The height of the blade of a wind turbine as it turns through an angle of is given by the function h()=8.5sin(+180⁰) + 40, with height measured in meters.
Find the maximum and minimum positions of the blade.
Explain what the value of 40 in the equation represents.
What is the amplitude? Explain what it represents.
Sketch the function over two cycles.
Answers
Considering the sine function in this problem, we have that:
The minimum position in the table is of: 31.5The maximum position in the table is of: 48.5.The value of 40 is the vertical shift of the function.The amplitude is of 8.5.The graph of two cycles is given by the image at the end of the answer.How is the sine function defined?
The general sine function has the definition presented as follows:
f(x) = asin(b(x+c))+d.
The coefficients are given as follows:
a is the amplitude of the sine function.b: The period of the sine function is of 2π/b.c is the phase shift of the sine function.d is the vertical shift of the sine function.For this problem, the function is:
h(θ ) = 8.5 sin (θ + 180°) + 40
The amplitude is of:
a = 8.5.
The function should oscillate between:
-8.5 and 8.5.
However, with the vertical shift of 40, the minimum and maximum values are given as follows:
Minimum value: -8.5 + 40 = 31.5.Maximum value: 8.5 + 40 = 48.5.The measure of each cycle of the cosine function is of:
2π = 360º.
The function has a phase shift to the right of 180º, hence the graph is given by the image at the end of the answer, for two cycles, that is, between 0 and 4π.
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Related Questions
evaluate: p2(square) +3q2(square). p= -1/2. q= -2
Answers
Answer:
12 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
substitute the given values for p and q into the expression
p² + 3q²
= (- [tex]\frac{1}{2}[/tex] )² + 3(- 2)²
= [tex]\frac{1}{4}[/tex] + 3(4)
= [tex]\frac{1}{4}[/tex] + 12
= 12 [tex]\frac{1}{4}[/tex]
A 5 foot woman stands 3 feet from a lamppost and casts a 9 foot shadow
as shown. What is the height of the lamppost, rounded to the nearest tenth
of a foot?
O A) 6.5
OC) 6.9
O E) 6.7
O B) 6.8
OD) 6.6
Answers
Answer: e) 6.7
Step-by-step explanation:
This is a Similarity of Triangles problem (geometry)
if x is the height of the lamp post, then:
x/5 = (3 + 9) / 9
x (9) = (12) (9)
x = 60/9 = 6.7
Find the distance between 7 and 18 on a number line.
Answers
Answer:
11
Step-by-step explanation:
Find the difference using subtraction:
18 - 7 = 11
So, the numbers are 11 units apart.
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = −7 and x = 5 and passes through the point (0, −2).
Answers
The formula of the parabola is y = 2/35(x + 7)(x - 5)
How to determine the formula of the parabola?The parameters in the question are given as
Horizontal intercepts (roots) at x = −7 and x = 5 Passes through the point (0, −2).These parameters can be represented as
x₁ = -7 and x₂ = 5
(x, y) = (0, -2)
The quadratic function can be represented as
y = a(x - x₁)(x - x₂)
Substitute the known values in the above equation So, we have the following equation
y = a(x + 7)(x - 5)
At (x, y) = (0, -2), we have
-2 = a(0 + 7)(0 - 5)
Evaluate
a = -2/-35
Divide
a = 2/35
So, we have
y = 2/35(x + 7)(x - 5)
Hence, the equation is y = 2/35(x + 7)(x - 5)
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The measures of the angles of a triangle are shown in the figure below. Find the measure of the largest angle.
Answers
The measure of the Largest angle using the angle sum property of a triangle is: 80°
What is the Angle sum property of a triangle?
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.
In the given figure, we have:
Measure of 1st angle = 64°
Measure of 2nd angle = (2x + 14)°
Measure of 3rd angle = (6x + 14)°
and we know the angle of the property,
using the angle of property,
64° + (2x + 14)° + (6x + 14)° = 180°
⇒64° + 8x + 14° + 14° = 180°
⇒92° + 8x = 180°
⇒ 8x = 180° - 92°
⇒8x = 88°
⇒ x = 11°
So,
Measure of 2nd angle = (2x11 + 14)°
Measure of 2nd angle = (36)°
Measure of 3rdangle = (6x11 + 14)°
Measure of 2nd angle = (80)°
Hence,
The measure of the Largest angle using the angle sum property of a triangle is: 80°
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a point lies on the line y=3x-2, its y coordinate is 25. what is the coordinates of this point?
Answers
Answer:
x=9 (9,25)
Step-by-step explanation:
9*7=27
27-2=25
...........................................PLEASE HELP ME
Answers
So 1% of 3000 is 30
So 6% of 3000 is 180
180 + 3000 = 3180
Answer:
They should pay AED 180 as interest.
Step-by-step explanation:
Simple interest:
P = The amount borrowed = AED 3000
R = rate of interest = 3% per year
t = time = 24 months = 24 ÷ 12 = 2 years
[tex]\sf \boxed{Interest = PRt}[/tex]
Substitute the values,
[tex]\sf = 3000 * \dfrac{3}{100}*2\\\\ = 30*3*2\\\\=AED \ 180[/tex]
9) A shark descends from the surface of the water at a rate of 15 feet each minute. What is the depth of the shark
after 5 minutes?
Answers
Answer:
75
Step-by-step explanation:
1 minute=15
2 minutes=30
3 minutes=45
4 minutes=60
5 minutes=75
A copy machine makes 32 copies per minute. How long does it take to make 136 copies?
Answers
Answer:
4.25 minutes
Step-by-step explanation:
[tex]\frac{32 \:copies}{1\:min} = \frac{136\: copies}{x \: min} \\\\x\: min = \frac{136 \: copies}{32 \: copies} \\\\x=4.25 \: min[/tex]
Answer: 4 mins 15 seconds (4.25 mins)
Step-by-step explanation:
136 copies/32 copies per minute = 4.25 minutes
So we know it will take 4.25 mins. 4.25 mins is equal to 4 mins and 15 seconds.
given f(x)=2x-2, find f (-3)
Answers
Answer:
-8
Step-by-step explanation:
f(-3) = 2(-3)-2
f(-3) = -6 -2
f(-3) = -8
Answer:
[tex] \huge{f( - 3) = - 8}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x - 2[/tex]
In order to find f(-3) we substitute the value of x that's -3 into f(x) that's wherever we find x in f(x) we substitute it with -3 and solve for f(-3).
We have
[tex]f( - 3) = 2( - 3) - 2 \\ = - 6 - 2 \\ = - 8[/tex]
We have the final answer as
[tex] \bold{f( - 3) = - 8}[/tex]
Hope this helps you
2) Bethany, a pilot with a commercial airline, flew from NY to Pittsburgh and back. It took % hours to get to
Pittsburgh. With the help of the jet stream, the return trip took only 4/5 the time. How long was the round trip?
Answers
Total time taken by Bethany to make a round trip of NY to Pittsburgh as per given conditions is equal to 1 (7/ 20)hours.
As given in the question,
Time taken by Bethany to flew from NY to Pittsburgh is equal to 3/4 hours
Now using jet stream ,
Time taken by airlines from Pittsburgh to NY is (4/5) th of (3/4) hours
= (4/5) × (3/4) hours
= 3/5 hours
Total time taken by airlines to make a round trip from NY to Pittsburgh is given by:
= [(3/4) + (3/5)] hours
= [(15 +12)/20] hours
= 27/20 hours
= 1 7/20 hours
Therefore, total time taken by Bethany to make a round trip of NY to Pittsburgh as per given conditions is equal to 1 (7/ 20)hours.
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Triangles ABD and BCD are right-angled triangles.
A
5 cm
B
x cm
Work out the value of x.
Give your answer correct to 2 decimal places.
10 cm
D
4 cm
C
Answers
In triangle ABC,
Angle ABC = 90 degrees
AD= h = 10 cm
AB= p =5cm
BD = b = ?
Now,
Tan 90= p/b
or, 1/0= 5/BD
or, BD = 0 cm
In triangle BCD,
Let,
BC = h = xcm
BD = b = 0 cm
DC = 4cm
Using the Pythagoras theorem,
h = ( p^2 + b^2)^1/2
or, x = (4^2 + 0^2)^1/2
or, x = (16 + 0)^1/2
or, x = (16)^1/2
or, x = 4 cm
Hence, The value of x is 4 cm.
The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high
school preparation class, and no preparation class. Use the information from the table to answer the remaining questions.
Treatment
Private prep class
High school prep class
No prep class
Number of Observations
Source
Between treatments
Within treatments
60
60
60
Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean
times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.)
Sum of Squares (SS)
21,000.00
442,500.00
df
2 ▼
Sample Mean
650
645
625
177
Sum of Squares (SS)
132,750.00
147,500.00
162,250.00
Mean Square (MS)
Answers
The F Test statistic is 1.58.
Given data is
Source SS df MS
between 21,000.00 2 6,000.00
within 442,500.00 117 3,782.00
The SStotal is sometimes easier to calculate than SSbetween Since ......
SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween.
= 442,500+21,000 = 463,500
In ANOVA, the F test statistic is the ratio of the between - treatments variance and the within-treatments variance. The value of the F test statistic is 1.58 when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely large in general, you should reject null hypothesis for larger values of the F test statistic.
Hence the answer is the F Test statistic is 1.58.
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1. A circle is divided into 9 uneven pie shaped pieces. Each section is labeled 1, 2, ... 9. The circle is then spun and the number pointing north recorded. Estimate the probability that the next number pointing north will be between 2 and 7 inclusive.
4 3 2 1 9 8 5 6 7 4 3 2 1 5 8 6 5 4
13/18
5/18
5/8
8/5
2. How many shoppers made a purchase at a big-box store, or online, or at a locally- owned store?
250
359
380
400
3. How many shoppers made a purchase online and at a locally owned store, but not at a big box store?
38
56
109
179
Answers
The probability that the next number pointing north is between 2 and 7 is 13/18 .
1) The circle is divided into 9 parts.
Now the parts are uneven.
So the data about the spins is required to calculate the probability .
The total number of items in the box = 18
favorable outcomes (between 2 and 7) = 13 possible outcome.
Required probability
= favorable outcome / total outcome
= 13 / 18
2) Using the Venn diagram we can calculate the various parts of the problem:
Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers
3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.
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Which of the following is a disadvantage to a questionnaire?
A.
They are inexpensive to administer.
B.
The respondent controls the validity.
C.
The results can be confidential.
D.
They are time efficient.
Answers
A disadvantage of using a questionnaire is that B. The respondent controls the validity.
What is a disadvantage of using questionnaires?Questionnaires are a means of gathering data in research in order to find out more about a certain phenomenon. They involve writing questions and giving them to a respondent to fill out the answers.
Questionnaires are inexpensive to administer and can lead to confidential results which is good. However, they have the disadvantage that respondents control the validity of questionnaire results and can decide to lie if they feel it would make them look better, which would confuse the research results.
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Please show your work:
-5/2(8a - 2b) =
Answers
[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)
How can the answer is zero?
The first thing that we should do is simplify questions.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]
After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.
[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]
Next step is find the "a" by enter the "b" into the same question.
[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]
After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]
So, the answer is zero (0).
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Answer:
[tex] - 20a + 5b[/tex]
Step-by-step explanation:
[tex] - \frac{5}{2} (8a - 2b)[/tex]
[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]
[tex] - 20a + 5b[/tex]
Ordered pair for 2x+3y=5x-y
Answers
Draw and label the following figure.
Isosceles obtuse triangle with the obtuse vertex is angle T.
Answers
The Isosceles obtuse triangle in which the obtuse vertex is angle T is represented with the attached diagram.
What is an isosceles obtuse triangle?An isosceles obtuse triangle is a type of triangle which is formed by two equal sides of the triangle.
The vertex angle, which will be the obtuse one (x) can be x > 90°.The sum of the two base angles, y1 and y2, can be represented by y1 + y2 < 90 degrees.As long as the measures of the angles add up to 180°, it is an isosceles obtuse triangle.
An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.
A triangle is a polygon with three sides and three angles. There are different types of triangle, which includes:
Equilateral triangleScalene triangleObtuse triangleIsosceles triangleRight angle triangleSo therefore, an isosceles obtuse triangle is formed by having two equal sides of a triangle.
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A survey of 780 was conducted while visiting Sonoma county on vacation. Each person was asked if they drank wine on their trip. 532 people responded "Yes".
What proportion of people did NOT drink wine in the survey? Round your answer to two decimal places.
Answers
Answer:
0.32
Step-by-step explanation:
[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.
On rectangle ABCD below, if A is located at (3,4) and B is located at (7, 6), what is the slope of BC?
Answers
If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2 .
In the question ,
it is given that ,
In the rectangle ABCD , the coordinate of the point A is (3,4) and the coordinate of the point B is (7,6) .
since the sides of the rectangle are at 90° , that means they are perpendicular .
which means AB⊥BC ,
the slope of AB = (6-4)/(7-3)
slope = 2/4
slope = 1/2
Since , AB⊥BC ,
(slope of AB)×(slope of BC) = -1
substituting the values , we get
(1/2)×(slope of BC) = -1
slope of BC = -1/(1/2)
slope of BC = -2 .
Therefore , If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2 .
The given question is incomplete , the complete question is
On rectangle ABCD, if A is located at (3,4) and B is located at (7, 6), what is the slope of BC ?
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water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches express the volume v of the water in the cone as a function of the height h of the water
Answers
The volume V of the water in the cone as a function of the height h of the water is,
V = (1/48)πh³
Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.
We have to express the volume V of the water in the cone as a function of the height h of the water.
Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,
So, using the concept of similarity in triangles
we get, r/4 = h/16
r = h/4
Now, the volume of the water in the cone be,
V = (1/3)πr²h
V = (1/3)π(h/4)²h
V = (1/48)πh³
So, the function expressing the volume of the water in the cone be,
V = (1/48)πh³
Hence, the volume V of the water in the cone as a function of the height h of the water is,
V = (1/48)πh³
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calculate the surface area of a cube that has a width of 25 centimeters
Answers
The surface area of a cube that has a width of 25 centimeters is 3750 cm².
What is surface area?It should be noted that surface area simply implies the measure of the total area that the surface of an object occupies.
In this case, the surface area of a cube is measured as 6a² where a = side
In this case, the side is 25. Therefore, the surface area will be:
= 6a²
= 6 × 25²
= 3750 cm²
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Diego is solving this system of equations:
4x + 3y = 10
-4x + 5y = 6
Here is his work:
4x + 3y = 10
-4x + 5y =6
-4x + 5y = 6 +
0 + 8y = 16
y = 2
4x + 3(2) = 10
4x + 6 = 10
4x = 4
x = 1
Answers
The solutions of the equations are x = 1 and y = 2
The system of equations are
4x + 3y = 10
-4x + 5y = 6
Here we have to use the elimination method. Eliminate the x term and find the value of y term
Add both equation
3y + 5y = 10 +6
Add the like terms
8y = 16
y = 16 / 8
Divide the terms
y = 2
Substitute the value of x in the first equation
4x + 3y = 10
4x + 3×2 = 10
Multiply the terms
4x + 6 = 10
4x = 10 - 6
4x = 4
x = 4 / 4
Divide the terms
x = 1
Hence, the solutions of the equations are x = 1 and y = 2
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At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh. Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW. The market is currently bid at 95 pounds/MWh and offered at 105 pounds/MWh. What would you do, and why?
Answers
After 2 hours the plan needs to be changed, and purchase solar for the cost effect.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.
Total cost = 6x100 = 600 pounds
Total cost for 2 hours = 200 pounds
Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW.
Total cost for this:
From 8 AM to 12 PM = Number of hours 4 hours
4.5 GW = 4500 MW
= 105 pounds/MWh
Total cost for 4 hours = 630 pounds for 4500 MW per hour
Thus, after 2 hours the plan needs to be changed, and purchase solar for the cost effect.
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Frank makes $320 a week. If he works more than 8 hours in a day, he gets paid $10 for each hour of overtime. What did Frank earn if he worked 9 hours on 3 days last week?
Answers
Answer:
$55.71
Step-by-step explanation:
$320/7=$45.71 per day
45.71/8=5.71 per hour
45.71+10=$55.71 for 9 hours of work
45.71+ 45.71+55.71 =$147.13 for 3days +1 hour overtime
Let f(x) = -4x + 3 and g(x) = 6+ 7x Find the function. f/g (f/g)(x) =
Answers
The solution of the composite function (f/g)(x) is [tex]\frac{-4x+3}{6+7x}[/tex]
How to solve composite function?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Composite function involves the composition of functions is combining two or more functions as a single function.
Therefore, let's solve the function below:
f(x) = -4x + 3
g(x) = 6 + 7x
Hence,
(f/g)(x) = f(x) / g(x)
Therefore,
f(x) / g(x) = [tex]\frac{-4x+3}{6+7x}[/tex]
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Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four
Answers
Answer: 2(x+4) >3(x+7)-4
Step-by-step explanation:
Hope this helps
Answer:
2(n+4)≤3(n+7)-4
Step-by-step explanation:
The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4
What is a solution set to an inequality or an equation?
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.
We need to find the inequality of the statement given;
"Two times the sum of a number and four is no more; than three times the sum of the number and seven decreased by four"
Let n be the unknown number
Then it would be;
2(n+4) ≤ 3(n+ 7) - 4
Hence, The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4
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Draw and label the following figure.
Scalene Right triangle RGH.
Answers
The scalene right triangle RGH is given by the image shown at the end of the answer.
What are the classification of triangles?There are two classifications of triangles, either regarding the side lengths or the angles.
Regarding the side lengths, the classifications are given as follows:
Scalene: Three different side lengths.Isosceles: Two equal side lengths.Equilateral: Three equal side lengths.Regarding the measure of the greatest angle, the classifications are given as follows:
Acute: The greatest angle has a measure that is less than 90º.Straight: The greatest angle has a measure that is exactly 90º.Obtuse: The greatest angle has a measure that is greater than 90º.In this problem, RGH is a scalene right triangle, hence:
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The formula D = 5e -0.1h
can be used to find the number of milligrams D of a certain drug that is in a patient's
bloodstream h hours after the drug was administered. When the number of milligrams reaches 3, the drug is to be
administered again. What is the time between injections?
Answers
By Computing the Logarithmic Relation, we calculate that the time between injections is 5.1 hours or 5 hours and 6 minutes.
The given formula is
[tex]D = 5e^{-0.1h}[/tex]
where D is the amount of drug in milligrams in the patient's bloodstream and h is the number of hours after the drug was administered.
So, it is given that D = 3 and we need to evaluate the number of hours it took between the injections,
So, We have,
[tex]D = 5e^{-0.1h}[/tex]
[tex]\frac{D}{5} = e^{-0.1h}[/tex]
Taking Natural log on both sides, we have :
[tex]ln\frac{D}{5} =ln e^{-0.1h}\\\\ln\frac{D}{5} = -0.1h\\[/tex]
We have D = 3, putting it in the formula, we get
[tex]\ln\frac{3}{5} = -0.1h\\\\ln(0.6) = -0.1h\\\\-0.5108 = -0.1 h\\\\h = \frac{0.5108}{0.1} = 5.1[/tex]
Hence, the time between injections is 5.1 hours or 5 hours and 6 minutes.
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Use the calculator below to approximate √59 as a decimal to the tenths place.
Note that you must do the approximation without using a square root button.
Your answer must be within a tenth of the actual value.
Answers
The approximate of √59 is 7.7 when rounded off to the nearest tenth place.
Given, √59
we are asked to determine the approximation without using a square root button.
√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.
the square root of the number 59 is:
7.6811
You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.
= 7.7
When the digit to the right is 5 or greater we round away from 0.
7.6811 was rounded up and away from zero to 7.7
Hence we get the required approximation.
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