Answers
The equation is given to be:
[tex]\sec\theta=-\sqrt{2}[/tex]Recall that sec is the inverse of cos. Thus, we have:
[tex]\frac{1}{\cos\theta}=-\sqrt{2}[/tex]Rewriting the equation, we have:
[tex]\cos\theta=-\frac{1}{\sqrt{2}}[/tex]We can find the arccos of both sides:
[tex]\theta=\arccos(-\frac{1}{\sqrt{2}})[/tex]Since we know that:
[tex]\cos(-x)=\cos(x)[/tex]Then, we have:
[tex]\theta=\arccos(\frac{1}{\sqrt{2}})[/tex]Recall the identity:
[tex]\arccos(\frac{1}{\sqrt{2}})=\frac{3\pi}{4}+2\pi n,\:θ=\frac{5\pi}{4}+2\pi n[/tex]Therefore, the answer is the SECOND OPTION.
Related Questions
a rectangle has the perimeter of 116 cm and its length is 1cm more than twice its width. I got 39L and 19w but I'm having problems setting up the problems
Answers
To answer this question, we can proceed as follows:
1. We have that the perimeter of the rectangle is equal to 116cm, then, we have:
[tex]w+l+w+l=116\Rightarrow2w+2l=116[/tex]We know that a rectangle is a parallelogram. Then, its opposite sides are congruent.
2. We have that the length of the rectangle is 1 cm more than twice its width. We can translate this, algebraically, as follows:
[tex]l=2w+1[/tex]Now, to find the measures of the length and the width of the rectangle, we can substitute this last formula into the first one, as follows:
[tex]2w+2(2w+1)=116[/tex]We need to apply the distributive property to find w:
[tex]2w+4w+2=116[/tex]Adding like terms:
[tex]6w+2=116[/tex]Subtracting 2 to both sides of the equation, and then dividing by 6:
[tex]6w+2-2=116-2\Rightarrow6w=114\Rightarrow\frac{6w}{6}=\frac{114}{6}\Rightarrow w=19[/tex]Then, the width of the rectangle is equal to 19cm. The measure of the length can be calculated using either equation above. Let us use the first equation:
[tex]2w+2l=116\Rightarrow2\cdot19+2l=116\Rightarrow38+2l=116[/tex]Then, using similar properties as before, we have:
[tex]38-38+2l=116-38\Rightarrow2l=78\Rightarrow\frac{2l}{2}=\frac{78}{2}\Rightarrow l=39[/tex]In summary, we have that the measures of the length and width of this rectangle are:
• Width, ,(w) =, 19cm
,• Legth (l) = ,39cm
Which of the following equations is equivalent to log(y)= 3.994
Answers
ANSWER:
[tex]y=10^{3.994}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]log\mleft(y\mright)=3.994[/tex]Applying property of logarithms we have:
[tex]\begin{gathered} \log _a(b)=c\rightarrow b=a^c \\ \text{ in this case:} \\ log(y)=3.994\rightarrow y=10^{3.994} \end{gathered}[/tex]In order to pass a science lab, you have to measure a beaker (container) of water with 5% error or less. The beaker has 12 ounces of water in it. You measure 13.2 ounces of water. Did you pass the lab? Why or why not?
Answers
Data:
Error: 5%
Volume of water in the Beaker: 12oz
Your measure: 13.2oz
As the error is 5% it means that the measure can be actually 5% more or 5% less.
Then, you calculate the 5% of the measure you have to measure: 12oz
[tex]12\cdot\frac{5}{100}=0.6oz[/tex]Then, the measure you need to take to pass the lab is between: 11.4oz and 12.6oz
[tex]12oz\pm0.6oz[/tex][tex]\begin{gathered} 12oz+0.6oz=12.6oz \\ 12oz-0.6oz=11.4oz \end{gathered}[/tex]Then, your measure of 13.2oz is not between the 5% of error. You didn't pass the lab.
A quality control worker at a factory selects the first 10 items she sees as her sample for the day.What type of sample is this?
Answers
This is a convinience sample because the first 10 items are easy to select.
I need help with this questionthe question to this question is below is a graph of a logarithmic function, identify it key characteristics. match accordingly
Answers
The answers to the problem :
[tex]\begin{gathered} 1.\text{ Domain : x >-6} \\ 2\text{ Range : -}\infty\text{ to +}\infty \\ 3.\text{ Aymptote : x = -6} \\ 4\text{. Transformation : left 6, down 1} \\ 5.\text{ End behaviour : As x approaches }\infty,\text{ f(x) approaches }\infty.\text{ As x approaches -6, f(x) approaches -}\infty \\ 6.\text{ x-intercept : (-4,0)} \end{gathered}[/tex]Customers can pick their own blueberries at Blueberry Hill. They pay $5 toenter the patch and $4 per pound for the blueberries they pick. Write anequation to model the total cost, y, for x pounds of blueberries.
Answers
SOLUTION
Step1; Write out the parameters
[tex]\begin{gathered} \text{entry fe}e=\text{ \$5} \\ \cos t\text{ of blueberries per pound=\$4} \end{gathered}[/tex]Step2: Write out the variables
[tex]\text{let y=total cost and x=number of bluerries}[/tex]Step3: write out the model
[tex]\begin{gathered} \text{The total cost=number of blueberries}\times\text{\$}4+\text{ the entry fe}e \\ y=4x+5 \end{gathered}[/tex]There
A system of equations is given below.x + 2y = 24x − 5y = 8Identify the constant that can be multiplied by both sides of the first equation to eliminate the variable x when the equations are added together.thenWrite the revised system of equations.
Answers
Answer:
[tex]constant\rightarrow-4[/tex]Explanation: We have to find the constant that when multiplied to the first equation and added to the second, the variable x gets canceled out, the two equations are as follows:
[tex]\begin{gathered} x+2y=2\rightarrow(1) \\ 4x-5y=8\rightarrow(2) \end{gathered}[/tex]Multiplying the equation (1) by -4 and adding it to the equation (2) gives the following answer:
[tex]\begin{gathered} -4\times(x+2y)=-4\times2\rightarrow-4x-8y=-8 \\ \begin{equation*} -4x-8y=-8 \end{equation*} \\ + \\ \begin{equation*} 4x-5y=8 \end{equation*} \\ ---------------------- \\ -3y=0 \end{gathered}[/tex]Therefore the value of the constant is -4.
Use a graphing utility to find or to approximate the x-intercepts of the graph of the function.y=3x2−8x+
Answers
Answer:
The x-intercepts are x = 0.6667, 2
Explanation:
The graph of the function y = 3x² - 8x + 4 is:
Then, the x-intercepts are the points where the graph crosses the x-axis.
So, an approximation for the x-intercepts are x = 0.6667 and x = 2
Therefore, the answer is:
The x-intercepts are x = 0.6667, 2
10 Students share 1 hour to give their science reports
Answers
Answer:
1/10
Explanation:
If 10 students share 1 hour, we need to divide 1 hour into 10 students. So, the fraction is
[tex]\frac{1\text{ hour}}{10\text{ students}}=\frac{1}{10}[/tex]It means that each student has 1/10 hour to give the science report.
Hello am I correct, if not can you help me understand?
Answers
total kilometer of journey = 353miles
she stopped at mile 36
Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Answers
Using the Distributive Property of multiplication, the equation - 6(x + 3) = 30 is solved as x = -8.
What is the distributive property of multiplication?The distributive property of multiplication shows that a mathematical expression in the form of a(b + c) is also equal to ab + ac.
The distributive property applies to either addition or subtraction in multiplication.
- 6(x + 3) = 30
-6x - 18 = 30
-6x = 48
x = -8
Thus, x = -8 is the solution to the equation - 6(x + 3) = 30.
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A seven digit telephone number is of theform ABC-DEFG. In one particular state,the digit ‘A’ is restricted to any numberbetween 1 and 9. The digits B and Carerestricted to any number between 2 and9. The digits D,E,F, and G have norestriction. How many seven digit phonenumbers are possible with theserestrictions?
Answers
9 x 8 x 8 x 10 x 10 x 10 x 10 = 5760000 possible phone numbers
what is the shape of a cross section that is parallel to the bases
Answers
The cross-section that is parallel to the base will have a
RECTANGULAR Shape
It's just like cutting through the shape horizontally
For a winter-themed Valentine's Day party, Mr. Rivera made 12 cups of hot chocolate. Does he have enough hot chocolate to give 26 kids 1/2 of a cup each?
Answers
Multiply the number of kids by the number of cups for each kid. This is 26 times 1/2.
[tex]26\cdot\frac{1}{2}=\frac{26}{2}=13[/tex]It means 13 cups are needed to give each of the 26 kids 1/2 of a cup of chocolate.
Mr. Rivera does not have enough hot chocolate to give 26 kids 1/2 of a cup of chocolate.
Solving a trigonometric equation involving an angle multiplied by a constant
Answers
In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
[tex]2k\pi,k\in\Z[/tex]4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for x to get the solutions.
1 - To solve, we just use algebraic operations:
[tex]\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
[tex]+\frac{\sqrt[]{3}}{3}[/tex]is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
[tex]-\frac{\sqrt[]{3}}{3}[/tex]Are:
[tex]\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}[/tex]3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
[tex]\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}[/tex]Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
[tex]\theta=\frac{5\pi}{6}+k\pi,k\in\Z[/tex]4 - Now, we need to solve for x, because these solutions are for all the interior of the tangent function, so:
[tex]\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}[/tex]So, the solutions are:
[tex]x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z[/tex]The product of 5 – 2i and i is1) 72) 2 + 5i3) 5 – 2i4) -2 + 5i
Answers
Answer:
2) 2 + 5i
Explanation
Fom the given question, we are find the product of 5-2i and i
i(5-2i)
Expand
= 5i - 2(i^2)
From complex number i^2 = -1
Substitute
= 5i - 2(-1)
= 5i + 2
= 2 + 5i
Hence the product is 2 + 5i
This statics question has me stumped if you could hope me I would rlly appreciate it! Have a nice night :).
Answers
Spinner A
Sample space = 1,2,3,4,5,6
Number of total outcome = 6
Odd numbers = 1,3,5
Number of odd numbers = 3
[tex]\text{Probability = }\frac{n\text{umber of required outcomes}}{\text{total number of possible outcome}}[/tex]Probability of spinning an odd number = 3/6 = 1/2
Spinner B
Sample space = yellow, brown, red
Number of total outcome = 3
Not yellow = brown, red
Number of not yellow = 2
Probability of not yellow = 2/3
Since the two spinners are independent events, then the probability that you spin an odd number and not yellow are multiplied together
Thus we have,
Probability of spinning an odd number X Probability of not yellow
[tex]\frac{1}{2}\text{ X }\frac{2}{3}\text{ = }\frac{2}{6}[/tex]Final answer is 1/3.
Need help with this exercise. It’s from a review the real test is next week need more explanation so I already know what to do on the test.
Answers
ANSWER
Options 1 and 4
EXPLANATION
First, let us find the length of the third side of the right triangle. To do this apply the Pythagoras theorem.
Let the length of the third side of the triangle be x.
It implies that:
[tex]\begin{gathered} x^2+8^2=17^2 \\ x^2=17^2-8^2 \\ x^2=289-64=225 \\ x=\sqrt[]{225} \\ x=15 \end{gathered}[/tex]Now, we can find the value of sinA, tanA, and sinC.
According to trigonometric ratios, SOHCAHTOA, we have that:
[tex]\begin{gathered} \sin A=\frac{\text{opposite}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \sin C=\frac{\text{opposite}}{\text{hypotenuse}} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin A=\frac{15}{17} \\ \tan A=\frac{15}{8} \\ \sin C=\frac{8}{17} \end{gathered}[/tex]Hence, the correct options are options 1 and 4.
If f(1) = 2 and f(n) = f(n - 1)^2 – 5 then find the value of f (4).
Answers
We are asked to calculate f(4) by means of the following function:
f(n) = f(n - 1)² - 5
As you can see, in order to calculate f(n) first we have to specify the value of f(n - 1), we are given the value of f(1), so we can calculate the value of f(2), then f(3) and finally f(4), like this:
f(2) = f(2-1)² - 5 = f(1)² - 5 = 2² - 5 = 4 - 5 = -1
Then, f(2) = -1, now we can calculate f(3) like this:
f(3) = f(3 - 1)² - 5 = f(2)² - 5 = (-1)² - 5 = -4
Then f(3) = -4, now we can calculate f(4) like this:
f(4) = f(4 - 1)² - 5 = f(3)² - 5 = (-4)² - 5 = 16 - 5 = 11
Then, f(4) equals 11
Allen is choosing a 2 letter password from the letters ABCD. the password cannot be the same letter repeated in it .how many such passwords are possible?
Answers
Since we can choose 2 letters and they can not be the same, we have the following possibilities:
[tex]{}\lbrace AB,AC,AD,BC,BD,BA,CB,CA,CD,DA,DB,DC\rbrace[/tex]As we can note, there are 12 possible combinations of 2 different letters. So, How many such passwords are possible? The answer is 12 passwrods
Given the definitions of f(x) and g(x) below, find the value of g(f(-2)). f(x) = 5x + 4 g(x) = x^2 - 6x - 13
Answers
f(-2) = 5(-2) + 4
= -10 + 4
= -6
g(f(-2))
= -6^2 -6*-6 -13
= 36 + 36 - 13
= 59
Triangle ABC shown below has m B = 38°, a = 8, and c = 16. Find the area of the triangle. Round your answer to the nearest tenth and do not include units in your answer.
Answers
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times8\times16\times\sin 38=64\sin 38^{\circ}[/tex][tex]A=39.4\text{ squnit}[/tex]Thus the area of triangle is 39.4 sq.unit.
-7.9 cm 26.2 cm 6.2 cm 19.1 cm 2.8 cm The perimeter of the figure is (Type a whole number or a decal.) .
Answers
ANSWER
The perimeter is 81.5 cm
EXPLANATION
The perimeter of any polygon is the sum of the length of its sides. The perimeter of this figure is:
[tex]P=7.9+26.2+6.2+22.8+18.4=81.5\operatorname{cm}[/tex]Given `lim_(x -> 2) 2x - 3 = 1`, use the formal definition of a limit to find the value of δ that corresponds to ε = 0.3.
A. 0.05
B. 0.15
C. 0.30
D. 0.50
Answer: B. 0.15
Your Welcome :)
Answers
Each person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of ancestors a person has, going back five generations? twelve generations?
Answers
62
8190
1) Gathering the data:
So Adding the 2 + 4 +8 +16+32 Then we can write that up to the 5th generation each person has 62 ancestors.
2) Or we can check. Let's write out considering that the ratio is 2 and the first term is 2 since the person per se is not counted.
[tex]\begin{gathered} S=\frac{a_1(1-r^n)}{1-r} \\ S_5=\text{ }\frac{2(1-2^5)^{\square}}{1-2}=62 \\ S_{12}=\frac{2(1-2^{11})}{1-2}=8190 \end{gathered}[/tex]3) Hence, each person has counting back up to the 5th generations 62 ancestors and 4094 when it comes to 11 generations
A survey of a random sample of voters showsthat 56% plan to vote Yes to the newproposition and 44% plan to vote No. Thesurvey has a margin of error of +4%. What isthe range for the percentage of voters whoplan to vote Yes?
Answers
Answer:
G 52% to 60%
Explanation:
The percentage of voters that plan to vote Yes = 56%
The survey's margin of error = +/-4%
Therefore, the range for the percentage of voters who plan to vote Yes is:
[tex]\begin{gathered} 56\%\pm4\% \\ =56\%-4\%\text{ to }56\%+4\% \\ =52\%\text{ to }60\% \end{gathered}[/tex]The correct choice is G.
Write a quadratic inequality represented by the graph.
Answers
The quadratic inequality represented by the graph is y > -x².
What is meant by quadratic inequality?Simply put, an equation of the type with the highest degree of two and no equal sign is known as a quadratic inequality. There is a technique for resolving quadratic inequalities called the wavy curve approach. It is the same to solve quadratic equations as it is solving quadratic inequalities. When plotted, quadratic inequalities show a parabola, much like quadratic equations do. Quadratic inequalities can be solved to provide a variety of solutions. For instance, the quadratic equation x²+6x+5=0 has two solutions: x² + 6 x + 5 = 0 and x² + 6x + 5 = 0. A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign. The quadratic inequalities x- 6x - 16 0, 2x² - 11x + 12 > 0, x² + 4> 0, and x² - 3x + 20 are some examples.
From the graph, we can see that it is a parabola with vertex points (0,-9)
Thus, y= -3² is the equation at the vertex and the equation of the parabola will be y= -x².
The graph is an increasing function, so the inequality will be
y > - x²
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Convert the Fahrenheit temperature to the equivalent Celsius temperature round to 1 decimal Places if necessary
Answers
Given
[tex]19^0F[/tex]To convert the given to Celsius
Solution
The formula connecting Fahrenheit and degree Celsius is given as
[tex]\begin{gathered} =\frac{5(F-32)^{}}{9} \\ =\frac{5(19-32)}{9} \\ =\frac{5(-13)}{9}=-7.222^0C \end{gathered}[/tex]Hence
19⁰F = -7.2⁰C
Find the difference. (10m+ 3) - (4m-2) O A. 14m-1 OB. 6m+ 5 O C. 6m-1 D. 14m + 5
Answers
(10m + 3) - (4m -2)
Firstly, use the negative sign to open the parenthesis
(10m + 3) -1 x 4m -1 x (-2)
minus x minus = plus
(10m + 3) -4m + 2
10m + 3 - 4m + 2
Collect the like terms
10m - 4m + 3 + 2
m(10-4) + 5
m(6) + 5
6m + 5
The answer is OPTION B
Solve the equation.g−37=27g− 73 = 72 g, minus, start fraction, 3, divided by, 7, end fraction, equals, start fraction, 2, divided by, 7, end fractiong=g=g, equals
Answers
ANSWER
[tex]\text{ g = }\frac{5}{7}[/tex]EXPLANATION
We want to solve for g in:
[tex]g\text{ - }\frac{3}{7}=\frac{2}{7}[/tex]Collect like terms by moving 3/7 to the right hand side:
[tex]\begin{gathered} g\text{ = }\frac{2}{7}+\frac{3}{7} \\ \Rightarrow\text{ g = }\frac{5}{7} \end{gathered}[/tex]