Answers
The trigonometric identities can be proved as follows;
32. Using the substitution, tan(x) = sin(x)/cos(x), and cot(x) = cos(x)/sin(x), we get;
cot(x) - tan(x) = (1 - 2·sin²(x))/(sin(x)·cos(x)) = sec(x)·(csc(x) - 2·sin(x))
36. tan(θ)/(1 + sec(θ)) = sin(θ)/(1 + cos(θ)) = (1 - cos(θ))/(sin(θ)) = -cot(θ) + csc(θ)
What are trigonometric identities?Trigonometric identities are equations involving trigonometric functions which are valid for the values of the input variable.
as follows;
cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))
The left hand side of the equation can be expressed using sin(x) and cos(x) as follows;
cot(x) = cos(x)/sin(x)
tan(x) = sin(x)/cos(x)
Therefore;
cot(x) - tan(x) = cos(x)/sin(x) - sin(x)/cos(x) = (cos²(x) - sin²(x))/(sin(x)·cos(x))
cos²(x) = 1 - sin²(x), therefore
(cos²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - sin²(x) - sin²(x))/(sin(x)·cos(x))
(1 - sin²(x) - sin²(x))/(sin(x)·cos(x)) = (1 - 2·sin²(x))/(sin(x)·cos(x))
(1 - 2·sin²(x))/(sin(x)·cos(x)) = csc(x)·sec(x)·(1 - 2·sin²(x))
csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))
Therefore;
cot(x) - tan(x) = csc(x)·sec(x)·(1 - 2·sin²(x)) = sec(x)·(csc(x) - 2·sin(x))
cot(x) - tan(x) = sec(x)·(csc(x) - 2·sin(x))36. tan(θ)/(1 + sec(θ)) = -cot(θ) + csc(θ)
The left hand side can be manipulated as follows;
tan(θ) = sin(θ)/cos(θ)
sec(θ) = 1/cos(θ)
Therefore; tan(θ)/(1 + sec(θ)) = (sin(θ)/cos(θ))/(1 + (1/cos(θ)))
(sin(θ)/cos(θ))/(1 + (1/cos(θ))) = (sin(θ)/cos(θ))/((cos(θ) + 1)/(cos(θ)))
((sin(θ)/cos(θ))×cos(θ))/((cos(θ) + 1)/(cos(θ)) × cos(θ))) = sin(θ)/(cos(θ) + 1)
tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1)
sin(θ)/(cos(θ) + 1) = sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ)))
sin(θ)/(1 + cos(θ)) × ((1 - cos(θ))/(1 - cos(θ))) = ((sin(θ)·(1 - cos(θ))/(1 - cos²(θ)))
((sin(θ)·(1 - cos(θ))/(1 - cos²(θ))) = ((sin(θ)·(1 - cos(θ))/(sin²(θ)) = (1 - cos(θ))/(sin(θ))
sin(θ)/(cos(θ) + 1) = (1 - cos(θ))/(sin(θ)) = csc(θ) - cot(θ) = -cot(θ) + csc(θ)
tan(θ)/(1 + sec(θ)) = sin(θ)/(cos(θ) + 1) = -cot(θ) + csc(θ)
Therefore;
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Related Questions
Calculate the marked price on a bag of Cement selling 570 ksh after a discount of 5% is offered.
Answers
Answer:
541.5 ksh
Step-by-step explanation:
3. Explain how "a" affects the graph of a parabola. (f(x) = ax²)
Answers
The effect of "a" in the graph of parabola is value from the quadratic function.
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
y = a(x – h)2 + k or x = a(y – k)2 +h
Where:
(h, k) - The vertex of the parabola.
p - Least distance between the vertex and the focus of the parabola.
Given that;
The equation of parabola is f(x) = ax².
Now, Let's look at the graph of f(x) = x^2 + 3x + 1, which is below. The b-value in this equation is 3.
We see that our graph is indeed a parabola. Our parabola is curving up. The x-value of the vertex, the tip of the parabola, is -3 / 2 or -1.5. We can actually calculate this x-value by evaluating the expression -b / 2a, where a and b are the values from the quadratic function.
Therefore, the role of a in parabola is stated.
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The Lopez family is looking to rent a large truck for their upcoming move. With Felipe's
Moving, they would pay $90 for the first day plus $1 per additional day. With Springdale
Rent-a-Truck, in comparison, the family would pay $40 for the first day plus $6 per additional
day. Before deciding on which company to use, Mrs. Lopez wants to find out what number of
additional days would make the two choices equivalent with regards to cost. How many
additional days would that be?
Write a system of equations, graph them, and type the solution.
Answers
The system of equation is written as follows
y = 90 + x
y = 40 + 6x
With regards to cost the choices will be equivalent in 10 day
How to write the system of system of equationsAssuming additional day is x
Felipe's Moving, they would pay $90 for the first day plus $1 per additional day:
= 90 + x
Rent-a-Truck, the family would pay $40 for the first day plus $6 per additional day.
= 40 + 6x
Equating both costs gives
90 + x = 40 + 6x
90 - 40 = 6x - x
50 = 5x
x = 10
in 10 days the cost will be same
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The grass in the photo above can be found in the __________ ecosystem.
Answers
The tropical savanna environment is home to the grass in the picture above.
What is Southeast Asia's ecosystem like?The two primary types of forests are deciduous or monsoon rainforests and tropical evergreen rainforests, which have leaves all year round (these loose their leaves during the dry season). Human activity causes deforestation because it endangers the local ecosystem's ability to sustain life.
What is the ecosystem of the rainforest?Rainforests are a type of forest habitat that have a dense canopy, great species variety, and high rainfall rates. The Amazon is made up of a variety of ecosystems and plant life, including savannas, deciduous woods, seasonal forests, and rainforests.
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Mike is working on solving the exponential equation 37^x= 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation
Hint Use the change of base formula: logby=
log y over log b
Answers
Answer:
should" (and any subsequent words) was ignored because we limit queries to 32 words.
1/4x
10. Last night, 4 friends went out to dinner at a restaurant. They split the bill evenly. Each friend paid $12.75 for his or her meal and each left the same amount for a tip, t. The total dinner bill including the tip was $61. What equation could you use to describe the situation?
Answers
Answer:
Step-by-step explanation:
Let's call the number of friends "f". Since each friend paid $12.75 for their meal, the cost of the meals can be represented as f * 12.75. And since each friend left the same amount for a tip, the cost of the tips can be represented as t * f.
The total cost of the dinner including the tip was $61, so we can write the following equation:
f * 12.75 + t * f = 61
Expanding the left side of the equation:
12.75f + t * f = 61
Combining like terms:
13.75f + t = 61
Solving for t:
t = 61 - 13.75f
So, the equation that describes the situation is t = 61 - 13.75f.
Chose the fraction that correctly represents the ratio 5 to 15 in simplest form
Answers
The fraction that correctly represents the ratio of 5 to 15 in it's simplest form is option C. 1/3.
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
The given ratio is 5 to 15.
Fraction in simplest form means that, the numerator and denominator cannot be factored by a common factor again.
In order to find the given ratio in simplest form, find the greatest common factor of both 5 and 15.
5 = 5
15 = 3 × 5
5 is the only common factor and so the greatest common factor of both 5 and 15.
5 / 15 = (5 × 1) / (5 × 3)
= 1/3
Hence 1/3 is the simplest form of the ratio 5 to 15.
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Your question is incomplete. The correct question is as follows.
Chose the fraction that correctly represents the ratio 5 to 15 in simplest form.
A. 2/3
B. 10/30
C. 1/3
D. 1/5
Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?O The theoretical probability for selecting a red card in each pick is 0.5. O For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far. O This is an example of the law of large numbers. O The relative frequency of selecting a red card changes with the increase in number of selections.
Answers
He then constructs a graph to visualize his results, For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far is FALSE.
Probability refers to potential. A arbitrary event's circumstance is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to read the liability of colorful events. The degree to which commodity is likely to be is principally what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
We are only interested in finding red card so we can't differentiate between diamond or hearts at any time. Hence,
The false statement is:
For a given number of selections, we can use Josephs graph to find the number of diamonds that he has picked so far.
Option B is correct.
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find an expression for sin (5 theta) as a fifth degree polynomial in the variable sin(theta) ?
Answers
On solving the provided question, we can say that the trigonometry sin3θcos2θ+cos3θsin2θ = 4sin3(1−2cos2θ)+sinθ
What is trigonometry?The area of mathematics knοwn as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, arοund the third century BC. frοm the use of geometry in astronοmical study.
The area of mathematics knοwn as exact methods deals with specific trigonometric functions and hοw they might be used in calculations. There are six popular trigonοmetric functions in trigonometry. Sine, cosine, tangent, cοtangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics οf triangles, particularly right triangles, is called trigonοmetry. The study of geοmetry, however, is the characteristics of all geοmetric figures.
the trigonometry
sin3θcos2θ+cοs3θsin2θ=4sin3(1−2cos2θ)+sinθ
Use the variation cοs2θ=1−sin2θ to express sin(5θ) in terms of sinθ
sin5θ=4sin3θ(1−2(1−sin2θ))+sinθ(8(1−sin2θ}
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Find the value of x that makes AABC~ADEF.
B
8
12
光
A x+7 C
X =
D
24
E
48
3(x+3)
F
Answers
Answer:e
Step-by-step explanation:t
A city bowling league is holding a tournament in which the top 8 bowlers with the highest three-game totals are awarded cash prizes. First place will win $1250, second place $1132, third place $1014, and so on.
(a) Write a sequence a, that represents the cash prize awarded in terms of the place n in which the bowler finished
(b) Find the total amount of prize money awarded at the tournament.
Answers
The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.
What exactly is a sequence?
A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.
Now,
given award money for 1, 2, 3 places is given as $1250, $1132 and $1014
that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)
So, the sequence will be aₙ=$1250-118ⁿ⁻¹
where
n=place at which a bowler is placed.
Hence,
The sequence will be aₙ=$1250-118ⁿ⁻¹.
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PLEASE HELP ASAP WILL GIVE BRAINLIEST
Answers
The value of the length /MK/ is 10 units
How to find the length?Recall that in an isosceles reangle, two sides are equal and the base angles are equal
We can use the cosine rule to find the length MK
N² = K²+M² - 2KMCosN
This implies that /MK/² = 5²+5²-2*5*5*cos110
⇒25+25-50*-0.9990
= 50+49.95
=99.95 this can be approximated to 100
the /MK/ = √100= 10 units
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PLEASE ANSWER!!!
Russell surveys 200 randomly selected seventh-graders in his school and finds that 30 attend summer camp. If there are 780 seventh-graders in his school,
about how many are expected to attend summer camp?
Answers
Answer:
To estimate the number of seventh-graders who attend summer camp, we can use the sample proportion of 30 out of 200 students.
Let's call the population proportion of seventh-graders who attend summer camp "p".
The sample proportion can be estimated as:
p = 30/200 = 0.15
To estimate the number of seventh-graders in the entire school who attend summer camp, we can multiply the population size by the sample proportion:
Estimated number of seventh-graders attending summer camp = p * population size = 0.15 * 780 = 117
So, about 117 seventh-graders in the school are expected to attend summer camp.
Answer:
117 seventh-graders in the school are expected to attend summer camp.
Step-by-step explanation:
Find the perimeter of the figure.
Answers
Answer:
≈29.93 [units].
Step-by-step explanation:
according to the attachment the required perimeter is:
P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].
Solve for the equation of the tangent line. Question is attached below. Please show full working.
Answers
Answer:
y = 1/8x +1/64
Step-by-step explanation:
You want the equation of the line that is tangent to the curve y = x³ -x⁴ in exactly two places.
Points of intersectionSince the tangent line is not crossed, the difference between the line and the given curve is a 4th-degree polynomial with two roots, each of multiplicity 2. If those are 'a' and 'b', we can write for line y = mx +p, ...
mx +p -(x³ -x⁴) = (x -a)²(x -b)² = 0
x⁴ -x³ +0x² +mx +p = x⁴ -2(a+b)x³ +(a²+4ab+b²)x² -2ab(a+b)x +a²b²
Equating coefficients, we have ...
x⁴: 1 = 1x³: -1 = -2(a+b)x²: 0 = (a+b)² +2abx: m = -2ab(a+b)constant: p = a²b²SolutionThe coefficient of x³ tells us ...
a +b = 1/2
The coefficient of x² tells us ...
0 = (a +b)² +2ab
0 = (1/2)² +2ab
ab = -1/8
LineUsing these value, we can find the equation of the line to be ...
m = -2ab(a+b) = -2(-1/8)(1/2) = 1/8
p = (ab)² = (-1/8)² = 1/64
The equation of the line is ...
y = 1/8x +1/64
__
Additional comment
To find the line, we did not need the coordinates of the points of tangency. They are ((1-√3)/4, (3-2√3)/64) and ((1+√3)/4, (3+2√3)/64).
The slope of the line is equal to the slope of the quartic at the point of inflection of its derivative, at x=1/4.
I need to know why the medians differ relative to the data set and the best measure of center?
Answers
Explanation:
In this case the median value is more representative of the 'center' of the population. The median is a better measure when the data set is skewed, has fat tails as compared to a normal didtribution, or has outliers. Otherwise you should use the arithmetic mean.
the function of G takes a student's first name for its input and gives the number of letters in the first name for its output
Describe the meaning of G(jada)=4
Find the value of G(Diego).
Answers
Answer:
Step-by-step explanation:
The meaning of the function notations are
G(Jada) = 4 means that the first name Jada has four letters
C(11-15)= chemistry means that the Monday class for 11-15 is chemistry
How to interpret the function notations?
The meaning of the function G
From the question, we have the following parameters that can be used in our computation:
Function G gives the number of letters in the first name for its output.
Next, we have
G(Jada) = 4
Using the meaning of the function, we have
G(Jada) = 4 means that the first name Jada has four letters
The meaning of the function C
From the question, we have the following parameters that can be used in our computation:
Function C gives a student's Monday class for its output.
Next, we have
C(11-15)= chemistry
Using the meaning of the function, we have
C(11-15)= chemistry means that the Monday class for 11-15 is chemistry
9. Find the sum of the first multiples of 5.
Answers
Answer:
75
Step-by-step explanation:
Use the arithmetic progression formula: S =n/2(2a + (n-1)d)
a = 5, d = 5, n = 5
S = 5/2((2(5) + (5-1)(5)) = 75
Last week's and this week's low temperatures are shown in the table below Low Temperatures for 5 Days This Week and Last Week Low Temperatures This Week (F) Low Temperatures Last Week (F) Which measures of center the mean of this wer O the mean of the range of this O the mean absolute deviat the mean absolute devi 10 ariability are greater than 5 degrees? Select three choices temperatures temperature
Answers
The measures of the center or variability that are greater than 5 degrees are :
a) the mean of this week’s temperaturesb) the mean of last week’s temperaturesc) the range of this week’s temperaturesHow to find the center of variability ?The mean of the data on temperature this week and the last is :
= ( 4 + 10 + 6 + 9 + 6 ) / 5
= 7 degrees Fahrenheit 4+ 10+ 6+9+ 6
The mean of the data on temperature last week and the last is :
= ( 13 + 9 + 5 + 8 + 5 ) / 5
= 8 degrees Fahrenheit
The range of this week's temperature is :
= 10 - 4
= 6 degrees Fahrenheit
All these measures of center are above 6 degrees.
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The full question is:
Temperatures for 5 Days This Week and Last Week
Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.
a) the mean of this week’s temperatures
b) the mean of last week’s temperatures
c) the range of this week’s temperatures
d)the mean absolute deviation of this week’s temperatures
e) the mean absolute deviation of last week’s temperatures
Find the surface area (in square feet) of a right circular cylinder of height 4 feet whose base has radius 3 feet. Round the answer to the nearest tenth of a square foot.
Answers
Answer:
After rounding the nearest tenth of a square foot, the surface area of the circular cylinder is 131.88 feet^2.
Step-by-step explanation:
To find surface area of a right circular cylinder we can use the formula,
A = 2πrh + 2πr^2
Here A is surface area,
π is mathematical constant ,
r is radius, and h is the height of the cylinder.
We have
r = 3 ft
h = 4 ft,
Now we put the values to find the surface area,
A = 2π × 3 × 4 + 2π ×3^2
A = 24π + 18π
A = 42π
A= 42×3.14 (we know π = 3.14 )
A = 131.88
After rounding the nearest tenth of a square foot, the surface area of the circular cylinder is 131.88 feet^2.
Help with my algebra homework
Answers
The evaluation of the function expressions gives:
(q + f)(5) = 1
(f - q)(2) = -2
(q f)(4) = 9
(f /q)(0) = 1
How to use the graph to evaluate the function expressions?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
From the graph, when c = 5, q(5) = 0, f(5) = 1. Thus:
(q + f)(5) = 0 + 1 = 1
From the graph, when c = 2, f(2) = 0, q(2) = 2. Thus:
(f - q)(2) = 0 - 2 = -2
From the graph, when c = 4, q(4) = 3, f(4) = 3. Thus:
(q f)(4) = 3 * 3 = 9
From the graph, when c = 0, f(0) = 4, q(0) = 4. Thus:
(f /q)(0) = 4/4 = 1
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Box plot pls answer what is the outlier and a box plot represents the data excluding the outlier
Answers
Answer: The outlier is $95 and the plot is D.
Step-by-step explanation:
An outlier is the data value that's much larger or much smaller than the other data values. Here, that is $95.
Excluding this value, our smallest is $15 and the largest is $60. We plot a dot at both of these points.
The middle dot is the median. To find this, we will arrange the values in order and find the middle value. (We are excluding $95.) After doing this process, we see the middle dot is at 39.
$15, $20, $38, $60, $45, $40, $35, $50
$15, $20, $35, $38, $40, $45, $50, $60
----, ----, ----, $38, $40, ----, ----, ----
[tex]38 + 40 = 78, \;\;78 / 2\;\;\boxed{= 39}[/tex]
This means we have dots at 15, 39 and 60, leading us to answer D.
1 The difference between the simple interest and compound interest on a sum put out for 2 years at 5% was 6.90 .find the sum
Answers
so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]
now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90
[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]
2 Δ Δ Δ Δ Δ
Δ.
57. If t is any real number, which of the following
statements must be true?
A. -t <0
B. -t
C. -t=t
D. ts|-t
E. (-t)2 = -12
58. Let a and h be positive real num
Answers
When t is any real number, the true statements will be:
A. -t < 0:
B. -t = 0
E. (-t)^2 = -t^2
How to get the true statementsIf t is any real number, then the following statements are true:
A. -t < 0: This statement is true if t > 0, and false if t <= 0.
B. -t = 0: This statement is true if t = 0, and false if t ≠ 0.
C. -t = t: This statement is false for all real numbers t, since the negative of any non-zero real number is not equal to the original number.
D. t|-t: This statement is false for all real numbers t, since the absolute value of any real number is non-negative.
E. (-t)^2 = -t^2: This statement is true for all real numbers t, since squaring a real number gives a non-negative result. Note that the negative sign in front of the square is distributive and can be moved inside the square.
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Select the graph of y = 2 sinz+2
O A
O
2₁
0
24
0
KIN
Inter
R
te
#
3m
1月1~
2
Ad
3m
285
Alo
2t
M
Answers
The graph of y = 2 sin(x) + 2 is given by the following option:
Graph A.
How to graph the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function in this problem has an amplitude of 2, meaning that before the vertical shift, it oscillates between -2 and 2.
Due to the vertical shift, the function is going to oscillate between 0 and 4, with a period of 2π and no phase shift, crossing the midline of y = 2 at the origin, hence Graph A is the correct graph.
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Please Explain and solve this problem. What trigonometric function would you use based upon the given information in the triangle shown below? ASAP
Answers
To solve the problem we would use tangent as a trigonometric function and find the unknown value.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
From the given triangle we observe that the given values are:
Angle B, side a and side b.
To find any of the unknows in the three we use the trigonometric function tangent.
Tan α = opposite side / adjacent side
For the given figure:
Tan B = b / a
Hence, to solve the problem we would use tangent as a trigonometric function and find the unknown value.
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write an absolute value inequality for each length x with the given tolerance
1. a length of 4.2 cm with a tolerance of 0.01 cm
2. a length of 3.5 cm with a tolerance of 0.2 cm
show work pls
Answers
The absolute value inequalities for the different lengths are
1) 4.19 ≤ x ≤ 4.21
2) 3.3 ≤ x ≤ 3.7
What is an absolute value inequality?
The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|.
An expression using absolute functions and inequality signs is known as an absolute value inequality. One example of an absolute value inequality with a larger than symbol is the statement |x + 3| > 1.
1) length x = 4.2 cm with a tolerance of 0.01 cm
Absolute value inequality is:
|x - 4.2| ≤ 0.01
This can be written as:
x - 4.2 ≤ 0.01x ≤ 4.21
x - 4.2 ≥ - 0.01x ≥ 4.19
2) length x = 3.5 cm with a tolerance of 0.2 cm
Absolute value inequality is:
|x - 3.5| ≤ 0.2
This can be written as:
x - 3.5 ≤ 0.2x ≤ 3.7
x - 3.5 ≥ - 0.2x ≥ 3.3
Therefore the absolute value inequalities for the different lengths are
1) 4.19 ≤ x ≤ 4.21
2) 3.3 ≤ x ≤ 3.7
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*Please help, I will mark brainest*
A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 532,000 gallons. Tank card with three different carrying capacities are available: 7,000 gallons, 14,000 and 28,000. How many of each type of tank car should be leased?
Fill in the blank: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1=_t+(_), x2=_t+(_) & x3=t
Answers
Answer:
Let's call the number of 7,000 gallon tank cars "x1", the number of 14,000 gallon tank cars "x2", and the number of 28,000 gallon tank cars "x3".
We can write the following constraints based on the total carrying capacity of the fleet:
7,000x1 + 14,000x2 + 28,000x3 = 532,000
x1 + x2 + x3 = 25
x1, x2, x3 >= 0 (since we can't have a negative number of tank cars)
This is a linear programming problem, which can be solved using simplex method or the graphical method.
By using the graphical method, we find that there are multiple optimal solutions. For example, one solution is x1 = 11, x2 = 7, and x3 = 7. This means that the manufacturer should lease 11 7,000 gallon tank cars, 7 14,000 gallon tank cars, and 7 28,000 gallon tank cars to meet the total carrying capacity requirement of 532,000 gallons.
So, the answer to the question is: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1 = 11 + 7t, x2 = 7 + 7t, and x3 = 7 + 7t.
The answer to this problem
Answers
Answer:
A. (f+g)(x)=-2x^2-2x+8
Step-by-step explanation:
You combine like terms by adding
Find all real numbers z for which the equation (z-5)x^2-zx+5=0 has exactly one real solution.
Answers
By making the discriminant equal to zero, we can see that the quadratic equation has one real solution only for z = 10.
For which values of z the quadratic equation has only one real solution?For a general quadratic equation:
a*x^2 + b*x + c = 0
We define the discriminant as:
D = b^2 - 4ac
The quadratic equation will have only one real solution only if the discriminant is equal to zero.
Here the quadratic is:
(z - 5)*x^2 - z*x + 5 = 0
Then the discriminant is:
(-z)^2 - 4*5*(z - 5)
And that must be equal to zero, then we need to solve:
z^2 - 20*(z - 5) = 0
z^2 - 20z + 100 = 0
Using the quadratic formula we will get:
[tex]z = \frac{20 \pm \sqrt{(-20)^2 - 4*1*100} }{2} \\\\z = \frac{20 \pm 0}{2} \\\\z = 10[/tex]
So the quadratic equation has one real solution only for z = 10.
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