The final answer is:
-1/7 < 5 < 2
Or, in interval notation:
(−1/7, 2)
What is interval?
In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded. For example:
First, let's simplify the expression inside the parentheses:
3 + 2 = 5
Now we can substitute this value into the expression and simplify further:
-14 < -7(5) < 1
-14 < -35 < 1
To solve this compound inequality, we need to isolate the variable (in this case, there is no variable) to find the range of values that satisfy the inequality. We can do this by dividing all three parts of the inequality by -7. However, we need to reverse the direction of the inequality signs since we are dividing by a negative number:
-14/-7 > -35/-7 > 1/-7
2 > 5 > -1/7
Therefore, the solution to the inequality is:
-1/7 < 5 < 2
In interval notation, this can be written as:
(−1/7, 2)
To sketch the solution, we can plot the interval on a number line. The interval does not include the endpoints, so we use open circles to indicate this:
<-------------(○======○)------------->
-1/7 5 2
The open circle at -1/7 indicates that -1/7 is not included in the interval, and the open circle at 2 indicates that 2 is also not included in the interval. The line segment between the circles represents the range of values that satisfy the inequality.
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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77
∘
∘
with the ground. Find the length of the ladder.
The length of the extension ladder that is against the outside wall of the house is 22.58 feet.
What is the length of the ladder?
The ladder forms a right triangle when it is placed up against a home. The hypotenuse of a ladder is its length. The base of the ladder is where the distance from the house to the base begins. The length is the distance from the home.
Here, we have
Given: An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77
To find the length of the ladder, Sin would be used:
Sin = opposite / hypotenuse
Sin77 = 22 / h
h = 22 / 0.9743 = 22.58 feet
Hence, the length of the extension ladder that is against the outside wall of the house is 22.58 feet.
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Amanda was watching her little brother Mike play on a swing
set. She decided that she would like to find his distance above
the ground using a sine or cosine curve. She starts timing and
finds that at t-2 seconds Mike is at his highest point. He
reachers his lowest point exactly 1.5 seconds later. Amanda
also records the highest Mike gets as 9 feet whle the lowest
point occurs at 1 foot. Write an equation that will find Mike's
height after t seconds.
Putting all these values together, we get the equation: h(t) = 4 cos(2π/3 (t - 2)) + 1 with Mike's height above the ground as a function of time t in seconds, where h(t) is measured in feet.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) and at least two expressions on either side of the equals sign. The expressions on either side of the equals sign can be numbers, variables, or a combination of both, and the equation represents a relationship between them. Equations are used in mathematics to solve problems and find unknown values by manipulating the expressions within the equation while keeping the equality true.
Here,
Assuming that Mike's motion on the swing set follows a periodic pattern, we can model his height above the ground using a sinusoidal function. Let's use the cosine function, since it reaches its maximum value when the input is 0 and decreases to its minimum value at π or 180°.
The general form of a cosine function is:
y = A cos(Bx + C) + D
where:
A = amplitude (half the distance between the maximum and minimum values)
B = frequency (the number of cycles per unit of x)
C = phase shift (horizontal shift of the graph)
D = vertical shift (vertical shift of the graph)
We are given that Mike's highest point is at 9 feet and his lowest point is at 1 foot. Therefore, the amplitude A = (9 - 1) / 2 = 4.
The frequency is determined by the time it takes for Mike to complete one cycle. We know that it takes him 1.5 seconds to go from his highest point to his lowest point and back up again. Therefore, the period of the function is 3 seconds (2 x 1.5), and the frequency is 1/3 cycles per second. Hence, B = 2π/3.
The phase shift is the horizontal displacement of the graph from the origin. We know that at t = 2 seconds, Mike is at his highest point. Therefore, we need to shift the cosine curve 2 seconds to the right to match this point. Thus, C = -2.
Finally, the vertical shift D is the position of the center of the curve. Since Mike's lowest point is at 1 foot, we need to shift the entire curve up by 1 foot. Thus, D = 1.
Putting all these values together, we get the equation:
h(t) = 4 cos(2π/3 (t - 2)) + 1
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Veronica's meal cost $11.92. She pays 8% tax. She then adds a 15 % tip to the total. What is the total cost of the meal to the nearest cent?
The cost of Veronica's supper was $11.92, plus an additional 8% tax of $0.954 and a 15% gratuity on top of tax of $2.0681, for a total price of $14.94.
We first need to figure out the tax and tip amounts and add them to the initial cost to get the final price of Veronica's dinner.
Let's first figure out the tax amount. The cost of the meal is multiplied by the 8% tax rate to determine the tax:
Tax = 11.92 * 0.08 = 0.954
Hence, the meal's tax is $0.954.
Next, let's figure out how much to tip. We multiply the price of the meal plus the tax by the 15% tip percentage to determine the tip:
Tip = (11.92 + 0.954) x 0.15 = 2.0681
Thus, $2.0681 is the total tip for the lunch, tax included.
The original price of the meal, the tax, and the tip can now be added to determine the final price:
Total Cost: 11.92 plus 0.9544 plus 2.0681
Veronica's total bill, rounded to the nearest cent, is therefore $14.94.
In conclusion, Veronica's dinner cost $11.92, plus an additional 8% tax of $0.954 and a 15% tip on top of the meal plus tax of $2.0681, for a total of $14.94.
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Pls help me
How long is the side CD? (Hint: opposite sides are equal. Put the expressions equal to each other and solve for x. Then, plug back into the expression for CD to find CD).
the side CD will be 27 units.
What is parallelogram?
A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.
Here CD=AB
2x+13=5x-8
3x = 13+8
x= 21/3
x=7
CD= 2*7+13=14+13=27
Hence the side CD will be 27 units.
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3/2=4x what is x
Solve the equation.
3
2
=
4
�
2
3
=4xstart fraction, 3, divided by, 2, end fraction, equals, 4, x
�
=
x=x, equals
Answer:
x = 3/8
Step-by-step explanation:
You want the solution to 3/2 = 4x.
One-step equationYou solve this one-step linear equation by multiplying both sides by the inverse of the x-coefficient:
[tex]\dfrac{3}{2}=4x\qquad\text{given}\\\\\\\dfrac{1}{4}\times\dfrac{3}{2}=\dfrac{1}{4}\times4x\\\\\\\dfrac{3}{8}=\dfrac{4}{4}x\\\\\\\boxed{x=\dfrac{3}{8}}[/tex]
__
Additional comment
The "one step" is multiplying both sides by 1/4. The rest is simplifying the result.
Of course, this is the same as dividing both sides by 4. The result is x = (3/2)÷4 = 3/(2·4) = 3/8.
Which of the following similarity statements is correct?
Answer:
Two
Step-by-step explanation:
Trangles are labled n named alphabetically therefore on the bigger triangle D comes first than E and E comes forsr than R wich means that itvis triangle DER not any ather way around.
On the second triangle A comes first than N and N comes first then T thetefore it is triangle ANT
Answer:
Option A is the correct answer
Triangle RED IS SIMILAR TO TRIANGLE TAN
A side of a inner circle trapezium is a diameter of the circle. The non-parallel sides are equal to the radius of a circle. If the radius of the circle is 2 units, the area of the trapezium can be written as n√n. What is the value of n?
The value of n = 12, and the area of the trapezium can be written as 12√12.
How to determine the the value of nLet's call the diameter of the circle (and one of the parallel sides of the trapezium) "AB", and let's call the non-parallel sides "CD" and "EF". We know that CD and EF are both equal to the radius of the circle, which is 2 units.
We know that AB is a diameter of the circle, which means that its length is twice the radius, or 4 units.
We also know that CD and EF are each 2 units long.
To find the height of the trapezium, we can draw a perpendicular line from point C to line AB:
We can see that the height of the trapezium is the distance from point H to line AB. Since point H is directly above the center of the circle (point O), we can use the Pythagorean theorem to find its distance from point A (or point B, since AB is a diameter):
The length of the hypotenuse (OB) is 2 units (the radius of the circle), and the length of one of the legs (OA) is 2 units (half of AB). To find the length of the other leg (HB), we can use the Pythagorean theorem:
HB^2 + OA^2 = OB^2
HB^2 + 2^2 = 2^2
HB^2 = 0
This tells us that HB (and therefore the height of the trapezium) is 0 units.
Since the height is 0, the area of the trapezium is simply the average of the two parallel sides (AB and CD) multiplied by the distance between them (which is also AB).
Area = (AB + CD) / 2 * AB
= (4 + 2) / 2 * 4
= 3 * 4
= 12
Therefore, n = 12, and the area of the trapezium can be written as 12√12.
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Suppose you have $50 in a savings account and deposit an additional $10 each week.
a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26
weeks? Show all work.
a. The recursive formula to represent the sequence is aₓ = aₓ₋₁ + 10.
b. The explicit formula to represent the sequence is aₓ = 50 + 10x.
c. We have $310 in savings after 26 weeks.
What is sequence?
A progression or sequence of numbers known as an arithmetic sequence keeps the difference between any subsequent term and its preceding term constant throughout the entire sequence. In that arithmetic progression, the constant difference is known as the common difference.
We are given that there are $50 in a savings account and each week additional $10 are deposited.
a. Let x be the number of weeks
a₀ = $50
aₓ = aₓ₋₁ + 10
So, the recursive formula to represent the sequence is aₓ = aₓ₋₁ + 10.
b. Let x be the number of weeks.
So, the explicit formula is given by
aₓ = 50 + 10x
c. Now, we are given x = 26.
So, by substituting this, we get
⇒ a₂₆ = 50 + 10 * 26
⇒ a₂₆ = 50 + 260
⇒ a₂₆ = $310
Hence, the required solutions have been obtained.
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Which is a solution for the following system of inequalities?
Find the trigonometric ratios as simplified fractions and as decimals to the nearest thousandths (as necessary).
Sin X: Fraction ______ Decimal _______
Cos X: Fraction ______ Decimal ______
Tan X: Fraction _______ Decimal ______
(30 points)
By answering the presented question, we may conclude that tan(X): trigonometry Fraction 3/4, Decimal 0.750
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Using the Pythagorean theorem,
hypotenuse² = opposite² + adjacent²
hypotenuse² = 4² + 3²
hypotenuse² = 16 + 9
hypotenuse² = 25
hypotenuse = √25
hypotenuse = 5
Now we can find the trigonometric ratios:
sin(X) = opposite / hypotenuse = 3/5
sin(X) = 0.600 (rounded to the nearest thousandth)
cos(X) = adjacent / hypotenuse = 4/5
cos(X) = 0.800 (rounded to the nearest thousandth)
tan(X) = opposite / adjacent = 3/4
tan(X) = 0.750 (rounded to the nearest thousandth)
Therefore, the trigonometric ratios for angle X are:
sin(X): Fraction 3/5, Decimal 0.600
cos(X): Fraction 4/5, Decimal 0.800
tan(X): Fraction 3/4, Decimal 0.750
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A survey is taken at a movie theater in Winterville. The first 150 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 150 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Winterville.
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.
The population is the number of people in the town of Winterville, and the sample is the number of people who go to the movie theater.
Answer:
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.
Step-by-step explanation:
The population is the potential people that could be sampled, and the sample is the people who are being asked the question.
Answer:ccccccccccccccccccccccccccc
Step-by-step explanation:
Solve 9+5x-x^2 by completing the square
Text → Graphing Exponential Functions: Mastery Test
2
Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function f?
f(x) = e - 4
g(x) =
- 4
OA.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function f to the left.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the right.
The graph of function g is a vertical compression of the graph of function f.
Answer:
x=2
Step-by-step explanation:
4 x1,2 =2
The correct statement which compares the graph of function g with the graph of function f is,
⇒ The graph of function g is a vertical compression of the graph of function f.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions are,
f (x) = eˣ - 4
g (x) = 1/2eˣ - 4
Now, We have to find that;
The graph of function g is a vertical compression of the graph of function f.
Hence, The correct statement which compares the graph of function g with the graph of function f is,
⇒ The graph of function g is a vertical compression of the graph of function f.
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if the volume of a cube can be represented by a polynomial of degree 9, what is the degree of the polynomial that represents each side lenght
Answer:
Each side length of the cube will be a polynomial of degree 3.
A cannon on a 1m raised platform fires a cannonball at a speed of 200m/s. It lands in a field of equal elevation 2km away.
At what angle did the cannon fire the shot, and when did it land? Disregard air resistance.
For an easier problem, eliminate the raised platform
Note: Please show all work!
The cannonball will land approximately 20.4 seconds after it was fired.
What is the name of a cannon ball?A round shot is a solid, spherical projectile fired from a gun that is also known as a decent shot or simply a ball. Its diameter is just a little bit smaller than the diameter of the barrel that it is fired from.
A cannon ball's composition.An iron anti-personnel bullet having a hollow internal cavity filled with leads or iron round pellets and a tiny explosive charge that explodes with just enough power to crack open the iron projectile's thin walls. A time fuse was put into a receptacle at the projectile's outer edge after a powder trains in a tiny iron sleeve.
We can use the equations of motion for projectile motion to solve this problem. Let's assume that the cannonball is fired at an angle θ above the horizontal and lands at a distance of x = 2000 meters from the cannon. We also know that the initial speed of the cannonball is 200 m/s.
The horizontal and vertical components of the velocity can be expressed as:
vₓ = v₀ cos(θ)
vₐ = v₀ sin(θ) - gt
where v₀ is the initial velocity (200 m/s), g is the acceleration due to gravity (9.8 m/s²), and t is the time taken for the cannonball to land.
Using the equation for the horizontal motion, we can find the time taken for the cannonball to travel a distance of 2000 meters:
x = v₀ cos(θ) * t
t = x / (v₀ cos(θ))
Using the equation for the vertical motion, we can find the time taken for the cannonball to reach the ground:
y = v₀ sin(θ) * t - (1/2) * g * t²
0 = v₀ sin(θ) * t - (1/2) * g * t²
Solving for t in the second equation gives:
t = 2 * v₀ sin(θ) / g
Substituting this expression for t into the first equation gives:
x = (v₀² / g) * sin(2θ)
We can now solve for θ:
sin(2θ) = (g * x) / v₀²
θ = 0.5 * arcsin((g * x) / v₀²)
Plugging in the given values for g, x, and v0, we get:
θ = 0.5 * arcsin((9.8 m/s² * 2000 m) / (200 m/s)²) ≈ 20.3 degrees
Therefore, the cannon fired the shot at an angle of approximately 20.3 degrees above the horizontal.
To find the time taken for the cannonball to land, we can use the expression for t derived earlier:
t = 2 * v₀ sin(θ) / g
t = 2 * 200 m/s * sin(20.3°) / 9.8 m/s² ≈ 20.4 seconds
Therefore, the cannonball will land approximately 20.4 seconds after it was fired.
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HELP I NEED THIS ASAP PLS HELP
Answer:
A
Step-by-step explanation:
I added a photo of my notes (the angles I've marked as equal are cross angles)
[tex]w = 180° - 30° - x°[/tex]
[tex]w = 150° - x°[/tex]
Here is a pattern made from sticks with a triangle what is n
find x if 2x+3x+3x-4x=32x^2
Answer: x=0, x=1/8
Step-by-step explanation:
Simplifying the equation give us: 4x=32x^2
Subtract 4x from both sides: 32x^2-4x=0
Factor:4x(8x-1)=0
Using the Zero Product Property, x=0, x=1/8
Answer:
x equals 0 it wont only let me put answer so i am typing more
you ride a bike to campus a distance of 5 miles and return home on the same route. Going to campus, you ride mostly downhill and average 9 miles per hour faster than on your return trip home. If the round trip one hour and ten minutes that is 7/6 hours; what is your average velocity on your return trip
Tammy ran 4 2
5 miles on Saturday.
On Sunday she ran for 1
2 of the distance
she ran on Saturday. Write and solve an
equation that will help you figure out how
far Tammy ran on Sunday. Explain the
steps you took to solve the problem
Tammy ran 2.25 miles on Sunday.
What is Linear Equation?A linear equation is a mathematical expression that describes a straight line on a graph. It is of the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.
Let's start by figuring out how far Tammy ran on Sunday. We know that she ran for 1/2 of the distance she ran on Saturday. Therefore, if we let "x" be the distance Tammy ran on Sunday, we can set up the following equation:
x = 1/2(4.5)
Here, we used the fact that Tammy ran 4.5 miles on Saturday.
To solve for "x", we simply need to simplify the right-hand side of the equation:
x = 1/2(4.5)
x = 2.25
Therefore, Tammy ran 2.25 miles on Sunday.
In summary, we used the equation x = 1/2(4.5) to represent the distance Tammy ran on Sunday, where "x" is the unknown distance. We then solved for "x" by simplifying the equation and found that Tammy ran 2.25 miles on Sunday.
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A ladder forms the hypotenuse of a right triangle with a building and the ground, as shown. The ladder reaches to a height of 30 feet on the building, while the base of the ladder is 6 feet from the bottom of the building. What is the length of the ladder?
The length of the ladder is approximately 30.6 feet. The height of the building is 90 degrees.
Let "θ" be the angle between the ladder and the ground. Then, we have:
sin(θ) = 30 ÷ x
Solving for "x", we get:
x = 30 ÷ sin(θ)
Since the ladder is the hypotenuse, we know that the angle opposite the height of the building is 90 degrees. Therefore, the angle between the ladder and the ground is the complement of this angle, which is:
θ = 90 - arcsin(30 ÷ x)
Substituting this expression for "θ" into the equation for "x", we get:
x = 30 ÷ sin(90 - arcsin(30 ÷ x))
Using the identity sin(90 - θ) = cos(θ), we can simplify this to:
x = 30 / cos(arcsin(30 ÷ x))
Using the identity cos(arcsin(x)) = [tex]\sqrt[] 1-x^{2}[/tex] , we can simplify this further to:
x = [tex]\frac{30}{\sqrt{(1-(30/x^{2}))\\} }[/tex]
Squaring both sides and simplifying, we get:
x² = 30² + 6²
x² = 900 + 36
x² = 936
x = [tex]\sqrt{936}[/tex]
x = 30.6 feet is height of ladder
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PLEASE HELP ILLL MAKE BRAINLY
By looking at the 0 and 1 column, 200 people own less than two smartphones
HELP!!!
The graph represents a relation where x represents the independent variable and y represents the dependent variable. a coordinate plane with points at negative 5 comma 1, negative 2 comma 0, 0 comma 2, 1 comma negative 2, 3 comma 3, and 5 comma 1 What is the domain of the relation?
The domain of the relation is the set {-5, -2, 0, 1, 3, 5}.
The domain of a relation is the set of all possible input values (independent variable) that correspond to an output (dependent variable).
The domain of a function or relation is the set of all possible input values (independent variable) that correspond to an output (dependent variable). It represents the values for which the function or relation is defined.
Looking at the given points, we can see that the x-coordinates of the points are -5, -2, 0, 1, 3, and 5. Therefore, the possible input values for this relation (i.e., the domain) are:
Domain: {-5, -2, 0, 1, 3, 5}
So the domain of the relation is the set {-5, -2, 0, 1, 3, 5}.
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PLEASE SHOW WORK FOR BRAINLIST!!!
In circle A what is angle DAR?
Answer:
68°
Step-by-step explanation:
because the inscribed angle (at B) is half of the arc angle (at A).
angle B = 1/2 × angle A
34 = 1/2 × angle A
angle A = 34×2 = 68°
Find the area <<<<<<
Answer:
Area = 100 units^2
Step-by-step explanation:
This shape is a trapezoid. The area of a trapezoid is:
A = 1/2(Base+Base)•h
What you do is average the bases and times by the height. The only thing is in your picture the bases are the 12 and 8. And the height is the 10.
Area = 1/2(12+8)•10
= 1/2(20)•10
= 10•10
= 100
The area is 100 square units.
there are several possible heights at which the higher end of the bridge can be attached to the higher end of the mountain. Fill in the table below to use 5 possible values for y, and calculate the resulting values for r
The resulting values for r will be sqrt(140).
Let's assume that the bridge is a straight line segment that connects the top of the mountain (point A) to a point on the ground (point B).
Let's also assume that the distance from the top of the mountain to point B is a fixed value d.
If we attach the higher end of the bridge to the top of the mountain at a height y, the distance between point A and the attachment point can be calculated using the Pythagorean theorem as:
x = sqrt([tex]d^2[/tex] - [tex]y^2[/tex])
The length of the bridge, which is also the hypotenuse of the right triangle formed by points A, B, and the attachment point, can then be calculated as:
r = sqrt([tex]x^2[/tex] + [tex](d-y)^2[/tex])
To find the values of r for different heights y, we can simply substitute different values of y into these equations and calculate the resulting values of r.
For example, if we use the values d=10 and y=3, we get:
To calculate the values for "r" given 5 possible values for "y," we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the bridge is the hypotenuse, and we know the height of the mountain (x) and the distance from the mountain to the lower end of the bridge (d). So we can write:
r^2 = [tex]x^2[/tex] + [tex](d + y)^2[/tex]
x = sqrt([tex]10^2[/tex] - [tex]3^2[/tex])
x = sqrt(91)
r = sqrt((sqrt([tex]91))^2[/tex] + [tex](10-3)^2[/tex])
r = sqrt(91 + 49)
r = sqrt(140)
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Q10) use the accompanying graph of y = f(x)
1. What is the domain and range of f.
2. find f(-4) and f(-6).
3. find lim f(x)
x-4
4. find lim f(x)
5. Does lim f(x) exist? If it does, what is it?
6. Is f continuous at 0?
(-2,2)
(-4,1)
-6-4-2
(-6,2)
4
2
-2-
(3 marks)
The limits [tex]\lim_{x \to 0 } f(x)[/tex] exists and the function f(x) is continuous at x = 0
Other solutions are shown below
The domain and the range of the functionThe domain of a function is the set of all possible input values, while the range is the set of all possible output values.
From the graph, we have the domain and the range to be:
Domain: [-6, -4) ∪ (-4, -2) ∪ [-2, 0] ∪ (0, 2) ∪ (2, 5) ∪ (5, 6]Range: (-∝, ∝)The values of the functionFrom the graph, we have the values of the function to be
f(-4) = 1 and f(-6) = 2
The function limitsFrom the graph, we have the values of the limits to be
[tex]\lim_{x \to 4^{-} } f(x) = -2[/tex]
[tex]\lim_{x \to 4^{+} } f(x) = 2[/tex]
Checking if the limits exist at x = 0Yes, the limit [tex]\lim_{x \to 0 } f(x)[/tex]
Checking if the function is continuousTo check if a function is continuous at x=0, you need to check three conditions:
The function must be defined at x=0 i.e. f(0) = 4The limit of the function as x approaches 0 from the left must be equal to the limit of the function as x approaches 0 from the rightThese limits must be equal to the function's value at x=0. If all three conditions hold, the function is continuous at x=0.Hence, the function is continuous at x = 0
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You can get 52 to point if you answer every single answer hurry up this a test
Determine the number of units a given figure would be translated using the given notation.
The number of units a given figure would be translated using the given notation are shown below.
What is a translation?In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
Based on each of the transformation rule, the number of units a given figure would be translated using the given notation include the following:
(x, y) → (x + 7, y - 6)
7 units right.
6 units down.
(x, y) → (x - 9, y + 2)
9 units left.
2 units up.
(x, y) → (x - 11, y)
11 units left.
0 units up/down.
(x, y) → (x - 8, y - 5)
8 units left.
5 units down.
(x, y) → (x + 13, y + 3)
7 units right.
3 units up.
(x, y) → (x, y + 9)
0 units right/left.
9 units up.
(x, y) → (x - 14, y + 12)
14 units left.
12 units up.
(x, y) → (x, y - 4)
0 units right/left.
4 units down.
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A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. (Hint use Logarithms)
Actual time is much longer than the 50-year timeframe suggested by the speaker.
How to verify the statement?
This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.
To verify this claim, we can use the following formula to calculate the expected total pollution after n years:
Total pollution after n years = [tex]Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n[/tex]
Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.
We can set the expected total pollution after n years equal to the present pollution level and solve for n:
[tex]Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n[/tex]
Simplifying this equation, we get:
[tex]1 = 1.03^n \times 0.2^n[/tex]
Taking the logarithm of both sides of the equation, we get,
[tex]n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56[/tex]
Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.
It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.
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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"
what is 1/7 divided by 2/5
Step-by-step explanation:
[tex] \frac{ \frac{1}{7} }{ \frac{2}{5} } = \frac{1}{7} \times \frac{5}{2 } = \frac{5}{14} \\ [/tex]
Answer: 5/14
Step-by-step explanation:
It would help if you used the KCF (Keep, Change, Flip) method. First, you write 1/7 as a fraction, then change the division sign to a multiplication sign, and flip the fraction 2/5 to 5/2. Then multiply 1/7 by 5/2 to get 5/14.