which of the following is a solution to 4cos^2x-1=0?
60°
150°
210°
330°
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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What is greater, 7/9, or 7.81 times 10 to the 1 power?
7/4 - 1.76
Please help -.-
the tax on a $400 painting is $34 what should be the tax on a $700 painting
In timra’s math class, there are 12 boys and 15 girls. What is the ratio of boys to girls in timra’s math class
In Timra's math class, the ratio of boys to girls is 12:15, which can be simplified to 4:5. This means for every 4 boys, there are 5 girls.
Explanation:In Timra's math class, there are 12 boys and 15 girls. The ratio of boys to girls in this case would be represented by the number of boys followed by the number of girls, separated by a colon. Therefore, the ratio of boys to girls is 12:15. You can also simplify this ratio by dividing both numbers by their greatest common divisor which is 3. After doing so, you will get a simplified ratio of 4:5. This means that for every 4 boys in the class, there are 5 girls.
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A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 48 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth are cut from the square?
(π = 3.14)
Answer Choices:
150.72 in2
192.00 in2
1,152.00 in2
1,808.64 in2
Answer:
D). 1,808.64 in2
Step-by-step explanation:
Diameter - 48 in.
Therefore, the radius is half of 48. 48/2 = 24.
Area = 3.14(24) 24 = 1,808.64in2
Hope this helps
Which expression is equal to 4−−√40−3−−√45 ?
0.2(x+50)-6=0.4(3x+20)
( show work please)
Tommy rote down all the whole numbers greater than -1 and less than 3. what is the average value of these numbers
What is the product of −2 1/2 and −3 1/3 ? a−8 1/3 b−616 c6 1/6 d8 1/3
Answer:
d 8 1/3
Step-by-step explanation:
Can someone help my do step by step 579 divided by 3
Answer: 193
Step-by-step explanation: an image is included to show you the steps.
From the division of given numbers we get quotient as 193 and the remainder as 0.
The two given numbers are 579 and 3.
Here, 579 divided by 3.
That is, 579/3
3|579|193
3
_____
279
27
_____
09
09
_____
00
So, the quotient is 193 and the remainder is 0.
Therefore, from the division of given numbers we get quotient as 193 and the remainder as 0.
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Which equation will help you solve this problem?
You have 16 books and 2 shelves to store them.
If you split them equally between the 2 shelves, how many books will be on each shelf?
State the slope of the line in simplest form.
Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $ 2 0 0 $200dollar sign, 200 a month and an additional $ 1 2 $12dollar sign, 12 for each album that he sells. Last month he earned a total of $ 6 4 4 $644dollar sign, 644. Write an equation to determine the number of albums ( a ) (a)left parenthesis, a, right parenthesis Floyd sold last month. Find the number of albums Floyd sold last month.
To find the number of albums Floyd sold last month, we calculate it using the linear equation $644 = $200 + ($12 \u00d7 a), where $644 is the total earnings, $200 is the base rate, and $12 is the amount earned per album. Floyd sold 37 albums last month.
Explanation:To determine the number of albums Floyd sold last month, we can set up a linear equation based on the information provided. Floyd is paid a base rate of $200 per month, and he earns an additional $12 for every album sold. The total amount Floyd earned last month was $644.
Let's let a represent the number of albums sold. The equation that represents the total earnings for the month would be:
Total Earnings = Base Rate + (Number of Albums Sold × Price per Album)
Based on what has been given, we can express this as:
$644 = $200 + ($12 × a)
To find the number of albums sold, we subtract the base rate from the total earnings, then divide by the additional amount earned per album:
$644 - $200 = $12 × a
$444 = $12 × a
a = $444 / $12
a = 37
So, Floyd sold 37 albums last month.
Use the associative property to identify which expression is equal to (10)(5x)(7).
A. (7)(5x)(10)
B. 10(5x + 7)
C. (10*5)(x*7)
D. (5x)(10)(7)
Help please, thanks in advance!
HELP PLEASE!!!!! HELP
What is the number in scientific notation?
Drag the answer into the box to match the number.
855,000,000,000
A: 8.055 x 10 ^-8
B: 8.5 x 10^9
C: 8.55 x 10 ^-11
D: 8.55 x 10^11
E: 8.5 x 10^7
F: 8.055 x 10^8
7 is what percent of 25
. Rotate 270 clockwise around the origin, and then translate 2 units up. (2, 10) (9, 5) (12, 2) (12, 10)
Your local bakery charges $6.00 for one dozen of doughnuts. (One dozen is 12 doughnuts). If you purchase any number of doughnuts over one dozen, you will only have to pay $0.40 per doughnut. The total cost of any number of doughnuts is given by the expression below.
6+.40(d−12)
Which part of the expression represents the number of doughnuts purchased at the discounted rate?
A. d
B. (d−12)
C. 6
D. .40(d−12)
The line segment is rotated 270 degrees counterclockwise about the origin to form A'B'. Which statement describes A'B'?
A.) A'B' is parallel to AB.
B.) A'B' is half the length of AB.
C.)A'B' and AB are equal in length.
D.) A'B' is greater than twice the length of AB.
8/9(54x−36)+2=−3/4(−40+16x)+90x solve for x
Farmer Ed has 3,500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
Answer:
Because it is a rectangle, the area is expressed as A = xy, or length times width.
Step-by-step explanation:
Because it is next to the river, he only needs to fence three sides, so F = x + 2y.
Knowing the amount of fencing available is 7500m, we get:
7500 = x + 2y solve for x
x = 7500 - 2y substitute into the area equation
A = (7500 - 2y)y distribute
A = -2y2 +7500y
You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875
x = 7500 - 2(1875) = 3750
A = 3750(1875) = 7,031,250 m2
If Farmer Ed has 3,500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, Then 7,031,250 is the largest area that can be enclosed.
What is Rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.
As it is next to the river, he only needs to fence three sides, so F = x + 2y.
Knowing the amount of fencing available is 7500m, we get:
7500 = x + 2y
solve for x
x = 7500 - 2y
substitute into the area equation
A = (7500 - 2y)y
Distribute
A = -2y2 +7500y
You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875
x = 7500 - 2(1875) = 3750
A = 3750(1875) = 7,031,250 m².
Hence 7031250 is the largest area that can be enclosed.
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A popular chain of superstores made 3.0479×108 dollars in profit last year. One particular store in the chain made 2.102×106 dollars in profit last year.
How many times greater is the profit made by the entire chain last year than by this particular store?
Drag and drop the values into the boxes to represent the answer in scientific notation.
0.145 1.45 145 10^2 10^14 10^48
____X_____times greater
Jack is mixing a cleaning solution that is 12% bleach.After mixing the solution,jack has 150 ounces of cleaning solution.how many ounces of bleach did jack use?
I am 5 more than 6 times 10?what number am i?
jon weighs 148 lbs and hopes to gain 2 lbs a week matt weighs 193 lbs and hope to lose 1 lb a week how many weeks till the weight is the same
To make 3.7 a whole number, multiply by ?
at the soda shop they sold forty eight hotdogs on monday and eighty on tuesday. how many times as many did they sell in monday than they sold on tueday?
What is the equation of the graphed line?
suppose that Y and Z are points on the number line if YZ=11 and Y lies on -9 where would Z be located
Final answer:
Point Z is located at 2 on the number line, found by adding the distance YZ=11 to the location of Y at -9.
Explanation:
If Y and Z are points on the number line, YZ=11, and Y lies on -9, to find where Z would be located, you simply add the distance between Y and Z to the point Y. Since the distance YZ=11, and Y is at -9 on the number line, you add 11 to -9 to find Z.
Therefore, the location of point Z will be:
-9 + 11 = 2
So, point Z is located at 2 on the number line.