The engine in a airplane has a power curve approximated by x2 270 y = + 14 15000 44 where I is the RPin and y is the horsepower generated. - At what RPM is the engine putting out maximum horsepower?. Round your answer to three decimal places. RPM What is the maximum horsepower? Round your answer to three decimal places.
Answers
A)For this question, we will use the first and second derivative criteria. First, we compute the first and second derivative of the given function:
[tex]\begin{gathered} \frac{dy}{dx}=-\frac{2x}{15000}+\frac{27}{44} \\ \frac{d^{2}y}{dx^{2}}=-\frac{2}{15000} \end{gathered}[/tex]Setting the first derivative equal to zero and solving for x we get:
[tex]\begin{gathered} -\frac{2x}{15000}+\frac{27}{44}=0 \\ \frac{2x}{15000}=\frac{27}{44} \\ x=\frac{27(15000)}{44(2)}=4602.273 \end{gathered}[/tex]Evaluating the first second derivative at x=4602.273 we get a negative number, therefore the function has a maximum value at x=4602.273. At 4602.273 RPM the engine puts out its maximum horsepower.
B) Now, to compute the maximum horsepower we evaluate the given function at x=4602.273:
[tex]\begin{gathered} y=-\frac{(4602.273)^{2}}{15000}+\frac{27}{44}(4602.273)-14 \\ y=1398.061 \end{gathered}[/tex]Therefore, the maximum horsepower is 1398.061.
Related Questions
Which expression is equivalent to 64 -1/2
A. 8
B. 8^2
C. 1/4
D. 1/8
Answers
The expression is 64 - 1/2 is equivalent to 127/2.
Given,
In the question:
Which expression is equivalent to 64 -1/2
Now, According to the question:
The ex[pression is given as:
64 - 1/2
Find common denominator and write the numerator above common denominator
[tex]= \frac{64 . 2}{2} - \frac{1}{2}[/tex]
Calculate the product or quotient:
128/2 - 1/2
Write the numerator over common denominator:
(128 - 1)/2
= 127/2
Hence, The expression is 64 - 1/2 is equivalent to 127/2.
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a boat can travel 57 miles upstream against the current in the same amount of time it can travel 84 miles down stream with the current. if the boat's average speed in still water is 20 miles per hour. find the speed of the current
Answers
a boat can travel 57 miles upstream against the current in the same amount of time it can travel 84 miles down stream with the current. if the boat's average speed in still water is 20 miles per hour. find the speed of the current
Let
x -----> the speed of the current
we have that
speed *time=distance
upstream
(20-x)t=57 --------> equation A
down stream
(20+x)t=84 -----> equation B
solve the system of equations
Adds the equation A and B
20t-xt=57
20t+xt=84
------------------
40t=141
t=3.525 hours
Find the value of x
(20+x)t=84
substitute the value of t
20+x=84/3.525
x=84/3.525 - 20
x=3.83 mph
therefore
the answer is
3.83 mphA protractor is user on an angle. One ray of the angle is at 46 degrees and the other ray is at 95 degreesWhat is the measure of the angle? Choices are:141 degrees95 degrees49 degrees46 degrees
Answers
A protractor is used to measure angles. The range is from 0 degrees to 180 degrees. One ray of the angle is at 46 degrees and the other ray is at 95 degrees. The measure of the angle can be calculated below
[tex]undefined[/tex]A plastic candy container and its dimensions are shown in the figure.What is the closest to the value of the volume?
Answers
The volume of this composite figure is the sum of the volume of the cylinder and the cone.
Volume of Cylinder
The formula is
[tex]V=\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
Given,
r = 5
h = 17.8
Substituting, we find the volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(5)^2(17.8) \\ V=1398.01 \end{gathered}[/tex]Volume of Cone
The formula is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
Given,
r = 5
h = 6.2
Substituting, we find the volume:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V=\frac{1}{3}\pi(5)^2(6.2) \\ V=162.32 \end{gathered}[/tex]The total volume of the figure is:
1398.01 + 162.32 = 1560.33
Factorise 3x^2 + 5x + 2
Answers
After factorizing the expression we get the result as -1 and -2/3.
Given,
the expression is:
3x²+5x+2
Multiply the terms and get the factors.
6x²
Now split the numbers according to the term
3x² + 3x + 2x + 2
collect the like terms.
Arrange the like terms.
3x(x+1) + 2(x+1)
re arrange the terms.
(x+1)(3x+2)
now get the value of x:
x+1 = 0
x = -1
or
3x+2 = 0
3x=-2
x=-2/3
Hence the factors of x are -1 and -2/3
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I A family of G holds a ceremony to determine each child's favorite Teenage Mutant Ninja Turtle. The ceremony involves each child's results of choosing 10 numbers out of a hat. If Raphael, Michelangelo, Donatello, and Leonardo are represented with the numbers 1, 2, 3, and 4, respectively, which Teenage Mutant Ninja Turtle would become the favorite of a Child having the following results? Construct a 90% confidence interval estimate of the mean to develop the reasoning for your answer 2 21 4 3 3 3 3 11
Answers
Solution
Step 1
Write an expression for the mean
[tex]\bar{x}=\text{ }\frac{\sum ^{\square}_{\text{ of terms}}}{\text{mumber of terms}}[/tex][tex]\begin{gathered} \bar{x}=\frac{2+2+1+\text{ 4 +3+3+3+3}+4+1}{10} \\ \bar{x}=\text{ }\frac{26}{10} \\ \bar{x}=2.6 \end{gathered}[/tex]Step 2
Find the standard deviation
[tex]SD=\sqrt[]{\frac{\sum |x-\bar{x}|^2}{n}}[/tex][tex]SD=\sqrt[]{\frac{|2-2.6|^2+|2-2.6|^2+|1-2.6|^2+|4-2.6|^2+|3-2.6|^2+|3-2.6|^2+|3-2.6|^2+|3-2.6|^2+|4-2.6|^2+|1-2.6|^2}{10}}[/tex][tex]\begin{gathered} SD=\sqrt[]{\frac{0.36+0.36+2.56+1.96+0.16+0.16+0.16+0.16+1.96+2.56}{10}} \\ =\sqrt[]{\frac{10.4}{10}}\text{ =}\sqrt[]{1.04} \\ =1.02 \end{gathered}[/tex]Find the Z (confidence interval level) value for 90%
[tex]Z_{90}=1.645[/tex]Find the confidence interval
[tex]\begin{gathered} CI=\bar{x}\pm_{}_{}z\times\frac{s}{\sqrt[]{n}} \\ \bar{x}\Rightarrow\operatorname{mean} \\ s\Rightarrow\text{standard deviation} \\ n\Rightarrow\text{sample size} \\ z\Rightarrow\text{confidence level} \end{gathered}[/tex][tex]\begin{gathered} CI=2.6\pm1.645\times\frac{1.02}{\sqrt[]{10}} \\ =2.6\pm1.645\times0.32 \\ =2.6\pm0.53 \\ \text{Thus,} \\ CI=2.6+0.53\text{ 0r 2.6-0.53} \\ CI=3.13\text{ or 2.07} \end{gathered}[/tex]Hence, a 90% confidence interval estimate of the mean lies between 2 and 3
Therefore, either Michelangelo or Donatello
Look at this diagram: GHIJKLMNIf HJ and KM are parallel lines and mJIG = 43°, what is mKLN?
Answers
We are given that lines HJ and KM are parallel. We notice that the angles:
[tex]\begin{gathered} \angle KLN \\ \angle HIL \end{gathered}[/tex]Are corresponding angles, and therefore they are congruent, that is:
[tex]\angle KLN\cong\angle HIL[/tex]Also, angles:
[tex]\begin{gathered} \angle HIL \\ \angle JIG \end{gathered}[/tex]Are vertical angles, therefore, they are equal:
[tex]\angle HIL\cong\angle JIG[/tex]Therefore, combining the two statements we get:
[tex]\angle KLN\cong\angle JIG[/tex]Therefore:
[tex]\angle KLN=43[/tex]Angle KLN equals 43 degrees.
18 is 32% of what number w? what is w?
Answers
Given: 18 is 32% of a number
To Determine: The number
Let the number be w. Therefore:
[tex]\begin{gathered} 32\%ofw=18 \\ \frac{32}{100}\times w=18 \end{gathered}[/tex][tex]\frac{32w}{100}=18[/tex][tex]\begin{gathered} 0.32\times w=18 \\ 0.32w=18 \end{gathered}[/tex]Divide both sides by 0.32
[tex]\begin{gathered} \frac{0.32w}{0.32}=\frac{18}{0.32} \\ w=56.25 \end{gathered}[/tex]Hence,
an equation is 18 = 0.32 . w
The solution is w = 56.25
HELP graph the solution of system of linear inequality's
y< - 5x - 3
y>x+5
Answers
The graph of solution of system of linear inequality can be obtained by plotting the given equations and and then shading the region according to the inequality sign.
How to graph two linear inequality?
To graph Linear equations with inequality consider the equations as linear equation in two variable.Obtain two points for each line which satisfies the equations and plot them on graph. For example (1,6) and (-1,4) satisfies the equation y=x+5.Now shade the region according to the inequality: < : below the line> : above the lineHence you obtain the graph for the solution of system of the given linear equation with inequality.Any point in this region will satisfy both the linear inequalities (check the graph attached below).To know more about linear inequality visit
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10 Which number line represents the solution to the inequality -7x - 13 2 8?A-10-5НЕН1005B-10-50510с-10-50510D-10-50510оооо
Answers
The correct option is option A
Explanation:
First we solve the inequality:
-7x -13 ≥ 8
collect like terms:
-7x ≥ 8 + 13
-7x ≥ 21
Divide through by -7:
x ≤ 21/-7
Note: when you divde an inequality by negative number, the iequality sign changes.
x ≤ -3
Since x is less than or equal to -3, the number line starts at -3 and moves towards the left of the number line.
The correct option is option A
Unit 3 homework 3 proving lines are parallelI need help on 1,2,3,4
Answers
ANSWER
Not enough information
EXPLANATION
2. We want to see if the lines l and m are parallel based on the information given in the diagram.
In the figure given, we have two angles that lie on the same line m (128 and 52 degrees).
This information is not enough to conclude that the two lines are parallel. To be able to determine that, we need at least an angle that lies on the line l.
Therefore, the information is not enough to determine that l and m are parallel.
5. Read the givens about the diagram shown and then state all conclusions you can draw from these givens. Explain your conclusions
Answers
We are given the following information
[tex]\bar{TV}\perp\bar{US}[/tex]Which says the line TV is perpendicular to the line US.
From this we can conclude that the angle VRU, angle TRU and angle TRS are 90°
We are also given that
[tex]undefined[/tex]What is the value of the digit in the tens place?3,847O A. 3,000OB. 4C. 40D. 800
Answers
Expand the given number as,
[tex]3847=(3\times10^3)+(8\times10^2)+(4\times10^1)+(7\times10^0)[/tex]The tens place is the second from the right.
It is observed that the value of the digit at tens place is 4
So, option B is the correct choice.
What is the equation of this line? Responses y=−2x y equals negative 2 x y = 2x y, = 2, x y=−1/2x y equals fraction negative 1 half end fraction x y=1/2x y equals 1 half x
Answers
The equation of line which shown in graph will be;
⇒ y = 2x
Option 3 is true.
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph for the equation of line is shown in figure.
Now,
Take two points on the line of the graph.
Two points are ( 1, 2) and (2, 4)
Find the slope of the line with two points (1, 2) and (2, 4) as;
⇒ m = (4 - 2) / (2 - 1)
⇒ m = 2 / 1
⇒ m = 2
Thus, The equation of line passing through the points (1, 2) and (2, 4) with slope 2 is;
⇒ y - 2 = 2 ( x - 1 )
⇒ y - 2 = 2x - 2
⇒ y = 2x - 2 + 2
⇒ y = 2x
Therefore,
The equation of line will be;
⇒ y = 2x
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Brian glues together 4 wooden cubes as shown. Each cube has an edge of 5 centimeters. He covers the surface area of this new figure with metallic paper that is cut to size for each face.A. 125 square cm B. 150 square cm C. 450 square cm D. 600 square cm
Answers
Explanation:
The new figure is a square prism, with the sides that measure 4x5 = 20 cm.
We have to find the surface area of this prism. To do this we have to find the area of the rectangular faces and the area of the base, which is the same as the area of the top. The total surface area is 4 times the area of the rectangular face plus 2 times the area of the base/top.
[tex]A_{\text{rectangular face}}=20\operatorname{cm}\times5\operatorname{cm}=100\operatorname{cm}^2[/tex][tex]A_{\text{base}}=5\operatorname{cm}\times5\operatorname{cm}=25\operatorname{cm}^2[/tex][tex]\begin{gathered} S=4\cdot A_{\text{rectangular face}}+2\cdot A_{base} \\ S=4\cdot100\operatorname{cm}+2\cdot25\operatorname{cm}^2 \\ S=400\operatorname{cm}+50\operatorname{cm}^2 \\ S=450\operatorname{cm}^2 \end{gathered}[/tex]Answer:
C. 450 cm²
What is the result of performing these steps?1. Draw a line segment with endpoints A and B.2. Draw point Canywhere on AB.3. Fold the paper through C So As lies on top of itself.4. Draw a line segment from C to any point along the fold.O A. A line segment parallel to ABB. A line segment perpendicular to ABC. A bisected angleD. The perpendicular bisector of AB
Answers
As AB lies on top of itself after folding the paper, the fold would be perpendicular to AB. Drawing a line from C to any point of the fold would result in a line segment perpendicular to AB.
Answer:
B. A line segment perpendicular to AB
step by step on how to solve -6.43 - 22.3
Answers
The given expression is
[tex]-6.43-22.3[/tex]Given that the numbers have the same sign, we have to sum.
The result must be negative because both numbers are negative.
Hence, the result is -28.73.Answer:
-28.73.
Step-by-step explanation:
What is the volume of this cylinder in terms of Pi? radius=2height=5a.5πb.10πc.20πd.50πWhat is the volume of this cylinder? radius=7height=11a.77 cubic cmb.241.9 cubic cmc.539 cubic cmd.1,693.32 cubic cmWhat is the volume of this cylinder in terms of Pi? radius=10height=20a.2000πb.500πc.200πd.100πWhat is the volume of this cylinder? radius=34height=27a.98,055.39 cubic metersb.2,883.98 cubic metersc.24,513.85 cubic metersd.1,441.99 cubic meters
Answers
What is the volume of this cylinder in terms of Pi?
Volume
please explain steps to get correct answer in pic below
Answers
Let's use the properties of the sum:
[tex]\begin{gathered} \sum ^{11}_{i\mathop=1}(3i^2+17)=\sum ^{11}_{i\mathop{=}1}3i^2+\sum ^{11}_{i\mathop{=}1}17 \\ =3\sum ^{11}_{i\mathop{=}1}i^2+17\cdot11 \end{gathered}[/tex]Therefore the answer is the last option.
To simplify this we use the properties listed below:
[tex]\sum ^n_{i\mathop{=}1}na_i=n\sum ^n_{i\mathop{=}1}a_i[/tex][tex]\sum ^n_{i\mathop{=}1}(a_i+b_i)=\sum ^n_{i\mathop{=}1}a_i+\sum ^n_{i\mathop{=}1}b_i[/tex][tex]\sum ^n_{i\mathop{=}1}c=cn[/tex]Graph the line that passes through the points (-2,-7) and (5,0) anddetermine the equation of the lineKuationSubmit Answer
Answers
Given points:
(-2,-7) and (5,0)
To get the equation of the line, we will use the formula below:
[tex]y_{}-y_1=m(x_{}-x_1)[/tex]From the points given
[tex]\begin{gathered} x_1=-2,y_1=-7 \\ x_2=5,y_2=0 \end{gathered}[/tex]Where
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-7)}{5-(-2)}=\frac{7}{7}=1 \\ m=1 \end{gathered}[/tex]Substituting the values into the equation
[tex]\begin{gathered} y-(-7)=1(x-(-2)) \\ y+7=1(x+2) \\ y+7=x+2_{} \\ \end{gathered}[/tex]simplifying further
The equation of the line is:
[tex]y=x-5[/tex]The graph of the points (-2,-7) and (5,0) is given below:
3x² + 11x > 4
How to slove this and the answer for it with it I really do need help with this
Answers
Using the factorization, the solution of given inequality is x>1/3 and x< -4.
In the given question we have to solve the given inequality.
The given inequality is 3x^2+11x>4.
Solving the given inequality
Subtract 4 on both side we get
3x^2+11x-4>0
Now factoring the binomial equation.
The multiplication of first and third term is 12 and middle term is 11.
So the possible factors are 1 and 12
3x^2+(12-1)x-4>0
3x^2+12x-x-4>0
3x(x+4)-1(x+4)>0
(3x-1)(x+4)>0
Equating equal to zero
3x-1>0 or x+4>0
Solving for x
x>1/3 or x< -4
Hence, the solution of given inequality is x>1/3 and x< -4.
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Bethany is paid time-and-a-half for each hour she works above her normal 40 hours each week. Last week, Bethany worked 44 hours and her gross pay was $575. how much did Bethany earn for each hour of overtime she worked?
Answers
Bethany worked a total of 44 hours, which means that she worked 40 normal hours and 4 extra hours.
Let x be the amount earned per 1 normal working hour since she earns a half more for each extra hour we can express the money earned above her 40 normal hours as 1.5 times x ( x+0.5*x = 1.5x), then we can express the gross pay like this:
gross pay = earnings per normal hour * normal hours + earnings per extra hour * extra hours
gross pay = x * normal hours + 1.5x * extra hours
As mentioned, she worked 40 normal hours and 4 extra hours, then we get:
gross pay = x*40 + 1.5x*4
gross pay = 40x + 1.5*4x
gross pay = 40x + 6x
gross pay = 46x
From the given information, we know that the gross pay equals $575, then we get:
575 = 46x
46x/46 = 575/46
x = 575/46
x=12.5
The amount earned with extra hours is 1.5x, then we get:
Extra hour earning = 1.5*12.5=18.75
Then, Bethany earned $18.75 for each extra hour
How many meters of binding are required to bind the edge of a rectangular quilt that measures 5 m by 7 m?
Answers
Answer: 24
Step-by-step explanation: To find the perimeter, add all of the sides. 5+5=10 and 7+7=14. 10+14=24.
Answer:
24 m of binding required===============
GivenDimensions of rectangle 5 m and 7 m.Find its perimeterP = 2(l + w)P = 2(5 + 7) = 2(12) = 24 mPoint M is the midpoint of segment QR. If QM = 2x + 5 and MR = 5x – 1, find the length of QR. QR = 18 QR = 9 QR = -9QR = 8
Answers
Asnwer:
QR = 18
Explanation:
If Point M is the midpoint of segment QR, then the following expressions are true
QM = MR and;
QM + MR = QR
Given
QM = 2x + 5 and MR = 5x – 1,
Recall that QM = MR
2x + 5 = 5x - 1
2x - 5x = -1-5
-3x = -6
x = -6/-3
x = 2
Get the length of QR
QR = QM + MR
QR = 2x+5 + 5x -1
QR = 7x +4
QR = 7(2) + 4
QR = 14+4
QR = 18
Hence the length of QR is 18
6Question(15 Points)6. The volume of the cylinder below is 150 cubic centimeters. What is the area of its base?a. 20 cmb. 20 cmc. 10 cmd. 10 cm7.5 cm
Answers
The given cylinder has a height of 7.5 cm and volume of 150 cubic centimeters,
[tex]\begin{gathered} h=7.5\text{ cm} \\ V=150\text{ cm}^3 \end{gathered}[/tex]Consider that the volume and base area of a right circular cylinder are related as,
[tex]V=A\times h[/tex]Substitute the values and solve for A,
[tex]\begin{gathered} 150=A\times7.5 \\ A=\frac{150}{7.5} \\ A=20 \end{gathered}[/tex]Thus, the base area of the given cylinder is 20 sq. cm.
Therefore, option b is the correct choice.
I need help to determine weather the slope on this graph is A. ZeroB. Negative C. Positive
Answers
The slope usually indicates the behavior of a line:
In the above picture there are 3 different lines with different slopes, let's describe them:
-L1. This red line has a positive slope, it means that as "x" increases, then "y" increases as well.
-L2. This blue line has a negative slope, which means that as "x" increases, then the value of "y" decreases.
-L3. This green line is horizontal and has zero slope . This means that it doesn't matter the value of "x", "y" always has the same value.
Using this description, we can now assure that the slope in your graph is NEGATIVE
26 is what % of 65.
Answers
Suppose that 65 is the 100%, then we can find the percentage that is 26 from 65 using a rule of three:
[tex]\begin{gathered} 65\rightarrow100\% \\ 26\rightarrow x\% \\ \Rightarrow x=\frac{26\cdot100}{65}=\frac{2600}{65}=40 \\ x=40\% \end{gathered}[/tex]therefore, 26 is 40% of 65
For which inequality would x = 8 not be a solution?4x + 3 > 09x - 5 < 100x + 4 ≤ 1072 ÷ x ≥ 4
Answers
Given:
Given the inequalities:4
[tex]\begin{gathered} 4x+3>0 \\ 9x-5<100 \\ x+4\leq10 \\ 72\div x\ge4 \end{gathered}[/tex]Required: Identify the inequality in which x = 8 is a solution.
Explanation:
Substitute 8 for x in each inequality and check whether it satisfies the inequality.
Consider 4x + 3 > 0.
[tex]4\cdot8+3=35>0[/tex]So, x = 8 satisfies the inequality 4x + 3 > 0.
Consider 9x - 5 < 100.
[tex]9\cdot8-5=67<100[/tex]So, x = 8 satisfies the inequality 9x - 5 < 100.
Consider x + 4 ≤ 10.
[tex]8+4=12>10[/tex]So, x = 8 not satisfies the inequality.
Consider 72 ÷ x ≥ 4.
[tex]72\div8=9\ge4[/tex]So, x = 8 satisfies the inequality.
Final Answer: The inequality in which x = 8 is not a solution is x + 4 ≤ 10.
10. There is a carnival at a local state park. It cost $5 to get in and $1.50 per ride. .Suppose Maya Mapleton has $25 to spend for the day. Which inequality wouldmodel this situation?5+ 1.50x 2 255x + 1.50 s 255 + 1.50x s 2525x + 1.50 s 5
Answers
Let:
B = Maya's budget = $25
c = cost of the entrance = $5
a = cost of each ride = $1.50
x = number of rides
T = total money spent
Therefore:
[tex]\begin{gathered} T\le B \\ where_{} \\ T=c+ax \\ so\colon \\ 5+1.5x\le25 \end{gathered}[/tex]At a parking garage in a large city, the charge for parking consists of a flat fee of $1.00 plus 1.60 /hr.(a) Write a linear function to model the cost for parking for hours.(Pt)(b) Evaluate P(1.4 )and interpret the meaning in the context of this problem.please make this right I keep making it wrong
Answers
Given:
The charge for parking consists of a flat fee of $1.00 and $1.60 per hour.
To find:
a) Write a linear function P(t).
b) Evaluate P(1.4)
Explanation:
a)
Since the flat fee is $1.00 and the varying fee is $1.60 per hour.
So, the linear function of the total cost for parking is,
[tex]P(t)=1.00+1.60t[/tex]Where t be the number of hours.
b)
Substituting t = 1.4 in the above function we get,
[tex]\begin{gathered} P(1.4)=1.00+1.60(1.4) \\ =1+2.24 \\ P(1.4)=\text{ \$}3.24 \end{gathered}[/tex]That means,
The total cost for parking for 1.4 hours is $3.24.
Final answer:
a) The linear function is,
[tex]P(t)=1.00+1.60t[/tex]b) The value is,
[tex]P(1.4)=3.24[/tex]