Answers
Answer:
[tex]f(\theta)=\cos(\theta)[/tex] is an even function.
Step-by-step explanation:
Recall when it means when a function is even or odd. An even function has the following property:
[tex]f(-x)=f(x)[/tex]
And an odd function has the following property:
[tex]f(-x)=-f(x)[/tex]
So, let's test some values for cos(x).
Let's use π/3:
[tex]f(\pi/3)=\cos(\pi/3)[/tex]
From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).
Now, let's find -π/3. This is the same as 5π/3. Thus:
[tex]f(-\pi/3)=\cos(-\pi/3)[/tex]
And again from the unit circle, we can see that this is 1/2.
Therefore, despite the negative, the function outputs the same value.
Cosine is an even function.
Notes:
Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!
Related Questions
The change in kinetic energy (in joules) as a horse accelerates from canter to gallop is found using the expression 1/2 times 350 times (12 2 Minus 6 2
Answers
Answer:
[tex]\mathtt{\Delta K.E = 10500 \ J}[/tex]
Step-by-step explanation:
Given that:
the expression for the change in kinetic energy = [tex]\dfrac{1}{2} \times 350 \times ( 122 -62)[/tex]
Recall that
Kinetic energy K.E = [tex]\dfrac{1}{2}mv^2[/tex]
where,
m = mass of the horse
v = velocity of the horse
The change in kinetic energy between two instant times can be expressed by the relation
[tex]\Delta K.E = K.E_2 - K.E_1[/tex]
[tex]\Delta K.E =\dfrac{1}{2}mv^2_2- \dfrac{1}{2}mv^2_1[/tex]
[tex]\Delta K.E =\dfrac{1}{2}m(v^2_2-v^2_1)[/tex]
where;
m = 350
[tex]v_2[/tex] = 122
[tex]v_1[/tex]= 62
[tex]\Delta K.E =\dfrac{1}{2} \times 350 \times (122-62)[/tex]
[tex]\Delta K.E =\dfrac{1}{2} \times 350 \times (60)[/tex]
[tex]\Delta K.E = 350 \times 30[/tex]
[tex]\mathtt{\Delta K.E = 10500 \ J}[/tex]
w-5<17 solve the inequality for w
Answers
Answer:
w < 22
Step-by-step explanation:
w - 5 < 17
Add 5 to both sides:
w - 5 + 5 < 17 + 5
w < 22
In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now? In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?
Answers
Answer:
x = 45
45 years old
Step-by-step explanation:
x + 3 = 4(x - 33)
x + 3 = 4x - 132
x - 4x = - 132 - 3
-3x = -135
x = -135/-3
x = 45
Sally spends 90% of her weekly income on rent. If her rent is $720 each week, find her weekly income.
Answers
Answer:
$800
Step-by-step explanation:
We are told that ...
0.90 × (weekly income) = $720
Dividing by 0.90 gives ...
(weekly income) = $720/0.9 = $800
Sally's weekly income is $800.
Nick and Pam are paid $38.25 for their work network one hour and five minutes and Pam work three hours they split the money according to the amount of time each of them worth how much is make sure of the money explain
Answers
Answer:
Nick get = $10
Pam get = $28.25
Step-by-step explanation:
Given:
Total amount paid = $38.25
Nick work = 1 hour 5 minutes = 1.0833 hr
Pam work = 3 hour
Find:
Amount they get
Computation:
Assume each get x in 1 hour
So,
3x + 1.0833x = 38.25
4.0833x = 38.25
x = 9.3674
Nick get = 1.0833(9.3674) = 10.14 = $10
Pam get = $38.25 - $10 = $28.25
Find the distance between the points (-16,10) and (2,-14)
Answers
Answer: The distance is 30
Step-by-step explanation:
To find the distance between the two points,find the difference between the x and y values, square them and add them to find their square root.
10 - (-14) = 24
-16 - 2= -18
24^2 + 18^2 = d^2 where d is the distance
576 + 324 = d^2
900 =d^2
d = [tex]\sqrt{900}[/tex]
d= 30
Answer:
d=30
Step-by-step explanation:
distance between 2 points: d
d=√(x2-x1)²+(y2-y1)² (-16,10) and (2,-14)
d=√(2-(-16)²+(-14-10)²
d=√18²+(-24)²
d=√324+576
d=√900
d=30
The population of Austin, Texas, was about 494,000 at the beginning of a decade. The population increased by 3% each year. Write an exponential growth model that represents the population y (in thousands) t years after the beginning of the decade. Find and interpret the y-value when t = 10.
Answers
Answer:
y(t) = 494 (1.03)^t
y(10) = 663,89
Step-by-step explanation:
An increase in population by 3% each year means that at the end of each year, the population is 1.03 times what it was at the start of the year
This increase in population continues for t years
Exponential growth model that represents the population y (in thousands) t years after the beginning of the decade is
y(t) = 494 (1.03)^t
Where,
y = population
t = number of years
Find y when t = 10
y(t) = 494 (1.03)^t
y(10) = 494 (1.03)^10
= 494 ( 1.3439)
= 663.8866
Approximately y(10) = 663.89
This means that after 10 years from when the population was 494,000, it increased to 663,89.
Here is a list of numbers:
9, 3, 15, 19, 4, 2, 18,8,13
State the median.
Answers
Please help me out please!!!!!!
Answers
Answer:
you're nearly there
x/4, x/44x, 4xStep-by-step explanation:
You have obviously determined the correct entry in the top box of each pair. What you seem to have failed to observe is that the bottom box in each pair needs exactly the same entry as the top box.
_____
You figure this out by looking at the stuff that is outside the box. The numbers and symbols for the second box show how the function indicated outside the first box is evaluated. That is f(x) at the top becomes 4x at the bottom, where x (in this case) is x/4 for both.
What is the answer for 2/3 x -4 = -2
Answers
Answer:
x=3
Step-by-step explanation:
2/3x -4 = -2
2/3x = 2
(3/2)*(2/3x) = (2*3/2)
x=3
Answer:
x=3 I hate asking for things but may i have brainliest I need to rank up
Step-by-step explanation:
Step 1: Add 4 to both sides.
2/3x−4+4=−2+4
2/3x=2
Step 2: Multiply both sides by 3/2.
(3/2)*(2/3x)=(3/2)*(2)
then you get x=3
A recipe needs a ratio of 2.5 of sugar to flour. If Joe uses 60g of sugar, how much flour should he use?
Answers
Explanation for equation:
Answer:
150 g
Step-by-step explanation:
The 2 part of the ratio represents 60 g , thus
60 g ÷ 2 = 30 g ← value of 1 part of the ratio, then
5 parts = 5 × 30 g = 150 g ← amount of flour required
??? help plssss ????
Answers
Answer:
18
Step-by-step explanation:
12(3/2)=36/2=18
Answer:
18Step-by-step explanation:
[tex]12\left(\frac{3}{2}\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=12\times \frac{3}{2}\\\\\mathrm{Multiply\:fractions}:\quad \:a\times\frac{b}{c}=\frac{a\:\times\:b}{c}\\=\frac{3\times\:12}{2}\\\\\mathrm{Multiply\:the\:numbers:}\:3\times\:12=36\\=\frac{36}{2}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{36}{2}=18[/tex]
5.3x10 4 in standard form.
Answers
Answer:
5.3× 10⁴= ?
Step-by-step explanation:
10⁴ can also be written as 10×10×10×10= 10000
so, 5.3 × 10000= 53000
Scientific notations are the way through which a very small or a very large number can be written in shorthand. The value of 5.3×10⁴ in standard form is equal to 53,000.
What are Scientific notations?Scientific notations is the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.
For example, 6,500,000,000,000 can be written as 6.5e+12.
Given the numerical value 5.3×10⁴ which is needed to be written in the standard form, therefore, we can write,
5.3 × 10⁴
= 5.3 × 10,000
= 53,000
Hence, the value of 5.3×10⁴ in standard form is equal to 53,000.
Learn more about Scientific notation here:
https://brainly.com/question/1740231
#SPJ2
Which of the following is the set of all points in a plane that are a given distance from a point? A.Angle B.Circle C.Line D.Ray
Answers
Answer:
Circle
Step-by-step explanation:
just took test and got it correct
Circle is the set of all points in a plane is equidistant at a given distance from a point.
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.
Since, we know that
A two dimensional figure in which the set of all the points in a plane is equidistant from a given is called circle.
Therefore, option B is correct.
Find out more information about circle here:
https://brainly.com/question/23519482
#SPJ3
Perform the indicated operation.
Answers
Answer:
-22
Step-by-step explanation:
-18 - 4 =
We are subtracting both number so add them and then give them a negative sign
-( 18+4)
-22
Answer:
-22
Step-by-step explanation:
Combine the like terms to create an equivalent expression:
8t+1+(−4t)+(−6)
Answers
Answer:
4t-5
Step-by-step explanation:
Answer:
4t-5
Step-by-step explanation:
8t+1+(-4t)+(-6)
= 8t+(-4t)+1+(-6)
=(8t-4t)+(1-6)
=(8-4)t+(-5)
=(4)t+(-5)
=4t-5
This is true of false??
Answers
Answer:
It's TRUE!
CLOSURE PROPERTY IS USED !
Please help and show your work TwT
Answers
Answer:
≤
Step-by-step explanation:
First we solve 5(x + 2) ≥ 2(x + 8).
5x + 10 ≥ 2x + 16
3x ≥ 6
x ≥ 2.
Now we place an equal sign into the box:
4(x - 6) = 2(x - 10)
4x - 24 = 2x - 20
2x = 4
x = 2.
For the solution to only have 1 value, the solution must be x = 2.
Therefore we must have x ≥ 2 and x ≤ 2.
How do you find the domain and range of a function and write it in set notation? What is the process of finding it? Tips and tricks are very much appreciated. I literally have no clue how to get them. Send help?
Answers
Answer:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis
Step-by-step explanation:
plz forgive me if my answer is wrong
Domain = looking for the very far left value and the very far right value on the x-axis, and only x-axis, so the farthest left x-axis value and the farthest right x-axis value.
Range = very bottom y-value, and very top y-value
In both cases, if the arrows extend forever then that means you could have the value of infinity.
I dont understand this can you help
Answers
Answer:
C
Step-by-step explanation:
To answer a multiple choice question process of elimination can be very helpful
A isnt correct because CED is 90 degrees
B isnt correct since the line equals 180 degrees
C is correct because CED and AEC are a linear pair that add up to 180 degrees so if CED is 90 then so is AEC
Answer:
i did not understand it either
Step-by-step explanation:
but it means so like you would see what statement is ture so like say ced measured right then you would say it is right, you want to see what angel is right with this question your answer is the third answer
hope this help
It takes 2 gallons of milk to make a batch of ice cream. How many gallons of milk does it take to make 15.2 batches of ice cream?
Answers
Answer:
30.4
Step-by-step explanation:
2 times 15.2
−2, −1, 0, 1 Which pair of numbers has a sum of zero? A . 1, −1 B. −2, 0 C.−2, 1 D.−1, 0
Answers
Answer:
The correct answer i would think would be A. 1 + -1= 0
Step-by-step explanation:
Mia is taking a multiple choice test with a total of 50 points available. Each question is worth exactly 2 points. What would be Mia's test score (out of 50) if she got 3 questions wrong? What would be her score if she got x questions wrong?
Answers
Answer:
Mia's test score is 44 if she got 3 questions wrong.
Mia's test score is (50-2x) if she got x questions wrong.
Step-by-step explanation:
It is given that, Mia is taking a multiple choice test with a total of 50 points available. Each question is worth exactly 2 points.
If she got 3 questions wrong, then
Deducted marks [tex]=2\times 3=6[/tex]
Marks obtained by Mia = Total marks - Deducted marks
[tex]=50-6[/tex]
[tex]=44[/tex]
So, Mia's test score is 44 if she got 3 questions wrong.
If she got x questions wrong, then
Deducted marks [tex]=2\times x=2x[/tex]
Marks obtained by Mia = Total marks - Deducted marks
[tex]=50-2x[/tex]
So, Mia's test score is (50-2x) if she got x questions wrong.
Solve:
Please help solve the equation 1.5x-0.5=x+3.25
Answers
Answer:
x = 7.5
Step-by-step explanation:
Step 1: Subtract x from both sides.
1.5x−0.5−x=x+3.25−x
0.5x−0.5=3.25
Step 2: Add 0.5 to both sides.
0.5x−0.5+0.5=3.25+0.5
0.5x=3.75
Step 3: Divide both sides by 0.5
0.5x ÷ 0.5 = 3.75 ÷ 0.5
Hoped this helped!
☆*: .｡. o(≧▽≦)o .｡.:*☆
helpppp
Which of the following statements is the most precise and correct to define perpendicular lines?
A. Two lines are perpendicular if they intersect.
o
B. Two lines are perpendicular if they meet at a single point such that the two lines make a "T".
o
C. Two lines are perpendicular if they meet at one point and one of the angles at their point of
intersection is a right angle.
Answers
Answer:
C
Step-by-step explanation:
you can add that they meet at a 90° angle
Simplify ( 2^5/3^2)^4
Answers
Answer:
[See Below]
Step-by-step explanation:
✦ First simplify parts of the equation to make it easier:
✧ 2⁵ = 32
✧ 3² = 9
✦ Rewrite and solve parenthesis:
✧ (32 ÷ 9)⁴ = 3.55555556⁴
✦ Now solve the exponent:
✧ 3.55555556⁴ = 159.819541
✦ Simplify your answer:
✧ 159.82 (I rounded to the nearest hundredths)
~Hope this helps Mate. If you need anything feel free to message me.
Larry pours 11 gallons of water equally into 4 containers. Which equation shows how to find how many gallons of water there are in each container? A. B. C. D.
Answers
Answer:
2 3/4 gallons in each container
Step-by-step explanation:
Gallons of water = 11
Containers = 4
Larry pours 11 gallons of water equally into 4 containers
Gallons of water in each container = Total gallons of water / number of containers
= 11 / 4
= 2 3/4
There are 2 3/4 gallons of water in each containers
The equation is
Gallons of water in each container = Total gallons of water / number of containers
Rodney rented a machine for $70.00 to make popcorn at a school event. In addition to the machine rental cost, the popcorn supplies cost him $0.15 per bag sold. Rodney sold the popcorn for $1.00 per bag. How much profit did Rodney make if he sold 200 bags of popcorn?
Answers
Answer:
100$
Step-by-step explanation:
he profit from 1 popcorn=0.85$
from 200=170$
170$-70$=100
Answer: 100 dollars
Step-by-step explanation:
you answer should be a polynomial in standard form (x- 4) ( x + 7)
Answers
= x•x + 7x - 4x - 4 + 7
= x*2 + 7x - 4x - 28
= x*2 + 3x - 28
what is the solution to the equation 1/x=x+3/2x^2
Answers
Answer:
3.
Step-by-step explanation:
1/x = (x+3)/(2x^2), where x ≠ 0.
Cross-multiply to give 2x^2 = x(x+3).
2x^2 - x^2 - 3x = 0
x^2 - 3x = 0
x(x - 3) = 0
x = 3 or x = 0 (rejected because equation will be undefined)
Answer:
d
Step-by-step explanation: