The windmill's blade measures 7 feet in length.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.To find the measure of the windmill's blade:
We have the equation: [tex]h=sin(\frac{\pi }{21t} )+28[/tex]At the time 't' = 0, the end of the blade is parallel to the ground and pointing to the right, indicating that it is the same height as the other end. (Ф = 0°)We may calculate the length of the blade by calculating the greatest height of this end at = 90°.We now know that the general model equation of a circular simple harmonic motion is written as follows: y = A sinωt + kWhere A is the maximum displacement from mean to maximum positionThe angular frequency is ω.When eq1 and eq2 are compared:A = 7As a result, the difference in blade end height at = 0° and = 90° is 7 feet.Therefore, the windmill's blade measures 7 feet in length.
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The correct question is given below:
The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet
PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3
How to determine the graph of f(x) + g(x)?The functions are given as:
f(x) = x + 3
g(x) = x
From the above functions, we can see that the function g(x) is the parent function of a linear function.
When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points
(x, y)= (0, b) and (-b, -b)
Where b is the y-intercept of the other function
i.e b = 3 from f(x) = x + 3
So, we have the following points
(0, 3) and (-3, -3)
Next, we draw the points and we connect the points
When the equation of f(x) + g(x) is calculated, we have
f(x) + g(x) = 2x + 3
See attachment for the graph of the functions
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Find the absolute maximum and minimum values of f on the set d. f(x, y) = xy2 7, d = {(x, y) | x ≥ 0, y ≥ 0, x2 y2 ≤ 3}
Assuming you mean [tex]f(x,y) = xy^2[/tex] over the domain
[tex]D = \left\{(x,y) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } x^2 + y^2 \le 3\right\}[/tex]
we first observe that [tex]f(x,y) = 0[/tex] for all [tex](x,y)[/tex] on the coordinate axes.
There are no critical points elsewhere in the interior of [tex]D[/tex], since
[tex]\dfrac{\partial f}{\partial x} = y^2 = 0 \implies y=0[/tex]
[tex]\dfrac{\partial f}{\partial y} = 2xy = 0 \implies x = 0 \text{ or } y = 0[/tex]
Parameterize the circular arc boundary by [tex]x=\sqrt3\cos(t)[/tex] and [tex]y=\sqrt3\sin(t)[/tex], where [tex]0\le t\le\frac\pi2[/tex]. Then
[tex]f(x(t), y(t)) = g(t) = 3\sqrt3 \cos(t) \sin^2(t) = 3\sqrt 3 (\cos(t) - \cos^3(t))[/tex]
Find the critical points of [tex]g[/tex].
[tex]g'(t) = -3\sqrt3 \sin(t) + 9\sqrt3 \cos^2(t) \sin(t) = 0[/tex]
[tex]-3 \sin(t) (1 - 3 \cos^2(t)) = 0[/tex]
[tex]\sin(t) = 0 \text{ or } 1 - 3 \cos^2(t) = 0[/tex]
[tex]\sin(t) = 0 \text{ or } \cos^2(t) = \dfrac13[/tex]
[tex]\sin(t) = 0 \text{ or } \cos(t) = \pm\dfrac1{\sqrt3}[/tex]
In the first case, we get
[tex]t = \sin^{-1}(0) + 2n\pi \text{ or } t = \pi - \sin^{-1}(0) + 2n\pi[/tex]
where [tex]n[/tex] is an integer; the only solution on the boundary of [tex]D[/tex] is [tex]t=0[/tex] corresponding to the point [tex](\sqrt3,0)[/tex].
In the second case, we get
[tex]t = \cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]
with only one relevant solution at [tex]t=\cos^{-1}\left(\frac1{\sqrt3}\right)[/tex] corresponding to [tex](1,\sqrt2)[/tex].
In the third case, we get
[tex]t = \cos^{-1}\left(-\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]
but there is no [tex]t[/tex] in this family of solutions such that [tex]0\le t\le\frac\pi2[/tex].
So, we find
[tex]\min\left\{xy^2 \mid (x,y) \in D\right\} = 0 \text{ at } (0,0)[/tex]
(but really any point on either axis works)
[tex]\max \left\{xy^2 \mid (x,y) \in D\right\} = 2 \text{ at } (1,\sqrt2)[/tex]
G.CO.5 △ABC undergoes a series of transformations to create △A'B'C'. Which of the following series of transformations will carry △ABC onto △A'B'C'?
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
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Geometry: complete this proof (ASAP!!! It’s urgent)
Answer:
1. BD bisects <CBE, AE || BD (Given)
2. <EBD ~= <CBD (Definition of < Bisectors)
3. <AEB ~= <EBD (Alternate Interior Angles Theorem)
4. <CAE ~= <CBD (Corresponding Angles Postulate)
5. <CAE ~= <AEB (Transitive Property of Congruence)
6. AB ~= BE (Converse of Isosceles Triangles Theorem)
Given that a randomly chosen flight arrives in los angeles (lax), what is the probability that the carrier is american airlines (aa)?
Using concepts of probability, it exists found that there exists a 4.7% probability that it arrives at American airlines (aa).
What is probability?A probability exists given by the number of expected outcomes divided by the number of total outcomes.
Over a large number of trials, a percentage can also define the probability of a single event.
In this question, analyzing the problem on the internet, we have that over a considerable number of flights, of those which came on time, 4.7% of them were in American airlines.
There exists a 4.7% probability that it arrives on American airlines(aa).
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Answer: 2316/16924 = 0.137 = 13.7%
Step-by-step explanation:
Perfect pizza has 16 toppings listed on their menu. how many ways could a customer choose a pizza that contains 5 different toppings?
Answer:
4368 ways
Step-by-step explanation:
Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.
can someone please help mee ( will give brainliest 20 points!!!)
The piecewise function graphed below is given as follows:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex][tex]f(x) = x + 2, -2 < x \leq 3[/tex][tex]f(x) = -1, 3 < x \leq 5[/tex]What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex]
For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:
[tex]f(x) = x + 2, -2 < x \leq 3[/tex]
For x greater than 3 until 5, the function is constant at -1, hence the definition is:
[tex]f(x) = -1, 3 < x \leq 5[/tex]
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(08.07 HC)
An expression is shown below:
f(x) = 2x²-3x - 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Answer:
Below in bold.
Step-by-step explanation:
Part A
At the x-intercepts f(x) = 0, therefore:
2x^2 - 3x - 5 = 0
(2x - 5)(x + 1) = 0
x = 5/2, -1)
So the x intercepts are (-1, 0) and (5/2, 0).
Part B
The Coefficient of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.
Convert f(x) to vertex form, by completing the square:
f(x) = 2x^2 - 3x - 5
= 2(x^2 - 3/2x) - 5
= 2[(x - 3/4)^2 - 9/16] - 5
= 2(x - 3/4)^2 -18/16 - 80/16
= 2(x - 3/4)^2 - 49/8
So the coordinates of the vertex are
(3/4, -49/8) or
(0.75, -6.125) in decimal form.
Part C
To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.
The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).
You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.
Suggest x = - 2 and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 = 11.
- that is the point (-2,11) and the other would be x = 4, f(x) = 15. (4, 15)
Once you have plotted these points draw a smooth u shaped curve through them.
find the value of n:
[tex]\frac{10}{n} =\frac{15}{6}[/tex]
The function f(x) = –Two-sevenths (five-thirds)x is reflected over the y-axis to create g(x). Which points represent ordered pairs on g(x)? Check all that apply.
The values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
Reflection of coordinatesReflection is a transformation technique that changes the position of an object on an xy-plane.
If the function f(x) is reflected over y-axis, the resulting function is y = f(-x). Given the following function;
f(x) = -2/7(5/3)x
This can also be written as;
f(x) = -10/21 x
Replace x as -x
f(-x) = -10/21(-x)
f(-x) = g(x) = 10/21x
Hence the values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
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Rick runs 5 miles which burns approximately 500 calories. how many miles would rick have to run to burn one pound of adipose tissue?
35miles Rick have to run to burn one pound of adipose tissue.
According to the given question.
Rick runs 5miles to burn 500 calories.
⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.
As we know that
1 pound = 3,500 calories.
So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles
Hence, 35miles Rick have to run to burn one pound of adipose tissue.
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A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles. event a = drawing a brown marble on the first draw event b = drawing an orange marble on the second draw if two marbles are drawn from the jar, one after the other and not replaced, what is p(b|a) expressed in simplest form?
The probability of event A and event B IS 15/91.
What is the probability?
Probability determines the odds that a random event would occur. The odds lie between 0 and 1.
The probability of event A = number of brown marbles / total number of marbles
= 6/14
The probability of event B = number of orange marbles / total number of marbles -1
= 5/13
P(A and B) =6/14 x 5/13
= 30/182
= 15/91
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Answer:
B.) 5/13
Step-by-step explanation:
15/3=5
91/7=13
5/13
BRAINEST IS VERYYYY APPRECATED
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]h = \frac{2A}{b}[/tex]
Step-by-step explanation:
We are given:
[tex]A = \frac{1}{2} b h[/tex]
To solve for [tex]h[/tex], we have to rearrange the equation to make [tex]h[/tex] the subject:
[tex]A = \frac{1}{2} b h[/tex]
⇒ [tex]2A = bh[/tex] [multiplying both sides by 2]
⇒ [tex]\frac{2A}{b} = h[/tex] [dividing both sides by b]
⇒ [tex]h = \frac{2A}{b}[/tex] [swapping sides]
A dairy farmer decides to sell three fifth of her 500 cows. How many cows will she be left with after the deal is complete?
What are angles <3 and <4 ?alternate interior angles
alternate exterior angles
vertical angles
corresponding angles
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation: 4x − 3y = 34
Second equation: 3x + 2y = 17
Answer:
Multiply both sides of the first equation by 2.
Multiply both sides of the second equation by 3.
Step-by-step explanation:
The y terms are
-3y
2y
The LCM of 2 and 3 is 6.
We need the y terms to add to zero.
Multiply both sides of the first equation by 2 to get -6y.
Multiply both sides of the second equation by 3 to get 6y.
Then -6y + 6y = 0 eliminating the y terms after adding the equations.
A bird (B) is spotted flying 6,000 feet from a tower (). An observer (0) spots the top of tower (T) at a distance of 9,000 feet. What is the angle of depression from the bird (B) to the
observer (0)?
Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.The adjacent side to the angle is the distance to the bird, of 6000 feet.Hence, considering θ as the depression angle, we have that:
tan(θ) = 9000/6000
tan(θ) = 1.5
θ = arctan(1.5)
θ = 56.31º.
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Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]
[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]
next,
g(f(-5)) represents value of y at x = f(-5) = 1
hence,
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\sf \:g(f( - 5)) = 5[/tex]Which of the equations below represents
this ellipse?
a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1
The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
What is the equation of the ellipse represented in the graph?
Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Coordinates of the centera, b - Lengths of the semiaxesPlease notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
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(b) Expand and simplify (x - 3) (2x + 3)(4x + 5)
Answer:
8x³ - 2x² - 51x - 45
Step-by-step explanation:
(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL
= (x - 3)(8x² + 10x + 12x + 15)
= (x - 3)(8x² + 22x + 15)
multiply each term in the second factor by each term in the first factor.
x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis
= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms
= 8x³ - 2x²- 51x - 45
Expand first 2 bracket first to get:
2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.
2x^2 - 3x - 9 (4x + 5)
2x^2 x 4x = 8x^4
2x^2 x 5 = 10x^2
Repeat for the next two numbers next to the bracket.
You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45
Final simplified answer of:
8x^3 - 2x^2 - 51x - 45
Hope this helps!
Please help!
The graph shows a system of inequalities.
Which point is a solution to the system?
(0,-1)
(2,3)
(4,0)
(6,-6)
Check the picture below.
In using the multiple regression method, we can model the effects of the different levels of a qualitative independent variable by using a(n) ____________
For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
According to the statement
we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.
So, For his purpose, we know that the
A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.
And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.
By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.
So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
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10. Ali's crystal ball grants two-fifths of one-fifth of
all wishes. This is ?% of all wishes.
(A)
2
(B)
25
(C) 8
(D) 60
Answer:
C
Step-by-step explanation:
2/5 x1/5 = 2/25 If you divide 2 by 25, you get.08. To change a decimal into a percent, you move the decimal two places to the right to get 8%
write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-6,6) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of -15
Answer:
[tex]y=-\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
Slope of line with given x and y intercepts
The x-intercept is when y = 0.
Therefore, if the x-intercept is 5 ⇒ (5, 0).
The y-intercept is when x = 0.
Therefore, the y-intercept is -15 ⇒ (0, -15).
Inputting these two points into the slope formula to find the slope of this line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]
Slope of function f(x)
If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.
[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]
Equation of f(x) in point-slope form
Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]
Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:
[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]
[tex]\implies y=-\dfrac{1}{3}x+4[/tex]
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Select the correct answer what are the solutions to this quadratic equation 4x^2-10=10-20x
Answer:
x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2
Step-by-step explanation:
what expression is equivalent to 6+3(n-4)-8+2n
Answer:
Step-by-step explanation:
Comment
Begin by removing the brackets.
6+3(n-4)-8+2n
6 + 3n - 12 - 8 + 2n Collect like terms
3n + 2n + 6 - 12 - 8 Combine
5n - 14
Answer
5n - 14
What two nonnegative real numbers with a sum of have the largest possible product?.
The two non negative real numbers with a sum of 60 that have the largest possible product are 30 and 30.
What are non negative numbers?
Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.
An integer that is either positive or zero is considered a non-negative integer.
Let us assume the two non negative numbers are [tex]x[/tex] and [tex]y[/tex].
According to the question,
Sum of two non negative numbers = 60
⇒ [tex]x+y=60[/tex]
⇒ [tex]y=60-x[/tex]
Their product will be given as,
⇒ [tex]P=xy[/tex]
⇒ [tex]P=x(60-x)[/tex]
⇒ [tex]P=60x-x^2[/tex]
For the product to be largest [tex]P'(x)=0[/tex]
⇒ [tex]P'(x) = 60-2x[/tex]
⇒ [tex]60-2x=0[/tex]
⇒ [tex]2x=60[/tex]
⇒ [tex]x=30[/tex]
Now, for the value of [tex]y[/tex]
⇒ [tex]y=60-x[/tex]
⇒ [tex]y=60-30[/tex]
⇒ [tex]y=30[/tex]
Therefore, the two non negative numbers are 30, 30.
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A 2-quart carton of non-dairy creamer costs $1.04. What is the price per cup?
whats the surface area of the rectangular prism
The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.
What is the area of a rectangle?The area of a rectangle with length and width is
Area = length × width
I.e., A = l × w sq. units
How to calculate the area of the rectangular prism?A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.
So, the areas of each face are as follows:
A(R1) = l × w
A(R2) = l × h
A(R3) = w × h
A(R4) = l × w
A(R5) = l × h
A(R6) = w × h
Thus, the area of the prism = sum of areas of all the faces
⇒ Area of the prism = lw + lh + wh + lw + lh + wh
⇒ A = 2lw + 2lh + 2wh
⇒ A = 2(lw + lh + wh)
Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).
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Select the correct answer. emily wants to find the number that appears in the middle of a set of 25 numbers arranged in ascending order, in a spreadsheet. which statistical function will help her do so? a. mode b. rank c. median d. average
The correct answer is option (C) median.
The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
What is the mean, median and mode?The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.
The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.
When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.
The number that appears most frequently in a set of numbers is called the mode.
So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
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