Use trigonometric identities to solve each equation within the given domain.
–sin2(x) = cos(2x) from [–π, π]. PLEASE SHOW WORK!!!
It looks like the equation is
-sin²(x) = cos(2x)
Recall the half-angle identity for sine:
sin²(x) = (1 - cos(2x))/2
Then the equation can be written as
-(1 - cos(2x))/2 = cos(2x)
Solve for cos(2x):
-1/2 + 1/2 cos(2x) = cos(2x)
-1/2 = 1/2 cos(2x)
cos(2x) = -1
On the unit circle, cos(y) = -1 when y = arccos(-1) = π. Since cosine has a period of 2π, more generally we have cos(y) = -1 for y = π + 2nπ where n is any integer. Then
2x = π + 2nπ
x = π/2 + nπ
In the interval [-π, π], you get two solutions x = -π/2 and x = π/2.
match the absolute value functions with their vertices
Hi, I need help with this!!! I don’t understand this :-(
Answer: See image and explanation below
Step-by-step explanation:
The problem gives us 6 points to draw into the sketch.
The first and second point gives the domain and range of the sketch. The last 4 points tell us the coordinates.
Let's do the first two points. This tells us that the sketch should not go further (-3,0) and (3,0) of the x-axis, and should not go further (0,0) and (0,4) of the y-axis.
For the last 4 points, we can convert them to coordinates and graph them. The points would be (-2,3), (1,2), (-3,0), (3,0), and (0,4).
After we draw the 5 points listed above onto the graph, we can connect the points.
In the image I attached, the lines are straight, but when you draw it out, you should make your lines more curved.
The table below gives the distribution of milk
chocolate M&M's
Color
Brown
Red
Yellow
Green
Orange
Blue
Probability
0.13
0.13
0.14
0.16
0.20
0.24
If a candy is drawn at random, what is the probability
that it is not orange or red?
PLZ HELP!!!!!
Explanation:
The probability of picking red is 0.13
The probability of picking orange is 0.20
The probability of picking either of these is 0.13+0.20 = 0.33
So the probability of picking neither of them is 1 - 0.33 = 0.67
There's a 67% of this happening.
Answer:
0.34
Step-by-step explanation:
because the probability of red is 20 and the probability of orange is 14 20 + 14 is 34.
Help anyone can help me do this question,I will mark brainlest.
Answer:
Answer is in attached image
I hope it help...
A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle? The change in the area of the rectangle is
Answer:
no change in area
Step-by-step explanation:
The original area is
A = 12*5 = 60 ft^2
The new length and width
l = 12 + .25 (12) = 12+3 =15
w = 5 - .2 (5) =5-1 = 4
The new area is
A = l*w =15*4 = 60 ft^2
The area is the same
Does anyone know the answer to this? I’m getting confused
Answer:
0
Step-by-step explanation:
Substitute b into -3.
Hence,
(b+3)(b²-5b+7)=(-3+3)(-3²-15+7)
=(0)(1)
=0
which function is shown in the graph below?
pls helppp
Answer:
c
Step-by-step explanation:
Can someone please explain how to do this!!!
Hi there!
So we are given that:-
tan theta = 7/24 and is on the third Quadrant.In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.
Since we want to find the value of cos theta. cos must be less than 0 or in negative.
To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.
Using the Identity
[tex] \large \displaystyle{ {tan}^{2} \theta + 1 = {sec}^{2} \theta}[/tex]
Substitute tan theta = 7/24 in.
[tex] \large \displaystyle{ {( \frac{7}{24}) }^{2} + 1 = {sec}^{2} \theta }[/tex]
Evaluate.
[tex] \large \displaystyle{ \frac{49}{576} + 1 = {sec}^{2} \theta} \\ \large \displaystyle{ \frac{625}{576} = {sec}^{2} \theta}[/tex]
Reminder -:
[tex] \large \displaystyle{ sec \theta = \frac{1}{cos \theta} }[/tex]
Hence,
[tex] \large \displaystyle{ \frac{576}{625} = {cos}^{2} \theta} \\ \large \displaystyle{ \sqrt{ \frac{576}{625} } = cos \theta} \\ \large \displaystyle{ \frac{24}{25} = cos \theta}[/tex]
Because in QIII, cos<0. Hence,
[tex] \large \displaystyle \boxed{ \blue{cos \theta = - \frac{24}{25} }}[/tex]
Using the Pythagorean Theorem
[tex] \large \displaystyle{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]
Define c as our hypotenuse while a or b can be adjacent or opposite.
Because tan theta = opposite/adjacent. Therefore:-
[tex] \large \displaystyle{ {7}^{2} + {24}^{2} = {c}^{2} } \\ \large \displaystyle{49 + 576 = {c}^{2} } \\ \large \displaystyle{625 = {c}^{2} } \\ \large \displaystyle{25 = c}[/tex]
Thus, the hypotenuse side is 25. Using the cosine ratio:-
[tex] \large \displaystyle{cos \theta = \frac{adjacent}{hypotenuse}} [/tex]
Therefore:-
[tex] \large \displaystyle{cos \theta = \frac{24}{25} }[/tex]
Because cos<0 in Q3.
[tex] \large \displaystyle \boxed{ \red{cos \theta = - \frac{24}{25} }}[/tex]
Hence, the value of cos theta is -24/25.
Let me know if you have any questions!
The height, h, in metres, of a rocket t seconds after it is launched is approximately modelled by the quadratic relation h = 80t - 16t2. To the nearest second, how long is the rocket in the air?
Answer: 5 s
Step-by-step explanation:
Given
Height of the rocket can be modelled as [tex]h=80-16t^2[/tex]
Rocket will land on earth when it's height becomes 0
[tex]\Rightarrow 80t-16t^2=0\\\Rightarrow t(80-16t)=0\\\\\Rightarrow t=0\ \text{or}\ t=\dfrac{80}{16}=5\ s[/tex]
Neglecting 0 value
Thus, rocket remains in air for 5 s.
geometry!!!!!! helppp select the ones that are true!
Answer:
Through any three collinear points, there is exactly one plane.False [ i.e. non collinear points]
A segment is part of a line between two points on the line called the endpoints.False[I.e. mid point]
If there is a line and a point not on the line, then there exists exactly one line through the point
that is parallel to the given line.True
The midpoint of a segment is equidistant from the endpoints.True
If two angles are supplementary to the same angle, then the angles must be obtuse.True
If two angles form a linear pair, then the angles are complementary.False [I.e. supplementary]
The sum of twice a number and 9 is-25
What’s the answer? I don’t understand the question and I came to see if you all can help
Answer:
15/2 that is the answer man
Need help please !!!!!!!
Answer:
go to scan an solve on brainly and it should bring up the answer, your welcome
Step-by-step explanation:
here is the answer to your question
Which of the following will simplify to the
correct solutions of y = 2x2 + 5x - 7?
-5+ 25 - 56 525-56
A
с
4
4
-5 + 25 +56 5+25+ 56
B
D
4
4
Answer:
f the answer to the question is A
Answer:b
Step-by-step explanation:
The area of a rectangle is 33 ft^2, and the length of the rectangle is 5 ft less than double the width. Find the dimensions of the rectangle.
Answer:
Length = 6
Width = 5.5
Step-by-step explanation:
Let's use the variable x to represent the width:
x = width
The question says that the length of the rectangle is "5 ft less than double the width". This length can be represented like this:
2x - 5 = length
To find the area of a rectangle, you multiply the width and length, so we are going to write an equation where we multiply the width and length and set it equal to 33 ft^2, which is the area:
(x)(2x - 5) = 33
Now use basic algebra to solve for x:
2x^2 - 5x = 33
2x^2 - 5x - 33 = 0
2x^2 + 6x - 11x - 33 = 0
(2x^2 + 6x) + (-11x - 33) = 0
2x(x + 3) - 11(x + 3) = 0
(2x - 11) (x + 3) = 0
x = 11/2, -3
x either equals 11/2 or -3. However, remember that x represents the width, and you can't have a negative number for a width, so x = 11/2 or 5.5.
Now plug in 5.5 to the length expression and simplify:
2(5.5) - 5
11 - 5 = 6
The length is 6 and the width is 5.5.
Hope this helps (●'◡'●)
A A theatre show lasts 162 minutes. How many hours long is 162 minutes? Show any remaining minutes as a decimal.
Answer:
2. 42 hrs
Step-by-step explanation:
we know that there are 60 minutes in one hour.
60 mins = 1 hour
162 mins = 162/ 60
[tex] \frac{162}{60} = \frac{120 + 42}{60} \\ = \frac{120}{60} + \frac{42}{60} \\ = 2 hrs+ \frac{42}{60} hrs[/tex]
42/ 60 hourse would mean 42 mins ( multiply the fractions with 60)
= 42 mins
therefore,
2hrs 42 mins
= 2. 42 hrs.
A reporter announces that there is an 80% chance of a thunderstorm tomorrow, and if the thunderstorm materializes, there is a 14% chance that it will produce a tornado.What is the probability that there will be a tornado tomorrow? What is the probability that there is a storm, but does not produce a tornado?
Answer & Step-by-step explanation:
We will only get a tornado if there is already a thunderstorm materializing
0.80 * 0.14 = 0.112
Probability of a tornado = 11.2%
There is a 100 - 14 = 86% chance of a tornado not being produced.
0.80 * 0.86 = 0.688
Probability of a storm and no tornado = 68.8%
What must be true if [tex]\frac{x}{y}[/tex] / [tex]\frac{3a}{b} =\frac{3a}{b}[/tex]? Assume a[tex]\neq[/tex]0, b[tex]\neq[/tex]0, and y[tex]\neq[/tex]0.
Answer:
4th option is correct
Step-by-step explanation:
The diagram shows the graph of a quadratic dinction y=f(x).
State
(a) the roots of the equation when f(x) = 0,
(b) he equation of the akis of symmetry of the curve
Pls help me
Answer:
hodrvyeieiwb was the only one to win a lot
Answer:
the roots are x= -4 and x=6
the equation of the axis of symmetry is x^2-2x-24
Step-by-step explanation:
to find the roots you go to the area where the graph is touching the x axis because y is 0 on the x axis
to find the equation use the values of the x intercepts which are -4 and 6
(x+4)(x-6)
solve this into an equation by multiplying everything in the first brackets by every thing in the second the answer you are likely to come up with is x^2-2x-24
I hope this helps
How is volume calculated for a triangular prism?
Multiply the area of triangle base by the prism’s total area.
Multiply the area of the triangular base by the prism’s height.
Multiply the area of the triangular base by the triangle’s height.
Multiply the area of the rectangular face by the height of the prism.
Answer:
B
Step-by-step explanation:
The volume of any prism whose height is perpendicular to the base is
V = B * h
The base can be anything, even a 17 sided figure. As long as the base has an area that can be found, and the height is perpendicular to it, the volume can be calculated.
Answer:
How is volume calculated for a triangular prism?
Multiply the area of the triangular base by the prism’s height.
At a gas station during a road trip, Gerard has $32.00 to spend on fuel and windshield washer fluid for his car. Fuel costs $2.75 per gallon, and each bottle of windshield washer fluid costs $3.00. The car's average fuel efficiency is 38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles, what is the maximum number of bottles of windshield washer fluid Gerard can buy? (Note: all prices include taxes.)
Answer:
Step-by-step explanation:
Total amount with Gerald = $32
Cost of fuel per gallon = $2.75
Cost of each bottle of windshield = $3
38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,
Total gallons of fuel = 250 miles / 38 miles
= 6.5789473684210 gallons
Total cost of fuel = Total gallons of fuel × cost per gallon
= 6.5789473684210 × $2.75
= $18.1
Amount left for windshield = Total amount with Gerald - Total cost of fuel
= $32 - $18.1
= $13.9
what is the maximum number of bottles of windshield washer fluid Gerard can buy?
= Amount left for windshield / Cost of each bottle of windshield
= $13.9 / $3
= 4.6333333333333 bottles
Maximum number of bottles =
4 bottles
If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work.
Answer:Answer: - The Earth will be closest to Saturn. - The Earth and Saturn will be 38,800,000 miles apart in standard notation
Step-by-step explanation:
becuase the earth and saturn are pretty farr
Tulio will invest $1,000,000 at 5% annual interest. Determine how much money will Tulio have after 10 years if the interest is calculated using the following methods.
Answer:
$1,500,000
Step-by-step explanation:
Given
Principal = $1,000,000
Rate = 5%
Time = 10years
Interest = PRT/100
Interest = 1000000*5*10/100
Interest = 100000*5
Interest = $500,000
Amount after 10years = $1,000,000+ $500,000
Amount after 10years = $1,500,000
A student survey was conducted at a major university. Data were collected from a random sample of 206 undergraduate students, and the information that was collected included physical characteristics (such as height and handedness), study habits, academic performance and attitudes, and social behaviors. In this exercise we will focus on exploring relationships between some of those variables. The variables are:
Answer:
Students Major
Cheat reporting response
Number of Alcohols taken
Student's Height
Step-by-step explanation:
The Variables are the following:
Categorical variables
1. Major – The student's majors -
Arts & Social Science or STEM
2. Cheat - Response about reporting cheating - Yes or No
Quantitative Variables
3. Alcohol - Number of alcoholic beverages consumed in a typical week
4. Height - Self-reported height (in inches)
please help she wont go to the next aswer
Answer:
$9.04 /gal
Step-by-step explanation:
1 gallon = 128 oz
8 * 4.23 oz = 33.84 oz
$2.39 /33.84 oz = .0707 $/oz
.0707 $/oz * 128 = $9.04 $/gal
plzzz helppppp 111111
Answer:
233 or option D
Step-by-step explanation:
In all shapes, all the angles add up to 360
So . . .
95 + x + 32 + x = 360
127 + x + x = 360
360 - 127 = 233
Therefore, your answer is 233 or option D
Answer:
233, D
Step-by-step explanation:
First, we know that the angles of a quadrilateral add up to 360 degrees. Therefore,
m∠a+m∠b+m∠c+m∠d = 360
m∠a+95+m∠c + 32 = 360
m∠a+m∠c + 127 = 360
subtract 127 from both sides
m∠a + m∠c = 233
You need to design a rectangle with a perimeter of 11 cm. The length must be 2.8 cm. What is the width of the rectangle? (You might want to draw a picture.)
a) Let w = the width of the rectangle. Write the equation you would use to solve this problem.
Step-by-step explanation:
p = 2×( l+w)
p = 2×l + 2×w
=> 2×w = p - 2×l
w = (p - 2×l) / 2
w = (11 - (2×2.8))/2
= (11- 5.6)/2
= 5.4 /2
= 2.7 cm
can someone help me make these into square root graphs? i thought i knew how, but trying it is confusing me
Answer:
Step-by-step explanation:
Please help
Me find that last box I’m struggling
Answer:
(0,-4)
Step-by-step explanation:
To find the y-intercept, substitute x=0
y= -3(0)^2+12(0)-4
=-4
Answer:
Axis of symmetry: x=2Vertex: (2, 8)Y-intercept: (0, -4)Min/Max: MaximumStep-by-step explanation:
Concept:
Quadratic equation formula: y=ax²+bx+c
Axis of symmetry formula=-b/2a
Y-intercept formula=c
Minimum or maximum is determined by the first term of the equation, which is [a]. If [a] is positive, then it is a minimum equation as the parabola heads up. If [a] is negative, then it is a maximum equation as the parabola heads down.
Given:
y = -3x² + 12x - 4
Solve:
The axis of symmetry formula = -b/2a
-(12)/2(-3) = 2The Vertex
y=-3x²+12x-4=-3(2)²+12(2)-4=8(2, 8)Y-intercept=c=(0, -4)
Min/Max
Since [-3] is negative, it is maximumHope this helps!! :)
Please let me know if you have any questions
