Answer:
Step-by-step explanation:
To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:
2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)
We can then substitute this expression on the left-hand side of the original equation and simplify:
4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)
Rearranging terms, we have:
4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1
We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:
4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1
Simplifying further:
4sinxcosx^2 - (cosx)cos(1) = 1
Now we can divide both sides by cos(1):
4sinxcosx^2/cos(1) - cosx = 1/cos(1)
Rearranging terms:
cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:
(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
We can then divide both sides by (4sinxcosx^2/cos(1) - 1):
2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)
And finally, we can solve for cosx:
cosx = 1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)
This is the solution to the equation.
R=1(149×109meter)2−(298×109meter)2
Value of R = 1.72×10¹¹ meter
The correct option is B.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
For example, x + y is an expression, where x and y are terms having an addition operator in between.
Given, expression
R = √[1/{1/(149×10⁹)² - 1/(298×10⁹)²}]
R = √[1/{1/(149×10⁹)² - 1/(298×10⁹)²}]
R = √[1/{(6.71×10⁻¹²)² - (3.36×10⁻¹²)²}]
R = √[1/{4.50×10⁻²³ - 1.13 × 10⁻²³}]
R = √[1/3.37×10⁻²³]
R = √2.97×10²²
R = 1.72×10¹¹ meter
Hence, 1.72×10¹¹ meter is value of R.
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Complete question is here;
is x-1 a factor of x^4-3x^3+6x^2-12x+8
Answer:
32842
Step-by-step explanation:
837428942
The cost of laser eye surgery in Country A is $2000 for each eye. The same surgery in Country B is
of this amount. What is the cost of this procedure in Country B?
The cost of laser eye surgery in Country B is for each eye.
(Simplify your answer.)
The cost of laser eye surgery in Country B is $1500 for each eye.
What is the proportion?
Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
A proportion is two ratios that have been set equal to each other,
a proportion is an equation that can be solved.
When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.
For instance, 5/10 equals 1/2.
We have given,
The cost of laser eye surgery in Country A is $2000 for each eye.
The same surgery in Country B is 3/4 of this amount.
Based on the given conditions, formulate: 2000 * 3/4
Reduce the expression to the lowest term: 500 * 3
Calculate the product or quotient: 1500
Hence, The cost of laser eye surgery in Country B is $1500 for each eye.
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The cost of laser eye surgery in Country B is $1500 for each eye.
What is the proportion?Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
A proportion is two ratios that have been set equal to each other,
a proportion is an equation that can be solved.
When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.
For instance, 5/10 equals 1/2.
We have given,
The cost of laser eye surgery in Country A is $2000 for each eye.
The same surgery in Country B is 3/4 of this amount.
Based on the given conditions, formulate: 2000 * 3/4
Reduce the expression to the lowest term: 500 * 3
Calculate the product or quotient: 1500
Hence, The cost of laser eye surgery in Country B is $1500 for each eye.
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Washington, DC is on Eastern standard time, Minneapolis is on Central standard time (1 hr earlier than Eastern standard time), and Las Vegas is on Pacific standard time (3 hrs earlier than Eastern standard time).
A flight leaves Washington, DC at 9:45 A.M. Eastern standard time, stops for 2 hours and 20 minutes in Minneapolis, then arrives in Las Vegas at 4:30 P.M. Pacific standard time.
How long is the plane actually flying?
Answer:
Step-by-step explanation:
When the plane landed in Las Vegas it was 4:30PM Pacific time - this converts to 730 PM Eastern time.
The entire trip lasted from 9:45 am to 7:30 pm. This is a total of 9 hours and 45 minutes.
Subtract 2 hours and 20 minutes for the layover and the plane was flying
for 7 hours and 25 minutes.
9 - 2 = 7 hours and 45 minutes - 20 = 25 minutes
What is the coefficient of the variable in the expression 2 − 5x − 4 + 8? (3 points) a −5 b −4 c 2 d 8
In the expression 2 − 5x − 4 + 8, the coefficient of x is -5. Thus, option a is correct.
What is a coefficient?A number or quantity combined with a variable is referred to as a coefficient. The variable is usually multiplied by an integer, which is then written next to it. It is assumed that the variables with no associated value have a coefficient of 1. For instance, in the expression 3x, the coefficient of x is 3, whereas in the expression x2 + 3, the coefficient of x2 is 1.
A variable's coefficient is the number or letter that the variable contains. As an illustration, the coefficient of variable x in the formula 2x + 3y is 2, and the coefficient of variable y is 3 in the same formula.
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لعمل
2. According to Jacqeline's mother, what is the right way to speak? (Look at "the right way to speak" on
pes. 68-69.)
Therefore , as a result, after answering the question, we may state that the coordinates are -(68,-69); the answer is = x - y - 137 = 0.
What do coordinates mean?When locating points or other geometric objects precisely on a continuum, such as Euclidean space, a coordinate system is a technique that uses one maybe more integers or coordinates. Locating a point or item on an a double plane requires the use of coordinates, which are pairs of integers. Two numbers called the y and x coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations.
Here,
Given :
we provided with the coordinates as -
(68,-69)
so, the equation is = y -y1 = m(x-x1)
= y + 69 = x - 68
x - y - 137 = 0
Therefore , as a result, after answering the question, we may state that the coordinates are -(68,-69); the answer is = x - y - 137 = 0.
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10. 24 is 3/4% of what number?
well, the number is really "x", which oddly enough is the 100%.
we also know that 3/4% of "x" is 24, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\[1em] 24&\frac{3}{4} \end{array}\implies \cfrac{x}{24}~~ = ~~\cfrac{100}{~~ \frac{3 }{4 } ~~}\implies \cfrac{x}{24}=\cfrac{400}{3} \\\\\\ 3x=9600\implies x=\cfrac{9600}{3}\implies x=3200[/tex]
Juan's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 70 coffees in all, 70% of which were regular. How many regular coffees did the cafe serve?
The cafe served 49 regular coffees.
How to calculate thisYou can use the proportion of regular coffees to the total number of coffees to find out how many regular coffees were served.
If 70% of the coffees served were regular, that means that 100-70 = 30% of the coffees served were decaffeinated.
To find out how many regular coffees were served, you can use the following proportion:
(Number of regular coffees) / (Total number of coffees) = 70% / 100%
You can then cross-multiply and solve for the number of regular coffees:
Number of regular coffees = (70/100) * (Total number of coffees)
Given the Total number of coffees = 70, you can substitute that and get:
Number of regular coffees = (70/100) * 70 = 49
Therefore, the number of regular coffees which the cafe served was 49.
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What is the work done on the box from x = 0m to 4.0m?
The work done on the given box from x = 0 m to 4.0 m will be 100 Nm.
What is Work Done?Work is performed when an item moves as a result of a force, causing energy to flow from one store to another. Work is measured in Joules, and one joule equals one newton of force on an object traveling one meter.
The graph is given in the question, as shown
We have to determine the work done on the given box from x = 0 m to 4.0 m
As per the given graph, the required solution would be as:
Work done = Force × covered area between the graph and displacement axis
Work done = 1/2 × (30 × 4) + 10 × 4
Work done = 1/2 × 120 + 40
Work done = 100 Nm
The work done on the given box will be 100 Nm.
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Some students collected the data below. They will graph the data. What is the y-intercept? Your answer should be an ordered pair ( , )
Answer:
(0, 28)
Step-by-step explanation:
Overview
To answer the question given, we have to find the point on the line that goes through the points given in the table when the x-axis represents the month of the year (1 is Jan, 2 is Feb, etc.) and the y-axis represents the average temperature for that month.
Method 1
I've attached a graph of the line for reference.
When we look at the graph of the line that goes through the points given in the table, we can determine that its y-intercept is (0, 28).
Method 2
To determine the y-intercept of the line without actually graphing it, we can construct an equation using the given points.
We know that the line's slope is defined as [tex]\dfrac{\textrm{rise}}{\textrm{run}}[/tex].
Using that information, we can solve for the line's slope by using any two of the given points. I will use the points for January (1, 42) and February (2, 56).
[tex]\textrm{slope} = \dfrac{56-42}{2-1} = \dfrac{14}{1} = 14[/tex]
Then, we can plug this value into the point-slope form equation
[tex]y - b = m(x - a)[/tex]
along with one of the given points [tex](a,b)[/tex] -- I'll use January (1, 42):
[tex]y-42=14(x-1)[/tex]
Next, to solve for the y-coordinate of the line's y-intercept, we can plug 0 into the equation for x and solve for y.
[tex]y - 42 = 14(0 - 1)[/tex]
[tex]y - 42 = 14(-1)[/tex]
[tex]y - 42 = -14[/tex]
[tex]y = -14 + 42[/tex]
[tex]y = 28[/tex]
Finally, we can plug the solved y-coordinate and 0 for the x-value (because we solved for when y when x = 0) into the format of a Cartesian coordinate:
(0, 28)
A number is no more than negative three
Simplify the expression in exact terms (no decimals): 6√x+7√(54) - 12√(6)
Answer:
Step-by-step explanation:
First, we will use the property of radicals that states that (a √b) * (c √d) = (ac) √(bd). Since the expression has both multiplication and addition, we will break the expression down into its components and simplify each component separately.
6√x+7√(54) = 6√x + 7√(27*2) = 6√x + 7√27 * 7√2 = 6√x + 7√27 * (2*√2) = 6√x + 14√27 * √2 .
Next, we will simplify the second component of the expression: 12√(6) = 12√(2*3) = 12√2 * 6√3 = (4*3)√2 * 6√3 = 12√2 * 6√3.
Finally, we can combine the two separate parts of the expression to get the simplified version: 6√x + 14√27 * √2 - 12√2 * 6√3 = 6√x + 14√27 * √2 - 12√6.
The simplified version of the expression is 6√x + 14√27 * √2 - 12√6, in exact terms (no decimals).
The cost revenue functions for a company are given by C=1000+3.75q and R=6.25q the fixed costs of the company are
The periodic fixed costs of the company, based on the cost function, are $1,000.
What are the fixed costs?The fixed costs refer to the period costs that do not change in total concerning the production or activity level and they relate to a financial period.
The fixed cost per unit decreases as more units are produced and vice versa. However, within the relevant range, the fixed cost for the period remains the same.
What is a cost function?A cost function is a model or formula that shows the total costs based on different cost behaviors (fixed and variable) and the relationship of costs to the production quantity.
Cost functions can be used to predict the total costs to be incurred under different production levels.
In this situation, the cost function, C = 1000 + 3.75q, shows that the fixed cost per period is $1,000 and $3.75 per unit (variable).
Thus, based on the cost function, the fixed costs are $1,000.
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answer for 10 points
Answer:
30 = 2·2·3
48 = 2·2·2·2·3
GCF = 6 (2·3)
LCM = 240 (2·3·5·8)
Step-by-step explanation:
if solid line is the parent function, f(x) Which of the following dotted line graphs shows the translation f(x)=f(x)+1? the translation f(x)=f(x)+1
Answer:
The graph that shows the translation f(x) = f(x) + 1 is the graph that is shifted upward by one unit on the y-axis. All the points on the graph have been moved upward by one unit, but the shape of the graph remains the same as the parent function.
The dotted line graph that shows the translation f(x) = f(x) + 1 is the one where the graph is shifted upward by one unit on the y-axis.
If 692 = 4,761, then 4,761 / 69 =
Answer: 69
Step-by-step explanation:
In the equation 692 = 4,761, we can see that 692 is being multiplied by some number to get 4,761. To find that number, we can divide 4,761 by 692:
4,761 / 692 = 69.
So, 4,761 / 69 = 69
In this case, 692 is being multiplied by 69 to get 4,761, so 69 is the value we get when we divide 4,761 by 69.
Consider the quadratic function y = ax2. As |a| increases, the graph . As |a| decreases, the graph .
As the value of a decreases the graph will expand.
What is a quadratic function?In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Given that consider the quadratic function y = ax². When the function is plotted on the for the value of an increases the graph contracts and if the value a decreases the graph expands.
The graph is attached with the answer below. In the graph, the quadratic function is shown at the two values of a.
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State the domain and range for the following relationThen determine whether the relation represents a function \{(4, 7), (- 3, 7), (6, 9), (4, 12)\}
Answer:
Domain {-3, 6}
Range: 7, 12}
Not a function
Step-by-step explanation:
Domain
Domain is the set of all x values which result in real and defined values for y
Range
Range is the set of y values that are possible from the values of x in the domain
Both are expressed in the form {min-value, max-value}
For x we see the minimum is -3 and maximum is 6
So domain = {-3, 6}
For y values we see the minimum is 7 and maximum is 12
So range = {7, 12}
A function can have only one output(y) for a specific input(x)
Here we see that for different values of x, x = 4 and x = -3, we get the same y-value
Hence it is not a function
which equation is represented by the table? y=-|x+1|-4 y
An equation is represented by the table is y= -4x+3. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, we have coordinates (0, 3) and (1, -1)
Here, m=(-1-3)/(1-0)
m=-4
Substitute m=-4 and (x, y)=(0,3) in y=mx+c, we get
3=-4(0)+c
c=3
Substitute m=-4 and c=3 in y=mx+c, we get
y= -4x+3
Therefore, option B is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which equation is represented by the table?
y=-3x+1
y=-4x+3
y=3x-4
y=-2x+1
A family buys an apartment for 200000. They pay a down payment of 20000. Their down payment is what percent of the purchase price
Answer:
the down payment of 20000 is 10% of the purchase price of 200000.
Step-by-step explanation:
To calculate the percentage of the down payment to the purchase price, you can use the following formula:
(down payment / purchase price) x 100
So in this case:
(20000 / 200000) x 100 = 0.1 x 100 = 10
Therefore, the down payment of 20000 is 10% of the purchase price of 200000.
A hiker walks at a speed of 3 2 5 kilometers per hour. How many kilometers will the hiker walk in 5 hours
Answer:
17 km----------------------------------------
The distance is the product of the speed and time.
Given:
Speed = 3 2/5 km/h,Time = 5 hours.Find the distance:
3 2/5 × 5 = 3 × 5 + 2/5 × 5 =15 + 2 = 17 kmAssume that you earned $27,000 last year and paid $1,809 in social security taxes. What percent of your
earnings are paid in social security taxes?
Include the "%" sign in your answer.
He paid 6.7% in taxes of his annual income.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Income = $27000 and paid $1,809 in social security taxes.
Thus percentage of earnings paid as taxes is
1809/27000 × 100 =6.7%
Hence, He paid 6.7% in taxes of his annual income.
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Whats the answer for the radius the image is attached please help and provide work :)
The radius of the cylinder is 1.59 centimeters.
What is the radius of the cylinder?Remember that for a cylinder of radius R and height H, the volume is given by the formula:
V = pi*R^2*H
Where pi = 3.14
Here we know that the height is 76cm, and the volume is 600cm³, then we can replace these two in the equation to get:
600cm³ = 3.14*(76cm)*R^2
Solving for R, we will get:
R = √( 600cm³/3.14*(76cm)) = 1.59 cm
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The radius of the cylinder is r=50.129
What is the radius of a cylinder?The radius of the cylinder is the radius of a base. The altitude of the cylinder is a perpendicular segment from the plane of one base to the plane of the other and the height of the cylinder is the length of the altitude. The axis of a cylinder is the segment containing the centers of the two bases
The volume of a cylinder is 600,000.
The height is 76cm and the radius is unknown. How do you solve it?
The volume of a right cylinder can be determined by πr²h,
where
r is the radius,
h is the height, and
pi is a constant.
So:
76πr²=600000
πr²=600000/76=7894.736
r²=2512.972
r=50.129 cm^2
Hence, the radius is 50.129 cm^2
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A region’s average movie theater ticket price in 2007 was $6.96. For 2017, it was estimated to be $8.53. Find the percent of increase in average movie theater ticket price for this 10-year period.
Answer: To find the percent increase in average movie theater ticket price, you can use the formula:
percent increase = (new value - old value) / old value * 100
Plugging in the values, we get:
percent increase = ($8.53 - $6.96) / $6.96 * 100 = 22.9%
So, the percent of increase in average movie theater ticket price for the 10-year period from 2007 to 2017 is 22.9%.
Step-by-step explanation:
William put the tip of his pencil on the outer edge of a graph of the unit circle at He moved his pencil tip through a angle of % radians in the the point (0,"1)_ counterclockwise direction along the edge of the circle At what angle of the unit circle did William's pencil tip stop?
Therefore , the solution of the given problem of circle comes out to be
angle is 5π /6 .
Circle – what is it?A circle is created when every point as in plane that is specific distance apart from another point does so (center). As a result, it is a curve made up of points that are spaced apart from one another in the plane. It is rotationally symmetrical about the center at all angles. Every pair of endpoints in the plane that make up a circle are evenly spaced away from the "center" and form a closed, two-dimensional object. A specular symmetries line is produced by a line that passes through the circle. It is rotationally symmetrical about the center at all angles.
Here,
Given : 4π/3
=> 4π/3 * 180/π
=> 240°
Thus , Angle measured from positive x - axis is anticlockwise direction.
=> 90° + 60° = 150°
=> 150° * π/180°
=> 5π /6
Therefore , the solution of the given problem of circle comes out to be
angle is 5π /6 .
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Please help!!! Will give brainlest easy 6th grade math.
A ball is dropped from different heights. The table shows the height of the first bounce after the ball is dropped.
Bouncing Ball Experiment.
Height of Drop (in inches)
10
20
30
Height of Bounce (in inches)
5
10
15
Part A
Using the data from the table, which equation can be used to find y, the height of the first bounce, in inches, when the
ball is dropped from a height of x inches?
A. y=2x
B. y=x/2
C. y=5x
D. y=x/5
Answer:
The equation that can be used to find y, the height of the first bounce, in inches, when the ball is dropped from a height of x inches is y=x/2. This can be determined by analyzing the data in the table:
-When the ball is dropped from a height of 10 inches, the height of the first bounce is 5 inches (y=5).
-When the ball is dropped from a height of 20 inches, the height of the first bounce is 10 inches (y=10).
-When the ball is dropped from a height of 30 inches, the height of the first bounce is 15 inches (y=15).
In all these cases, the height of the first bounce is half the height of the drop, meaning that the equation y=x/2 is the correct one
Answer:
B) y = x/2
Step-by-step explanation:
When the ball is dropped 10 inches, the ball bounces 5 inches
5 = 10/2
When the ball is dropped 20 inches, the ball bounces 10 inches.
10 = 20/2
When the ball is dropped 30 inches, the ball bounces 15 inches.
15 = 30/2
Find and ordered pair (x , y) that is a solution to the equation.
4x + y = 3
(x, y) = (_, _)
Answer:
(0,3)
Step-by-step explanation
4x+y=3
anything multiplied by x would make it greater than 3 so x is 0 then y has to be equal to 3 so (0,3)
A researcher uses technology to estimate the effect of a car crash on different car models.a. experiment b. observational study C. survey d. simulation
The debriefing is an essential part of the informed consent process and is mandatory when the research study involves use of deception.
What is the researcher use to technology?The debriefing is an essential part of the informed consent process and is mandatory when the research study involves use of deception. The debriefing provides participants with a full explanation of the hypothesis being tested, procedures to deceive participants and the reason(s) why it was necessary to deceive them.
Research in science and technology is important because it contributes to knowledge and understanding of the world. It also contributes to the development of new technologies which are important in science and technology.
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pls help with this question asap
Therefore , the solution of the given problem of slope comes out to be
1/10 , 2/15 , 3/20 and 4/25 slopes are respectively.
Explaining slope.steep a line is defined by its slope. The phenomenon of gradient overflow occurs in equations based on gradients. By dividing the median of the run (width difference) at two points even by rise (vertical distinction) between these very same two points, one may calculate the slope. Modeling the fixed path problem involves using an equation of the hill variety, denoted by the formula y = mx + b. The location of the line's y-intercept, when the slope is m, a = b, and also the equation are all true (0, b).
Here,
Given:
To find the slope
we have to find dx/dy is the formula for slope,
Thus ,
=> x/y = 1/10
=> x/y = 2/15
=> x/y = 3/20
=> x/y = 4/25
Therefore , the solution of the given problem of slope comes out to be
1/10 , 2/15 , 3/20 and 4/25 slopes are respectively.
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ANSWER FAST HELPP!! GIVING BRANLIEST!
Answer:
152
Step-by-step explanation:
8*10+12*6 =80+72 =152
