Answer:
[tex]x \sqrt{1-9x^2} -3x \sqrt{1-x^2}[/tex]
Step-by-step explanation:
Since we have to analyze the cosine of an addition of angles, let's recall that cos of an addition is:
[tex]cos (\alpha +\beta ) = cos(\alpha ) cos(\beta) - sin(\alpha) sin(\beta)[/tex]
Let's also use those Greek letters [tex]\alpha[/tex] and [tex]\alpha[/tex] to represent the inverse functions we are dealing with:
[tex]\alpha =arcsin(3x)[/tex] and therefore, [tex]sin(\alpha ) = 3x[/tex]
[tex]\beta =arccos(x)[/tex] and therefore [tex]cos(\beta ) = x[/tex]
Now use these identities to re-write the equation for the cos of an addition given above:
[tex]cos (\alpha +\beta ) = cos(\alpha ) cos(\beta) - sin(\alpha) sin(\beta)\\cos (\alpha +\beta ) = cos(\alpha ) x - 3x sin(\beta )[/tex]
Now recall that the sine of an angle can be written in terms of the cos of the same angle via the Pythagorean identity: [tex]sin(\beta ) = \sqrt{1-cos^2(\beta) }[/tex]
In our case, and with our particular values, this gives:
[tex]sin(\beta ) = \sqrt{1-cos^2(\beta)} = \sqrt{1-x^2}[/tex]
Similarly we can write the cos of an angle in terms of the sine of the same angle:
[tex]cos(\alpha ) = \sqrt{1-sin^2(\alpha) }[/tex]
In ours case, using our values, this gives:
[tex]cos(\alpha ) = \sqrt{1-sin^2(\alpha) }= \sqrt{1-(3x)^2}= \sqrt{1-9x^2}[/tex]
So replacing these in the cos of an addition of angles formula, we obtain that the given expression equals:
[tex]x \sqrt{1-9x^2} -3x \sqrt{1-x^2}[/tex]
We can simplify the expression cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions by using sin(arccos(x)) = sqrt(1 - x^2). The simplified expression is sqrt(1 - (3x)^2) * x - 3x * sqrt(1 - x^2).
Explanation:To simplify the expression cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions, we can use the fact that sin(arccos(x)) = sqrt(1 - x^2). Let's start by finding sin(arccos(x)).
arccos(x) gives us an angle whose cosine is x. We can then take the sine of this angle to get sin(arccos(x)). We know that sin^2(arccos(x)) + cos^2(arccos(x)) = 1, so sin(arccos(x)) = sqrt(1 - x^2).
Now, let's substitute the values in the original expression:
cos(arcsin(3x) + arccos(x)) = cos(arcsin(3x)) * cos(arccos(x)) - sin(arcsin(3x)) * sin(arccos(x))
Substituting the values, we have: cos(arcsin(3x)) * cos(arccos(x)) - sin(arcsin(3x)) * sin(arccos(x)) = sqrt(1 - (3x)^2) * x - 3x * sqrt(1 - x^2)
This is the simplified expression of cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions.
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Kevin, Michael and Darren all do their own laundry at home. Kevin does his laundry every 9 days, Michael every 10 days, and Darren every 12 days. If they all did their laundry today, in how many days will the three of them all do their laundry again on the same day?
A. 100 Days
B. 144 Days
C. 180 Days
D. 212 Days
Answer:
In 180 days the three of them will do their laundry again on the same day.
Step-by-step explanation:
we need to find the least common factor or 9, 10 and 12:
LCM(9, 10, 12) = 180
1. A group of 36 students goes
on a school field trip. Of all the
students on the trip. 18 are in
third grade. What is 18 in simplest
form?
- No
The simplest form of '18' is '18'. In relation to the field trip, '18' represents the number of third-grade students who attended, which is half of the total group of 36 students.
Explanation:This question is asking for us to simplify the number '18'. The simplest form of a number is itself when it cannot be divided evenly by any other numbers except for 1 and itself. In this case, the number '18' can be divided by 1, 2, 3, 6, 9, and 18. It cannot be simplified further because it does not have any other divisors aside from these. Therefore, the simplest form of '18' is '18'.
In the context of this question, if '18' represents the number of students in the third grade who went for the field trip, that refers to exactly half of the total group since there were 36 students in total.
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The sum of two numbers is 14. When one number is added to twice the other number, the result is 25. Find the numbers
Let x and y be the two numbers. We have:
[tex]\begin{cases}x+y=14\\x+2y=25\end{cases}[/tex]
Subtract the first equation from the second to get
[tex]y=11[/tex]
And deduce
[tex]x+11=14 \iff x=3[/tex]
The two numbers are 3 and 11.
2.3.7
Solve x - 9y = 17 for y.
y=
(Use integers or fractions for any numbers in the expressions
Answer:
x - 9y = 17
x - 17 = 9y
( x - 17)/9 = y
How much will a $1.42 loaf of bread cost in 25 years based on inflation
Answer:
the bread will cost around 28 dollars.
Step-by-step explanation:
To estimate the future cost of a $1.42 loaf of bread in 25 years based on inflation, we can use the compound interest formula with an assumed average inflation rate.
Explanation:To calculate how much a $1.42 loaf of bread will cost in 25 years based on inflation, we need to consider the rate of inflation over that period. However, without that specific data, we can estimate the future cost of the bread using past inflation rates.
Let's assume an average inflation rate of 2% per year. To calculate the future cost, we can use the formula for compound interest: Future Price = Present Price * (1 + Inflation Rate)^Number of Years
For the loaf of bread, the future price will be: $1.42 * (1 + 0.02)^25 = $2.63
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How are the properties of reflection used to
transform a figure?
Answer:When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). ... Remember that each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure.
Step-by-step explanation:
Answer:
The properties of reflection are used when we want to reflect a figure across a specific line, it can be across y-axis, x-axis, y = x or y = -x.
In either case, the result is a reflection, that is, those lines will work as a mirror, having the same shape and size but reflected across the line.
It's important to say that a reflection is a rigid transformation, which means the shape or size of the figure won't chance.
If we want to reflect across the y-axis, the transformation is:
[tex](x,y) \implies (-x,y)[/tex]
Across the x-axis: [tex](x,y) \implies (x,-y)[/tex]
Across the line y = x: [tex](x,y) \implies (y,x)[/tex]
Across the line y = -x: [tex](x,y) \implies (-y,-x)[/tex].
I need help ASPA with these two questions!!! <3 GIVE THANKS
1. Classify the expression: 5x3 + 2x − 3
Quadratic expression
Linear expression
Cubic expression
Exponential expression
2. Choose the expression that represents a quadratic expression.
12x4 − 2x3 + 5x2 − 9x − 6
2x3 + 5x2 − 9x − 6
12x2 + 8x − 1
−8x − 1
Answer:
Part 1) Is a cubic expression
Part 2) The quadratic expression is 12x² + 8x − 1
Step-by-step explanation:
Part 1) Classify the expression: 5x³ + 2x − 3
we know that
Polynomials can be classified two different ways - by the number of terms and by their degree.
so
a) By the number of terms is a trinomial, because has three terms
b) By their degree The degree of the polynomial is found by looking at the term with the highest exponent on its variable
The highest exponent is 3 so this is a 3rd degree trinomial
therefore
Is a cubic expression
Part 2) Choose the expression that represents a quadratic expression
we know that
If the expression is a quadratic equation , then the highest exponent of the variable is 2
therefore
The quadratic expression is 12x² + 8x − 1
Answer:
1. Cubic expression
2. [tex]12x^2+8x-1[/tex]
Step-by-step explanation:
1. We have the expression [tex]5x^3+2x-3[/tex] and we have to classify it.
A quadratic expression has the form [tex]ax^2+bx+c,a\neq 0[/tex].
We can see that the first term is squared. And in the expression that we have to classify the first term is raised to the cubic, then it isn't a quadratic expression.
A linear expression has the form [tex]ax+b[/tex].
We can see that it only has two terms and the first term has exponent 1. The expression [tex]5x^3+2x-3[/tex] has 3 terms and the first term has exponent 2 then it isn't a linear expression.
A cubic expression has the form[tex]ax^3+bx^2+cx+d[/tex].
We can see that the first term is raised to the cubic. And [tex]5x^3+2x-3[/tex] is raised to the cubic.
We can rewrite it: [tex]5x^3+2x-3=5x^3+0x^2+2x-3[/tex]
[tex]a=5\\b=0\\c=2\\d=-3[/tex]
The expression [tex]5x^3+2x-3[/tex] agrees with the definition of a cubic expression. Then it's a cubic expression.
An Exponential expression has the form [tex]y=ab^x, a>0[/tex]
2. We said that a quadratic expression has the form [tex]ax^2+bx+c,a\neq 0[/tex].
Then the expression that agrees with the definition is [tex]12x^2+8x-1,a\neq 0[/tex]
With,
[tex]a=12\\b=8\\c=1[/tex]
9. Which number is rational?
(1) Square root of
(2) pi (symbol)
(3) 5 square root 9
(4) 6 square root 2
Answer:
5 square root 9
Step-by-step explanation:
A rational number is a number that can be put in fraction form.
You can easily take the square root of 9 to get 3, which you can multiply by 5 to get 15.
Since you can make 15 into 15/1, which is a fraction, it is rational.
If Camillo goes with the better buy, how much will he pay for the 25 loaves of bread that he needs for the gourmet peanut butter and jelly sandwiches? Enter your answer to the nearest cent.
Answer:
let me fill your answer with this picture
Step-by-step explanation:
48.75 i belive
what is the distance from A to B
Answer:
E is the same distance away from A, and A to B.
(3a) (a^-3) please help I'm very confused if possible please show your work! <:D
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (3a)(a^{-3})\implies 3a\cdot \cfrac{1}{a^3}\implies \cfrac{3a}{a^3}\implies \cfrac{3~~\begin{matrix} a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{aa~~\begin{matrix} a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{3}{a^2}[/tex]
6 - 0.617. WHAT IS SIX MINUS 0.617
Answer:
5.833
Step-by-step explanation:
SIX MINUS 0.617 IS 5.833
For which object would a geologist use carbon-14 dating to determine age?
Answer:
The correct option is the first one. An animal skull
Step-by-step explanation:
The correct option is the first one. An animal skull
The radiocarbon dating, also referred to as carbon -14 dating, is used for the determining of the age of an object containing organic matter based on the properties of the radiocarbon.
The age detection of the ancient objects are very tough,due to no records are available about the objects.
That's why scientists use carbon-14 dating process.
In this picture, the only object that contains organic material is the animal skull, thus it is the only one that can be dated with this method.
Answer:
The correct option is animal skull
Step-by-step explanation:
Carbon-14 dating is a method for determining the age of an object containing organic material by utilising the properties of a radioactive isotope of carbon. As we have no records of the object, it's become very difficult to detect the age of an object . In such a situation, carbon-14 dating process helps .
In the given picture, animal skull is the only object that contains organic material , so it is the only object for which geologist would use carbon-14 dating to determine age.
Therefore, the correct option is animal scull ( first one )
What is the result when the number 25 is increased by 20%?
Answer:
30
Step-by-step explanation:
First find 20% of 25
25 x .20 = 5
Then add the product to the original number
25 + 5
Your answer is 30.
3/4 of what number is 6 times 4?
the answer would be 32
'
Answer:
32
Step-by-step explanation:
3/4 of what number is 6 times 4?
[tex]\frac{3}{4}x = 6(4)[/tex]
[tex]\frac{3x}{4} = 24[/tex]
[tex]3x = 24.4[/tex]
[tex]3x = 96[/tex]
[tex]x = \frac{96}{3}[/tex]
[tex]x = 32[/tex]
2/3+1/6= I need Help understanding fractions example. need a break down.
Answer:
[tex]\large\boxed{\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{5}{6}}[/tex]
Step-by-step explanation:
You must have the same denominator to add two fractions.
LCD = 6
[tex]\dfrac{2}{3}=\dfrac{2\cdot2}{3\cdot2}=\dfrac{2}{6}[/tex]
[tex]\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{4}{6}+\dfrac{1}{6}=\dfrac{4+1}{6}=\dfrac{5}{6}[/tex]
Is angle 4 and angle 7 vertical angles? I think that they aren’t but I’m not quite sure..
Answer:
Yes
Step-by-step explanation:
∠4 = ∠7 ( vertical angles )
The angles are opposite angles of the vertex with the same straight lines
Angle 4 and 7 are vertically opposite angle.
What is vertically opposite angle?Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.
in the given systems of line,
Angle 1, 2, 3, 4, 5, 6, 7, and angle 8 are given.
To determine angle 4 and angle 7 are vertically opposite or not.
Use vertically opposite angle property,
Since, angle 4 and 7 are at same vertex and apposite to each other,
Therefore, angle 4 and 7 are vertically opposite angles.
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Correct Answers plz
In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
Hey!
-------------------------------------------------
Solution:
1/2 are younger than 10.
1/20 are 10 years old.
1/10 are older than 10 but younger than 12.
70 are 12 years old.
Find Common Denominators.
1/2 = 10/20
1/20 = 1/20
1/10 = 2/10
Add.
10/20 + 1/20 + 2/10 = 13/20
Subtract.
20/20 - 13/20 = 7/20
So we now see that 7/20 = 70
Now we can see that 1/20 = 10
-------------------------------------------------
Answer:
There are 10 students that are 10 years old.
-------------------------------------------------
Hope This Helped! Good Luck!
Answer:
10
Step-by-step explanation:
0.50 = x<10
0.05 = 10
0.10 = 10<x<12
70 students = 12+
How many are 10 yrs old?
0.50 + 0.05 + 0.10 = 0.65
To find the percent, multiply it by 100
0.65 * 100 = 65%
70 are 35%
70/0.35 = 200 total
200 * 0.05 = 10 ten-year-old students
10
Estimate the square root of 0.39 to the nearest 10th Place
Answer:
0.62
Step-by-step explanation:
Identity each pair
V each pair of angles as complementary, supplementary, or neither.
More than 5tps please help quickly
Answer:
#17 Complementary
#18 Neither
Step-by-step explanation:
Complementary Angle: If sum of two angles is right angle then both angles are complementary to each other.
Supplementary Angle: If sum of two angles is straight angle then both angles are supplementary to each other.
#17 In figure 1
∠1 + ∠2 = 90°
Sum of ∠1 and ∠2 is 90° which is right angle.
Therefore, ∠1 and ∠2 are complementary angles.
#18 In figure 1
Sum of ∠1 and ∠2 neither 90° not 180°
Therefore, ∠1 and ∠2 neither complementary angles nor supplementary angles.
Which shape has a larger area: a rectangle that is 7 inches by 3/4 inch or a square with side length of 2 1/2 inches
Answer:
an rectangle
Step-by-step explanation:
because it is 7 inches and it is 3/4 inches
Where does each answer belong in the boxes?? Right answers only, help please!! :))
Answer:
Box 1: Quadrant I
Box 2: Quadrant II
Box 3: Quadrant III
Hope this helps.
Write the value of the digit in the hundreds place and the value of the digit in the tens place in 440. What is the relationship between the values of those two digits
Both of the digits in the hundreds and tens place are 4, making it a relationship. The 4 in the hundreds place is worth 400, the 4 in the tens place is worth 40, and the 0 in the ones place is worth 0.
Hope this helped!
Nate
what is the value of the digit 3 in 20320
300
Step-by-step explanation:
It’s in the hundreds place
bart ran 500 meters from the cops and a speed of 6 meters/second before he got caught. how long did he run?
Answer:
He ran for 83.333 seconds before he was caught.
Hope this help.
The figure shows a diver diving from a platform, the diver reaches a depth of 4meters what is the change in the elevation of the diver
Answer:
15ft
Step-by-step explanation:
you have to add 11 and 4 to get 15
The change of elevation of the diver is of 15 metres.
---------------------
Initially, the diver is stopped at a height of 11 metres.Then, he jumps, falling a distance of 11 metres, meaning that the initial change in elevation is of 11 metres.Finally, he reaches a depth of 4 metres, that is, 4 metres below the water, adding 4 metres more to the change in elevation, 11 + 4 = 15, and thus, the change of elevation of the diver is of 15 metres.A similar problem is given at https://brainly.com/question/24150365
A recipe requires 1.5 kilograms of eggs. How much is this in pounds
Answer:
3.31 pounds of eggs will be required to prepare the recipe.
Step-by-step explanation:
Since 1 kilogram = 2.205 pounds is the scale by which we can convert the unit kilograms into pounds
∵ 1 kilogram = 2.205 pounds
∴ 1.5 kilograms = 1.5 × 2.205
= 3.3069 pounds
≈ 3.31 pounds
Therefore, 3.31 pounds of eggs will be required to prepare the recipe.
People wait for sales to
Answer:
go down
Step-by-step explanation:
They don¨t want to spend to much money on something so they wait.
-3y+5x=26,-2y-5x=-16
Answer:
x = 4 , y = − 2
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Answer:
x=4
y=-2
Step-by-step explanation:
We are give two linear equations and asked to solve them. The two equations are
-3y+5x=26
-2y-5x=-16
Adding both equations
-5y=10
Dividing both sides by -5
y=-2
Substitute y=-2 in first equation
-3(-2)+5x=26
6+5x=26
5x=20
Dividing both sides by 5
x=4
A race car travels 100 feet in .5 seconds. At this rate of speed, how many feeet will the race car travel in a minute?
Answer:
Step-by-step explanation:
[tex]\frac{100ft}{0.5s} * 60s[/tex]
[tex]\frac{100 * 60}{0.5}[/tex]
[tex]\frac{6000}{0.5}[/tex]
[tex]12000ft[/tex]
[tex]\text{Hello there!}\\\\\text{We know that a car travels 100 ft every .5 seconds}\\\\\text{Lets find how far it goes every second}\\\\100*2=200\,\text{ft per second}\\\\\text{We're trying to find how far it goes in a minute, so multiply by 60}\\\text{Since 60 seconds = 1 minute}\\200*60=12000\\\\\boxed{12,000 ft}[/tex]