Which are simplified forms of the expression cot^2θcos2θ. Select two of the following there must be two selections!
Answers
Answer:
Second Option and Fourth Option
Step-by-step explanation:
[tex]cot ^ 2(\theta) cos(2\theta)[/tex]
We know that:
[tex]cot(\theta) = \frac{1}{tan(\theta)}[/tex]
Then:
[tex]cot^2(\theta)cos(2\theta) = cos(2\theta)\frac{1}{tan^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =\frac{cos(2\theta)}{tan^2(\theta)}[/tex]
Also:
For the sum of angles identity:
[tex]cos(2\theta) = cos(\theta + \theta)\\\\cos(\theta + \theta) = cos(\theta)cos(\theta) - sin(\theta)sin(\theta)\\\\cos(2\theta) = cos^2(\theta) - sin^2(\theta)\\\\cos(2\theta) = (1-sin^2(\theta)) - sin^2(\theta)\\\\cos(2\theta) = 1-2sin^2(\theta)[/tex]
Then:
[tex]cot^2(\theta)cos(2\theta) = \frac{cos^2(\theta)}{sin^2(\theta)}[1-2sin^2(\theta)]\\\\cot^2(\theta)cos(2\theta) = \frac{cos^2(\theta)[1-2sin^2(\theta)]}{sin^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =cot^2(\theta) - 2\frac{cos^2(\theta)[sin^2(\theta)]}{sin^2(\theta)}\\\\cot^2(\theta)cos(2\theta) =cot^2(\theta) - 2cos^2(\theta)[/tex]
Related Questions
We are given a table that displays the current value of search engine giant Google. Using the table below, determine the closing price of Google’s stock the previous day.
a.
$342.64
c.
$336.36
b.
$335.00
d.
$348.92
Answers
Answer:
c
Step-by-step explanation:
The correct option is c. $336.36. The previous day's closing price of stock was:c. $336.36.
To determine the closing price of stock the previous day, we need to use the information provided in the table. The table shows the net change (Chg) in the stock price and the current closing price (Close). The net change is the difference between the current closing price and the previous day's closing price.
From the table:
- Current closing price (Close): $342.64
- Net change (Chg): $6.28
Since the net change represents the increase in the stock price from the previous day to the current day, we can calculate the previous day's closing price by subtracting the net change from the current closing price.
[tex]\[\text{Previous day's closing price} = \text{Current closing price} - \text{Net change}\][/tex]
[tex]\[\text{Previous day's closing price} = 342.64 - 6.28 = 336.36\][/tex]
Therefore, the previous day's closing price of stock was:
c. $336.36
Could 60ft,61ft and 11ft form a right triangle
Answers
let's recall something about a right-triangle.
it has a 90° angle, and the longest side, the hypotenuse, from the pythagorean theorem, is c² = a² + b², or namely c = √( a² + b²).
so, let's take a peek at the two smaller sides, 60 and 11, can we get the longest side from it using the pythagorean theorem?
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=\stackrel{adjacent}{60}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ 61=\sqrt{60^2+11^2}\implies 61=\sqrt{3600+121} \\\\\\ 61=\sqrt{3721}\implies 61=61~~\stackrel{\textit{yeap, it is}}{\checkmark}[/tex]
The given lengths of 60ft, 61ft, and 11ft can form a right triangle. This has been confirmed by applying the Pythagorean theorem, which gives equal results for both sides of the equation.
Explanation:In the field of Mathematics, the formation of a right triangle with given side lengths can be verified using the Pythagorean theorem. The theorem states: If a triangle is a right triangle, then the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, as represented by this formula: a² + b² = c².
Applying this theorem to your question, we can use the three lengths you've provided: 60ft, 61ft, and 11ft. Let's assign the longest length (considered as the hypotenuse in a right triangle) as 'c', which is 61ft in this case. The other sides 'a' and 'b' would be 60ft and 11ft.
Here's how the theorem fits: 60² + 11² = 61².
Calculating the squares gives us 3600 + 121 = 3721 for the left-hand side, and 3721 for the right-hand side as well. Since the results are equal, the given lengths can indeed form a right triangle according to the Pythagorean theorem.
Learn more about Pythagorean theorem here:https://brainly.com/question/28361847
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what is the mode of 6.0, 6.5,6.2,5.5,6.8,6.3,6.4,6.7,6.5,6.2
Answers
Answer:6.2 and 6.5
Step-by-step explanation:
First, make a plotline from least to greatest and organize your list of numbers from least to Greatest.
Next, go through your list of organized numbers and add a dot to that number on the plotline. Repeat until done with list of numbers.
Then, go through your plotline and find the number(s) with the most dots and you have your mode.
Definition of mode: The number which appears most often in a set of numbers.
Answer provided in the image attached.
What is the area of the original rectangle?
Answers
ANSWER
[tex]8 {cm}^{2} [/tex]
EXPLANATION
First let us determine the scale factor of the enlargement
[tex]k = \frac{image \: length}{corresponding \: object \: length} [/tex]
[tex]k = \frac{8}{1.6} [/tex]
[tex]k = 5[/tex]
This implies that that, the corresponding length of the smaller rectangle is
[tex]l = \frac{25}{5} = 5cm[/tex]
The area of the smaller rectangle is
[tex] = 5 \times 1.6 = 8 {cm}^{2} [/tex]
Solve 2(y – 3) = 1.2 – y.
Answers
Answer:
y = 2.4
Step-by-step explanation:
first distribute into the parenthesis' -
2(y-3) = 1.2 -y
2y - 6 = 1.2 - y
+y +y
3y -6 = 1.2
+6 +6
3y = 7.2
/3 /3
y = 2.4
hope this helps!!
Answer: y=2.4
Step-by-step explanation:
The work is below Hopefully this helps:)
* Mark me the brainliest:)!!
A tent company has a tent design that is a triangular prism. The following is a net of the design.
If a = 68 inches, b = 69 inches, c = 44 inches, and d = 64 inches, how much fabric is needed to make the tent?
A. 22,264 sq in.
B. 15,236 sq in.
C. 14,080 sq in.
D. 23,460 sq. in
Answers
Answer:
first...you have to split the net into three rectangles and two triangles
picture inserted
Step-by-step explanation:
step 1
triangular base area
1/2 bh = 1/2 (44 in)(64 in)
= 1/2 (2,816 sq in)
= 1,408 sq in.
2 x 1,408 sq in = 2,816 sq in.
step 2
end rectangle area
lw = (68 in)(69 in)
= 4,692 sq in
2 x 4,692 sq in = 9,384 sq in
Now find the area of the middle rectangle
lw - (69 in) (44 in) = 3,039 sq in.
then add all the areas together
2,816 + 9,384 + 3,036 = 15,236 sq in
The fabric that is required to make the tent should be B. 15,236 sq in.
Calculation of fabric required:triangular base area
1/2 bh = 1/2 (44 in)(64 in)
= 1/2 (2,816 sq in)
= 1,408 sq in.
Now
2 (1,408 sq in) = 2,816 sq in.
Now
end rectangle area
lw = (68 in)(69 in)
= 4,692 sq in
So,
2 (4,692 sq in) = 9,384 sq in
Now determine the area of the middle rectangle
So,
lw - (69 in) (44 in) = 3,039 sq in.
So, the fabric required is
= 2,816 + 9,384 + 3,036
= 15,236 sq in
Learn more about prism here: https://brainly.com/question/22474603
Complete the statements to find the measurements of ∠a and ∠b .
Answers
Answer:
Step-by-step explanation:
Which day was the weather forecast most accurate?
Answers
Answer:
Thursday
Step-by-step explanation:
Since the forecast being completely accurate would be 0, you would have to choose the closest number to 0, and if you look -2 or Thursday is the closest number the 0,
What is the product?
Answers
Answer:
The correct answer is,
| -8|
| 4 |
Step-by-step explanation:
It is given two matrices,
1)Let Matrix A = 5 -2
-6 2
2) Matrix B = -1
-1
Matrix A is 2 x 2 matrix and matrix B is 2 x 1 matrix
To find the product of two matrices
A x B = 5 -2 x -1 = -10+2 = -8
-6 2 -1 6 -2 4
Therefore the correct answer is
| -8|
| 4 |
The triangles are similar. Which side of triangle JGH corresponds to side PM of PMO? I think it’s JG.
Answers
It is JG! You must rotate the second triangle so both triangles are at the same angle. Then, look at the lines and find the corresponding line segment on the other triangle.
(3x3 - 2x2 + 4) - (2x2 + 14) =
A)
3x3 - 10
B)
3x3 + 10
C)
3x3 - 4x2 - 10
D)
3x3 - 2x2 + 18
Answers
Answer:
Option C is correct
[tex]3x^3-4x^2-10[/tex]
Step-by-step explanation:
Like terms are those terms which have same variable to the same power.
Find the difference of the following:
[tex](3x^3-2x^2+4)-(2x^2+14)[/tex]
Remove the parenthesis we get;
[tex]3x^3-2x^2+4-2x^2-14[/tex]
Combine like terms;
[tex]3x^3-4x^2-10[/tex]
Therefore, the difference of [tex](3x^3-2x^2+4)-(2x^2+14)[/tex] is, [tex]3x^3-4x^2-10[/tex]
How do Federal Reserve banks and the federal government typically calculate simple interest?
Answers
Interest (I) = Principal (P) X Rate (R) X Time (T)
They tend to use 'Exact Interest' in which Interest calculated using a 365-day year. Time that counts exact number of days in the month that the borrower has the loan
Hope this helps :)
Answer:
Interest (I) = Principal (P) X Rate (R) X Time (T)
Hope this helps you:)
5INGH
Step-by-step explanation:
two step Equations ... problem :
-6n - 5=31
plz explain the answer ....thank u have a great day !
Answers
Answer:
n = - 6Step-by-step explanation:
[tex]-6n-5=31\qquad\text{First step: add 5 to both sides}\\\\-6n-5+5=31+5\\\\-6n=36\qquad\text\qquad\text{Second step: divide both sides by (-6)}\\\\-6n:(-6)=36:(-6)\\\\n=-6[/tex]
What is the length of bd?
Answers
The length of the bd in the given triangle is 12 cm. This is obtained by applying the Pythagoras theorem.
What is the Pythagoras theorem state?The Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. I.e., [tex]a^2+b^2=c^2[/tex].
Given data from the diagram:The triangle is perpendicularly divided into two halves looking like right-angled triangles.
The side lengths for the given triangle are bc=13 cm and ac=10 cm
Finding the length of the arm bd:The line segment bd divides the triangle into two right-angled triangles symmetrically.
So, the base ac of the given triangle is divided at the mid-point d.
Thus,
ac = ad + dc
here, d is the mid point, ad = dc
So, ad=dc=5 cm
Now, the triangle forms a right-angled triangle with sides bd, dc, and bc. Where bc is the hypotenuse.
To find the length of bd, applying the Pythagoras theorem
[tex](bc)^2=(bd)^2+(dc)^2[/tex]
⇒ [tex](13)^2 = (bd)^2 + (5)^2[/tex]
⇒ [tex]169 = (bd)^2 +25[/tex]
⇒ [tex](bd)^2 = 169 - 25[/tex]
⇒ [tex](bd)^2 = 144[/tex]
∴ bd = 12 cm
Therefore, the length of the bd is 12 cm.
Learn more about Pythagoras's theorem here:
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What is the center of the circle given by the equation (x−6)2+(y+3)2=72? A. (-6, 3) B. (-3, 6) C. (6, -3) D. (6, 7)
Answers
The center of the circle is the x and y in the equation.
To find the center you need to solve for x and Y when the equations inside parenthesis are set to zero.
(x-6)=0
x = 6
(y+3)=0
y = -3
The center of the circle is (6,-3)
help me !!!!!!please im begging u all for help i really need it please help me im begging u find the zero's of the function
Answers
[tex]y = - 2(x - 2)(x - 10)[/tex]
[tex]0 = - 2(x - 2)(x - 10)[/tex]
[tex]x - 2 = 0 \\ x = 2[/tex]
[tex]x - 10 = 0 \\ x = 10[/tex]
Answer:
The zero's are x=2 and x=10
Step-by-step explanation:
y = -2(x-2) (x-10)
We want to find the zero's so we set y=0
0 = -2(x-2) (x-10)
Using the zero product property
x-2 = 0 and x-10 =0
x-2+2 =0+2 x-10+10 =0+10
x =2 x=10
The zero's are x=2 and x=10
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $55. For one performance, 40 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $1325. What was the price of each kind of ticket?
Answers
Answer:
advance tickets cost $20 each & same-day tickets cost $35 each
Step-by-step explanation:
Let cost of advanced ticket be x and cost of same-day ticket be y. Now we can write 2 equations and solve them simultaneously.
"The combined cost of one advance ticket and one same-day ticket is $55":
[tex]x+y=55[/tex]
and
"...40 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $1325":
[tex]40x+15y=1325[/tex]
We solve for x in the first equation to get x = 55 - y and substitute this into 2nd equation and solve for y:
[tex]40(55-y)+15y=1325\\2200-40y+15y=1325\\-25y=1325-2200\\-25y=-875\\y=\frac{-875}{-25}=35[/tex]
Now plugging in y = 35 into the first equation, we can solve for x:
[tex]x+y=55\\x+35=55\\x=55-35\\x=20[/tex]
Hence, advance tickets cost $20 each & same-day tickets cost $35 each
Help me with number 2 plss people
Answers
Answer:
3/8
Step-by-step explanation:
1/2 of a yard is 4/8 of a yard, so you can subtract 7-4 to get 3/8 of a yard.
A pharmacist has 80 milliliters of a 30% saline solution. The graph shows the percentage concentration by adding x milliliters of a 10% saline solution. Which statement is true about the graph of the function?
Answers
Answer: C. The y-intercept means the concentration will remain 30% if no solution is added. <-- on edgen2020
Explanation: The first person who answered is correct! I'm attaching a screenshot of my quiz with this- Good luck everyone! :)
Answer:
C. The y-intercept means the concentration will remain 30% if no solution is added.
Step-by-step explanation:
edge2022
A right triangle has coordinates
A(6, 0), B(0, 0), and C(0, 8). What is the perimeter of the triangle?
A. 18 units
B. 20 units
C. 24 units
D. 28 units
Answers
Answer:
The answer is c, 24 units.
I need help pls...???
Answers
Answer:
x < 61
Step-by-step explanation:
Given
x + 12 < 73
Isolate x on the left side by subtracting 12 from both sides
x < 63 ← is the solution
The decimal equivalent of 3/7 rounded to the nearest hundredth is
0.43
0.428
0.429
0.40
Answers
The decimal equivalent of 3/7 rounded to the nearest hundreds is 0.428
Answer: 0.43 cause hundredths place is the 3 and its rounded
Step-by-step explanation:
How do you solve it
Answers
D is the answer............
Answer:
5/13
Step-by-step explanation:
Since the triangles are similar, the cos F = cos C
Cos C = adjacent side/ hypotenuse
Cos C = 5/13
Cos F = 5/13
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The length of each side of a square increases by 2.5 inches to form a new square with a perimeter of 70 inches. The length of each side of the original square was inches.
Answers
Answer:
15 inches
Step-by-step explanation:
Suppose length of original square is L inches.
Now, to form a new square the length increases by 2.5 inches
So, new length=L+2.5 inches
Given that, perimeter of new square =70 inches.
Formula:-
Perimeter=4*length of square
Therefore 70=4*(L+2.5)
70 =4 L+10
4 L=60
L=15 inches
Answer:
The original length of each side was 15 inches.
Step-by-step explanation:
In this case we have to have clear that the perimeter of square consists in the addition of the length of each one of its four sides, this is:
[tex]perimeter=a+a+a+a[/tex]
The new square has a perimeter of 70, and we have to find the original length of each side, the equation will be:
[tex]70=a+2.5+a+2.5+a+2.5+a+2.5[/tex]
[tex]70=4a+10[/tex]
We have to clear a:
[tex]a=\frac{70-10}{4} \\a=\frac{60}{4} \\a=15[/tex]
The original length of each side was 15 inches.
What is the reciprocal of -b/3
Answers
Answer:
-3/b
Step-by-step explanation:
The reciprocal of -b/3 is -3/b
Brock exercises every day. The function E = 15m + 5 represents the number of sit-ups he can do in m minutes. After drinking a new sports drink to stay hydrated, he finds that he can increase the number of sit-ups per minute by a factor of 3, represented by the function S = 3E. Which function represents the number of sit-ups he can do after drinking the sports drink?
Answer:
S = 45m + 15
Answers
Answer:
[tex]S=45m+15[/tex]
Step-by-step explanation:
we have
E------>the number of sit-ups
m----> the time in minutes
S----> the number of sit-ups after drinking the sports drink
[tex]E=15m+5[/tex] ----> equation A
[tex]S=3E[/tex] ----> equation B
substitute the equation A in the equation B
[tex]S=3(15m+5)[/tex]
[tex]S=45m+15[/tex]
Answer: Its the Second one!
Step-by-step explanation: Ur welcome <3
Which algebraic expression is a polynomial?
Answers
Answer:
B
Step-by-step explanation:
Answer:
Option 2 - [tex]-6x^3+x^2-\sqrt5[/tex]
Step-by-step explanation:
To find : Which algebraic expression is a polynomial?
Solution :
Polynomial is defined is the expression consisting of several terms with variable and constant.
Polynomial is always positive not a negative exponential.
Option 1 - [tex]4x^2-3x+\frac{2}{x}[/tex]
This is not a polynomial because it has a negative exponent.
Option 2 - [tex]-6x^3+x^2-\sqrt5[/tex]
This is a polynomial by definition.
Option 3 - [tex]8x^2+\sqrt x[/tex]
This is not a polynomial as [tex]\sqrt x[/tex] is not considerable.
Option 4 - [tex]-2x^4+\frac{3}{2x}[/tex]
This is not a polynomial because it has a negative exponent.
Therefore, Option 2 is correct.
Solve the following equation for d:b=cd
Answers
Answer:
d = b/c.
Step-by-step explanation:
Just divide both sides by c:
b = cd
b / c = cd/ c
b/c = d.
Answer:
[tex] d = \frac { b } { c } [/tex]
Step-by-step explanation:
We are given the following equation and we are to solve it for d:
[tex] b = c d [/tex]
Since we are asked to solve this equation for d and it contains all variables, it means that we need to make the variable 'd' the subject of the equation by keeping all other variables at the other side of the equation.
[tex] b = c d [/tex]
[tex]d=\frac{b}{c}[/tex]
23.8 is 10% of what amount
Answers
10% × 23.8 =
(10 ÷ 100) × 23.8 =
(10 × 23.8) ÷ 100 =
238 ÷ 100 =
2.38
Proof
2.38 ÷ 23.8 =
0.1 =
0.1 × 100/100 =
0.1 × 100% =
(0.1 × 100)% =
10%
Answer:
238
Step-by-step explanation:
Question: Find 10% of 238.
Answer: 10% of 238 is 23.8.
Explanation
STEP 1: 1% of 238 = 238100=2.38
STEP 2: 10% of 238 = 10⋅2.38=23.8
Explanation 2:
STEP 1: Write 10% as a decimal number: 10%=10100=0.1
STEP 2: Multiply 0.1 by 238: 0.1⋅238=23.8
Result
Question: The number 238 is 10% of what number?
Answer: The number 238 is 10% of 2380.
Explanation
STEP 1: Write 10% as a decimal number:
10=10100=0.1
STEP 2: Divide 238 by 0.1:
2380.1=2380
Help Me Please!!!!
Find the Mean from the line plot. , , .
Answers
The mean is the same as the average. To calculate the mean, add all of the values together and divide that result by the number of values.
3 + 3 + 3 + 4 + 6 + 6 + 7 + 8 = 40
Now, since there are 8 numbers, divide by 8.
40 / 8 = 5
There’s the mean! 5!
Please consider marking this answer as Brainliest to help me advance.