 feet
So, the altitude of the top of the hill is -136 feet above sea level.
2) To find the difference in altitude between Checkpoint 1 and Checkpoint 5, we need to subtract the altitude of Checkpoint 5 from the altitude of Checkpoint 1.
Altitude difference = Altitude of Checkpoint 1 - Altitude of Checkpoint 5
Substituting the values given in the table, we get:
Altitude difference (AD) = 3,459 - (-99)
AD = 3,459 + 99
Thus, AD = 3,558
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Please helpppp
if y+3/y-3 = 6
What is the value of y?
f(x) =3(x-2) (x+4)
f(x) = (3x+12) (x-2)
f(x) =3(x+4) (x+2)
f(x) = 3 (x-4) (x+2)
Answers
Answer:
Step-by-step explanation:
The answer is d. f(x) = 3 (x-4) (x+2).
is 68/33 rational or irrational
Answers
Answer:
Given value is Rational. The value is 2.06
Step-by-step explanation:
Answer: Rational.
Step-by-step explanation:
An irrational number is one that terminates forever, and cannot be expressed as a fraction. 68/33 is a fraction, therefore it's rational. Irrational can be values like pi, which do not have a ratio form (e.g. fraction).
The pto is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 200 tickets sold. The winter gets a prize worth $76.
Answers
Answer:
Step-by-step explanation:
The profit the PTO makes from selling raffle tickets can be calculated by subtracting the cost of the tickets from the total revenue generated from ticket sales.
Let's first calculate the total revenue:
Number of tickets sold = 200
Price per ticket = $4
Total revenue = 200 * $4 = $800
Next, let's calculate the cost of the tickets:
Number of tickets sold = 200
Price per ticket = $4
Total cost = 200 * $4 = $800
Finally, we can calculate the profit by subtracting the cost of the tickets from the total revenue:
Profit = Total revenue - Total cost
Profit = $800 - $800 = $0
So, the PTO makes no profit from selling the raffle tickets. This is because the cost of the tickets and the prize are equal, and there are no other expenses. In this scenario, the prize money of $76 is given away to the winner, so the PTO does not get to keep the money for classroom supplies.
what could be a ratio between the lengths of the two legs of a 30-60-90 triangle
Answers
Answer:
Below
Step-by-step explanation:
One leg would be hyp * cos 30 and one would be hyp cos 60
hyp cos 30 : hyp cos 60
cos 30 : cos 60
= ratio sqrt (3) /2 : 1/2 or sqrt 3 : 1
Sara can type 90 words in
4 minutes. About how many words
would you expect her to type in
10 minutes at this rate?
Answers
[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]
(03.02 MC)
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 9 feet.
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 18 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Answers
Solving the provided question, we can say that By, Pythagorean theorem PR = √277 and b = 11.31
What is Pythagorean theorem?The Pythagοrean Theorem, sometimes known as the Pythagοrean Theorem, is the basic Euclidean geοmetry relationship between a right triangle's three sides. Accοrding to this rule, the area of a square with the hypotenuse side equals the sum οf the areas of squares with the other twο sides. The Pythagοrean Theorem, often knοwn as the generic algebraic nοtation a² + b² = c², states that the square that crοsses the hypotenuse οf a right triangle οpposite the right angle equals the sum of the squares that span the sides of a right triangle.
By, Pythagοrean theorem
PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
Again by Pythagorean theorem
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet of water weigh in pounds? In tons?
Answers
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
