(a) f(36) is equal to 6.
(b) (g+f)(4) = g(4) + f(4) = 9/4
(c) we cannot compute (f · g)(0).
(a) To find f(36), we substitute x = 36 into the function f(x) = √x:
f(36) = √36 = 6
Therefore, f(36) is equal to 6.
(b) To find (g+f)(4), we need to evaluate g(4) and f(4), and then add the results:
g(4) = 1/4
f(4) = √4 = 2
(g+f)(4) = g(4) + f(4) = 1/4 + 2 = 1/4 + 8/4 = 9/4
Therefore, (g+f)(4) is equal to 9/4 or 2.25.
(c) To find (f · g)(0), we need to evaluate f(0) and g(0), and then multiply the results:
f(0) = √0 = 0
g(0) = 1/0
However, g(0) is undefined because division by zero is not defined in mathematics.
Therefore, we cannot compute (f · g)(0) in this case.
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Take a factor out of the square root:
a) √6x^2, where x≥0
b)√9a^3
d)√50b^4
plz help 30 points will give brainliest
Answer:
Question A)
[tex]=\sqrt{6}x[/tex]
Question B)
[tex]=3a\sqrt{a}[/tex]
Question C)
[tex]=5\sqrt{2}b^2[/tex]
Step-by-step explanation:
A)
We are given:
[tex]\sqrt{6x^2}\, \text{ where } x\geq 0[/tex]
We can rewrite the expression:
[tex]=\sqrt{6}\cdot \sqrt{x^2}[/tex]
The square root and square will cancel each other out. Thus:
[tex]=\sqrt{6}x[/tex]
B)
We are given:
[tex]\sqrt{9a^3}[/tex]
Rewrite:
[tex]=\sqrt{9}\cdot \sqrt{a^3}[/tex]
Note that the square root of 9 is simply 3. We can also factor the second part:
[tex]=3\cdot \sqrt{a^2\cdot a}[/tex]
Rewriting:
[tex]=3\cdot\sqrt{a^2}\cdot\sqrt{a}[/tex]
Simplify:
[tex]=3a\sqrt{a}[/tex]
C)
We are given:
[tex]\sqrt{50b^4}[/tex]
Rewrite. Note that 50 = 25(2):
[tex]=\sqrt{25}\cdot \sqrt{2}\cdot \sqrt{b^4}[/tex]
Simplify. We can rewrite the factor as:
[tex]=5\cdot \sqrt{2}\cdot \sqrt{(b^2)^2}[/tex]
The square and square root will cancel out. Thus:
[tex]=5\sqrt{2}b^2[/tex]
Carla wants to save $55.50 to buy a new video game. Carla babysits her niece once a week and earns the same amount of money each week. After every time she babysits she donates $2 from the money she earned to the local food bank. Carla calculates that it will take her 6 weeks to save enough to buy her video game. Write and solve an equation to determine how much money Carla earns per week.
Answer:
$11.25
Step-by-step explanation:
55.50 divided by 6 = 9.25
9.25 + 2 = 11.25
Vince is saving for a new mobile phone. The least expensive model Vince likes costs $225.90. Vince has saved $122.35. He used this solution to determine how much more he needs to save.
225.90 less-than-or-equal-to 122.35 + a. 225.90 minus 122.35 less-than-or-equal-to 122.35 minus 122.35 + a. 103.55 less-than-or-equal-to a.
Vince says that based on the solution, he should save a maximum of $103.55.
Is Vince correct?
Vince is correct because he found the correct solution to the inequality.
Vince is correct because he should save at least $103.55.
Vince is not correct because he wrote the wrong inequality to represent the situation.
Vince is not correct because he should have interpreted the solution as having to save a minimum of $103.55.
Answer:
Vince is not correct because he should have interpreted the solution as having to save a minimum of $103.55.
Step-by-step explanation:my
my sister which is in college helped me with one.
Answer: its D
Step-by-step explanation:
Help please I’ll give brainlest
Answer:
1m²
Step-by-step explanation:
Answer:
A = 157.3 units²
Step-by-step explanation:
A = 1/2(6.9)(8 x 5.7) = 157.3 units²
simplify the expression.
Answer:
5^2
Step-by-step explanation:
Answer:
[tex]5^{2}[/tex]
Step-by-step explanation:
when dividing exponents with the same base (the number on the bottom) you subtract the exponents.
1.
What is the unit rate of pesos to dollars?
Answer:
the unit rate of pesos to dollars is 1 MXN = 0.04960 USD
Step-by-step explanation:
Quick Conversions from Mexican Peso to United States Dollar : 1 MXN = 0.04960 USD
$ or MEX$ 10 $, US$ 0.50
$ or MEX$ 50 $, US$ 2.48
$ or MEX$ 100 $, US$ 4.96
$ or MEX$ 250 $, US$ 12.40
the arc measure of a sector in a given circle is doubled. will the area of the sector also be doubled? explain your reason
Answer:
Yes. See explanation below.
Step-by-step explanation:
The central angle and the degree arc measure of a sector of a circle are equal. Doubling the arc measure, doubles the central angle measure and vice versa.
Area of the the original sector:
[tex] A_{sector} = \dfrac{n}{360^\circ}\pi r^2 [/tex]
where n = measure of the central angle of the sector
Since the central angle and the arc measure of the sector are equal, changing the arc measure has the same effect as changing the central angle measure.
Let's double the central angle to 2n which is the same as doubling the arc measure.
Area of the sector with a doubled central angle or a doubled arc measure:
[tex] A_{sector} = \dfrac{2n}{360^\circ}\pi r^2 [/tex]
Now we divide the area of the doubled sector by the area of the original sector.
[tex]\dfrac{\frac{2n}{360^\circ}\pi r^2}{\frac{n}{360^\circ}\pi r^2} =[/tex]
Simplify:
[tex]= \dfrac{2n}{n} \times \dfrac{360^\circ \pi r^2}{360^\circ \pi r^2}[/tex]
[tex] = \dfrac{2n}{n} [/tex]
[tex] = 2 [/tex]
The ratio of the areas is 2, so the area of the sector is indeed doubled.
Answer: Yes.
Kathleen has a $750 loan payment due in six months. What amount of money should she be able to pay today if the interest on her loan is 5.75% per annum? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
The Kathleen should be able to pay approximately $702.82 today to cover her $750 loan payment due in six months.
If the initial amount is $5000 and it grows at an annual interest rate of 4.5%, compounded annually, what will be the value of the investment after 10 years?To calculate the present value of Kathleen's loan payment, we can use the formula for present value of a future sum of money:
Present Value = Future Value / (1 + r)^nFuture Value = $750 (the loan payment due in six months)r = 0.0575 (annual interest rate of 5.75% expressed as a decimal)n = 6 (number of periods, in this case, six months)Substituting the values into the formula:
Present Value = $750 / (1 + 0.0575)⁶Calculating the present value:
Present Value = $750 / (1.0575)⁶ ≈ $702.82Learn more about Kathleen
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What is the area of this square?
4 km
____ square kilometers
Answer:
4 kilometers.
Step-by-step explanation:
use cylindrical coordinates to find the volume of the solid region bounded on the top by the paraboloid z = 12 − x2 − y2 and bounded on the bottom by the cone z = x2 y2 .
Using cylindrical coordinates, the volume of the solid region bounded on the top by the paraboloid z = 12 − x^2 − y^2 and bounded on the bottom by the cone z = x^2 y^2 can be found. The explanation below provides the step-by-step process.
In cylindrical coordinates, we can express the paraboloid and the cone equations as follows:
Paraboloid: z = 12 -[tex]r^2[/tex]
Cone: z = [tex]r^2 cos^2(θ) sin^2(θ)[/tex]
To find the volume of the solid region, we need to determine the limits of integration. The region is bounded by the paraboloid on top and the cone on the bottom. The paraboloid and the cone intersect when 12 - [tex]r^2[/tex] = [tex]r^2 cos^2(θ) sin^2(θ)[/tex]. Simplifying this equation, we get 12 = [tex]r^2[/tex](1 - [tex]cos^2(θ)[/tex] [tex]sin^2(θ[/tex])). Since r is always non-negative, we can rewrite the equation as 12 =[tex]r^2[/tex][tex]sin^2(θ) (1 - sin^2(θ)[/tex]). This equation defines the boundary curve in the polar coordinate plane (r, θ).
To determine the limits of integration for r, we need to find the values of r that satisfy the equation above for each θ. For a fixed value of θ, the equation becomes 12 = [tex]r^2 sin^2(θ) (1 - sin^2(θ))[/tex]. This equation represents a circle with radius [tex]\sqrt(12 sin^2(θ) (1 - sin^2(θ)))[/tex]. Thus, the limits for r are 0 and [tex]\sqrt(12 sin^2(θ) (1 - sin^2(θ)))[/tex].
For the limits of integration for θ, we need to consider the range in which the paraboloid and the cone intersect. The cone is defined in the range 0 ≤ θ ≤ π, and the paraboloid intersects the cone when θ satisfies 12 = [tex]r^2 sin^2(θ) (1 - sin^2(θ))[/tex]. By solving this equation, we find that 0 ≤ θ ≤ π/2.
To calculate the volume, we integrate over the cylindrical coordinates as follows:
V = ∫∫∫ dV
= ∫[0,π/2]∫[0,√[tex](12sin^2(θ)(1-sin^2(θ)))]∫[r^2cos^2(θ)sin^2(θ),12-r^2][/tex] r dz dr dθ
Evaluating this triple integral will yield the volume of the solid region bounded by the given surfaces.
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please help.I don’t understand
Answer:
y=13 degrees
Step-by-step explanation:
This is an isosceles triangle, we know this because NO and NM are equal.
In an isosceles triangle, the base angles are congruent. In this case, they are angle NOM and angle NMO.
We also know that the sum of the interior angles of a triangle are equal to 180.
With this information, we can make an equation by gathering all the interior angles:
8y+2(3y-1)=180
Solve for y.
8y+6y-2=180
14y-2=180
14y=182
y=13
THE ANSWER IS NOT LETTER b. 2
Independent Practice
Now practice solving some problems.
Which number is a solution of the inequality ?
4−m/m ≥ 5
A.
0.5
B.
2
C.
–4
D.
0.75
Answer:
A.
0.5
Step-by-step explanation:
PLSSSS HELP IN NEED OF HELP IMMEDIATELY! (check whole picture and pls don’t leave a link)
Finding a Function to Match a Current Grade: 0.0/1.0 Remaining Time: Unlimited Shape For this week's discussion, you are asked to generate a continuous and differentiable function f(x) with the following properties: - f(x) is decreasing at x=−6 - f(x) has a local minimum at x=−3 - f(x) has a local maximum at x=3 Your classmates may have different criteria for their functions, so in your initial post in Brightspace be sure to list the criteria for your function. Hints: - Use calculus! - Before specifying a function f(x), first determine requirements for its derivative f ′
(x). For example, one of the requirements is that f ′
(−3)=0. - If you want to find a function g(x) such that g(−9)=0 and g(8)=0, then you could try g(x)=(x+9)(x−8). - If you have a possible function for f ′
(x), then use the techniques in Indefinite Integrals this Module to try a possible f(x). You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did I Do?". Notice that the label " f(x)= " is already provided for you. Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the x-axis go from -6 to 6 .
To find a function that satisfies the given criteria, we can start by determining the requirements for its derivative, f'(x).
Let's break down the given properties and find the corresponding requirements for f'(x): f(x) is decreasing at x = -6: This means that the slope of the function should be negative at x = -6. Therefore, f'(-6) < 0. f(x) has a local minimum at x = -3: At a local minimum, the slope changes from negative to positive. Thus, f'(-3) = 0. f(x) has a local maximum at x = 3: At a local maximum, the slope changes from positive to negative. Hence, f'(3) = 0.
Now, let's integrate f'(x) to obtain f(x): Integrating f'(x) = -6 < x < -3 will give us a decreasing function on that interval. Integrating f'(x) = -3 < x < 3 will give us an increasing function on that interval. Integrating f'(x) = 3 < x < 6 will give us a decreasing function on that interval. To simplify the process, let's assume that f'(x) is a quadratic function with roots at -6, -3, and 3. We can represent it as: f'(x) = k(x + 6)(x + 3)(x - 3), where k is a constant that affects the steepness of the curve. By setting f'(-3) = 0, we find that k = -1/18.
Therefore, f'(x) = -1/18(x + 6)(x + 3)(x - 3). Integrating f'(x) will give us f(x): f(x) = ∫[-6,x] -1/18(t + 6)(t + 3)(t - 3) dt. Evaluating this integral is a bit complicated. Let's denote F(x) as the antiderivative of f(x): F(x) = ∫[-6,x] -1/18(t + 6)(t + 3)(t - 3) dt. Now, we can find f(x) by differentiating F(x): f(x) = d/dx[F(x)]. To get an explicit equation for f(x), we need to calculate the integral and differentiate the resulting antiderivative. Once you have the equation for f(x), you can plot it on the provided graphing option to verify that it matches the criteria mentioned in the question.
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How high is the hands of the superhero balloon above the ground? The hand is ____ feet above the ground.
Answer:
61 ft
Step-by-step explanation:
since it's equal
u look cute in that pfp
Finish the table using
the equation.
Anyone help please ! ?
Answer:
y = 0.5, 1, 1.5, 2
Step-by-step explanation:
x is twice as much as y, so when you multiply the input for y by 2, it should get the value of x. Example: if y is 1, then x is 2, because 1*2 = 2
hope this helped!
(12) Which equation has irrational solutions?
Group of answer choices
Answer:
9(x+3)²=27
Step-by-step explanation:
hello :
9(x+3)²=27 means : (x+3)²=27/9
(x+3)²=3 because 3 is not the perfect square
true or false: ignoring minor details, one can think of the circulation of a vector field f along c as the line integral f along c given by
Ignoring minor details, one can think of the circulation of a vector field f along c as the line integral f along c given by. The statement is False. The statement is incomplete and lacks the necessary information to determine its truth value.
It seems to be referring to the circulation of a vector field along a curve, which is commonly represented by a line integral. However, without specifying the complete expression for the line integral or providing further context, it is not possible to definitively determine if the statement is true or false.
The statement provided is incomplete and lacks context, making it difficult to provide a comprehensive explanation. However, it seems to suggest a relationship between the circulation of a vector field and the line integral along a curve. In vector calculus, the circulation of a vector field represents the flow or rotation of the field around a closed curve. This can be computed by evaluating the line integral of the vector field along the curve. However, without specific details or equations, it is challenging to provide a more precise explanation within the given word limit. Additional information or context would be required to clarify the statement further.
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please help!! it’s due asap
Answer:
x = -4 and 2
Step-by-step explanation:
When x = -4 and 2, y = 0 so -4 and 2 are the roots
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
a = √39 (exact)
a = 6.24 (dec.)
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 + 5^2 = 8^2
a^2 + 25 = 64
a^2 = 39
a = √39 (exact)
a = 6.24 (dec.)
Show that if a_1, a_2, ., a_n are n distinct real numbers, then exactly n-1 multiplications are used to compute the product of these n numbers no matter how parentheses are inserted into their product. (Hint: use the 2nd principle of mathematical induction and consider the last multiplication done).
we have shown that if [tex]$a_1, a_2, \ldots, a_n$[/tex] are n distinct real numbers, exactly [tex]$n-1$[/tex] multiplications are used to compute their product, regardless of how parentheses are inserted into the product.
What is the principle of mathematical induction?
The principle of mathematical induction is a powerful proof technique used to establish the validity of an infinite sequence of statements.
To prove that exactly [tex]$n-1$[/tex] multiplications are used to compute the product of n distinct real numbers, regardless of how parentheses are inserted into their product, we will use the principle of mathematical induction.
[tex]\textbf{Base Case:}[/tex]
For [tex]$n=2$[/tex], we have two distinct real numbers [tex]a_1$ and $a_2$.[/tex] The product is simply [tex]a_1 \cdot a_2$,[/tex] which requires only one multiplication. Thus, the base case holds true.
[tex]\textbf{Inductive Step:}[/tex]
Assume the statement holds true for [tex]$n=k$[/tex], where [tex]k \geq 2$.[/tex] That is, when multiplying k distinct real numbers, exactly [tex]$k-1$[/tex] multiplications are used.
Now, consider the case for [tex]$n=k+1$[/tex], where we have [tex]$k+1$[/tex] distinct real numbers [tex]$a_1, a_2, \ldots, a_{k+1}$[/tex]. The product can be computed by multiplying [tex]$a_1$[/tex] with the product of the remaining k numbers, which can be denoted as [tex]$(a_2 \cdot a_3 \cdot \ldots \cdot a_{k+1})$[/tex].
By our induction hypothesis, computing the product of k distinct real numbers requires [tex]$k-1$[/tex] multiplications. Therefore, multiplying[tex]$a_1$[/tex] with the product of the remaining [tex]$k$[/tex] numbers requires an additional multiplication, resulting in a total of k multiplications.
Hence, we have shown that if [tex]a_1, a_2, \ldots, a_n$ are $n$[/tex] distinct real numbers, exactly [tex]$n-1$[/tex] multiplications are used to compute their product, regardless of how parentheses are inserted into the product.
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PLEASE HELP I DON'T UNDERSTAND!!!!!! I WILL MARK!!!!!!!!!!!!!!
identify the pattern then write the next three terms in each sequence 2,8,32,128
Step-by-step explanation:
the difference is the previous term multiplied by 4 to get the next term
2,8,32,128,512,2048,8192
Hope that helps :)
find the slope of the line through each pair of points
a. (8,-7) and (5,-3)
b. (-5,9) and (5,11)
c. (-8,-4) and (-4,-9)
Answer:
I think the answers would be :
a . 4/3
b. 1/5
c . - 5/4
hope it helps u ^^
2 questions i need help with thanks!
Answer:
c for both
Step-by-step explanation:
Drag each tile to the correct box. Not all tiles will be used. Given the Pythagorean theorem x^2+y^2 = r^2 where r is the distance from the origin to the point (x, y) place the steps in the correct order to derive the Pythagorean identity cos^2 (0) + sin^2 (0) =1
Answer:
i just got it right.
Step-by-step explanation:
Eva has read over 25 books each year for the past three years.
A. Write an inequality to represent the number of books that Eva has read each year.
B. If Eva reads exactly 25 books this year, will the inequality from part A still be true? Explain how you know.
C. What is the smallest total number of books Eva can read over the next five years so that the inequality in part A remains true each year? Explain how to find your answer, and show all work to support your explanation.
Answer:
its 16 books
Step-by-step explanation:
iv had this problwm b4
How to do this question
9514 1404 393
Answer:
AB = [[-6, -1][-4, 6][-15, 10]]
Step-by-step explanation:
Any of a number of on-line, spreadsheet, or calculator tools will find the matrix product for you.
The input and output of one such tool is shown below.
__
As you know, each term in the product matrix is the sum of products of a row in the left matrix and a column in the right matrix. The coordinates of that row and column are the coordinates of the result in the product matrix.
For example, row 2, column 1 of the product matrix is the sum of products ...
(4)(-3) +(-2)(-4) = -12 +8 = -4 . . . . row 2, column 1 of the result
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What is the formula for finding the surface area of a square pyramid?
Answer:
a2 + 2al (or) a2 + √a24+h2 a 2 4 + h 2
Step-by-step explanation:
Answer:
SA=L²+2L√(L²/4+H²)
Step-by-step explanation:
Where H is the height and L is the length
Solve 7 sin(2x) = 6 for the two smallest positive solutions A and B, with A
To solve the equation 7 sin(2x) = 6 for the two smallest positive solutions A and B, we can use algebraic techniques and trigonometric properties.
The solutions A and B are approximately equal to A ≈ 0.287 and B ≈ 1.569, respectively.
To explain the solution, let's begin by rearranging the equation: sin(2x) = 6/7. Since the range of the sine function is between -1 and 1, the equation has solutions only if 6/7 is within this range. We can find the corresponding angles by taking the inverse sine (arcsin) of 6/7. Using a calculator, we find that the arcsin(6/7) is approximately 0.942.
However, this gives us only one of the solutions. To find the other solution, we can use the periodicity of the sine function. We know that sin(θ) = sin(π - θ), where θ is the angle in radians. Therefore, the second solution is π - 0.942, which is approximately 2.199. However, since we're looking for the smallest positive solutions, we need to consider only the values between 0 and 2π. Thus, the two smallest positive solutions are A ≈ 0.287 and B ≈ 1.569.
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