Use graphing calculator to solve system the equations in the interval from 0+2pi.round to the nearest hundredth. 7cos 2t=3
Answers
The solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.
How to solve trigonometric equations
Trigonometric functions are periodic functions, cosine function has a standard period of 2π radians. There are two approaches to solve the expression given, an analytical one and a graphical one. Now we proceed to show each approach:
Analytical method
Now we proceed to apply algebraic handling and inverse trigonometric functions to solve the expression for t:
7 · cos 2t = 3
cos 2t = 3/7
2 · t = cos⁻¹ (3/7)
There are two solutions:
2 · t₁ ≈ 0.359π + 2π · i ∨ 2 · t₂ ≈ 1.641π + 2π · i
t₁ ≈ 0.180π + π · i ∨ t₂ ≈ 0.821π + π · i
t₁₁ ≈ 0.180π ∨ t₁₂ ≈ 1.180π ∨ t₂₁ ≈ 0.821π ∨ t₂₂ ≈ 1.821π
The solutions of the trigonometric equations in [0, 2π] are approximately 0.18π, 0.82π, 1.18π and 1.82π.
Graphical approach
First, we add the definition of the following two functions (f(x) = 7 · cos 2t and g(x) = 3) and plot in the calculator through a graphing tool. The solutions of this trigonometric function are the points of intersection of the two functions.
According to the image attached below, the solutions of the trigonometric equation are approximately 0.56, 2.58, 3.71 and 5.72, all in concordance with the results found beside the analytical approach.
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Related Questions
A function has a constant halving time. What type of function does this represent?
A. Decreasing linear
B. Exponential decay
C. Exponential growth
D. Increasing linear
Answers
[tex]A(t) = A_{0} ( \frac{1}{2} )^ \frac{t}{h} [/tex]
Where: A₀ is the initial amount
h is the half life time or the halving time.
t is the time
A(t) the amount that remains at time t
The previous function represents an Exponential decay function.
so, The correct answer is option B. Exponential decay
Answer:
b
Step-by-step explanation:
The first painter can finish a paint job in 2 hours. The second painter can finish the same job in 8 hours. How long would it take them to finish the job if they were working together?
Answers
If two painters who can individually finish a painting job in 2 hours and 8 hours respectively work together, they will be able to finish the job in 1.6 hours.
Explanation:The question is about determining how fast two painters can finish a paint job if they work together, given their individual working speeds. This is related to the field of mathematics and specifically to the concept of rates. The first painter can finish the job in 2 hours, so, his rate of working is 1/2 of the job per hour. The second painter can finish the job in 8 hours, so his rate of working is 1/8 of the job per hour. When they work together, their rates are added together. So, the combined rate of both painters is 1/2 + 1/8 = 5/8 of the job per hour. To find out how long it would take them to finish the job together, we take the reciprocal of this, which gives us 8/5 or 1.6 hours.
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Working together, the two painters would take approximately 1.6 hours or 1 hour and 36 minutes to finish the job.
Explanation:To find how long it would take the two painters to finish the job together, we can use the concept of work rates. The first painter can finish the job in 2 hours, so they have a work rate of 1/2 job per hour. Similarly, the second painter can finish the job in 8 hours, so their work rate is 1/8 job per hour.
When the two painters work together, their combined work rate is the sum of their individual work rates. So, the total work rate when they work together is 1/2 + 1/8 = 5/8 job per hour.
To find the time it would take them to finish the job, we can use the formula time = 1 / work rate. Substituting in the combined work rate of 5/8 job per hour, we get:
time = 1 / (5/8) = 8/5 = 1.6
Therefore, it would take the two painters approximately 1.6 hours or 1 hour and 36 minutes to finish the job if they were working together.
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Julio considers the reduction of the triangle.
What is the correct cross product that he should use to solve for the missing dimension?
(8)(12) = 21x
(8)(21) = 12x
(12)(8) = 12x
(12)(21) = 8x
Answers
Therefore, we can use the following relationship:
(12) / (21) = (8) / (x)
From here, we can clear to know the value of the incognita x.
Answer:
the correct cross product that should be used to solve for the missing dimension is:
(12) / (21) = (8) / (x)
Answer:
(12)(21) = 8x or d
Step-by-step explanation:
What is the excluded value of the rational expression: x-4/6 divided by x+1/7?
A. -1
B. 4
C. -7
D. None of the above
Answers
((x-4) / (6)) / ((x + 1) / (7))
Rewriting we have:
7 (x-4) / 6 (x + 1)
We observe that the expression is not defined for the values where the denominator is equal to zero.
We have then:
x + 1 = 0
x = -1
Answer:
The excluded value of the rational expression is:
A. -1
If EFGH is a parallelogram, what is the value of x?
Answers
so we have: 34 + (4x-2) = 180
now we can solve for x
34 + 4x -2 = 180
simplify the left side by subtracting 2 from 34
32+4x =180
subtract 32 from each side:
4x = 148
divide both sides by 4 to get x
x = 148 / 4
x = 37
The answer is B
A quadrilateral in which opposite sides are parallel is called a parallelogram. The value of x is 37.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, any two adjacent angles are always supplementary. Therefore, we can write the sum of the two angles as,
(4x-2)° + 34° = 180°
4x - 2 + 34 =180
4x + 32 =180
4x = 180 - 32
4x = 148
x = 37
Hence, the value of x is 37.
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YOOOOOO!!!!!!NEEEED HELP!!!WILL GIVE BRAIN!!!!!!PART2!!!!
Answers
f (x) = x ^ 3
We have the following transformation of functions:
Expansions and vertical compressions:
To graph y = a * f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a. (It lengthens)
If 0 <a <1, the graph of y = f (x) is compressed vertically by a factor a. (Shrinks)
We have then:
h (x) = ((1/4) x) ^ 3
h (x) = (1/64) * (x) ^ 3
h (x) = (1/64) * f (x)
0 <1/64 <1
The graph f (x) shrinks,
Answer:
f (x) = x ^ 3
option A
Find the approximate surface-area-to-volume ratio of the Moon. The radius of the Moon is 1,080 miles. A. 0.0009 B. 0.0028 C. 360 D. 3,240
Answers
surface area of a sphere=4*pi*r²
volume of a sphere=(4/3)*pi*r³
the ratio surface area to volume
=4*pi*r²/[(4/3)*pi*r³]-----> 3/r----> 3/1080-----> 0.0028
the answer is
the option B. 0.0028
How to calculate 95th percentile from mean and standard deviation of an exponential distribution?
Answers
0down voteaccepted
The qthqth quantile of a random variable XX is the value xx such that
Pr[X≤x]=q.Pr[X≤x]=q.So in your case q=0.25q=0.25, and0.25=Pr[X≤x]=FX(x)=1−e−x/β.0.25=Pr[X≤x]=FX(x)=1−e−x/β.This gives us e−x/4=0.75e−x/4=0.75, orx=−4log0.75≈1.15073.x=−4log0.75≈1.15073.This assumes that the parametrization of the exponential distribution is by scale; i.e., if β=4β=4 this means E[X]=β=4E[X]=β=4, rather than by rate--in which case E[X]=1/β=1/4E[X]=1/β=1/4.A number is less than 20 units away from 7 on the number line. What numbers are within these parameters? Choose the inequality that represents the situation.
Answers
Answer:
For the pull out menu it was B
Step-by-step explanation:
How much does the school have to charge for each candy bar to make a profit of 10 dollars per box?
Answers
A school purchases boxes of candy bars.
• Each box contains 50 candy bars.
• Each box costs $30.
How much does the school have to charge for each candy bar to make a profit of
$10 per box?
step 1
charge for each box $10
so
the new box cost $10+$30=$40
step 2
divide the new box cost to total candy bars
$40/50=$0.80
the answer is
the school have to charge for each candy bar $0.80
What is -2(3x+12y-5-17x-16y+4) simplified?
-40x+8y+2
28x+8y+2
28x+6y+2
-28x-8y+2
Answers
Combine like terms:
[tex]=-2(-14x-4y -1)[/tex]
Distribute 02:
[tex]=28x + 8y + 2[/tex]
A simplified expression involves rewriting an expression in a simpler form
The simplified expression is: 28x+8y+2
The expression is given as:
-2(3x+12y-5-17x-16y+4)
Collect like terms
-2(3x-17x+12y-16y-5+4)
Evaluate the like terms
-2(-14x-4y-1)
Open the bracket
28x+8y+2
Hence, the simplified expression is: 28x+8y+2
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y=-6x^2+100x-180
x=selling price of each soccer ball
y=daily profit from soccer balls
The vertex is located at (8.33, 236.67). What does this point represent in context?
Answers
[tex]y = 236.67[/tex]
And this happens when the selling price of each soccer ball is:
[tex]x = 8.33[/tex]
So if you want to get the best daily profit, this is the price you must sell each soccer ball.
Refer the below solution for better understanding.
Step-by-step explanation:
Given :
[tex]y = -6x^2+100x-180[/tex]
where,
x = selling price of each soccer ball.
y = daily profit from soccer balls.
Solution :
The vertex shows the maximum value of y and x.
y = 236.67 shows the maximum daily profit and this happens when selling price of each soccer ball is x = 8.33.
Refer the below graph for better understanding.
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How would I find the diameter?
Answers
Help Please
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
First picture is how they want you to put the answers in & the second one is the grid with the numbers
Answers
According to the Venn diagram, 4 people own a car and a truck. 15+4=19 people own a car, and 4+9=13 people own a truck. This leaves us 36-(15+4+9)=36-28=8 people that do not own a car or a truck.
We put 8 in the Don't Own a Truck row under the Don't Own a Car column.
We put 4 in the Own a Truck row under the Own a Car column.
We put 19 in the Total row under the Own a Car column.
We put 15 in the Don't Own a Truck row under the Own a Car column.
We put 13 in the Own a Truck row under the Total column.
We put 9 in the Own a Truck row under the Don't Own a Car column.
We put 23 in the Don't Own a Truck row under the Total column.
We put 8 in the Down Own a Truck row under the Don't Own a Car column.
We put 36 in the Total row under the Total column.
We put 17 in the Total row under the Don't Own a Car column.
What is the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters? Round the answer to the nearest square meter.
A. 1,100 square meters
B. 1,112 square meters
C. 2,507 square meters
D. 2,605 square meters
Answers
[surface area of the cone]=pi*r²+pi*r*l
where
r is the radius
l is the slant height
l²=h²+r²
h=43 m
r=14/2---> 7 m
l²=43²+7²----> l²=1898--------> l=43.57 m
[surface area of the cone]=pi*7²+pi*7*43.57----> 1111.53 m²----> 1112 m²
the answer is the option
B. 1,112 square meters
What is the focus of the parabola? [tex]y= \frac{1}{4} x^{2} -x+3[/tex]
Enter your answer in the boxes.
(__ , __)
Answers
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=1/4x²−x+3
where
a=1/4
b=-1
c=3
the coordinates of the focus are
(-b/2a,(1-D)/4a)
where D is the discriminant b²-4ac
D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> 2
y coordinate of the focus
(1-D)/4a------> (1+2)/(4/4)---> 3
the coordinates of the focus are (2,3)
Please help me with 8, 9, and 10 thanks! Show work too
RANDOM ANSWERS WILL BE MODERATED!
Answers
8. hypotenuse / (short side) = 25/x = x/9
x² = 25*9 = 5²×3²
x = √(5²×3²) = 5*3 = 15
9. (long side) / (short side) = x/7 = 9/x
x² = 7*9
x = √(9*7) = 3√7
10. (short side) / (long side) = x/48 = 48/64
x = 48²/64 = 36
The size of a television is given by the length ofthe diagonal of the screen. the ratio of the height to the width of wide flat-screen tv is 8:15. find expressions for the width and height of a wide-screen tv in terms of the length of its diagonal.\
Answers
suppose:
width=8x
length=15x
let d be the diagonal
thus; using Pythagorean theorem:
d^2=(8x)^2+(15x)^2
=64x^2+225x^2
=289x^2
d=17x
or x=d/17
width=8x=8d/17
length=15x=15d/17
O'Farrell offers 2 different after school clubs. The Ukulele club has 30 students and attendance is increasing by 6 students per month. MESA has 45 students and attendance is increasing by 3 students per month. After how many months will there be the same number of students in each club?
Answers
months / students
0 30 45
1 36 48
2 42 51
3 45 54
4 51 57
5 57 60
6 63 63
Find the slope and the y-intercept of the line with equation y=-5/4x+5
Answers
Therefore, your slope, m, is -5/4 and your y-intercept, b, is 5.
Tom caught 4 fish and his son caught 12 fish.The number of fish that Tom caught was what percent of the total number of fish?
Answers
tom % of fish = 4 divided by 16 = 0.25 =25%
2. How many real number solutions are there to the equation 0 = –3x² + x – 4? (1 point)
Answers
[tex] - 3 {x}^{2} + x - 4[/tex]
finding the determinant will tell us how many solutions
the determinant is
[tex] {b}^{2} - 4ac[/tex]
so we have
a=-3
b=1
c=-4
so the determinant is
[tex] {1}^{2} - 4( - 3)( - 4) = 1 - 48 = - 47[/tex]
now we know if d=0 there is 1 real solution if d<0 there are complex solutions and if d>0 there are 2 real solutions.
since d=-47<0 there are no real solutions only complex ones
Final answer:
The equation has no real number solutions.
Explanation:
To find the number of real number solutions to the equation 0 = –3x² + x – 4, we can use the discriminant of the quadratic equation. The discriminant is calculated as b² - 4ac, where a, b, and c are coefficients of the equation in the form ax² + bx + c = 0. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. And if the discriminant is negative, the equation has no real solutions.
In this case, a = -3, b = 1, and c = -4. Let's calculate the discriminant:
b² - 4ac = (1)² - 4(-3)(-4) = 1 - 48 = -47
Since the discriminant is negative, the equation 0 = –3x² + x – 4 has no real number solutions.
After creating a new email address, Gareth initially receives n emails per year. The number of emails received increases by 7% each year after that. The following expression represents the number of emails received after x years.
x(1 + 0.07)^x
Which of the following best represents the expression?
the product of the number of emails received initially and one plus the factor of increase raised to the number of years that the amount of emails Gareth received has increased
the product of the number of emails received initially and the factor of decrease raised to a period of x years
the product of the number of emails received initially and one plus the factor of decrease raised to the number of years that the amount of emails Gareth received has increased
the product of the number of emails received initially and the factor of increase raised to a period of x years
Answers
The formula to find the number of emails x years after making the email account is:
[tex]N(x)= N_{o}(1+0.07)^{x} [/tex]
where, [tex] N_{o} [/tex] is the number of emails in the first year.
So, the number of emails x years after creating the account is the product of [tex] N_{o} [/tex], the number of emails in first year, and (1+0.07)^x, the sum of 1 and rate of increased raised to the number of years.
Hence option A is the correct answer.
Answer:
The correct answer is Option A.
Step-by-step explanation:
Write each of the equations below in standard form (i.e. y = ax^2+bx+c y=ax 2 +bx+c):
a. y = 3(x-7)(x+4) y=3(x−7)(x+4)
b. y = 2(x-3)^2 + 5 y=2(x−3) 2 +5
c. y = -2(x+3)(x+5) y=−2(x+3)(x+5)
d. y = -3(x-4)^2 + 8y=−3(x−4) 2 +8
Answers
Hope it helps
Which value of h makes 10/8+h=9/3-2 a true statement?
Answers
What’s the answer for this question:)
Answers
f (x) = x + 4 if -4 <= x <3
f (x) = 2x-1 if 3 <= x <6
We observe that the function is defined from x = -4 (including it) to x = 6 (without including it).
Therefore, the domain of the function is:
[-4, 6]
Answer:
[-4, 6]
option 3
through how many radians does the minute hand of a clock turn in three hours?
•3π
•6π
•9π
Answers
180 degrees is 1π, so therefore it going around 3 full rotations(1080 degrees) it would be 6π
A bunch bowl is in the shape of a hemisphere. The top rim has a circumference of 116cm.
A) determine the volume of the punch bowl to the nearest cubic centimeter.
B) If there are 1,000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.
Answers
[tex]C=2\pi r[/tex]
[tex]116\:cm=2\pi r[/tex]
[tex]r=\frac{116}{2\pi }=18.462\:cm[/tex]
Part A
We can now compute for the volume of the hemisphere.
[tex]V=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{1}{2}\times \frac{4}{3}\pi \left(18.462\right)^3=13179\:cm^3[/tex]
Part B
We just need to convert the volume into its corresponding gallons
[tex]13179\:cm^3\times \frac{1\:Liter}{1000\:cm^3}\times \frac{1\:gallon}{3.785\:Liters}=3.5\:gallons[/tex]
cheryl went on a 3-hour train traveled at an average speed of 75 miles per hour.what was the total distance in miles that cheryl traveled?
Answers
Cheryl went a total of 225 miles in 3 hours.
9. WILL GIVE BRAINLIEST IF CORRECT
Answers
Re-arrange formula to give: sin q = -1/square root of 2
Now, sin (3 pie/4) = sin(135) = -1/square root of 2
Also, sin(5 pie/4) = sin(235) = -sin(45) = -1/square root of 2
sinq = -2/2sqrt(2) = -1/sqrt(2)
answer is letter A. 3pi/4 , 5pi/4
Hope this helps your question! Goodluck