The area of the surface above the region R is 4096π square units.
Given that:
The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]
The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].
To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.
The integral for the area is given by:
[tex]Area = \int\int_R f(x, y) dA[/tex]
To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.
Using polar coordinates, we can parameterize the region R as follows:
x = rcos(θ)
y = rsin(θ)
where r goes from 0 to 8, and θ goes from 0 to 2π.
Now, rewrite the integral in polar coordinates:
[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]
Now, we can integrate with respect to r first and then with respect to θ:
[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]
Integrate with respect to r:
[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]
Now, we can integrate with respect to θ:
[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]
Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))
Area = 4096π + 128(0) - 0
Area = 4096π square units
So, the area of the surface above the region R is 4096π square units.
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may someone assist me?
Answer:
28
Step-by-step explanation:
Let x be the missing segment
We will use the proportionality property to find x
24/16 = 42/x
Simplify 24/16
24/16= (4×6)/(4×4)= 4/6 = 3/2
So 3/2 = 42/x
3x = 42×2
3x = 84
x = 84/3
x= 28
In a small private school, 55 students are randomly selected from 1313 available students. What is the probability that they are the fivefive youngest students?
Complete Question
In a small private school, 5 students are randomly selected from 13 available students. What is the probability that they are the five youngest students?
Answer:
The probability is [tex]P(x) = 0.00078[/tex]
Step-by-step explanation:
From the question we are told that
The number of student randomly selected is r = 5
The number of available students is n = 13
Generally the number of ways that 5 students can be selected from 13 available students is mathematically represented as
[tex]n(k)=\left n} \atop {}} \right.C_r = \frac{n ! }{(n-r ) ! r!}[/tex]
substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{13 ! }{(13-5 ) ! 5!}[/tex]
[tex]\left n} \atop {}} \right.C_r = \frac{13 * 12 * 11 * 10 * 9 *8! }{8 ! * 5 * 4 * 3 * 2 *1}[/tex]
[tex]\left n} \atop {}} \right.C_r = 1287[/tex]
The number of method by which 5 youngest students are selected is n(x) = 1
So
Then the probability of selecting the five youngest students is mathematically represented as
[tex]P(x) = \frac{n(x)}{n(k)}[/tex]
substituting values
[tex]P(x) = \frac{1}{1287}[/tex]
[tex]P(x) = 0.00078[/tex]
Each marble bag sold by Carmen's Marble Company contains 3 purple marbles for every 4 blue marbles. If a bag has 28 blue marbles, how many purple marbles does it contain?
Answer:
21 purple marbles
Step-by-step explanation:
my explanation is i looked at it like a ratio so ¾= x/28
then i took 28 ÷ 4 which equals 7, then i took 7 and multiplied it by 3 which gave me 21, so the answer is 21 purple marbles
The top and bottom margins of a poster are each 9 cm and the side margins are each 6 cm. If the area of the printed material on the poster is fixed at 864 cm2, find the dimensions of the poster with the smallest area.
Answer:
the dimensions of the poster with the smallest area is 36cm by 54cm
Step-by-step explanation:
✓Let us represent the WIDTH of the printed material on the poster as "x"
✓Let us represent the HEIGHT of the printed material on the poster as "y"
✓ The given AREA is given as 864 cm2
Then we have
864 cm2= xy ...................eqn(1)
We can make "y" subject of the formula.
y= 864/x .......................eqn(2)
✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is
(y+18)
✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is
(x+12)
✓Then AREA OF THE TOTAL poster
A= (y+18)(x+12) ...................eqn(3)
Substitute eqn (2) into eqn(3)
A= ( 18+ 864/x)(x+12)
We can now simplify by opening the bracket, as
A=18x +1080 +10368/x
A= 18x +10368/x +1080
Let us find the first derivative of A which is A'
A'= 18-(10368/x²)
If we set A' =0
Then
0= 18- (10368/x²)
18= (10368/x²)
x²= 10368/18
x²= 576
x=√576
x=24
The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum
The value of "y" when x=24 can now be be calculated using eqn(2)
y= 864/x
y= 864/24
y=36cm
✓The total width of the poster= (x+12)
= 24+12=36cm
✓The total height big the poster= (y+18)=36+18=54cm
the dimensions of the poster with the smallest area is 36cm by 54cm
Answer:
The total width of the paper [tex]=36 cm.[/tex]
The total height of the paper [tex]=54cm[/tex]
Step-by-step explanation:
Given information:
Top margin of the paper = 9 [tex]cm\\[/tex]
Bottom margin of the paper = 6 [tex]cm\\[/tex]
Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]
Let, the width of the printed material = [tex]x[/tex]
And the height of the printed material = [tex]y[/tex]
So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]
After including margins;
Width of the paper [tex]= (x+12)[/tex]
Height of the paper [tex]= (y+18)[/tex]
Area [tex](A) = (y+18) (x+12)[/tex]
[tex]A=18x+(10368/x)+1080\\[/tex]
Take first derivative:
[tex]A'= 18- (10368/x^2)[/tex]
When [tex]A'=0[/tex]
Then,
[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]
Now ,when we take second derivative and check if it is positive or not ,
We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.
Hence ,
[tex]x \times y=864\\y=864/24\\y=36\\[/tex]
Now ,
The total width of the paper
[tex]= 24+12\\=36 cm.[/tex]
And , total height of the paper
[tex]=36+18\\=54 cm.[/tex]
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Help ASAP!!!!
Identify the correct trigonometry formula to use to solve for x.
Sin (angle) = opposite leg / hypotenuse
Sin(62) = 18/x
The answer is the third choice.
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?
Answer:
its 14/C
Step-by-step explanation:
i got i right on edg U^U
Answer:
16
Step-by-step explanation:
i did edge test yea dont be imma fake :***
Find the slope of the line passing through the points (3, 4) and (8, -3).
Answer:
-7/5
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 -4)/(8-3)
= -7/5
Answer:
-7/5
Step-by-step explanation:
Hey there!
To find the slope of a line with 2 given points we'll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^2}[/tex]
-3 - 4 = -7
8 - 3 = 5
-7/5
Hope this helps :)
What is the size of the matrix resulting from...
Answer:
1 x 3
Step-by-step explanation:
The order of the first matrix is 1 × 3
The order of the second matrix is 3 × 3
that is (1 × 3 ) × (3 × 3 )
The bold values at the ends of the orders give the order of the product, that is
1 × 3
Square root of 5 + square root of 3 the whole divided by sqaure root of 5 - square root of 3
Answer:
The answer is 4 + √15 .
Step-by-step explanation:
You have to get rid of surds in the denorminator by multiplying it with the opposite sign :
[tex] \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]
[tex] = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } [/tex]
[tex] = \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } [/tex]
[tex] = \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } [/tex]
[tex] = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} [/tex]
[tex] = \frac{8 + 2 \sqrt{15} }{2} [/tex]
[tex] = 4 + \sqrt{15} [/tex]
Question 3
34° Celsius is equal to
o
Fahrenheit
Hi
Below the formulas to convert Celsius into Fahrenheit.
9/5 C +32 = degree in fahrenheit.
Where C is the degree in celsius. So have a try and find the answer.
When do you reject the null hypothesis?
You reject the Null Hypothesis when you have a small P-Value. Here is an example! Also we never accept the null hypothesis, think of it like this if we bring someone to court you wouldn't say their innocent of a crime, you only know that if they do not get convicted of the crime they are not guilty in the eyes of the law. Same thing applies here, since there could be several answers that satisfy our assumptions made, we can not be certain that 1 of those assumptions is the REAL answer it's just AN answer.
What is the Greatest Common Factor GCF between two expressions?
Answer:
The GCF is the largest expression that is factor of all expressions
Answer:
The GCF of two expressions is the greatest expression that is a factor of both the expressions.
Step-by-step explanation:
For example 7x² and 14x.
7x² = 1, 7, x, x
14x = 2, 7, x
The greatest common factor of the two expressions is 7x.
Rita ha decidido emprender un negocio de ventas de productos de protección personal, para lo cual tiene que inventir 1/3 de su dinero en mascarillas, 4/15 en guantes, 1/10 en protección facial y el resto en alcohol. ¿Que fracciónde dinero se invierte en alcohol?
Answer:
3/10
Step-by-step explanation:
Subtract the sum of 1/3, 4/15 and 1/10 from 1:
10/30 + 8/30 + 3/30 = 21/30, or 7/10
Then: 1 - 7/10 = 3/10
In figure, MN : NP = 9:1. If MP = 2. Find the distance from M to point K (not shown) that is a midpoint of PN.
Answer:
1.9 units
Step-by-step explanation:
Since we have ...
MN : NP = 9 : 1
then ...
NP : MN+NP = 1 : (9+1) = 1 : 10
If MP is 2 units, then NP is 1/10 × 2 units = 0.2 units. Point K will be half that distance from N or P, so will be 0.1 unit from P.
So, the distance from M to K, the midpoint of NP is ...
2 units - 0.1 units = 1.9 units
Answer:
1.9
Step-by-step explanation:
Determine the area under the standard normal curve that lies to the left of
(a) Z = 1.75, (b) Z=0.01, (c) Z= -0.01, and (d)Z = 1.29.
Click the icon to view a table of areas under the normal curve.
(a) The area to the left of Z= 1.75 is
(Round to four decimal places as needed.)
Answer:
a) 0.9599b) 0.5040c) 0.4960d) 0.9015Step-by-step explanation:
You did not provide the table, so I used a spreadsheet. Most have functions for finding the area under a standard normal curve.
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answer:
Step-by-step explanation:
Assume that f(x) = 0 for x outside the interval [4,7]. We will use the following
[tex]E[X^k] = \int_{4}^{7}x^k f(x) dx[/tex]
[tex]Var(X) = E[X^2]- (E[X])^2[/tex]
Standard deviation = [tex] \sqrt[]{Var(X)}[/tex]
Mean = [tex]E[X][/tex]
Then,
[tex]E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}[/tex]
[tex]E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31[/tex]
Then, [tex]Var(x) = 31-(\frac{11}{2})^2 = \frac{3}{4}[/tex]
Then the standard deviation is [tex]\frac{\sqrt[]{3}}{2}[/tex]
Solve for qqq. 3\left(q+\dfrac43\right) = 23(q+ 3 4 )=2
pls answer this
Answer:
19/3Step-by-step explanation:
Given the expression [tex]3\left(q+\dfrac43\right) = 23[/tex], we are to find the value of q;
[tex]3\left(q+\dfrac43\right) = 23\\on\ expansion\\\\3q + 4/3(3) = 23\\\\3q+4 = 23\\\\subtract \ 4\ from \ both\ sides \ of \ the \ equation\\\\3q+4-4 = 23-4\\\\3q = 19\\\\Diviide \both\ sides \ by \ 3\\\\3q/3 = 19/3\\\\q = 19/3[/tex]
Hence the value of q is 19/3
Answer:
-2/3
Step-by-step explanation:
Don't worry about it, i got connections.
Expedia would like to test the hypothesis that the average round-trip airfare between Philadelphia and Paris is higher for a flight originating in Philadelphia when compared to a flight originating in Paris. The following data summarizes the sample statistics for round-trip flights originating in both cities. Assume that the population variances are equal.
Originating City
Philadelphia Paris
Sample mean $1,240 $1,060
Sample size 15 19
Sample standard
deviation $270 $240
If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris, the degrees of freedom for this hypothesis test are _____
(a) 33
(b) 32
(c) 34
(d) 28
Answer:
(b) 32
Step-by-step explanation:
From the information given :
sample mean of Philadelphia μ₁ = $1240
Sample size of Philadelphia n₁ = 15
Sample Standard deviation σ₁ = $270
sample mean of Paris μ₂ = $1,060
Sample size of Paris n₂ = 19
Sample Standard deviation of Paris σ₂ = $240
If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris;
the degrees of freedom for this hypothesis test can be calculated as;
degree of freedom df = n - 1
degree of freedom for both hypothesis test = (n₁ - 1 + n₂ -1)
degree of freedom for both hypothesis test = (n₁ + n₂ - 2)
degree of freedom for both hypothesis test = ( 15 + 19 - 2)
degree of freedom for both hypothesis test are 32
The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?
Answer:
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
Step-by-step explanation:
Given that:
60% of the batteries are from manufacturer 1
90% of these batteries last for over 40 hours
Let the number of the battery duration be n = 0.90
Therefore n' = 1 - 0.90 = 0.10
Let p = manufacturer 1 and q = manufacturer 2
q = 1 - p
q = 1 = 0.6
q = 0.4
Thus ; 40% of the batteries are from manufacturer 2
However;
Only 75% of the batteries from manufacturer 2 last for over 40 hours.
Let number of battery duration be m = 0.75
Therefore ; m' = 1 - 0.75 = 0.25
A battery in a critical tool fails at 32 hours.
Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:
[tex]= \dfrac{q \times m' }{ p \times n' + q \times m' }[/tex]
[tex]= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }[/tex]
[tex]=\dfrac{0.1}{0.06+ 0.1}[/tex]
[tex]=\dfrac{0.1}{0.16}[/tex]
= 0.625
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
The probability that the battery was from manufacturer 2 is 62.5%.
Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:
You must establish the percentage of failure of the total batteries, and determine what percentage of failures corresponds to each manufacturer. Manufacturer 1 = 60 x 0.1 = 6 Manufacturer 2 = 40 x 0.25 = 10 Total = 16 16 = 100 10 = X 100 x 10/16 = X 62.5 = X
Therefore, the probability that the battery was from manufacturer 2 is 62.5%.
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Jessie is adept at Imagining abstract concepts and applying advanced mathematical formulas while creating flowcharts for her programs. Jessle has strength in which
skill?
communication
Answer:
Design thinking skills
Step-by-step explanation:
The design thinking skills is observable in individuals who can effectively use Intuition to create prototypes of abstract objects.
Jessie thus shows that she possess design thinking skills by been able to imagine abstract concepts at the same and she applies advanced mathematical formulas which in turn provides solutions to problems.
Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2
The lines of the inequalities are parallel, and the system of inequalities do not have any solution.
How to determine the solution of the inequalitiesThe system of inequalities are given as:
y ≥ 2x + 1 y ≤ 2x – 2The inequality y ≥ 2x + 1 has the following characteristics:
A slope of 2A y-intercept of 1A closed line, where the upper region is shadedThe inequality y ≤ 2x – 2 has the following characteristics:
A slope of 2A y-intercept of -2A closed line, where the lower region is shadedSee attachment for the graphs of the system of inequalities
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Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is found that 4% of the legitimate users originate calls from two or more metropolitan areas in a single day. However, 30% of fraudulent users originate calls from two or more metropolitan areas in a single day. The proportion of fraudulent users is 0.0130%. If the same user originates calls from two or more metropolitan areas in a single day, what is the probability that the user is fraudulent
Answer:
0.0009741
Step-by-step explanation:
The approach to solve this question is by the use of Baye’s theorem in conditional probability
Please check attachment for complete solution and explanation
Answer:
0.000974
Step-by-step explanation:
Let assume that;
P(Q) is the probability that the same user originated calls from two or more metropolitan areas in a single day
Also; Let consider M to be the event that denotes the legitimate users and N to be the event that denote the fraudulent users .
Then;
P(M) = 0.00013
P(N) = 1 - P(M)
P(N) = 1 - 0.00013
P(N) = 0.99987
P(Q|M) = 0.3
P(Q|N) = 0.4
The probability the same users originates calls from two or more metropolitan areas in a single day is calculated as follows:
P(Q) = (P(M) P(Q|M) ) + ( P(N) P(Q|N) )
P(Q) = ( 0.00013 × 0.3 ) + (0.99987 × 0.04 )
P(Q) = 0.000039 + 0.0399948
P(Q) = 0.0400338
However; The probability that the users is fraudulent given that the same users originates calls from two or more metropolitan areas in a single day is,
[tex]P(M|Q) = \dfrac{P(M) P(Q|M)}{(P(M) \ P(Q|M) ) + ((P(N) \ P(Q|N)) } \\ \\ \\ P(M|Q) = \dfrac{0.0001 \times 0.3}{0.0400338} \\ \\ \\ P(M|Q) = \dfrac{0.000039}{0.0400338} \\ \\ \\ \mathbf{P(M|Q) = 0.000974}[/tex]
need help with these 3 questions (giving brainiest if you can answer with equations)
Problem 10
Answer: approximately 57.39159 kmExplanation: You'll use the equation cos(28) = d/65 to solve for d to get d = 65*cos(28) = 57.39159 approximately. We use the cosine ratio because it ties together the adjacent and hypotenuse.
=====================================
Problem 11
Answer: approximately 10.46162 metersExplanation: This time we use the sine rule. We have the height as the opposite side (which is unknown, call it x) and the hypotenuse is the ladders length (11). So we have sin(72) = x/11 which solves to x = 11*sin(72) = 10.46162
=====================================
Problem 12
Answer: approximately 16.05724 cmExplanation: Now we use the tangent rule to connect the opposite and adjacent sides.
tan(37) = 12.1/x
x*tan(37) = 12.1
x = 12.1/tan(37)
x = 16.05724 approximately
Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary.
Age (yr) when award was won: 25-34, 35-44, 45-54, 55-64, 65-74, 75-84, 85-94
Frequency: 29, 34, 16, 3, 5, 1, 2
Step-by-step explanation:
kindly find attached detailed information of the remaining information as requested for your reference
1. The lower class limit is the left number in the age column
i.e in the 25-34 the lower class limit is 25
2. The upper class limit is the right number in the age column
i.e in the 25-34 the lower class limit is 34
3. The class width is the difference between the class boundaries of a single class
class width = 34.5-24.5= 10
4. The number of individuals is= 29+34+16+3+5+1+2= 90
Which statement describes this system of equations? 9x – 6y = 15, 3x – 2y = 5 The equations in the system are equivalent equations. There is no solution to the system of equations. The system of equations has one solution at (3, 2). The system of equations has one solution at (5, 5).
Answer:
There is no solution to the systems of equation.
Step-by-step explanation:
Graph the system by using y=mx+b
Both systems are y=2/5x+5/2.
Answer:
that guy is wrong. its the first option.
Step-by-step explanation:
i just took it
what is the approximate radius of a sphere with a volume of 1436cm to power of 3
Answer:
The radius is 7 cmStep-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
where r is the radius
From the question V = 1436 cm³
[tex]1436 = \frac{4}{3} \pi {r}^{3} [/tex]
Multiply through by 3
We have
[tex]4308 = 4\pi {r}^{3} [/tex]
Divide both sides by 4π
[tex] {r}^{3} = \frac{4308}{4\pi} [/tex]
[tex] {r}^{ 3} = \frac{1077}{\pi} [/tex]
Find the cube root of both sides
[tex]r = \sqrt[3]{ \frac{1077}{\pi} } [/tex]
r = 6.99
We have the final answer as
r = 7cmHope this helps
If mZNOM = 30°, then what is the length of the minor arc
NM?
Answer:
Option (B)
Step-by-step explanation:
To determine the length of arc of a circle we use the formula,
Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Where θ = measure of the central angle subtended by the arc
r = radius of the circle
For the circle given in the picture attached,
Length of arc NM = [tex]\frac{30}{360}(2\pi)(2)[/tex]
= [tex]\frac{4\pi }{12}[/tex]
= [tex]\frac{\pi }{3}[/tex]
Therefore, length of [tex]\widehat{NM}=\frac{\pi }{3}[/tex]
Option (B) will be the answer.
Answer: C
Step-by-step explanation:
4#/12 = #
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −7 and 6, and goes to −∞ as x→−∞.
Answer:
f( x ) = - x² - x + 42
Step-by-step explanation:
The polynomial function will have to include the zeroes with opposing signs, considering that when you isolate the value x say, you will take that value to the opposite side, changing the signs,
f(x) = (x + 7)(x - 6)
Now as you can see, x extends to negative infinity, such that,
f(x) = - (x + 7)(x - 6) - that negative makes no difference whatsoever on the zeroes of the function. All we want to do now is to expand this, and we receive out simplified solution.
Goal : [tex]expand\:-\:\left(x\:+\:7\right)\left(x\:-\:6\right)[/tex],
[tex]- xx+x\left(-6\right)+7x+7\left(-6\right)[/tex] = [tex]- xx-6x+7x-7\cdot \:6[/tex] = [tex]-\left(x^2+x-42\right)[/tex],
Expanded Solution : [tex]-x^2-x+42[/tex],
Polynomial Function : f( x ) = [tex]-x^2-x+42[/tex]
1. An architect is designing a house for the Mullet family. In the design he
must consider the desires of the family and the local building codes. The
rectangular lot on which the house will be built has 91 feet of frontage
on a lake and is 158 feet deep.
Answer:
An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
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The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
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2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
hope it helpsss
Step-by-step explanation:
Answer: An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
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length = 91 - 2*10 = 71 ft.
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The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
The amount of carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27% of its carbon-14. How old are the paintings?
Answer:
The painting is [tex]t = 10911.1 \ years \ old[/tex]
Step-by-step explanation:
From the question we are told that
The amount of carbon present after t year is
[tex]y(t) = y_o * e ^{-0.00012t}[/tex] {Note ; This is the function }
Here [tex]y(t)[/tex] is the amount of carbon-14 after time t
[tex]y_o[/tex] the original amount of carbon-14
Now given that the paint as at now contain 27% of the original carbon-14
Then it mean that
[tex]y(t) = 0.27 y_o[/tex]
So the equation is represented as
[tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]
=> [tex]0.27 = * e ^{-0.00012t}[/tex]
=> [tex]ln(0.27) = -0.00012t[/tex]
=> [tex]- 1.30933 = -0.00012t[/tex]
=> [tex]t = \frac{-1.30933}{-0.00012}[/tex]
=> [tex]t = 10911.1 \ years[/tex]