Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). If a turbine generates 700 kW in a 12 m/s wind, how much power does it generate in a 6 m/s wind?
(The formula for P as a power function of v is P = a ⋅ v3.
A. 88 kW
B. 175 kW
C. 125 kW
D. 1050 kW
Answers
Answer:
New power = 88 Kw (Approx.)
Step-by-step explanation:
Given:
P = a(v³)
Old power p = 700 Kw
Old wind speed v = 12 m/s
Find:
New power when v = 6m/s
Computation:
P = a(v³)
700 = a(12³)
a = 0.4050 m²
New power = a(v³)
New power = (0.4050)(6³)
New power = 87.48
New power = 88 Kw (Approx.)
Related Questions
utomobile trips there are major roads from city to city and major roads from city to city . how many different trips can be made from city to city passing through city ?
Answers
There are 8 different trips that can be made from City X to City Z, passing through City Y.
To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.
First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.
By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:
Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z
= 2 x 4
= 8
This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.
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Complete question is:
Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?
Jackson bought 5 ounces of raisins for \$4 dollar sign, 4. How much do raisins cost per ounce? \$
dollar sign How many ounces of raisins can be bought for \$1dollar sign, 1? ounces
Answers
Answer:
Answer:
Cost of raisin per ounce = $0.8
Step-by-step explanation:
Solution:
Number of ounces = 5 ounces
Price of 5 ounces= $4
Cost of raisin per ounce = ?
To find out the price per ounce, simply take the total dollar amount of the product and divide it by the number of ounces.
Formula = Price/Number of ounces
= 4/5
=$0.8
Cost of raisin per ounce = $0.8....
Step-by-step explanation:
Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is?
Answers
Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is 1 - 1/k².
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.
This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.
Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;
1 - 1/1.8² = 0.6914
= 69.14%
Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is 1 - 1/k².
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what is 4 / 4 + 8 - 9 + 15 - 50 + 1000
Answers
Answer:
965
Step-by-step explanation:
Each of Frank's notebooks is 2/5 inches wide. If he has 10 inches of space remaining on his bookshelf, how many notebooks will fit
Answers
We can fit 25 notebooks on the space.
Now, According to the question:
The width of the notebook is 2/5
The length of the space is 10 inches.
To find the number of the notebooks can put there divide 30 by 2/3
Number of the books : \(\frac{10}{\frac{2}{5} }\) = 10 × \(\frac{5}{2}\)
=> 50/2 = 25
The number of the notebook is 25
We can fit 25 notebooks on the space.
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A roller coaster’s height is given by the equation h = –.067t2 7t 50, where t represents the time in seconds. how long will it take riders to pass over the hill and reach ground level? hint: set h = 0. 13.40 seconds 50.07 seconds 52.24 seconds 111.19 seconds
Answers
The time it take riders to pass over the hill and reach ground level is 111.19 seconds .
Given :
the roller coaster's height expressed by the equation below;
h = -0.067t^2 + 7t + 50
where
t is the time in seconds
The driver will hit the ground at the point where h = 0
Substitute
-0.067t^2 + 7t + 50 = 0
Multiply through by -1
0.067t^2 - 7t +-50 = 0
Factorize :
On factorizing, the positive value of "t" is 111.19 seconds
Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds
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On the coordinate plane, point P is located at (3, y) and point Q is located at (1, -4). The distance between
points P and Q is 29 units.
What are the two possible values of y?
Answers
Answer:
y = 23, -31
Step-by-step explanation
ttyl
Can someone pls help me with this?
Answers
Associative prop: (3+5) +7 or (3+7) +5
And the last one, I don’t fully understand what it is asking, but I believe it is asking for the answer which would be 15
simplify the following 4 (45−52) ÷ 10 + 6
Answers
Answer:
the answer
Step-by-step explanation:
the answer will be 3.2 ( by using calculator)
Consider the following numerical example of the IS-LM model: C=233+0.47Y D I=143+0.22Y−1,094i G=299 T=239 i=0.06 Derive the IS relation. (Hint: You want an equation with Yon the left side of the equation and everything eise on the right.) Y= ( (Round your calculations of the intercept and slope terms to two decimal places.)
Answers
The IS relation is given by: Y = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places) in the numerical example of the IS-LM model.
To derive the IS relation, we need to equate aggregate demand (AD) to aggregate supply (AS). Aggregate demand consists of consumption (C), investment (I), government spending (G), and net exports (NX). In this case, we assume net exports to be zero.
Given:
C = 233 + 0.47YD
I = 143 + 0.22Y - 1,094i
G = 299
T = 239
Aggregate demand (AD) = C + I + G
Substituting the given equations into AD:
AD = (233 + 0.47YD) + (143 + 0.22Y - 1,094i) + 299
Simplifying:
AD = 233 + 143 + 299 + 0.47YD + 0.22Y - 1,094i
Combining like terms:
AD = 675 + 0.47YD + 0.22Y - 1,094i
Since we want an equation with Y on the left side, we need to express YD in terms of Y by substituting YD = Y - T.
AD = 675 + 0.47(Y - T) + 0.22Y - 1,094i
AD = 675 + 0.47Y - 0.47T + 0.22Y - 1,094i
Combining like terms again:
AD = (0.47Y + 0.22Y) + (675 - 0.47T - 1,094i)
AD = 0.69Y - 0.47T - 1,094i + 675
Comparing with the IS relation Y = a + bAD, we have:
Y = 0.69Y - 0.47T - 1,094i + 675
Rearranging terms to have Y on the left side:
Y - 0.69Y = -0.47T - 1,094i + 675
0.31Y = -0.47T - 1,094i + 675
Dividing both sides by 0.31:
Y = (-0.47T - 1,094i + 675) / 0.31
Now, we can calculate the intercept and slope terms:
Intercept term = (-0.47T - 1,094i + 675) / 0.31
Slope term = 1 / 0.31
Rounding these values to two decimal places, the IS relation is:
Y = Intercept term + Slope term = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places).
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If f(x)=5x^2-3x-1f(x)=5x 2 −3x−1, then what is the remainder when f(x)f(x) is divided by x+10x+10?
Answers
Answer:
\(5x-53+\frac{529}{x+10}\)
Step-by-step explanation:
A stock just paid a dividend of $1.55. The dividend is expected to grow at 26.56% for three years and then grow at 3.42% thereafter. The required return on the stock is 14.40%. What is the value of the stock?
Answers
Here, we are supposed to find the value of the stock. Let's begin by determining the expected dividends: Expected dividends1st year dividend (D1)
= $1.55(1 + 26.56%)
= $1.96Second-year dividend (D2) = $1.96(1 + 26.56%) = $2.48Third-year dividend (D3)
= $2.48(1 + 26.56%)
= $3.
= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4...∞Where r
= required rate of return Let us substitute the values now PV of the future dividends
= $1.96/(1 + 14.40%)^1 + $2.48/(1 + 14.40%)^2 + $3.14/(1 + 14.40%)^3 + $3.25/(1 + 14.40%)^4...∞PV of the future dividends = $1.96/1.1440^1 + $2.48/1.1440^2 + $3.14/1.1440^3 + $3.25/1.1440^4...∞PV of the future dividends
= $1.72 + $1.92 + $2.04 + $1.86...∞PV of the future dividends
= $7.54We know that the value of the stock is the present value of the expected dividends, so we can calculate it as follows: Value of the stock
= PV of the future dividends Value of the stock
= $7.54
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Can someone please explain? You don’t even have to answer, just explain how they are right or wrong ILL MARK AS BRAINLIEST!!!!!!
Answers
Answer:
Enrique is correct.
Step-by-step explanation:
He converted the mixed fraction into improper and multiplied which is correct where matt has done it incorrectly .
Find the domain of the graphed function.
3- 12
-10
OA. -6≤x≤ 9
OB. -10≤x≤0
OC. x≤0
OD. x is all real numbers.
10-
●
-10-
10
Answers
The domain is the collection of possible inputs (values of x) for which a function is defined, according to mathematical terminology. The domain of a function is usually determined by analyzing its graph, which represents all feasible inputs to the function.
The domain of a graphed function is given in the question; it is the range of values for x that are represented on the horizontal axis of the graph. The domain can also be written as an interval of the form [a, b], where a and b are the leftmost and rightmost values of x that appear on the graph respectively.
When looking at the graph, we can see that the leftmost value is -6, and the rightmost value is 9. As a result, the domain of the function is given by the inequality -6 ≤ x ≤ 9, which is option A: -6≤x≤9. This is because any value of x that lies between -6 and 9 (inclusive) is shown on the graph, and any other value of x is not displayed on the graph.
The domain is one of the most important elements of any function, as it determines the set of all possible input values that a function can accept. Knowing the domain of a function is critical in determining if a function is defined for a given input value, among other things.
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two tangents each intersect a circle at oppositea. endpoints of the same diameter. is it possible for the twob. tangents to intersect each other outside the c. circle? explain why or why not, using the information you d. learned in this lesson.
Answers
No, it is not possible for the two tangents to intersect each other outside the circle.
We have,
The concept used in this explanation is that a tangent to a circle is perpendicular to the radius at the point of tangency.
This is a fundamental property of circles and tangents, based on geometry and the definition of a tangent line.
No, it is not possible for the two tangents to intersect each other outside the circle.
This is because tangents to a circle are perpendicular to the radius at the point of tangency. If the tangents intersect with ed each other outside the circle, it would imply that they are not perpendicular to the radius, which contradicts the definition of a tangent.
Thus,
No, it is not possible for the two tangents to intersect each other outside the circle.
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Yes, it is possible for the two tangents to intersect each other outside the circle only when the tangents are perpendicular to the diameter. They will intersect at the point directly opposite to the center of the circle. This concept combines the properties of tangents and circles that are normally covered in high school geometry.
Explanation:In the context Mathematics and Geometry, the situation you have described where two tangents to a circle meet at opposite ends of a diameter is indeed possible, but only in one specific scenario: when the tangents are perpendicular to the diameter and they intersect each other at the point directly opposite to the center of the circle. This is because, by geometry, a tangent to a circle is perpendicular to the radius at the point of tangency. Thus, if the tangents are drawn at the endpoints of a diameter, they will be parallel and will not intersect each other outside the circle.
In contrast, if the tangents are drawn such that they are perpendicular to the diameter, they will intersect at a point that is a distance from the center of the circle equivalent to the length of the radius, and directly opposite the center of the circle. This point of intersection of the tangents is outside the circle.
The properties of tangents and circles, which we use in the explanation, are part of the standard curriculum in high school geometry.
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20. lan used 9½ cups of flour to make 1 batches of oatmeal cookies. One batch makes 18
cookies. If he follows the same recipe, about how many cookies can he make with 15 cups of
flour?
Answers
Answer:
To solve this problem, we can set up a proportion:
9.5 cups of flour / 18 cookies = 15 cups of flour / x cookies
To solve for x, we can cross-multiply:
9.5 cups of flour * x cookies = 18 cookies * 15 cups of flour
Dividing both sides by 9.5 cups of flour gives us:
x cookies = 18 cookies * 15 cups of flour / 9.5 cups of flour
x cookies ≈ 28.42
Since we can't make a fraction of a cookie, we'll round down to the nearest whole number. Therefore, Lan can make about 28 cookies with 15 cups of flour using the same recipe.
Solve 2X squared plus X equals 15
Answers
Answer:
x=5
Step-by-step explanation:
2x+x= 3x
3x=15
15/3=5
Answer:
x=15 and x=7
Step-by-step explanation:
2x^2+x=15
x(2x+1)=15
x=15
2x+1=15
2x=15-1
x=14/2
x=7
solve the system of equations by the addition method3x - 7y = 45x - 5y = 4
Answers
Evaluate the expression 2x - 15, for x = 4 PLSSSSS HELPPPPP
Answers
Answer:
-7
Step-by-step explanation:
2x4=8
8-15=-7
not sure if it's right
what is the missing number
Answers
Answer i believe the rule is y= x/2 so n=6
Step-by-step explanation:
find the distance of a speed of 15m/s for 5 minutes
Answers
15m/s * 1km/1000m*60s/1 min*60 min/1hr=
You do the calculation.
Here are the conversions used in the conversion.
1km = 1000 m, 60 seconds = 1 minute, 60 minutes = 1 hour.
When you set up the problem the 15 meters is in the numerator and 1 second is in the denominator. To convert the 15 meters to km the next conversion factor needs to have 1km in the numerator and 1000 meters in the denominator. Now the 15 m will be divided by 1000 m which cancels the meters and leaves km.
The seconds in 15 m/s is in the denominator so to convert seconds to hours multiply by 60 seconds placing it in the numerator over 1 minutes. Use the same idea to set up the conversion from minutes to hours.
Practice this conversion. It is a fundamental conversion that any middle school student should know how to do.
the expression x^3+ax^3+bx-3 where a and b are constants, has a factor of x-3 and leaves a remainder of 15 when divided by x+2. find the value of a and b
Answers
The values of a and b in the expression x³ + ax³ + bx - 3 are a = 1 and b = -17
How to determine the values of a and b?From the question, we have the following parameters that can be used in our computation:
x^3+ax^3+bx-3
Rewrite properly
So, we have
x³ + ax³ + bx - 3
The expression has a factor of x - 3
This means that
(3)³ + a(3)³ + b(3) - 3 = 0
So, we have
27 + 27a + 3b - 3 = 0
Evaluate the like terms
27a + 3b = -24
Divide by 3
9a + b = -8
The expression has a remainder of 15 when divided by x + 2
This means that
(-2)³ + a(-2)³ + b(-2) - 3 = 15
So, we have
-8 - 8a - 2b - 3 = 15
Evaluate the like terms
-8a - 2b = 26
Divide by -2
4a + b = -13
So, we have
9a + b = -8
4a + b = -13
Subtract the equations
5a = 5
Divide
a = 1
Recall that 4a + b = -13
So, we have
4(1) + b = -13
So, we have
b = -13 - 4
Evaluate
b = -17
Hence, the values are 1 and -17
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Which of the following statements must be true based on the diagram below
Answers
Answer:
i think its the 2nd and 4th
Step-by-step explanation:
helppp me with this eee
Answers
Answer:
6 lessons mark me as brainliest
Step-by-step explanation:
200-50=150-25=125-25=100-25=75-25=50-25=25-25=0
1 2 3 4 5 6
Answer:
6
Step-by-step explanation:
10 pints equals how many quarts
Answers
Answer:
5
Step-by-step explanation:
2 pints are in a quart
Answer:
5 quarts
Step-by-step explanation:
2 pints = 1 quart
10 pints = 5 quarts
Hope this helps!
find an equation for F minus one the inverse function. Verify that your equation is correct by showing that
Answers
Explanation
We are to first find the inverse of the function:
\(f(x)=\frac{x+12}{x-4}\)\(\mathrm{A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:\)To do so, we will follow the steps below:
Step 1:
\(\begin{gathered} write\text{ the function interms of y} \\ y=\frac{x+12}{x-4} \end{gathered}\)Step2: Interchange x with y
\(x=\frac{y+12}{y-4}\)Step 3: solve for y
\(\begin{gathered} xy-4x=y+12 \\ xy-y=12+4x \\ y(x-1)=12+4x \\ y=\frac{12+4x}{x-1} \end{gathered}\)Thus, the inverse of the function is
\(\begin{gathered} f^{-1}(x)^=\frac{12+4x}{x-1} \\ \\ for \\ x\ne1 \end{gathered}\)Part 2
\(f(f^{-1}(x))=f(\frac{12+4x}{x-1})\)Simplifying further
\(\begin{gathered} f(\frac{12+4x}{x-1})=\frac{\frac{12+4x}{x-1}+12}{\frac{12+4x}{x-1}-4}=x \\ Thus \\ f(\frac{12+4x}{x-1})=x \end{gathered}\)Also
\(f^{-1}(f(x))=f^{-1}(\frac{x+12}{x-4})\)Simplifying further
\(\begin{gathered} f^{-1}(\frac{x+12}{x-4})=\frac{12+4\times\frac{x+12}{x-4}}{\frac{x+12}{x-4}-1}=x \\ \\ Thus \\ f^{-1}(\frac{x+12}{x-4})=x \end{gathered}\)One hundred volunteers who suffer from depression are available for a study involving a new drug that is thought to be effective in treating depression. Researchers want to compare the new drug with the drug currently in use. The researchers believe that men and women may respond differently to the drugs. Fifty of the volunteers are selected at random and are given the new drug, and the other 50 are given the drug currently in use. A psychiatrist evaluates the symptoms of all volunteers after four weeks to determine if there has been substantial improvement in the severity of the depression. Which of the following is correct?
A. This is an example of a block design.
B. Both answer options are correct.
C. This is an example of a completely randomized design.
Answers
Step-by-step explanation:
jffkjfkfkro3p2009uh2 that is c my answer
1) Ed invests $1,000 into a money market account that earns 8% annual interest compounded quarterly. How much money will
he have earned after 8 years?
Answers
The money market account earns 8/4 = 2% interest per quarter.
In one year, there are 4 quarters.
so, the formula to calculate the balance after 8 years is:
A = P (1 + r/n)^(nt)
where A is the final balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested for.
Substituting in the given values,
A = 1000 (1 + .02)^(4*8)
A = 1000 (1.02)^32
A = 1000 (1.8587)
A = 1858.7
So after 8 years, Ed will have earned $1858.7.
The highest and lowest recorded temperatures for the state of Texas are 109°F and -21°F. Find
the difference in these extreme temperatures.
Answers
Answer:
130
Step-by-step explanation:
suppose that the radius is expanding at a rate of 0.6 inches per second. how fast is the volume changing when the radius is 2.3 inches? use at least 5 decimal places in your answer.
Answers
Using the theories of Application of derivative,we got that 59.11221inches³/sec is rate of volume changing when the radius is 2.3 inches.
We are given rate of change of radius (dr/dt)=0.6inches
We know very well that volume of sphere is given by (4/3)πr³
where r is the radius of the sphere.
Now, differentiating the volume with respect to radius, we get
=>dV/dr=4πr²
=>dV/dt=(dv/dr)·(dr/dt)
=>dV/dt=4πr².(dr/dt)
We are given that dr/dt=0.6inches/sec
So, dV/dt=4πr²·(0.6)
Now, putting values of r=2.3
dV/dt=4π(2.3)²×(0.6)
=>dV/dt=4×3.14×2.3×2.3×0.6
=>dV/dt=59.11221inches³/sec
Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.
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