Answer:
The given complex number is (-2.5 + i4.2).
To express it in exponential form, we need to find the modulus (r) and argument (θ) of the complex number.
The modulus is given by:
|r| = √((-2.5)^2 + (4.2)^2) = √(6.25 + 17.64) = √23.89 ≈ 4.888
The argument is given by:
θ = tan⁻¹(4.2/(-2.5)) = tan⁻¹(-1.68) ≈ -1.03 radians
Therefore, the exponential form of the complex number is:
(-2.5 + i4.2) = 4.888e^(-i1.03)
What is the radical expression (6–√4)3
written in exponential form?
Responses
634
61
643
612
The radical expression (6–√4)3 written in exponential form is 612.
What is expression?Expression is a term used to describe the process of making clear or conveying one's thoughts, ideas, and feelings. It is a way of communicating with others and expressing oneself in a meaningful and effective manner. Expression can be done through verbal and non-verbal communication, including writing, art, music, dance, and other creative outlets. It can also be used to express emotions such as joy, sadness, fear, anger, and love. Expression is essential to healthy communication and can be a powerful tool for self-expression, personal growth, and development.
This is because raising a number to an exponent is the same as multiplying that number by itself the number of times specified by the exponent. In this case, the base number is 6, and the exponent is 12. When a number is multiplied by itself 12 times, it is referred to as an exponential expression. To convert the radical expression to an exponential expression, the radical needs to be converted to an exponent. The radical of 4 is 2, so the exponent is 12. This results in the answer 612.
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Chris throws a ball upward. The height of the ball, in meters, t seconds after being
thrown is modeled by h (t)= 8t-5t² +4. After how many seconds will the ball reach
the ground?
Answer:
When the ball hits the ground, its height will be 0 meters. Therefore, we need to solve the equation:
h(t) = 0
8t - 5t^2 + 4 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula, but in this case, it's easier to use factoring:
(5t - 4)(t - 1) = 0
From this equation, we can see that either 5t - 4 = 0 or t - 1 = 0. Solving for t in each case, we get:
5t - 4 = 0 ==> t = 0.8 seconds
t - 1 = 0 ==> t = 1 second
Therefore, the ball will reach the ground after either 0.8 seconds or 1 second, depending on the initial height of the ball.
7. What is the order of these numbers from least to greatest?
2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10¹2, 4.8 x 10²1
21
The order of these numbers from least to greatest is 2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10^12, 4.8 x 10^21
What are index forms?Index forms are simple described as the mathematical expressions or models used to represent numbers that are large or small in more appropriate ways.
They are also termed as scientific notations or standard forms.
Examples of index forms are;
2³ = 8
2 ² = 4
3 ³ = 27
From the information given, we have that;
2.7 x 10³
This is represented as; 2.7 × 10 × 10 × 10
Multiply the values
2700
2.3 x 10¹¹
This is represented as 2. 3 multiply by 10 in 11 times
6. 5× 10^12
This is represented by 6.5 multiplied by 10 in 12 places
4.8 × 10^21
This is represented by 4.8 multiplied by 10 in 21 places.
Hence, the exponent shows the greatest number
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The polynomial of degree 4, P(x) has a root of multiplicity 2 at a = 2 and roots of multiplicity 1 at
x = 0 and x = -3. It goes through the point (5,36).
Find a formula for P(x).
P(x)
Answer:
the answer is px and at ako
Write a formula for the function g(x) obtained when the graph of f(x)=√x is shifted up 1 unit and to the left 6 units.
g(x).
Answer:
The formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.
Step-by-step explanation:
To obtain the formula for the function g(x) when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units, we can use the following transformations:
A vertical shift up by 1 unit is represented by adding 1 to the function: f(x) + 1
A horizontal shift to the left by 6 units is represented by replacing x with (x + 6): f(x + 6)
Therefore, the formula for the function g(x) is:
g(x) = f(x + 6) + 1
Substituting the expression for f(x), we get:
g(x) = √(x + 6) + 1
So, the formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.
A mean ogre stole 20
of your muffins 5/8 of all of them how many are left?
Answer:
Let's start by finding out how many muffins were there in total before the ogre stole 20 of them. Let's call that number "x".
If 5/8 of them were left after the ogre stole 20, then 3/8 of them were taken.
So we can set up an equation:
x - 20 = 3/8x
To solve for x, we can start by multiplying both sides by 8 to get rid of the fraction:
8(x - 20) = 3x
8x - 160 = 3x
Now we can solve for x by subtracting 3x from both sides:
5x - 160 = 0
5x = 160
x = 32
So there were originally 32 muffins.
Now we can find out how many are left:
5/8 of 32 = 20
So there are 20 muffins left.
Step-by-step explanation:
The question is present in the problem
The solution to the given equation √(2x + 9) = 7 is x = 20.
What is the radical equation?Any equation that contains a radical symbol is considered a radical equation. To find the square roots, cubic roots, and higher, radical symbols are used.
The equation is given as follows:
√(2x + 9) = 7
Square both sides of the above equation,
2x + 9 = 7²
2x + 9 = 49
Subtract 9 from both sides of the above equation,
2x = 49 - 9
2x = 40
Divide by 2 into both sides of the equation,
x = 40/2
x = 20
Thus, the solution to the given equation is x = 20.
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Nicholson purchased a piece of equipment on for $60,000. The equipment has an estimated useful life of eight years or 50,000 units of production and an estimated salvage value of $6,000. The amount of depreciation to be recorded for year 2 using the straight-line method of calculating depreciation, is
The amount of depreciation to be recorded for year 2 using the straight-line method of calculating depreciation is $6,750.
What is the amount of depreciation to be recorded for year 2?Straight-line depreciation is calculated by dividing a fixed asset's depreciable base by its useful life. The depreciable base is the difference between an asset's all-in costs and the estimated salvage value at the end of its useful life.
By using the straight-line method of calculating depreciation, the annual depreciation expense would be calculated as follows:
= (Purchase Price - Salvage Value) / Useful Life
= ($60,000 - $6,000) / 8 years
= $54,000 / 8 years
= $6,750.
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The average annual interest rate r (in decimal form) of a savings account is
V₂
represented by the formula r =
1, where Vo is the initial investment
Vo
and V₂ is the balance of the account after 2 years. Find the average annual
interest rate r of a savings account with an initial investment of $400 and a
balance of $422 after 2 years.
The interest rate of the saving account is 2.71%
What is simple interest?Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
Given, the interest rate of a savings account is represented by the formula such that:
r = [tex]\sqrt{\frac{V_2}{V_0} } - 1[/tex]
Where V₀ is the initial investment,
and V₂ is the balance of the account after 2 years.
In our case,
V₂ = 422
V₀ = 400
So the interest rate,
r = [tex]\sqrt{\frac{422}{400} } - 1[/tex]
r = 1.0271 - 1
r = 0.0271
therefore, the interest rate of the saving account is 2.71%
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Complete question:
The average annual interest rate r (in decimal form) of a savings account is V₂ represented by the formula r = [tex]\sqrt{\frac{V_2}{V_0} } - 1[/tex], where Vo is the initial investment, and V₂ is the balance of the account after 2 years. Find the average annual interest rate r of a savings account with an initial investment of $400 and a balance of $422 after 2 years.
need help now i have like so much questions that need to be done
The measures of the angles are JKN = 27 degrees and JNK = 126
How to determine the measures of the anglesFrom the question, we have the following parameters that can be used in our computation:
The rectangle
On the rectangle, we have
JKN = NJK
Using the above as a guide, we have the following:
JKN = 27 degrees
The sum of angles in a triangle is 180
So, we have
JNK = 180 - 27 * 2
Evaluate
JNK = 126
Hence, teh angle is 126 degrees
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If the two shakes below are similar, calculate the value of x.
X=
Answer:
try 1/2
Step-by-step explanation:
The list below shows how many students attended a school dance in each of the past six
years.
120, 132, 100, 150, 132, 140
Which measure of data should NOT be used to predict the number of students that will attend
the dance this year?
A Mean
B Median
C Mode
D Range
Answer:
The answer should be D.)
6TH GRADE MATH, SOMEONE PLSS HELP!!! TY! ALSO THE ANSWERS GO IN ORDER FOR EXAMPLE, SLOPE IS FIRST NUMBER, AND Y INTERCEPT IS SECOND NUMBER, TYSMM
Answer:
4/3, -3
Step-by-step explanation:
slope is the number in front of the variable x, and y intercept is when x=0
Be wise as thou art cruel; do not press
My tongue-tied patience with too much disdain;
Lest sorrow lend me words, and words express
The manner of my pity-wanting pain.
If I might teach tee wit, better it were,
Though not to love, yet, love, to tell me so;
As testy sick men, when their deaths be near,
No news but health from their physicians know;
For, if I should despair, I should grow mad,
And in my madness might speak ill of thee:
Now this ill-wresting world is grown so bad,
Mad slanderers by mad ears believed be.
That I may not be so, nor thou belied,
Bear thine eyes straight, though thy proud heart go wide.
What is the rhyme scheme of the poem?
A. aabb ccdd eeff gg
B. aaaa bbbb cccc dd
C. abab cdcd efef gg
D. abcb defe ghih jj
The rhyme scheme of the poem is abab cdcd efef gg. The rhyme scheme creates a sense of symmetry and balance in the poem.
what is rhyme scheme?A poem's rhyme system is its regular pattern of final rhymes. It is written using alphabetical letters, each of which stands for a particular rhyme sound. A poem with the rhyme scheme ABAB, for instance, follows a pattern where the first and third lines rhyme, and the second and fourth lines rhyme.
According to question:The poem's rhyme scheme can be mathematically described by utilising letters to denote the various rhyming sounds. "Abab cdcd efef gg" is the rhyme pattern used in this poem. This can be written as follows using letters to represent the various sounds:
The last word of the first line rhymes with the last word of the third line (a)The last word of the second line does not rhyme with any other line (b)The last word of the fourth line does not rhyme with any other line (c)The last word of the fifth line rhymes with the last word of the seventh line (d)The last word of the sixth line does not rhyme with any other line (e)The last word of the eighth line does not rhyme with any other line (f)The last word of the ninth line rhymes with the last word of the tenth line (g)This pattern is repeated throughout the entire poem, creating a consistent and structured rhyme scheme.
Therefore the rhyme scheme is abab cdcd efef gg.
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QUESTION 10
Consider the following argument: If Bryony has her baby before next week, Bryony does not need dress alterations before
her sister's wedding next month. But Bryony does need dress alterations before her sister's wedding next month. So
Bryony does not have her baby before next week. This argument is
O a. valid
O b.invalid
O c. true
O d. false
Oe. None of the above
Answer:
Valid
Step-by-step explanation:
This argument is Valid because there could be many other reasons she needs dress altercations, however the most likely one is that she did not have her baby before next week.
Answer:
Step-by-step explanation:
The argument is valid.
We can analyze it using the following symbols:
Let A be the event that Bryony has her baby before next week.
Let B be the event that Bryony needs dress alterations before her sister's wedding next month.
Then the argument can be represented as follows:
If A, then not B.
B.
Therefore, not A.
This is a valid deductive argument form called modus tollens. The conclusion follows logically from the premises. Therefore, the argument is valid.
The elementary school in your town wants to replace its current playground. The space used for the new playground will be similar to that of the current playground. The current space is rectangular and has a length of 35 feet and a width of 45 feet. The length of the new space is 42 feet. Find the perimeter of the space used for the new playground. Perimeter: feet
By answering the above question, we may infer that Thus, the 159 feet that make up the perimeter of the area used for the new playground.
What is perimeter?A limit is a closed path that encircles, separates, or encompasses a one-dimensional length, a two-dimensional shape. A circle's or an ellipse's perimeter refers to its outermost region. Many practical uses may be made of the perimeter calculation. The radius of an edge is used to calculate a shape's perimeter. Get the circle's radius by multiplying the lengths of the sides of irregular shapes. Every form's perimeter may be determined by multiplying its side lengths. The area around an object is called its perimeter. Your home's walled garden serves as a wonderful example of this. A thing's perimeter is the area surrounding it. A 200 foot barrier will be needed to contain a 50 by 50 foot yard.
Current playground size is 1,575 square feet, or 35 feet by 45 feet.
The difference between the old and new playgrounds is 1,575 square feet.
New playground length = 1,575 square feet / 42 feet 37.5 feet, where new playground width equals new playground area.
We can calculate the perimeter now that we know the new playground's width is around 37.5 feet:
The new playground's perimeter is equal to 2 (length + width).
The new playground's perimeter is 2 (42 feet plus 37.5 feet).
2 is the new playground's perimeter (79.5 feet)
The new playground's perimeter is 159 feet.
Thus, the 159 feet that make up the perimeter of the area used for the new playground.
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tool to form the correct answer on the provided number line.
ven functions.
Function 1
f (x) =-52 + 1 + 10
-6
-2
Function 2
g(x)
30-
20+
the interval where both functions are decreasing on the number line provided.
The interval where both functions are decreasing is {-1, 2} and it is shown on the number line below.
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph of g(x), we can logically deduce that the function g(x) decreases over the interval {-2, 2}. On the other hand (conversely), the function f(x) = -5|x + 1| + 10 decreases over the interval {-1, ∞}.
Therefore, the interval over which both functions decrease is denoted by the intersection of both functions;
Interval = {-1, 2}
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Angie packed same-size cubes into a rectangular prism. A 1 What is the number of cubes needed to fill this prism? 20 cubes Area of the base is 6 yd.² pls helpppppppppp
There are 42 cubes needed to fill this prism.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Angie packed same-size cubes into a rectangular prism.
And, Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall.
Hence, Number of cubes to fill the prism is,
⇒ 3 × 2 × 7
⇒ 42
Thus, There are 42 cubes needed to fill this prism.
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Complete question is this,
Angie packed same-size cubes into a rectangular prism.
Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall. PLEASE HELP ME
What is the number of cubes needed to fill this prism?
URGENT!!
In the picture below, there are three right trangles. Complete the following.
The similar triangles are Δ SRQ ~ Δ RPQ ~ Δ SRP
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given is right triangle PRQ, a perpendicular line is drawn to the side PQ from angle R
we need to tell the similar triangles,
From the figure we have,
Δ SRQ ~ Δ RPQ ~ Δ SRP
And, according to the definition of similar triangle,
SP / RP = PR / RQ
PQ / RQ = RQ / SQ
Hence, the similar triangles are Δ SRQ ~ Δ RPQ ~ Δ SRP
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Please help with this thank you
Answer:
D.
Step-by-step explanation:
Answer:
the answer for the problem is D.
Which is greater?
0.59 or 1/4
The area of a rectangular pool is 6x²−11x+3
Use the dimensions (length and width) of the pool to determine an expression that gives the perimeter of the rectangular pool. Reminder: P=2l+2w
After using the dimensions (length and width) of the pool to determine an expression that gives the perimeter of the rectangular pool is P = 2 (5x- 4)
What is perimeter?
When defining a length in one dimension or a form in two dimensions, a perimeter is a closed path. The perimeter of a two-dimensional figure is the region that surrounds it. It provides the length of the shape, whether it is a circle, triangle, square, or rectangle. Area and perimeter are a 2D shape's two main properties.
The area of a given rectangular pool is
6x²−11x+3
⇒6x²− (9 + 2) x + 3
⇒ 6x²− 9x - 2x + 3
⇒ 3x(2x - 3) - 1 (2x - 3)
⇒ (3x - 1) (2x - 3)
An expression that gives the perimeter of the rectangular pool is,
P = 2 [ (3x - 1) + (2x - 3) ]
P = 2 [ 3x - 1 + 2x - 3 ]
P = 2 (5x - 4)
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Find all points having an x-coordinate of 2 whose distance from the point (-2,-4) is 5
The two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)
What is distance formula?
Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively.
Distance formula: [tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
We can solve this problem using the distance formula, which gives us the distance between two points in a plane:
[tex]distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
Let (x, y) be a point with an x-coordinate of 2. Then we can write the distance from (-2, -4) to (x, y) as:
[tex]distance = \sqrt{((x - (-2))^2 + (y - (-4))^2)}[/tex]
Simplifying this expression, we get:
[tex]distance = \sqrt{((x + 2)^2 + (y + 4)^2)}[/tex]
We know that the distance between (-2, -4) and (x, y) is 5. Therefore, we can write:
[tex]\sqrt{((x + 2)^2 + (y + 4)^2)} = 5[/tex]
Squaring both sides, we get:
[tex](x + 2)^2 + (y + 4)^2 = 25[/tex]
Expanding the left side, we get:
[tex]x^2 + 4x + 4 + y^2 + 8y + 16 = 25[/tex]
Simplifying this expression, we get:
[tex]x^2 + 4x + y^2 + 8y - 5 = 0[/tex]
To find all points with an x-coordinate of 2 that satisfy this equation, we can substitute x = 2 and simplify the resulting equation:
[tex]2^2 + 4(2) + y^2 + 8y - 5 = 0[/tex]
Simplifying this equation, we get:
[tex]y^2 + 8y + 3 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
y = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 8, and c = 3.
Plugging in these values, we get:
y = (-8 ± sqrt(8^2 - 4(1)(3))) / 2(1)
Simplifying this expression, we get:
y = (-8 ± √52) / 2
y = (-8 ± 2√13) / 2
y = -4 ± √13
Therefore, the two points with an x-coordinate of 2 and a distance of 5 from (-2, -4) are: (2, -4 + 2√13) and (2, -4 - 2√13)
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Suppose C(t) is the cost, in thousands of dollars, of producing t tons of white paper. If
C'(10) = 380,
estimate the cost of producing an additional 500 lb of paper once 10 tons have been produced.
It is estimated that producing an additional 500 lb of paper once 10 tons have been produced would cost approximately $95,000.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To estimate the cost of producing an additional 500 lb of paper, we need to first convert 500 lb to tons.
1 lb = 0.0005 tons
So, 500 lb = 0.25 tons
Now, we can use the marginal cost formula:
MC = C'(t)
where MC is the marginal cost and C'(t) is the derivative of the cost function with respect to t.
We are given that C'(10) = 380, which means that the marginal cost of producing the 10th ton of paper is $380,000.
To estimate the cost of producing an additional 500 lb of paper once 10 tons have been produced, we need to find the marginal cost at t = 10.
Therefore, the estimated cost of producing an additional 500 lb of paper is:
MC(10) ≈ C'(10) ≈ $380,000 per ton
0.25 tons x $380,000 per ton = $95,000
Hence, it is estimated that producing an additional 500 lb of paper once 10 tons have been produced would cost approximately $95,000.
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need help with problem 4 test stastic and p value
The p-value for this sample is approximately 0.004655 which is smaller than the significance level of 0.005. This means that we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population proportions are not equal.
What is the test statistic for this sample?To test the hypothesis Hₐ : p₁ ≠ p₂ at a significance level of α = 0.005, we can use the two-sample z-test for proportions, where the test statistic is given by:
z = (p₁ - p₂) / sqrt{p(1-p)(1/n₁ + 1/n₂)}
where p = (x₁ + x₂) / (n₁ + n₂) is the pooled sample proportion, x₁ and x₂ are the number of successes in the two samples, n₁ and n₂ are the sample sizes for the two samples, and p₁ and p₂ are the sample proportions for the two samples.
Plugging in the given values, we have:
p₁ = 119/687 ≈ 0.1732
p₂ = 137/577 ≈ 0.2374
n₁ = 687
n₂ = 577
p = (119 + 137) / (687 + 577) ≈ 0.202
z = (0.1735 - 0.2376) / √{0.202 * (1 - 0.202) * (1/687 + 1/577)} ≈ -2.83
The test statistic for this sample is approximately -2.83
To find the p-value for this sample, we need to find the probability of observing a test statistic as extreme as -2.83, assuming that the null hypothesis is true. Since this is a two-tailed test, we need to find the area in the tails of the standard normal distribution that corresponds to a significance level of 0.005:
α/2 = 0.005/2 = 0.0025
Using a standard normal table or a calculator, we can find that the z-score corresponding to an area of 0.0025 in the left tail of the standard normal distribution is approximately -2.81. The z-score corresponding to an area of 0.0025 in the right tail is approximately 2.81.
The p-value for this sample is the sum of the areas in the tails beyond the test statistic:
p-value = P(Z ≤ -2.83) + P(Z ≥ 2.83)
P = 0.004655
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What is the equation for calculating the area of a triangle?
A =
base · height
A = length · width
A = pi · height
A =
base · height
The equation for calculating the area of a triangle is:
A = 1/2 * base * height
where A represents the area of the triangle, base represents the length of the base of the triangle, and height represents the height of the triangle measured perpendicularly to the base.
you find sneakers for $79.95. In the paper you see they will be on sale for 63.96 next week what is the percent discount that they will be offering?
The percent discount being offered is 20%.
What is percentage ?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol %, which means "per cent" or "out of 100". Percentages are used to compare two quantities and express the relationship between them in terms of the fraction of one quantity that the other quantity represents.
To find the percent discount, we need to first calculate the amount of discount that is being offered. We can do this by subtracting the sale price from the original price:
Discount = Original Price - Sale Price
Discount = $79.95 - $63.96
Discount = $15.99
Next, we can calculate the percentage discount by dividing the discount by the original price and then multiplying by 100:
Percent Discount = (Discount / Original Price) x 100
Percent Discount = ($15.99 / $79.95) x 100
Percent Discount = 20%
Therefore, the percent discount being offered is 20%.
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you decide to install a rope swing at the bend in the river. the
time t in seconds for the rope swing to make one swing is
given by 2√1/3.3, where I is the length of the rope swing in
feet. If one swing takes 3.5 seconds, how long is the rope
swing? Round your answer to the nearest tenth foot.
?
The length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).
Describe Algebraic Expression?Algebraic expressions are used to represent mathematical relationships and formulas, and can be used to solve equations and manipulate equations in order to isolate variables or solve for unknown quantities. They are used extensively in algebra, calculus, and other branches of mathematics.
We are given that the time for one swing is given by the formula:
t = 2√(L/32.2)
where L is the length of the rope swing in feet, and 32.2 is the acceleration due to gravity in feet per second squared.
We are also given that one swing takes 3.5 seconds, so we can write:
3.5 = 2√(L/32.2)
Squaring both sides, we get:
12.25 = 4(L/32.2)
Multiplying both sides by 32.2/4, we get:
L = 32.2 × 12.25/4
L ≈ 98.9 feet
Therefore, the length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).
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Determine the inverse of the function f(x)=2(x-3)^2 +4
The correct statement regarding the inverse function is given as follows:
[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex], with a domain of x ≤ 3.
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = 2(x - 3)² + 4.
The axis of symmetry of the function is of x = 3, hence the domain of the inverse function is given as follows:
x ≤ 3.
The inverse function is obtained exchanging x and y and then isolating y, hence:
x = 2(y - 3)² + 4
2(y - 3)² = x - 4.
[tex](y - 3)^2 = \frac{x - 4}{2}[/tex]
[tex]y - 3 = \sqrt{\frac{x - 4}{2}}[/tex]
[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex]
More can be learned about inverse functions at https://brainly.com/question/3831584
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What is the area of the half circle below?
Answer:
25.12cm
Step-by-step explanation:
The area of a circle is (π) x (radius)^2.
Here, you are given the diameter.
To find the radius, divide the diameter by 2, which results in 4.
(π) x (4)^2
Now square the 4, which results in 16
3.14 x 16 = 50.24
50.24 would be the area of the circle not cut in half, so divide 50.54 by 2 to get half.
50.24/2 = 25.12
Answer:
Step-by-step explanation:
The area of Circle is [tex]\pi r^{2}[/tex]
So, the area of half circle is [tex]\frac{\pi r^{2} }{2}[/tex]
Diameter is given = 8cm
so radius will be 4 cm
[tex]A = \frac{\pi 4^{2} }{2} \\A = \frac{\pi 16}{2} \\A = 8\pi[/tex]
A = 8 × 3.14
A = 25.12cm Square