Answer:
Option A- 60°
Step-by-step explanation:
Given : Function - [tex]4cos^2x-1=0[/tex]
To solve the function
Step 1 - Write the function
[tex]4cos^2x-1=0[/tex]
Step 2- Add 1 both side
[tex]4cos^2x=1[/tex]
Step 3- Divide 4 both side
[tex]cos^2x=\frac{1}{4}[/tex]
Step 4 - Taking root both side
[tex]cosx=\sqrt{\frac{1}{4}}[/tex]
Step 5 - solve
[tex]cosx=\pm{\frac{1}{2}}[/tex]
Either [tex]cosx={\frac{1}{2}}[/tex] or [tex]cosx=-{\frac{1}{2}}[/tex]
When [tex]cosx={\frac{1}{2}}[/tex]
[tex]\rightarrow cosx={cos\frac{\pi}{3}}[/tex]
[tex]\rightarrow x={\frac{\pi}{3}} or 60^{\circ}[/tex]
or when [tex]cosx=-{\frac{1}{2}}[/tex]
[tex]\rightarrow cosx={cos(\pi-\frac{\pi}{3})}[/tex]
[tex]\rightarrow x={\frac{2\pi}{3}} or 120^{\circ}[/tex]
Therefore, Option A is correct solution of function is at 60°.
The solution of the given trigonometric ratio for the expression 4cos²x - 1 = 0 is equal to 60°
To find the solutions to the equation 4cos²x - 1 = 0, we first need to isolate the cosine term and then solve for x.
Let's go through the steps,
Add 1 to both sides of the equation:
4cos²x = 1
Divide both sides by 4:
cos²x = 1/4
Take the square root of both sides:
cosx = ±√(1/4)
Now, we have two cases to consider: positive and negative square roots.
Case 1,
cosx = √(1/4)
The cosine of an angle can never be negative when expressed in degrees, so we ignore the negative square root.
cosx = √(1/4) = 1/2
To find the angles for which the cosine is 1/2, we look at the unit circle or use a calculator to find the inverse cosine (arccos) values:
x = arccos(1/2)
The principal angle that satisfies this is x = 60°.
Case 2,
cosx = -√(1/4)
Again, we ignore the negative square root as the cosine is not negative in degrees.
Therefore, the only solution to the equation is:
x = 60°
Therefore, among the given options, the solution to 4cos²x - 1 = 0 is 60°.
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Which letter would it be ??
A game normally cost $53.00, but Isabel used a coupon and got the game for $37.10. The coupon was for what percent off.
A block of wood has a mass of 120g and a volume of 200cm3. What is the density of the wood?
Please provide an explanation!
Answer: [tex]0.6\ g/cm^3[/tex]
Step-by-step explanation:
We know that the formula to find density is given by :_
[tex]\text{Density}=\dfrac{\text{Mass}}{\text{Volume}}[/tex]
Given : Mass of block of wood = 120 g
Volume = [tex]200\ cm^3[/tex]
Then, the density of wood is given by :_
[tex]\text{Density}=\dfrac{120}{200}=0.6\ g/cm^3[/tex]
Hence, the density of wood = [tex]0.6\ g/cm^3[/tex]
what is the slope of this line −4x+7=2y−3
The slope of the line −4x + 7 = 2y − 3 is 2.
Explanation:To find the slope of the line, we need to rewrite the equation in the form y = mx + b, where m represents the slope.
Start by rearranging the given equation:
−4x + 7 = 2y − 3
Add 4x to both sides:
7 = 2y − 4x − 3
Combine like terms:
7 = 2y − 4x − 3
Now, isolate the y variable:
2y = 4x + 10
Divide both sides of the equation by 2:
y = 2x + 5
The equation is now in the form y = mx + b.
So, the slope of the line is 2.
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Four football fans took turns driving the distance from new York to Oklahoma to see a big game
Rewrite as a square or a cube:
3 3/8 =_____
1 11/25=_____
Answer:
3 3/8=1.5^3
1 11/25= 6/5^2
Step-by-step explanation:
i just tried until i got it
i hope this helps
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jane, andre, and marIA pick apples. andre picks three times as many pounds as maria. Jane picks two times as many pounds as andre. the total weight of apples is 840 pounds. how many pounds of apples does andre pick?
Rosaries cat weights 9.8 pounds. Her dog weighs 25.4 pounds. What's the weight of both animals combined.
I don't get this I need help
A culture of 1.08×1015 bacteria is in petri dish A. A culture of 2.7×1011 bacteria is in petri dish B.
How many times greater is the number of bacteria in petri dish A than petri dish B?
PLEASE ANSWER QUICKLY
Answer:The number of bacteria in petri dish A is 4000 times greater than petri dish B.
Step-by-step explanation:
Culture of bacteria in petri dish A=[tex]1.08\times10^{15}[/tex]
Culture of bacteria in petri dish B=[tex]2.7\times10^{11}[/tex]
Dividing culture of bacteria in petri dish A bu culturebacteria in petri dish B ,we get
[tex]\frac{1.08\times10^{15}}{2.7\times10^{11}}=\frac{108\times10^{15-11}}{270}\\\\=\frac{108}{270}\times10^{4}=0.4\times10^4=4000[/tex]
Therefore, the number of bacteria in petri dish A is 4000 times greater than petri dish B.
Farmer bob has a lot of chickens and pigs. If the pigs and chickens had the total of 17 heads and 46 legs, how much of each animal does farmer bob have?
I need help I don’t get the question
A number minus 6 equals 12
Find and compare the unit prices. Which one is the better buy?
3 for $1.00
Or
10 for 3:00
Plz answer both parts ibe been really stuck on this one :)
There are 946 milliliters in a quart. There are 2 pints in a quart. How many milliliters are in a pint?
Answer:
Find out the how many milliliters are in a pint .
To prove
As given
There are 946 milliliters in a quart.
There are 2 pints in a quart.
Thus
946 milliliters = 1quart = 2 pint
Than
946 milliliters = 2 pint
[tex]1\ pint = \frac{946}{2}\ millilitre[/tex]
1 pint = 473 millilitre
Therefore 473 milliliters are in a pint .
Answer:
there are 473
Step-by-step explanation:
0.009 is 1/10 of which decimal
Eli need to save $235 to earn money he plans to mow lawn’s and charged $21 for each write two estimate you like you to determine the number of lawns he need to mow decide which estimate you think is the better one Eli to use explain your reasoning
Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M'N'O'. Which statement shows the measure of angle M'N'O'?
m∠ M'N'O' = 90 degrees
m∠ M'N'O'= 180 degrees
m∠ M'N'O' = 2 ⋅ m∠MNO
m∠ M'N'O' = m∠MNO
Answer:
The answer is m∠ M'N'O' = m∠MNO
Step-by-step explanation:
If the Angle MNO is rotated 90 degrees counterclockwise about the origin. The new angle formed by ' will be the same as the rotation doesn't alter neither the shape or size of the figure. Therefore, we can conclude that MNO and M'N'O' are congruent (Same lenght and angle).
How many 1760 got in 4710
"The correct answer is 2.675.
To find out how many times 1760 is contained within 4710, we simply divide 4710 by 1760:
[tex]\[ \frac{4710}{1760} = 2.675 \][/tex]
This means that 1760 is contained exactly 2 times in 4710 with a remainder.
The decimal part (0.675) represents the fraction of the third 1760 that is not complete.
To express this as a fraction, we can write 0.675 as [tex]\(\frac{675}{1000}\),[/tex] which can be simplified by dividing both the numerator and the denominator by 125, giving us [tex]\(\frac{5.4}{8}\) or \(\frac{27}{40}\)[/tex] when expressed in lowest terms. Therefore, 4710 contains 2 complete sets of 1760 and a partial set equivalent to [tex]\(\frac{27}{40}\)[/tex] of 1760."
We want to partition 100 mL into 10 equal parts. How many milliliters should we pour in each cup?
What is the y-intercept of the graph that is shown below?
(–2, 0)
(–1, 2)
(0, 4)
(4, 0)
Answer:
The correct answer is C- (0,4)
Step-by-step explanation:
edge 2021
The y-intercept of the given graph is (0,4).
What is y-intercept?The y-intercept is the point where the graph intersects the y-axis.
Given a graph, where a straight line is intersecting x-axis at -2 and y-axis at 4.
So, x-intercept = (-2,0)
y-intercept = (0,4)
Hence, The y-intercept of the given graph is (0,4).
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a cube has a volume of 8 cubic inches what is the length of each edge of the cubes
The length of each edge of the cube is 2 in.
Given:
Volume of cube = [tex]8 in.^{3}[/tex]
*image of a cube is shown in the attachment.
Recall:
Formula for volume of a cube is given as:
[tex]V = a^{3}[/tex]
where,
[tex]a =[/tex] length of each edge of the cube
[tex]V = 8[/tex]
Plug in the value into the formula to find a.
[tex]8 = a^{3}\\\sqrt[3]{8} = \sqrt[3]{a^{3} } \\2 = a\\a = 2[/tex]
Therefore, the length of each edge of the cubes is 2 inches.
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The scale on the map says that 1.5 cm represents 40 miles. On the map the distance between Columbia, SC and Atlanta is 7 cm. Which is the correct proportion to use for finding the real distance between the cities?
A) none of these
B)
1.5
40
=
7
x
C)
1.5
7
=
x
40
D)
40
1.5
=
7
x
R=5(CA−0.3) solve for c
Final answer:
To solve the equation R=5(CA−0.3) for C, divide both sides by 5, add 0.3 to both sides and then divide by A.
Explanation:
To solve the equation R = 5(CA - 0.3) for C, you would first divide both sides of the equation by 5 to isolate the (CA - 0.3) term on one side:
R / 5 = CA - 0.3
Next, you would add 0.3 to both sides of the equation to get CA by itself:
(R / 5) + 0.3 = CA
Finally, to solve for C, you would divide the entire equation by A, assuming A is not zero:
C = [(R / 5) + 0.3] / A
determine whether the ordered pair (12, -5) is a solution to the equation 3x-3y=21
a root beer factory produces 132 554 cases in 100 days. About how many cases does the factory produce in 1 day? round your answer to the nearest tenth of a case. Show yohr thinking on the number line.
The robot beer company produces [tex]\fbox{\bf1325.5}[/tex] cases in one day.
Further explanation:
Given:
There is a robot beer factory that produces 132554 cases in 100 days.
Calculation:
As it is know that m objects produces [tex]x[/tex] cases in [tex]n[/tex] days, then [tex]m[/tex] objects produces cases in 1 day is [tex]\dfrac{x}{n}[/tex].
As it is given that the robot beer factory that produces 132554 cases in 100 days.
That means robot factory has total 132554 case which is produced by the worker of this company in 100 days.
Then the robot beer factory produces [tex]x[/tex] cases in 50 days is,
[tex]\begin{aligned}x&=132554\times\frac{{50}}{{100}}\\&=66277\\\end{aligned}[/tex]
That means if the robot beer company works for 50 days then the company produces 66277 cases which is the half of the 132554 cases as the number of days reduces to half.
The robot beer factory produces [tex]x[/tex] cases in 1 days is,
[tex]\begin{aligned}x&=132554\times\frac{1}{{100}}\\&=1325.54\\\end{aligned}[/tex]
That means if the robot beer company works for 1 days then the company produces 1325.54 cases which is the one hundredth of the 132554 cases as the number of days reduces to hundred times.
Since, we have to round the cases up to one decimal, the robot beer company produces [tex]\fbox{\bf1325.5}[/tex] cases in one day.
The robot beer company produces [tex]\fbox{\bf1325.5}[/tex] cases in one day.
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Answer detail:
Grade:Middle school
Subject:Mathematic
Chapter: Time and Work
Keywords:robot, factory, beer, 132554, cases, 100, days, 1, time, work, ratio, multiplication, division, 1325.54, 1325.5, produces.
Factory produces 1325.5 cases to the nearest tenth in 1 day.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Number of cases produced by factory = 132,554
Number of days = 100 days
Thus, Number of cases produce in 1 day = Number of cases produced / Number of days
⇒ Number of cases produce in 1 day = 132,554/100
⇒ Number of cases produce in 1 day = 1325.54
Round to nearest tenth, We look at the second decimal place which is 4
that is less than 5 so we leave the tenth place alone
⇒ Number of cases produce in 1 day = 1325.5
Thus, Factory produces 1325.5 cases to the nearest tenth in 1 day.
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You are heating liquid in a chemistry lab. Four minutes ago, the temperature of the liquid was -4 degrees Celsius. Since then, it has been going up at a steady rate of 2 degrees per minute.
A. Write an equation that tells you the relationship between temperature and time at any given time. Designate the current time as 0.
B.Use your equation to predict the temperature of the liquid 15 minutes from now.
Hank estimated the width of the door to his classroom in feet. What is a reasonable estimate?
How do solve -1.3m=3.12
what will be the 15th shape in the pattern. .