The value of the Fourier cosine series at x = 2 is -3/8.
a0 = -3/4 for 0 ≤ x < 2 and a0 = 1/4 for 2 ≤ x ≤ 4.
The value of the Fourier cosine series at x = -3 is -3/8.
To compute the Fourier cosine coefficients for the function f(x) = {0 - (4 - x) for 0 ≤ x < 2, 4 - x for 2 ≤ x ≤ 4}, we need to evaluate the following integrals:
a0 = (1/2L) ∫[0 to L] f(x) dx
an = (1/L) ∫[0 to L] f(x) cos(nπx/L) dx
where L is the period of the function, which is 4 in this case.
Let's calculate the coefficients:
a0 = (1/8) ∫[0 to 4] f(x) dx
For 0 ≤ x < 2:
a0 = (1/8) ∫[0 to 2] (0 - (4 - x)) dx
= (1/8) ∫[0 to 2] (x - 4) dx
= (1/8) [x^2/2 - 4x] [0 to 2]
= (1/8) [(2^2/2 - 4(2)) - (0^2/2 - 4(0))]
= (1/8) [2 - 8]
= (1/8) (-6)
= -3/4
For 2 ≤ x ≤ 4:
a0 = (1/8) ∫[2 to 4] (4 - x) dx
= (1/8) [4x - (x^2/2)] [2 to 4]
= (1/8) [(4(4) - (4^2/2)) - (4(2) - (2^2/2))]
= (1/8) [16 - 8 - 8 + 2]
= (1/8) [2]
= 1/4
Now, let's calculate the values of the Fourier cosine series at the given points:
x = 2:
The Fourier cosine series at x = 2 is given by a0/2 + ∑[n=1 to ∞] an cos(nπx/4).
For x = 2, we have:
a0/2 = (-3/4)/2 = -3/8
an cos(nπx/4) = 0 (since cos(nπx/4) becomes zero for all values of n)
x = -3:
The Fourier cosine series at x = -3 is given by a0/2 + ∑[n=1 to ∞] an cos(nπx/4).
For x = -3, we have:
a0/2 = (-3/4)/2 = -3/8
an cos(nπx/4) = 0 (since cos(nπx/4) becomes zero for all values of n)
x = 5:
The Fourier cosine series at x = 5 is given by a0/2 + ∑[n=1 to ∞] an cos(nπx/4).
For x = 5, we have:
a0/2 = (1/4)/2 = 1/8
an cos(nπx/4) = 0
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I WILL GIVE BRAINLY A dairy farmer wants to mix a 60% protein supplement and a standard 20% protein ration to make 1400 pounds of a high-grade 40% protein ration. How many pounds of each should he use?
The number of pounds of 60% protein and 20% protein supplement used is 700 and 700 pounds respectively.
Simultaneous equationlet
Pounds of 60% protein used = xPounds of 20% protein used = yx + y = 1400
0.60x + 0.20y = 1400×0.40
0.60x + 0.20y = 560
From (1)
x + y = 1400
x = 1400 - y
Substitute into (2)
0.60x + 0.20y = 560
0.60(1400 - y) + 0.20y = 560
840 - 0.60y + 0.20y = 560
- 0.60y + 0.20y = 560 - 840
-0.40y = -280
y = -280/-0.40
y = 700 pounds
Recall,
x + y = 1400
x + 700 = 1400
x = 1400 - 700
x = 700 pounds
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I dont know how to do this
Answer:
Option C = 78,125Step-by-step explanation:
First prime factorize 135,
135 = 5×3×3×3
Now prime factorize 128,
128=2×2×2×2×2×2×2 = 2^7
the highest prime factor of 135 is 5,
Let 5 be x
the highest power of the lowest prime factor of 128 which is the power 2 is 7
Let 7 be y
According to the question x^y = 5^7
= 78,125A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress.
A weather balloon is 529 meters above the ground. Weather stations A and B are on the ground to form a triangle. A horizontal line is drawn at the top of the triangle to form angle v on the left and angle w on the right. The angle formed with A is x and the angle formed with B is y. A vertical line is drawn from the weather balloon to the ground to form a right angle and split the distance between A and B into 2 parts. The distance from A to the vertical line is 229 meters, and the distance between the vertical line and point B is 347 meters.
Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.
x > y
v > x
w = y
y < v
v = w
x < w
A, C, D are correct. In this question the options that are correct are
x > yw = y y < vHow to solve for the correct statements in the questionWe have first with legs height to be =529 m and 229 m;
second with legs height =529 m and 347 m.
Then tan x = 529/229
tan y = 529/347
We can see that tanx > tany
Hence x> y
We have alternate angles in the question. This makes x=v, y=w
For D
x > y while x = v
This tells us that v>y
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Answer:
acd
Step-by-step explanation:
Green’s Sport Shop offers its salespeople an annual salary of $10,000 plus a 6% commission on all sales above $20,000. Every employee receives a Christmas bonus of $500. What are Mr. Cahn’s total earnings in a year in which his sales amounted to $160,000?
(A) $18,900
(B) $18,400
(C) $19,600
(D) $20,100
Answer:
A
Step-by-step explanation:
His commision was 0.06(160000-20000) = $8400.
His salary was $10,000.
His bonus was $500.
Adding these together, we get $18,900.
Find the difference. write your answer as a fraction in simplest form. 5/8-(-7/8)
Answer:
1 1/2
Step-by-step explanation:
When you are subtracting a negative number is is the same as adding a positive. So the problem is really 5/8 + 7/8, since the denominators are the same, just add the numerators to get 12/8 divide the top and bottom by 4 to get 3/2 or 1 1/2, if I divide 3 by 2.
Find the side length of the equilateral triangle whose area is the square root of 3 cm2
Here, Given
Area of Equilateral triangle = 3cm2
therefore, we know;
Area of Equilateral triangle =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]
so,
3 =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]
3÷( [tex]\sqrt{3}[/tex]÷4) = [tex]a^{2}[/tex]
2.63 cm = a .
The area of an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of the shape is the number of unit squares that fit inside.
Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.
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When researching for a business report, you should find reliable sources whose information is accurate, unbiased, and .
Answer:
Creditable
Step-by-step explanation:
Could also be:
up-to-date
Theresa needs twice as many feet of wood as samuel how many pieces of wood does teresa need?
Using addition or multiplication, Teresa has twice a number of wood as Samuel.
According to the question,
Teresa needs twice as many feet of wood as Samuel in order to find the number of pieces of wood Teresa need only if we add the number Teresa has by itself or multiply it by 2.
Hence, we need to do only multiply it by 2
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Solve: 5(x + 2) = 3x + 5
Answer:
Exact Form: x = -5/2
Decimal Form: x = -2.5
Mixed Form: x = 2 1/2
Answer:
Step-by-step explanation:
5(x+2)=3x+5
5x+10=3x+5
5x=3x-5
2x=-5
x=-0.4
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the
resulting statements true.
(a) B __ A (b)C __ A (c) B __ C (d) ∅ __ B (e) C __C
Answer:
Answer
Step-by-step explanation:
(a) B ⊄ A (b) C ⊂ A (c) B ⊄ C (d) ∅ ⊂ B (empty set is an element of any set)
(e) C ⊂ C (reflexitivity).
Find the smallest number by which the following numbers should be multiplied to obtain a perfect cube. (a) 3087 (b) 2560
Check each number's prime factorization, then add any factors necessary to make each one a cube.
(a) 3
[tex]3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3[/tex]
(b) 25
[tex]2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3[/tex]
can someone please help me
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{3\pi }{4}[/tex] is an angle in the second quadrant where sin > 0 and cos < 0
cos([tex]\frac{3\pi }{4}[/tex] )
= cos (π - [tex]\frac{3\pi }{4}[/tex] )
= - cos ([tex]\frac{\pi }{4}[/tex] )
= - [tex]\frac{\sqrt{2} }{2}[/tex]
and similarly
sin ([tex]\frac{3\pi }{4}[/tex] )
= sin ([tex]\frac{\pi }{4}[/tex] )
= [tex]\frac{\sqrt{2} }{2}[/tex]
Check all that apply
X^2+7x-8
Answer:
x = -8, 1.
Step-by-step explanation:
x^2 + 7x - 8 = 0
(x + 8)(x - 1) = 0
x = -8, 1.
Answer:
-8 and 1
Step-by-step explanation:
Quadratic expression.
A quadratic expression is an expression with 2 as the highest power of the unknown.
Solving the question:
[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation ℎ()=−2+10+9.5 h ( x ) = − x 2 + 10 x + 9.5 , where x is the number of feet away from the sprinkler head (along the ground) the spray is.
Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.
How to determine the maximum height?For any quadratic equation with a parabolic curve, the axis of symmetry is given by:
Xmax = -b/2a
Xmax = -10/2(-1)
Xmax = 5.
Thus, the maximum height on the vertical axis is given by:
h(x) = -x² + 10x + 9.5
h(5) = -(5)² + 10(5) + 9.5
h(5) = -25 + 50 + 9.5
h(5) = 34.5 feet.
Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.
Also, the spray reaches all the way to the ground at about:
Maximum distance = √34.5 + 5
Maximum distance = 10.87 feet.
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Complete Question:
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.
1. The irrigation system is positioned____ feet above the ground to start.
2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
3. The spray reaches all the way to the ground at about_____ feet away
Writing equivalent ratios and ordered pairs Gallons 1 2 3 Quarts 4 8 12 which ordered pairs represents the equivalent ratios in the table? (1,2) (1,4) (2,8) (4,1) (3,12)
Step-by-step explanation:
gallons to quarts have the ratio 1:4.
there are 4 quarts in a gallon (hence the name of quarts by the way).
so, the question is really, which order pair have also a 1:4 ratio between x and y ?
(1, 4)
(2, 8)
(3, 12)
the (4, 1) would represent a 4:1 ratio.
and as you know, 4/1 is different to 1/4.
a ratio is nothing else than a fraction. just the "whole" is different.
the pure fraction 1/4 means that the whole is 4/4, has 4 times 1/4.
a ratio 1:4 (you can also write as 1/4) means that the whole has 5 (1+4) parts.
other than that they are compared and calculated with the same way as normal fractions.
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Mrs. Lindy is purchasing notebooks for her students. She spends $52 on n notebooks. Each notebook costs $3.25
Select the equation that matches this situation.
Answer:
B. 52= 3.25n
Step-by-step explanation:
Unit price multiplied by quantity equals total. So, each notebook cost $3.25 and she buys 'n' notebooks.
She totally spends $52.
In conclusion, 3.25 (unit price × n [quantity]) = 52.
And that is.. 52 = 3.25n.
<3
Answer:
B
Step-by-step explanation:
Let's think about what does the given info mean.
Because of n notebooks, she spent $52
One notebook is $3.25.
So 3.25n = 52
Take it this way if you don't understand
Let's say I spent 4$ on two (2) pens
What's the value of one pen?
We want to find the value of one pen and then multiply it by 2, to get 4$
So we normally would do 4/2
However, to set up an equation, we would create
v (value of one pen) x 2 (pens) = 4$ (cost)
v = 4$/2 = 2$
Determine the missing side of a rectangle with an area
of 144 cm² and a width of 8 cm. Please show your work.
O
Answer:
Length is equal to 18
Step-by-step explanation:
The formula for finding the area(A) of a rectangle in Length(L) times width(W): A=(W)(L). If we plug in the given information into the equation, you will get 144=(8)(L). From there we solve for L.
144 = (8)(L)
144/8 = (8)/8 (L)
18 = L
Question 4 of 18
in a group of 60 students, the probability that at most 40 of them like to swim
is 67%. what is the probability that at least 41 of them like to swim?
a. 28%
b. 33%
c. 74%
d. 44%
submit
Answer b. The probability that at least 41 of them like to swim is 33%.
Solution:
The probability of an event is always 1 or 100%
The probability of at most 40 of them like to swim is 67% = 0.67
The probability of at most 40 not swimming = 1 - 0.67 = 0.33
Hence the probability of at least 41 people swimming is 33%.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half.Learn more about Probability brainly.com/question/24756209
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Identify the solutions to the quadratic equation 6x^2+x-1=0
Answer:
1/3 and -1/2
Step-by-step explanation:
You can use the factoring method to identify the solutions of x
6x^2+x-1
2 numbers have to multiply to 6 and subtract to 1 because x is the same as 1x
So, you get 3x and 2x
since you know that -1x1 is -1 you will get
(3x-1)(2x+1)=0
Now, since (3x-1) and (2x+1) multiply to get 0, if either (3x-1) or (2x+1) is 0 the statement will be valid
3(1/3)-1=0
2(-1/2)+1=0
So, your answers are 1/3 and -1/2
Solve the system of equations 4x+5y=-14 and -5x-8y=10 by combining the equations.
The solution of the system is:
x = 62/7
y = 30/7
How to solve the system of equations?
Here we have the system:
4x + 5y = -14
-5x - 8y = 10
To solve it by combining the equations, we need to try to remove one of the variables.
If we take the sum of 5 times the first equation and 4 times the second equation we get:
5*(4x + 5y) + 4*(-5x - 8y) = 5*(-14) + 4*10
If we simplify that we get:
20x + 25y - 20x - 32y = -30
-7y = -30
Now we can solve that for y:
y = -30/-7 = 30/7
Now to get the value of x, we can replace the value of y in any of the given equations:
Using the first one:
4x + 5y = -14
x = (-14 - 5y)/4
x = (-14 - 5*30/7)/4 = (-98/7 - 150/7)/4 = 248/28 = 124/14 = 62/7
The solution of the system is:
x = 62/7
y = 30/7
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The table shows your height on a water slide at various time intervals
1. Find the average rate of change in a riders height between 1 and 3 seconds
2. Find the average rate of change in a riders height between 0 and 5 seconds
3. What is another word for rate of change in this situation?
Time(s) Height (ft)
0 120
1 90
2 60
3 30
4 0
5 0
1. The average rate of change in a riders height between 1 and 3 seconds -30 ft/s
2. The average rate of change in a riders height between 0 and 5 seconds -24 ft/s
3. Another word for rate of change in this situation is speed
What is speed?Speed is defined as the rate of change of the distance travelled with time. Mathematically, it can be expressed as:
Speed = distance / time
With the above idea, we can obtain the answers to the question given above.
1. How to determine the rate of change between 1 and 3 secondsChange in height = 30 - 90 = -60 ftChange in time = 3 - 1 = 2 sRate of change =?Rate = Change in height / change in time
Rate = -60 / 2
Rate = -30 ft/s
2. How to determine the rate of change between 0 and 5 secondsChange in height = 0 - 120 = -120 ftChange in time = 5 - 0 = 5 sRate of change =?Rate = Change in height / change in time
Rate = -120 / 5
Rate = -24 ft/s
3. what is another word for rate of change?From the definition of speed given above, we can say that: another word for rate of change is speed
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Theo earns a base salary plus commission. At the end of September, he was paid $3,835.25 based on his monthly sales of $12,850. At the end of October, he earned $3,641 based on $9,875 in sales. What was Theo’s base salary?
Theo's base salary using a simultaneous equation approach is $2,996.22 .
In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary
Bear in mind that total earnings are determined as base salary plus commission
Let X be the base salary
Let R be the rate of commission
commission =sales*rate of commission
When earnings were $3,835.25 and sales is $12,850, we have the below equation:
X+(12,850*R)=3,835.25
X+12850R=3,835.25 .................... equation (1)
When earnings were $3,641 and sales is $9,875, we have the below equation:
X+(9,875*R)=3641
X+9875R=3641 ......................... equation (2)
subtract equation 2 from 1
2975R=194.25
R=194.25/2975
R=commission rate=6.52941176470588%
substitute for R in equation 1 to arrive at X(base salary)
X+(12850*6.52941176470588%)=3,835.25
X=3,835.25-(12850*6.52941176470588%)
X=base salary=$2,996.22
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if you buy a computer game for $54, you have a $5 mail-in rebate, and you pay 8% sales tax, how much does your game cost?
Answer:53.32
Step-by-step explanation:
$54 retail price
sales tax 8%
$54x8%= 4.32
sales tax is $4.32
$54+$4.32= $58.32
total with tax is $58.32
$58.32-$5= 53.32
Shawnice Smith
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Addition Word Problems
Directions: Solve the following addition word problems.
MATH
1. 100 students participated in a sports card show in the school gym. Brad brought his
entire collection of 2,000 cards to show his friends. He had 700 football cards and 400
basketball cards. If the rest of his cards were baseball cards, how many baseball cards
did he bring with him?
Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
The student with the correct list of steps is student B
How to determine the correct student?The list of steps is to create a line parallel to line AB
Both students are correct in step (1).
However, the step (2) of student A is incorrect.
This is so because, the student did not provide how points C and G are created
Hence, the student with the correct list of steps is student B
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Complete the equation describing how x and y are related.
X | Y
0 | -1
1 | -1.5
2 | -2
3 | -2.5
4 | -3
5 | -3.5
Y= [?]x + [?]
What number is the height changing by each minute
The height is changing by 0.5 each minute
How to determine the number?The question implies that we calculate the slope of the table
From the table of values, we have the following points
(0, 150) and (1, 150.5)
The slope is then calculated as:
m = (y2 - y1)/(x2 -x1)
This gives
m = (150.5 - 150)/(1 - 0)
Evaluate
m = 0.5
Hence, the height is changing by 0.5 each minute
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A lab received and produce a sample of plutonium which has a half life of 138 days suppose you have an initial sample of 52 g which equation can be used to calculate the remaining amount of the sample “t” days after being processed by the lab
The remaining amount of the sample after 't' days would be 51. 74g
How to determine the amountWe have the formula for amount to be;
A = Ao × (1/2)^ t/t^1/2
Where
t1/2 = half -life = 138 days
t = 1
Ao = 52g
A = Amount after decay
Substitute into formula
A = 52 × (1/2) ^ 1/138
A = 52 ×
[tex] { \frac{1}{2} }^{0.00724} [/tex]
A = 52 × 0. 9950
A= 51. 74 g
Thus, the remaining amount of the sample after 't' days would be 51. 74g
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I’ve tried everything and yet don’t understand this
Snow reaches at a 15 inches after 16 hours. and 8 inches melt in next 6 hours.
According to the statement
we have a given that there was 1 inch snow on the ground before the snowstorm starts.
then snow fell at constant rate of 3 inches every 2 hours until the snow level reaches at 12 inch had fallen
It means after that there was 13 inch snow on the ground.
and in 1 hour only 1.5 inches snow increases
and if snow takes 2 hours to increase at 3 inches then
it takes 10 hours to reach at 12 inches.
So, snow falls for 10 hours to increase at 12 inches.
And then the snow falls at constant rate of 1 inch per hour for 2 hours.
It means now snow reaches at a 15 inches after 16 hours.
Then sun melt the snow at a 4 inches per 3 hours and sun came for 6 hours then
it means now the level of snow reduced and came at the 7 inches.
because sun reduced 8 inches snow in 6 hours.
So, this is the data collected by a person.
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PLEASE FIND X
NOTE: Angles not necessarily drawn to scale.
x =x=x, equals
\Large{{}^\circ}
∘
degrees
Check the picture below.