The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is 1/20 degree/sec.
What is angle of elevation?It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.
Calculation for the rate of change of angle of elevation-
According to the question,
A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.
The balloon is 100 feet above the ground.
Let the height of the balloon be 'h' ft.
Then tanØ = h/100
h = 100tanØ
Differentiate the above equation with respect to time.
dh/dt = 100 sec² Ø (dØ/dt)
We know dh/dt = 10 ft/sec.
when h = 100
tanØ = 100/100 = 1/1
tanØ = Perpendicular/Base
On comparing above two equations,
Perpendicular = 1; Base = 1.
By Pythagoras the hypotenuse is,
H² = P² + B²
= 1² + 1²
= 2
H = √2
Now, calculate the value of cosØ.
cosØ = B/H = 1/√2
Squaring both side
cos² Ø = 1/2
sec² Ø = 1/cos² Ø
sec² Ø = 2
The main equation was,
dh/dt = 100 sec² Ø (dØ/dt)
Substitute the values,
dØ/dt = (dh/dt )/100 sec² Ø
= (10)/(100×2)
dØ/dt = 1/20 degree/sec.
Therefore, the rate of change of the angle of elevation of the balloon from the observer is 1/20 degree/sec.
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v(t)=37,036(0.84)¹ What is the initial cost of the car, and what will the car be worth after 4 years? Round to the nearest whole number.
The initial value is 37,036 dollars and in 4 years, the value will be 18,439.16 dollars.
How to work with the exponential decay equation?Here we have an exponential decay that models the value of a car as time passes, the exponential decay is:
[tex]v(t) = 37,036*(0.84)^t[/tex]
The initial value is what we get when we evaluate in t = 0.
[tex]v(0) = 37,036*(0.84)^0 = 37,036[/tex]
The initial value is 37,036 dollars.
The value in 4 years is what we get when we evaluate in t = 4:
[tex]v(4) = 37,036*(0.84)^4 = 18,439.16[/tex]
In 4 years, the value will be 18,439.16 dollars.
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The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
(4, −7)
(−4, −7)
(4, 7)
(−4, 7)
Answer: (4,-7)
Step-by-step explanation:
when f(x) = [tex]x^3[/tex] the vertex is (0,0). when g(x)= [tex](x-4)^3-7[/tex] the vertex will be (4,-7). The equation is put into vertex form, in order for us to find the vertex (h,k), followed by [tex]y=a(x-h)^3+k[/tex]. With h=4 and k=-7.
Therefore, the answer is (4,-7)
l=10m,b=8m,h=5m
Please answer
Step-by-step explanation:
we have given
l=10m
b=8m
h=5m
volume =?
area=?
volume =l*b*h
= 10*8*5
=400
area=2(lb+lh+bh)
=2(10*8+10*5+8*5)
=2(80+50+40)
=2(170)
=340
hope this is helpful please make me brainliest
Which system is equivalent to startlayout enlarged left-brace 1st row y = 9 x squared 2nd row x y = 5 endlayout
The set of equations that corresponds to the specified function are
y = 5 - x and 5 - x = 9x².
What is linear equation in two variables?
If an equation is expressed as ax + by + c=0, where a, b, and c are all real integers and a and b, the coefficients of x and y, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
The given equation is :
[tex]y=9x^{2}[/tex] equation 1.
[tex]x+y=5[/tex] equation 2.
From equation 2.
[tex]x+y=5\\y=5-x[/tex]
substituting into 1 equation.
[tex]5-x=9x^{2}[/tex]
The system of equations that is equivalent to the provided function is shown by the resulting equation, which is y = 5 - x and [tex]5-x=9x^{2}[/tex]
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verbal scale uses a representative fraction to describe the ratio between the map and the real world
Verbal scale uses a representative fraction to describe the ratio between the map and the real world is a "true" statement.
What is verbal scale/expression?A verbal scale is also known as a "word statement" or a "scale expression," and it is one of the possibilities for entering "scale text" in the ArcGIS software.
It is presented as a relationship between map distance and ground distance that is stated in common units that both parties can agree upon.
Uses of the verbal scale:
Verbal scales are widely employed on large-scale maps and planning documents, most frequently by civil engineers, just like representative fractions. On some smaller-scale maps, you can discover them, although not as frequently as you can with representative fractions. The verbal scales have already been calculated in some common map scales, so you might utilize those. The best treatment of verbal scales and the other scale indications may be found in Map Use by Kimerling, Muehrcke, and Muehrcke.To know more about the verbal expression(scale), here
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The complete question is-
Verbal scale uses a representative fraction to describe the ratio between the map and the real world.(True/False).
Total area=
Help me please thanks so much
The surface area of the parallelpiped is equal to 800 square units.
What is the surface area of a parallelpiped?
The surface area of the parallelpiped seen in the picture is equal to the sum of the areas of its six faces, which are combination of areas of quadrilaterals and triangles. There are four parallelograms and two squares. Thus, the surface area of the solid is:
A = 2 · 8 · 20 + 2 · 7 · 20 + 2 · 10²
A = 800
The surface area of the parallelpiped is equal to 800 square units.
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Which is the graph of the function f() = x2 + 2x - 6?
The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards
Quadratic graphQuadratic functions are functions that has a leading coefficient of 2.
According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.
The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.
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The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what is the wavelength for radio waves with frequency 3 × 109?
The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.
What's the relation between frequency and wavelength of electromagnetic waves?For electromagnetic waves travelling in vaccum, the product of frequency and wavelength is the speed of light in vaccum.Mathematically, frequency × wavelength = 3×10⁸ m/s (which is speed of light)So, wavelength= 3×10⁸/ frequencyWhat's the wavelength of radio wave with frequency 3×10⁹ Hz ?Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m
Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.
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2. (4)1 point possible (graded, results hidden)Recall for Define the kernel function Write as a function of the dot product . To answer, let , and enter in terms of . z^2 submitted
The Kernel Function K (x,x') written as a function of the dot product x *x' is K (x, x') = Z². See the working below.
What is a Kernel Function?A kernel function is a way for taking input data and transforming it into the needed form of processing data.
The term "kernel" refers to a collection of mathematical functions used in Support Vector Machine to provide a window to alter data.
What is the solution deriving the expression given above?Given x = [x₁, x₂][tex]^{T}[/tex]
β(x) = [x²₁, √2 x₁ x₂, x²₂]
K (x₁, x') = β(x)[tex]^{T}[/tex] β(x')[tex]^{T}[/tex]
Hence, X' = [x₁, x₂][tex]^{T}[/tex]
→ β(x') = [x'²₁, √2 x'₁ x'₂, x'²₂]
K (x, x') = [x²₁, √2 x₁ x₂, x²₂][tex]^{T}[/tex] [x'²₁, √2 x'₁ x'₂, x'²₂]
K (x, x') = [x²₁, [x'²₁ + 2x₁ x₂ x'₁ x'₂ + x²₂ x'²₂
Because Z = x · x' (dot product of x·x')
= x₁ x'₁ + x₂x₂'
Expressing K (x,x') as a function of Z, we have
K (x₁, x') = x²₁ x'²₁ + 2x₁x₂ x'₁ x'² + x²₂ x'²₂
Simplified, we have
(x₁ x₁¹ + x₂x¹₂)² = Z²; and
[(a+b)² = a²+2ab+b₂] = z x₁x₁¹ + x₂x₁²
Therefore,
K (x, x¹) = Z²
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The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a v
In a 10-year period, Bakersfield, CA population grew from 558,000 to 718,000. What is the percentage of increase? (Round to the nearest tenth of a percent)
The percent increase to the nearest tenth is 22.2%
Calculating percent increasePercent increase is the percent it takes from a value to change from its initial value
Given the following
Initial value = 558,000
Final value = 718,000.
Determine the percent increase
% increase = (718,000-558000)/718,000 * 100
% increase = 160000/718000 * 100
% increase = 22.2%
Hence the percent increase to the nearest tenth is 22.2%
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Charlie owns a computer repair service. For each computer, they charge $50 plus $45 per hour of work. A linear equation that expresses the total amount of money Charlie earns per computer is y
The linear equation is 45x+50
Linear equation is the equation having the degree 1
Given that the charge per computer repair service is $50
The charge per hour of work is $ 45
We need to show the linear equation that expresses the total amount of money Charlie earns per computer is y
So , Let the number of hours be x
Therefore, the Charlie working hours charge will be 45x
The total amount of money Charlie earns per computer is y
Therefore the linear equation will be
y = 50+45x
Where y = Total amount of money
x = number of hours
Hence the linear equation is y = 45x+50
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In your opinion, what are the pros and cons of each projection? What are the limitations? In which circumstances, environments, or occupations is one type of projection likely preferred over the other? Describe any special tools that might be needed to create the projection. Which projection is easiest for you to interpret visually? Why?
The projection discussed are the isometric and the orthographic projection.
How to illustrate the information?The isometric projection is how the object look to the eyes when seen from a distance. It should be noted that orthographic projection give the actual measurements of the object.
The isometric drawing is through 100% true measurement of the height, width, and the depth.
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The sum of the reciprocals of three consecutive integers is 47/60. What is the sum of the three integers
Answer:
56
Step-by-step explanation:
small brain :(
Need help with this problem
put into quadratic formula
Answer: [tex]\frac{-7+\sqrt{49-4(15)(-12)} }{30}[/tex]
Step-by-step explanation:
Use the quadratic formula:
[tex]\frac{-b+-\sqrt{b^{2}-4(ac) } }{2a}[/tex]
Substitute the values, A = 15, b = 7, c = -12
[tex]\frac{-7+-\sqrt{7^{2}-4*(15*-12) } }{2*15}[/tex]
Simplify to answer:
[tex]\frac{-7+49-4(15)(-12)}{30}[/tex]
I hope this helps!
Which is the graph of a quadratic equation that has a positive discriminant?
Answer:
CORRECT graph is Graph C.
________________________________
HOPE IT HELPS
43. Consider the equation 4(x-8)+y=9(x-2)
[Part 1]
Find an expression for y of the form ax+b expression for y such that the equation has infinitely many solutions. Is there more than one such solution? Explain your reasoning using complete sentences.
[Part 2]
Find an expression for y of the form ax+b expression for y such that the equation has no real solutions. Is there more than one such solution? Explain your reasoning using complete sentences.
The expression of the equation 4(x - 8) + y = 9(x - 2) in slope intercept form is; y = 5x + 14
How to write an equation in Slope Intercept form?We want to express 4(x - 8) + y = 9(x - 2) in slope intercept form of y = mx + b.
Let us expand the equation to get;
4x - 32 + y = 9x - 18
Isolate y to get;
y = 9x - 4x - 18 + 32
y = 5x + 14
Thus;
Slope = 5
y - intercept = 14
x - intercept = -2.8
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I can't figure out the equivalent fraction. Whoever gets it first gets brainliest, and please do explaination
Factorize the numerator and denominator. You'll see that they both have a factor of 4 that can be canceled. The introduce a factor of 3 to change the denominator to 36.
[tex]\dfrac{28}{48} = \dfrac{4\times7}{4\times12} = \dfrac7{12} = \dfrac{3\times7}{3\times12} = \boxed{\dfrac{21}{36}}[/tex]
Ruthie is trying to choose what reading material she wants to take on a vacation. She wants to read 1 fiction book, 1 nonfiction book, and 3 magazines. If Ruthie has 8 fiction books, 7 nonfiction books, and 3 magazines to choose from, how many possible combinations of books and magazines could she take with her.
E. 3 F.8 G.56 H.112
The number of possible combinations would be 56.
What is permutation?Permutation is the changing of the order in which things have been arranged or the arranging of things in a certain order.
Analysis:
Total number of fiction books available = 8
number of fiction books Ruthie wants = 1
Number of combination for Ruthie = 8C1 = 8 ways
Total number of non fiction books available = 7
number of non fiction books needed by Ruthie = 1
possible combination = 7C1 = 7 ways
Total number of magazines available = 3 ways.
Total possible combinations for all the Reading materials = 8 x 7 x 1 = 56 ways.
number of magazines Ruthie wants = 3C3 = 1 way
In conclusion, the number of possible combinations of The reading materials is 56.
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Find the measure of each numbered angle.
Answer:
m∠1 = 51°
m∠2 = 16°
Step-by-step explanation:
First ,check the attached photo.
=================
In the right triangle ABC :
m∠1 = 90 - 39
= 51°
……………………
In the right triangle ABD :
m∠2 = 90 - 74
= 16°
Answer:
• ∠ 1 = 51°
• ∠ 2 = 16°
Step-by-step explanation:
• ∠ 1, the 39° angle, and the right angle marked in red are angles of a triangle.
∴ ∠ 1 + 90° + 39° = 180° [Angles in a triangle add up to 180°]
⇒ ∠ 1 = 180° - 90° - 39°
⇒ ∠ 1 = 51°
• The small triangle on the top-left of the image consists of ∠ 2, a right-angle (marked in red) and a 74° angle.
∴ ∠ 2 + 90° + 74° = 180° [Angles in a triangle add up to 180°]
⇒ ∠ 2 = 180° - 90° - 74°
⇒ ∠ 2 = 16°
uan recently hired a roofer to do some necessary work. On the final bill, Juan was charged a total of $1131.5. $450 was listed for parts and the rest for labor. If the hourly rate for labor was $47, how many hours of labor was needed to complete the job?
Based on the total cost that Juan incurred to hire the roofer including the charge for parts and labor, the number of hours that was needed to complete the job was 14.50 hours.
How many hours did the roofer use?The first thing to do is to find out the amount that went to labor:
= Final bill - cost of materials
= 1,131.5 - 450
= $681.50
Now that you have the cost of labor, you can find out the number of labor hours that were used based on the hourly rate:
= Cost of labor / Hourly rate
Solving gives:
= 681.50 / 47
= 14.5 hours
In conclusion, the number of labor hours that the roofer used to complete the work, based on the total amount charged to Juan is 14.50 hours.
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Select all the correct answers.
Consider functions f and g.
f(x) = - 2 cos (x - 1) + 3
g(x) = 2 cos (x + 3) - 3
Which statements describe transformations of the graph of fresulting in the graph of function g?
A. The graph of function f has been vertically stretched by a factor of 4.
B. The graph of function fhas been reflected over the y-axis.
C. The graph of function fhas been reflected over the x-axis.
D. The graph of function fhas been translated 3 units down.
D. The graph of function fhas been translated 4 units left.
E. The graph of function fhas been translated 3 units left.
((More than one))
The function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
How to determine the characteristics of rigid transformations by comparing two functions
In this problem we have two functions related to each other because of the existence of rigid transformations. Rigid transformations are transformations applied to geometric loci such that Euclidean distance is conserved at every point of the geometric locus.
Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:
f'(x) = - 2 · cos (x - 1 + 4) + 3
f'(x) = - 2 · cos (x + 3) + 3 (1)
Now we apply a reflection over the x-axis:
g(x) = - [- 2 · cos (x + 3) + 3]
g(x) = 2 · cos (x + 3) - 3
Therefore, the function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)
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Add the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of x. 2x^3+4x-6 3x^3-8x+7
The addition of the polynomials [tex]2x^3+4x-6[/tex] and [tex]3x^3-8x+7[/tex] in the proper location on the grid is [tex]5x^3-4x+1[/tex]
How to find the addition of two polynomials is proper location on the grid ?
Polynomials addition in proper location means add the coefficient of same power of variable
So the addition of polynomials like this
[tex]2x^3+4x-6+3x^3-8x+7[/tex]
[tex]2x^3+3x^3=5x^3\\4x-8x=-4x\\-6+7=1[/tex]
The addition of the polynomials is [tex]2x^3+4x-6+ 3x^3-8x+7=5x^3-4x+1[/tex]
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What is the slope of the line that contains the points (4, 3) and (2, 7)?
OA-1
B. -5
C. -2
OD. -
Answer:
B. -2
Step-by-step explanation:
To find a slope of a line, you have to identify x and y variables:
(4, 3) => (x1, y1) (2, 7) => (x2, y2).We use the formula;
m = ∆y/∆x
= (y2 - y1)/(x2 - x1)
m is slopeSubstitute the values into the formula above.
m = (7 - 3)/(2-4)
= 4/-2
= -2
Therefore, the slope of the line is passing through points (4,3) and (2,
7) is -2.
A 1500 pound car is stopped in traffic on a hill that is at an incline of 10°. determine the force that is required to keep the car from rolling down the hill.
Answer: about 260 Lb
Step-by-step explanation:
successor of -501 is
Answer:
-500
Step-by-step explanation:
since 501 has a negative sign,add 1 to to the number,the next number will be -500
-501 +1 = -500
successor in this case means a number that succeeds another
True or false: If neither variation in an A/B is statistically better, you pick the variation you like best and proceed to make the change.
It is false to state that " If neither variation in an A/B is statistically better, you pick the variation you like best and proceed to make the change."
What is A/B Testing?A/B testing compares two variations of a website element, often by evaluating users' responses to variant A vs. variant B and determining which of the two variants is more successful.
When the variation seems to be equal, then another factor must be introduced into the metric analysis that helps to make the testing objective.
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Which term describes the red curve in the figure below?
• A. Parabola
O B. Circle
• C. Hyperbola
O D. Ellipse
Answer:
the red curve is a hyperbola
A farmer has a piece of land with an area of 4 square yards. If a cow can graze grass at a rate of 2 square feet per hour, how long will it take 3 cows to graze the entire piece of land
Answer:
2 hours
Step-by-step explanation:
4 square yards to feet: 4*3 = 12ft
3 cows grazing grass at 2 ft per hour: 2*2 = 6 square ft per hour
Time taken: 12ft/6ft per hour = 2 hours
The shape of f(x) = √ x, but shifted nine units to the left and then reflected in both the x-axis and the y-axis
Answer:
g(x) = -√(-x +9)
Step-by-step explanation:
The relevant transformations are ...
f(x -h) . . . . . shifts the graph of f(x) right h unitsf(x) +k . . . . . shifts the graph of f(x) up k units-f(x) . . . . . . . reflects the graph of f(x) over the x-axisf(-x) . . . . . . . reflects the graph of f(x) over the y-axisApplicationApplying the transformations in the specified order, we have ...
f(x) = √x
f(x +9) = √(x +9) . . . . . . . shifted 9 units to the left
-f(x +9) = -√(x +9) . . . . . . shifted 9 left, reflected in the x-axis
-f(-x +9) = -√(-x +9) . . . . shifted 9 left, reflected in x-axis, reflected in y-axis
The shifted, reflected function is ...
g(x) = -√(-x +9)
__
Additional comment
The graph shows the original f(x) = √x function in red. The shifted, reflected function is shown in blue. Note that the initial left shift changes appearance to a right shift when it is reflected over the y-axis.