7.2. I have a question about advanced trig equations that I really need help with picture included
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1) Let's start out isolating the cosine by dividing both sides by 2
[tex]\begin{gathered} 2\cos \mleft(\theta\mright)=\sqrt{3} \\ \frac{2\cos\left(θ\right)}{2}=\frac{\sqrt{3}}{2} \\ \cos \mleft(\theta\mright)=\frac{\sqrt{3}}{2} \\ \end{gathered}[/tex]2) From that we can find two general solutions in which the cosine of theta yields the square root of 3 over two:
[tex]\begin{gathered} \cos (30^{\circ})or\cos (\frac{\pi}{6})\text{ and }cos(330^{\circ}or\frac{11}{6}\pi)=\frac{\sqrt[]{3}}{2} \\ \theta=\frac{\pi}{6}+2\pi n,\: \theta=\frac{11\pi}{6}+2\pi n \end{gathered}[/tex]But not that there is a restraint, so we can write out the solution as:
[tex]\theta=\frac{\pi}{6},\: \theta=\frac{11\pi}{6}[/tex]Related Questions
Use the drawing tool(s) to form the correct answer on the provided graph, The function fx) is shown on the provided graph. Graph the result of the following transformation on f(X). f(x) + 6
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We have that the line passes by the points (0, -2) & (1, 2). Using this we determine the slope (m) and then the function. After that we transformate the function. We proceed as follows:
[tex]m=\frac{2-(-2)}{1-0}\Rightarrow m=4[/tex]Now, using one of the points [In our case we will use (0, -2), but we can use any point of the line] and the slope, we replace in:
[tex]y-y_1=m(x-x_1)[/tex]Then:
[tex]y-(-2)=4(x-0)[/tex]Now, we solve for y:
[tex]\Rightarrow y+2=4x\Rightarrow y=4x-2[/tex]And we apply the transformation to our line, that is f(x) -> f(x) + 6:
[tex]y=4x-2+6\Rightarrow y=4x+4[/tex]Therefore our final line (After the transformation) is y = 4x + 4, and graphed that is:
Find the coordinates of point p that partition AB in the ratio 1: 4,
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Given:
[tex]A(1,-1)\text{ ; B(}4,4)\text{ m:n =1:4}[/tex][tex](x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex][tex](x,y)=(\frac{4+4}{1+4},\frac{4-4}{1+4})[/tex][tex](x,y)=(\frac{8}{5},0)[/tex]Therefore the point P be ( 1.6 ,0)
The from y=mx passes through the points (2, - 15) and (6, - 45)
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y = -7.5x
Explanation:The given points: (2, -15) and (6, -45)
The equation of the proportional relationship given:
y = mx
m = slope
We apply slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=2,y_1=-15,x_2=6,y_2\text{ = }-45 \\ m\text{ = }\frac{-45\text{ - (-15)}}{6\text{ - 2}} \\ m\text{ = }\frac{-45+15}{4} \end{gathered}[/tex][tex]\begin{gathered} m\text{ = }\frac{-30}{4} \\ m\text{ = -15/2} \\ m\text{ = -7.5} \end{gathered}[/tex]The relationship of the equation becomes:
y = -7.5x
Which is the better buy: $40.00 for 30 gallons of gas or $8.50 for 8 gallons ofgas?
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Ok, we need to calculate the value of each gallon and see which is the cheapest:
First Option: 40/30=1.33
Second Option: 8.5/8=1.0625
This mean that the better buy is $8.50 for 8 gallons of gas.
1) f(x) = 60.73(0.95)x2) f(x) = 0.93(60.73)x3) f(x) = 60.04 – 8.25 ln x4) f(x) = 8.25 – 60.04 ln x
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A logarithmic function is expressed as
y = a + blnx
We would substitute corresponding values of x and y into the function. This will give us two equations. We would solve the equations for a and b. We have
From the table, when x = 1, y = 60
Thus,
60 = a + b * ln1
60 = a + b * 0
60 = a
when x = 2, y = 54
Thus,
54 = a + bln2
54 = a + 0.693b
Substituting a = 60 into 54 = a + 0.693b, we have
54 = 60 + 0.693b
0.693b = 54 - 60 = - 6
b = - 6/0.693
b = - 8.65
The function would be
f(x) = 60 - 8.65lnx
Given a and b are first quadrant angles, sin a=5/13 and cos b=3/5 evaluate cos (a+b)1) 56/652) 33/653) 16/65
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The graph below shows the length of Jutta's hair over 6 months period. Each month point represents a measurement at the beginning of a month. How many inches did her hair grow between the beginning of February and the beginning of July?
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Given:
Length of hair at the beginning of february is 4.1''
Length of hair at the beginning of July is 7.7''
[tex]\begin{gathered} \text{Hair grown between beginning of February an beginning of July=7.7''-4.1''} \\ =3.6^{\doubleprime} \end{gathered}[/tex]model and solve. 3/5 ÷ 1/2 =
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Solution:
Consider the following diagram
extremes and means are multiplied in the diagram. Then we have that:
[tex]\frac{\frac{3}{5}}{\frac{1}{2}}\text{ = }\frac{3\text{ x 2}}{5\text{ x1}}\text{ = }\frac{6}{5}\text{ = 1.2}[/tex]and this number is represented on the real line as follows:
A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1100 feet, whatare the dimensions of the field?The width of the field isfeet.The length of the field isfeet.
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Given:
The perimeter of the rectangular field is 1100 feet.
According to the question,
l=9w
To find the dimensions:
Substitute l=9w in the perimeter formula,
[tex]\begin{gathered} 2(l+w)=1100 \\ 2(9w+w)=1100 \\ 20w=1100 \\ w=55\text{ f}eet \end{gathered}[/tex]Since the width of the rectangle is 55 feet.
The length of a rectangle is,
[tex]55\times9=495\text{ f}eet[/tex]Hence,
The width of the rectangle is 55 feet.
The length of a rectangle is 495 feet.
I need help part two and three of this question:A line passes through the following points: (6,3) and (2,9)1. Write the equation of the lineWhich I got y=-3/2 x+122. Write an equation of a line that is perpendicular to the original form. 3. Write the equation of a line that is parallel to the original form.
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Part 2:
To determine an equation that is perpendicular to the line equation y = -3/2x + 12, get the negative reciprocal of the slope of the line equation.
[tex]\begin{gathered} \text{Given slope: }m=-\frac{3}{2} \\ \\ \text{The negative reciprocal is} \\ -\Big(-\frac{3}{2}\Big)^{-1}=\frac{2}{3} \\ \\ \text{We can now assume that any line in the form} \\ y=\frac{2}{3}x+b \\ \text{where }b\text{ is the y-intercept} \\ \text{is perpendicular to the line }y=-\frac{3}{2}x+12 \end{gathered}[/tex]Part 3:
An equation that is parallel to the line y = -3/2x + 12, is a line equation that will have the same slope as the original line.
Given that the slope of the line is m = -3/2, then any line equation in the form
[tex]\begin{gathered} y=-\frac{3}{2}x+b \\ \text{where} \\ b\text{ is the y-intercept} \end{gathered}[/tex]The day's high temperature in Detroit, Michigan was recorded as 50°F. Use the formula C=59(F−32) to write 50°F as degrees Celsius.
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Given:
The day's high temperature in Detroit, Michigan was recorded as 50°F.
[tex]C=\frac{5}{9}(F-32)[/tex]Required:
To convert the 50°F as degrees Celsius.
Explanation:
Consider
[tex]C=\frac{5}{9}(F-32)[/tex]For F=50,
[tex]\begin{gathered} C=\frac{5}{9}(50-32) \\ \\ =\frac{5}{9}(18) \\ \\ =5\times2 \\ \\ =10\degree C \end{gathered}[/tex]Final Answer:
[tex]C=10\degree C[/tex]A restaurant has 5 desserts, 3 side dishes and 4 main dishes. A student chooses one side dish, one main dish, and one dessert. How many different meals could he make?
Answers
30
Explanation
if the first event occurs in x ways, and the second event occurs in y ways, then two events occur in as sequence of xy ways.
so
event A ; choose (1) dessert , 5 ways
event B , chosen (1) side dish, 3 ways
event C, choose (1) main dish, 2 ways
so
a meal( 1 dessert+1 side dish+main dish) is the product of the 3 ways
[tex]\begin{gathered} \text{ways a meal could be made= (5}\cdot3\cdot2)\text{ ways} \\ \text{ways a meal could be made=}30\text{ ways} \end{gathered}[/tex]therefore, the answer is
30
I hope this helps you
Write the inverse of the given conditional statement.Conditional Statement: "If a shape has four sides, then theshape is a rectangle."Inverse Statement: Ifthen
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Given: A conditional statement, "If a shape has four sides, then the
shape is a rectangle."
Required: To write the inverse of the statement.
Explanation: The given statement has two following statements:
[tex]\begin{gathered} p\rightarrow\text{ A shape has four sides} \\ q\rightarrow\text{ The shape is rectangle} \end{gathered}[/tex]The inverse of the statement will be
[tex]\text{ If }∼q\text{ then \thicksim}p[/tex]Hence the inverse statement is
Final Answer: The inverse statement is- "If the shape is not a rectangle, then the shape doesn't has four sides."
what is quotient of 0.5?
A.25÷5
B.2.5÷5
C.25÷0.5
D.25÷0.05
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Answer:
B
Step-by-step explanation:
2.5/5=0.5
Answer: the answer is b
Step-by-step explanation:
because 2.5 goes into 5 0.5 times also written as 1/2 and said as one half i hope this helps have a great day (brainly pls)
Find the distance between the two points. 15.) (-3, -1), (-1, -5)-use Pythagorean Throrem
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Answer:
4.5 units
Explanation:
First, we need to draw the points (-3, -1) and (-1, -5) as follows
Therefore, the distance between the points is the length of the yellow line. This distance is the hypotenuse of a triangle with legs a and b.
The length of a is 2 and the length of b is 4
Then, using the Pythagorean theorem, we can calculate the length of c as follow
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=2^2+4^2 \\ c^2=4+16 \\ c^2=20 \end{gathered}[/tex]So, using the calculator, we get that the value of c is equal to
[tex]\begin{gathered} \sqrt{c^2}=\sqrt{20} \\ c=\sqrt{20} \end{gathered}[/tex]To find an approximate value for c, we will use the following:
We know that √16 = 4 and √25 = 5
Since 20 is between 16 and 25, the square root of 20 is a number between 4 and 5, so we can approximate it to 4.5.
Therefore,
c = 4.5
Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Construct the probability distribution and histogram of the random variable Z.
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ANSWER and EXPLANATION
Let R represent the number of red balls.
Let B represent the number of blue balls.
There are four possible outcomes when the balls are picked:
[tex]\lbrace RR,RB,BR,BB\rbrace[/tex]We have that Z is the random variable that represents the number of blue balls.
This implies that the possible values of Z are:
To construct the probability distribution, we have to find the probabilities of each of the outcomes:
[tex]\begin{gathered} P(RR)=\frac{5}{11}*\frac{4}{10}=\frac{2}{11} \\ P(RB)=\frac{5}{11}*\frac{6}{10}=\frac{3}{11} \\ P(BR)=\frac{5}{11}*\frac{6}{10}=\frac{3}{11} \\ P(BB)=\frac{6}{11}*\frac{5}{10}=\frac{3}{11} \end{gathered}[/tex]Hence, the probabilities for the possible outcomes of the random variable are:
[tex]\begin{gathered} P(Z=0)=\frac{2}{11} \\ P(Z=1)=\frac{3}{11}+\frac{3}{11}=\frac{6}{11} \\ P(Z=2)=\frac{3}{11} \end{gathered}[/tex]Therefore, the probability distribution is:
Now, let us plot the histogram:
That is the answer.
Mariana, who rents properties for a living, measures all the offices in a building she is renting. Size (square meters) Number of offices 60 3 70 2 98 5 X is the size of a randomly chosen office. What is the expected value of X? Write your answer as a decimal.
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The expected value formula is
[tex]E=\Sigma x\cdot P(x)[/tex][tex]\begin{gathered} E=60\cdot\frac{3}{10}+70\cdot\frac{2}{10}+98\cdot\frac{5}{10} \\ E=18+14+49 \\ E=81 \end{gathered}[/tex]Hence, the expected value is 81.We need to know how to Convert the fraction into its decimal representation on level seven using step by step instructions. We especially need to know how to solve 1/7 in level seven
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We want to convert our fractions in a way the denominators are potencys of 10. Let's start with the first one.
[tex]\frac{32}{40}[/tex]If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{32\times25}{40\times25}=\frac{800}{1000}=0.8[/tex]Now, with the next fraction
[tex]\frac{12}{48}[/tex]Dividing both numerator and denominator by 12, we have
[tex]\frac{12}{48}=\frac{1}{4}[/tex]Again, If we multiply both the numerator and denominator by 25, we're going to have
[tex]\frac{1}{4}=\frac{25}{100}=0.25[/tex]For the next fraction, it is enough to multiply both numerator and denominator by 4
[tex]\frac{3}{25}=\frac{12}{100}=0.12[/tex]For the next one, we can again multiply both the numerator and denominator by 25
[tex]\frac{18}{40}=\frac{450}{1000}=0.45[/tex]How many different amounts of money can be made
with six pennies, two nickels, and one quarter?
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Based on the number of pennies, nickels, and quarters, the number of different amounts of money that can be made are 42.
How to find the different amounts that can be made?First, find out the number of ways to select the different amounts.
There are six pennies so there are 7 ways to collect them including:
(0 times, 1 time, 2, 3, 4, 5, 6)
There are 3 ways to collect nickels and there are two ways to collect quarters.
The number of different amounts of money that can be made are:
= 7 x 3 x 2
= 42 different amounts of money
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- 9 = 12 what is the value of K?
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For this case we have the following expression given:
k/3 -9 = 12
We can add 9 in both sides and we got:
k/3 = 12+9
k/3= 21
And if we multiply in both sides by 3 we got:
k = 21*3 = 63
Can I please just have the answer I’m in a hurry to complete this lol
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By rearranging the triangles side by side and making sure the triangles vertices touches each other. The image below is formed
What you notice : The image formed by placing the triangle side by side with the vertices touching each other is that, the shape formed is a trapezium.
a) If the triangles are cut out at equal proportion, then the angles are equal and the the triangles are equiangular; the angles are 60 degrees each
b) If the triangles are not cut out equally, then the greatest number of right angle that we can get in a triangle is one (1) and the greatest number of obstuse angle in a triangle is one (1)
Reason:
The sum of the three angles of a triangle is 180 degrees, of which if one angle is 90 degrees (right angle) then the other two angles will be less than 90 degrees each, as their sum will give 90 degrees
Also if one of the three angles is an obtuse angle ( say 115 degrees) then the other two angles will be acute angles each.
would this be (0, -1) since if b is greater than 1 but it is also -2
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The y-intercept is the point where the graph cuts the y-axis. The y-axis is the line x = 0, therefore, to find the y-coordinate of this point we just need to evaluate x = 0 in our function.
[tex]\begin{gathered} y(x)=b^x-2 \\ y(0)=b^0-2 \end{gathered}[/tex]Any nonzero real number raised to the power of zero is one, therefore
[tex]y(0)=b^0-2=1-2=-1[/tex]The y-intercept is (0, -1).
Question 2 write an expression to represent the perimeter of Melissa‘s garden in the terms of X type the correct answer in each box use numerals instead of words
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From the given statement in part A,
There are given that square patch for the tomatoes
Now,
Let x is the length of the tomato patch, w is the width of the garden and L is the length of the garden
So,
[tex]\begin{gathered} L=3x+2 \\ W=x+5 \end{gathered}[/tex]Then,
From the perimeter of the vegetable garden:
[tex]\begin{gathered} P=2(L+W) \\ P=2(3x+2+x+5) \\ P=2(4x+7) \\ P=8x+14 \end{gathered}[/tex]Hence, the perimeter is, 8x + 14.
Write a linear function f with f (- 1/2) = 1 and f (0) = -4
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The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.
What is linear equation?Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on cartesian plane with axes of those variables, give a straight line.
We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4
Let the equation in variable x and y can be written in the form y = mx + c
So f (- 1/2) = 1
this gives, 1 = -1/2m+c -----------eq 1
Also f (0) = -4
This gives -4 = c. --------------eq2
Now Putting value of c in equation in eq1 we get m=0.
So 1 = -1/2m+c
1 = -1/2m - 4
m = -5
Then we get;
y = -5x -4.
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What is the solution to14h + 6 = 2(5 + 7h) - 4 ?
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14h + 6 = 2(5 + 7h) - 4
First , apply distributive porperty to solve the parentheses:
14h+6 =2(5)+2(7h)-4
14h+6 = 10+14h-4
Move the "h " terms to the left:
14h-14h = 10-4-6
0 = 0
h has infinite solutions.
Nancy plans to take her cousins to an amusement park. She has a total of $100 to pay for 2 different charges. • $5 admission per person • $3 per ticket for rides Which inequality could Nancy use to determine y, the number of tickets for rides she can buy if she pays the admission for herself and x cousins? A. 5y + 3(x + 1) >= 100 B. 5(x + 1) + 3y > 100 C. 5(x + 1) + 3y =< 100 D. 5y + 3(x + 1) < 100
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ANSWER
[tex]C.5(x\text{ + 1) + 3y }\leq100[/tex]EXPLANATION
Nancy has $100.
The charges are:
=> $5 admission per person. She has x cousins and herself to pay for, this means that she pays $5 for (x + 1) persons.
The admission charge is therefore:
$5 * (x + 1) = $5(x + 1)
=> $3 per ticket for rides. The number of rides she can pay for is y. So the charge for rides is:
$3 * y = $3y
Since she only has $100, everything she pays for can only be less than $100 or equal to $100.
This means that, if we add all the charges, they must be either less than or equal to $100.
That is:
[tex]5(x\text{ + 1) + 3y }\leq100[/tex]That is Option C.
1. Write a linear equation of the form y1 = mx + b for your first set of data.2. Write a linear equation of the form y2 = mx + b for the other equation in your system. 3. Graph and explain the solution.
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Given:
Company A: transport 56 people in one hour for $40 per person in 30 minutes
Company B:
Describe the relationship between average velocity of a car in motion versus the instantaneous velocity of the same car in motion. Which one matters more if you get pulled over on the freeway for speeding and why?
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Answer:
During a typical trip to school, your car will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often. The speedometer of a car reveals information about the instantaneous speed of your car. It shows your speed at a particular instant in time.
Step-by-step explanation:
The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure of the distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio. Suppose that during your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The average speed of your car could be determined as
On the average, your car was moving with a speed of 25 miles per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 miles per hour. Yet, on average, you were moving with a speed of 25 miles per hour.
hope this helps might not be the answer your looking for but a better explanation on how too figure it out :))
y=6/5x+9 how would I graph it
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To graph this linear function, we can find both intercepts of the function. To achieve this, we need to solve the equation when y = 0 (for this function) (this will be the x-intercept), and then we need to solve the resulting equation for this function when x = 0 (this will be the y-intercept). Then, we will have two points for which we can graph the function - we need to remember that a line is defined by two points.
Then, we can proceed as follows:
1. Finding the x-intercept[tex]y=\frac{6}{5}x+9,y=0\Rightarrow0=\frac{6}{5}x+9[/tex]Then, we have:
a. Add -9 to both sides of the equation:
[tex]\frac{6}{5}x=-9[/tex]b. Multiply both sides of the equation by 5/6:
[tex]\frac{5}{6}\frac{6}{5}x=-9\cdot\frac{5}{6}\Rightarrow x=-\frac{45}{6}=-\frac{15}{2}=-7.5[/tex]Therefore, the x-intercept is (-7.5, 0).
2. Finding the y-interceptWe have that x = 0 in this case. Then, we have:
[tex]y=\frac{6}{5}x+9\Rightarrow y=\frac{6}{5}(0)+9\Rightarrow y=9[/tex]Therefore, the y-intercept is (0, 9).
Now, we have the points (-7.5, 0) and (0, 9), and we can draw both points on the coordinate plane. The line will pass through these two points:
Solve for u-6u+3(u-3)=12
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Answer: u=7
Given:
[tex]-6u+3(u-3)=12[/tex]- Distribute 3(u-3):
[tex]\begin{gathered} -6u+3(u-3)=12 \\ \Rightarrow-6u+3u-9=12 \end{gathered}[/tex]- Combine like terms:
[tex]\begin{gathered} \begin{equation*} -6u+3u-9=12 \end{equation*} \\ \Rightarrow-6u+3u=12+9 \\ \Rightarrow-3u=21 \end{gathered}[/tex]- Divide both sides by -3:
[tex]\begin{gathered} \begin{equation*} -3u=21 \end{equation*} \\ \Rightarrow\frac{-3u}{-3}=\frac{21}{-3} \\ \Rightarrow u=7 \end{gathered}[/tex]Therefore, u=7.