Yes, b(-6, 9, 2) is in the span of the other given vectors [tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6).
b as a linear combination of the other vectors [tex]a_1[/tex] and [tex]a_2[/tex]
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
A vector is a quantity that has magnitude and direction.
We say that a vector u spans vectors v, w if u = av + bw where a and b are scalars.
As per the given data:
[tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6), b = (-6, 9, 2)
We need to write vector b as a linear combination of vectors [tex]$a_1[/tex] and [tex]a_2$[/tex].
Let c and d be scalars.
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
(-6, 9, 2) = c(-1, 3, -1) + d(-2, -3, 6)
(-6, 9, 2) = (-c - 2d, 3c - 3 d, -c + 6d)
-6 = -c - 2d........(i),
9 = 3c - 3d ...... (ii),
2 = -c + 6d .......(iii)
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
On solving equations (i) and (ii), we get c = 4, d = 1
Now, we will check if c = 4, and d = 1 satisfy equation (iii).
= - c + 6d
= -4 + 6(1)
= -4 + 6
= 2
As it satisfies this equation, so b is a linear combination of [tex]$a_1[/tex] and [tex]a_2[/tex]
For more questions on vectors
https://brainly.com/question/14677899
#SPJ4
Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. (if b cannot be written as a linear combination of the other two vectors, enter done in both answer blanks.) a1=[-1 3 -1],a2=[-2 -3 6],b=[-6 9 2]
In an examination ,55%examines passed in english,60%In mathematics .if 40% examines passed in both subject.
1.By using Venn diagram
2.Find the percentage of students who failed in both the subject.
A simple way to depict sets visually is with a Venn diagram, also called an Euler-Venn diagram. A circle is used for the sets that are being considered, and a rectangle is used as the standard representation.
What is a Venn Diagram?Consequently, we'll talk about issues with variables two and three in this post.
Let's look at some fundamental Venn diagram formulas for two and three members.
n (A ∪ B) = n (A + B) - n (A ∪ B)
n (A ∪ B ∪ C ) = n(A) + n (B) + n (C) - n (A ∩ B) - n (B ∩ C) - n (C ∩ A) + n (A ∩ B ∩ C)
Then, where n(A) is the quantity of elements in set A, goes on.
You won't need to memorize these formulas once you've understood the notion of a Venn diagram using diagrams.
In this scenario, X is the number of elements that only belong to set A, Y is the number of elements that only belong to set B, and Z is the number of elements that both sets A and B (A + B) contain.
W is the number of objects that are not part of either set A or set B.
n(A) = x + z; n(B) = y + z; n(A B) = z; and n (A B) = x + y + z are all easily deduced from the above diagram.
w = total number of elements = x + y + z.
The Complete Question.
To Learn more About Venn diagram Refer To:
https://brainly.com/question/2099071
#SPJ1
y=3x²-5x+4 is there a relationship between the degree of a polynomial and how steep it is on the left and right edges. If it is so, what is it?
Answer:
Step-by-step explanation:
The revenue can be modeled by the polynomial function
R
(
t
)
=
−
0.037
t
4
+
1.414
t
3
−
19.777
t
2
+
118.696
t
−
205.332
where R represents the revenue in millions of dollars and t represents the year, with t = 6 corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.
Multiplicity and Turning Points
Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Suppose, for example, we graph the function
f
(
x
)
=
(
x
+
3
)
(
x
−
2
)
2
(
x
+
1
)
3
.
Notice in the figure below that the behavior of the function at each of the x-intercepts is different.
Graph of h(x)=x^3+4x^2+x-6.
The behavior of a graph at an x-intercept can be determined by examining the multiplicity of the zero.
The x-intercept
x
=
−
3
is the solution to the equation
(
x
+
3
)
=
0
. The graph passes directly through the x-intercept at
x
=
−
3
. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.
The x-intercept x=2
is the repeated solution to the equation (x−2)2=0
. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.
(x−2)2=(x−2)(x−2)
Consider the logistic equation ˙=(1−) y ˙ = y ( 1 − y ) (a) Find the solution satisfying 1(0)=14 y 1 ( 0 ) = 14 and 2(0)=−3 y 2 ( 0 ) = − 3 .
Answer:
The logistic equation is a differential equation that describes the growth of a population over time. The solution of this equation can be found using separation of variables or other methods of solving differential equations. The general solution for the logistic equation is given by:
y(t) = y_0 * e^(rt) / (1 + (y_0 - 1)e^(rt))
Where y_0 is the initial population size, r is the growth rate, and t is time.
For the specific case given in the question, we have the initial conditions y1(0)=14 and y2(0)=-3. We can use these to find the specific solution for each case.
1(0)=14 => y1(t) = 14e^(rt) / (1 + (14 - 1)e^(rt))
2(0)=−3 => y2(t) = -3e^(rt) / (1 + (-3 - 1)e^(rt))
It is important to note that we can not find the exact value of r without additional information.
Answer:
y(t) = 1 / (1 + (-4e^(-t))
Step-by-step explanation:
The logistic equation is a nonlinear differential equation that describes how a population grows. The solution for the logistic equation is given by y(t) = 1 / (1 + (Ce^(-t)) where C is the constant of integration, which can be determined by the initial conditions.
For the first initial condition, 1(0)=14, we can substitute the initial condition into the solution to get:
y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = 14
Solving for C, we get C = 13.
So the solution for the first initial condition is:
y(t) = 1 / (1 + (13e^(-t))
For the second initial condition, 2(0)=-3, we can substitute the initial condition into the solution to get:
y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = -3
Solving for C, we get C = -4.
So the solution for the second initial condition is:
y(t) = 1 / (1 + (-4e^(-t))
A spherical gasoline tank has been drained. If the result was 65,450 cubic feet of gasoline, what was the diameter?
The required diameter of the spherical gasoline tank is given as 50 feet.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The volume of the cylinder = 4/3πr³
4/3πr³ = 65450
r³ = 15625
r = 25 feet
Diameter = 2 × r
= 2 × 25
= 50 feet
Thus, the required diameter of the spherical gasoline tank is given as 50 feet.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ1
consider the continuous random variable x, which has a uniform distribution over the interval from 40 to 44. the variance of x is approximately . a. 46 b. 1.333 c. 1.155 d. 0.333
Consider the continuous random variable x that has a uniform distribution over the interval from 40 to 44. The variance of 'x' is approximately C: 1.155.
The variance of a continuous uniform distribution over the interval [a, b] is determined by the formula given as follows:
Var(x) = (b-a)^2 / 12
For the given distribution, a = 40 and b = 44, so the variance is calculated by putting these values into the above formula:
Var(x) = (44 - 40)^2 / 12 = 1.155
Therefore, the variance of 'x' is approximately 1.155
You can learn more about variance at
https://brainly.com/question/28426562
#SPJ4
The volume of a cube is 96 cubic millimeters. What is the length of each edge of the cube?
A.32 mm
B.212 mm
C.62 mm
D.48 mm
The length of each edge of the cube : C : 2∛12
What is meant by volume?Three-dimensional space is quantified by volume. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it. Volume is a term used in mathematics to describe the volume of three-dimensional space inhabited by an object or a closed surface. The measurement of volume is done in cubic units, like m3, cm3, in3, etc. Volume is also referred to as capacity on occasion.Three-dimensional space is quantified by volume.
V= a³ => 96 = a³ => a= ∛96 =2∛12
The length of each edge of the cube : C : 2∛12
To learn more about volume refer to:
https://brainly.com/question/463363
#SPJ1
compare and
contrast the
different types of
monetary Incentives
Profit sharing, project bonuses, stock options, warrants, scheduled bonuses (like Christmas and performance-linked), and increased paid vacation time are a few examples of financial incentives.
What are the different types of monetary Incentives?Financial incentives are used to financially commend employees for doing a great job. Cash or presents having a clear monetary value are examples of monetary rewards and incentives that employers give to their staff.
In addition to employee benefits, leadership and human resources departments offer and create financial incentive programmed to reward employee achievement and motivate team members to surpass their objectives.
Unlike non-monetary incentives, these perks and advantages are provided to employees in addition to their base pay and other benefits.
Therefore, these monetary incentives can take the form of lifestyle budgets, profit-sharing, end-of-year bonuses, spot bonuses, stock options, and end-of-year bonuses.
Learn more about monetary Incentives here:
https://brainly.com/question/1068495
#SPJ1
the temperature of a body falls from -5 degrees Celsius to -14 degrees Celsius. by how many degrees does the temperature fall?
Answer:
Temperature falls by - 9 degree Celsius
Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between -2.9 million and 4.5 million?
The probability that the mean profit for the sample was between -2.9 million and 4.5 million is of:
0.0475 = 4.75%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 6.54, \sigma = 10.45, n = 73, s = \frac{10.45}{\sqrt{73}} = 1.22[/tex]
The probability that the mean profit for the sample was between -2.9 million and 4.5 million is the p-value of Z when X = 4.5 subtracted by the p-value of Z when X = -2.9, hence:
X = 4.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (4.5 - 6.54)/1.22
Z = -1.67
Z = -1.67 has a p-value of 0.0475.
X = -2.9:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (-2.9 - 6.54)/1.22
Z = -7.73
Z = -7.73 has a p-value of 0.
Hence:
0.0475 - 0 = 0.0475 = 4.75%.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
5/6 divided by 1/2 in a fraction
Answer:5/3
Step-by-step explanation:
In the following intermediate step, cancel by a common factor of 2 gives 5/3
Answer:
[tex]1\dfrac{2}{3}[/tex]
Step-by-step explanation:
Fraction division:Use KCF method:
Keep the first fraction.Change division to multiplication.Flip the second fraction.[tex]\dfrac{5}{6} \ \div \dfrac{1}{2}=\dfrac{5}{6}*\dfrac{2}{1}[/tex]
[tex]\sf = \dfrac{5}{3}\\\\= 1\dfrac{2}{3}[/tex]
A hexagon can be created with 2 parallelograms. Find
cos CAB in terms of x.
BA= CA = 10. Hint DE=BC
The answer is cos CAB = 5 × √(10² + h²) in terms of x.
What is cos CAB in terms of X?"h" denotes the parallelogram's height.
We know that the base of parallelogram A and B is 10, so the area of parallelogram A and B can be found by:
Area = base * height = 10 * h
Since parallelogram A and B make up a hexagon, their combined area must equal the area of the hexagon:
2 * (10 * h) = 6 * h * a/2
Where a is the length of one of the sides of the hexagon.
Solving for a, we get:
a = 5 * h
Next, let's find the length of DE, which is equal to BC.
We know that the height of parallelogram A is h, and the base is 10.
So, the diagonal of parallelogram A can be found using the Pythagorean theorem:
DA = √(10² + h²)
Since DE = DA, we can substitute DA with DE:
DE = √(10² + h²)
Now we can find cos CAB using the Law of Cosines:
cos CAB = (AB² + BC² - AC²) / 2 * AB * BC
AB = 10
BC = DE = √(10²+ h²)
AC = 10
So,
cos CAB = (10² + (√(10² + h²))² - 10²) / 2 * 10 * √(10² + h²)
= (√(10² + h²))² / 2 * 10 * √(10² + h²)
= 5 × √(10² + h²)
Since h is a variable, we cannot simplify the expression further.
Therefore, cos CAB = 5 × √(10² + h²) in terms of x.
To learn more about cosine refer:
https://brainly.com/question/28355770
#SPJ1
Asp please
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 28 fU/sec. The function s(1) = - 16? + 281 + 5 gives the height of the ball, in feet, t seconds after it has been thrown. Determine
the time at which the ball reaches its maximum height and find the maximum height.
The ball reaches its maximum height of [ ft [ sec(s) after the bal is thrown.
(Type integers or decimals.)
The ball reaches a maximum height of 35.375 ft.
The height of the ball can be expressed as:s(t) = -16t^2 + 28t + 5
To find the time at which the ball reaches its maximum height, we can take the derivative of the height function with respect to time:
s'(t) = -32t + 28
And then set the derivative equal to zero and solve for t:
-32t + 28 = 0
32t = 28
t = 28/32 = 7/8 sec
So, the ball reaches its maximum height 7/8 seconds after it was thrown.
Next, we can plug this value of t back into the height function to find the maximum height:
s(7/8) = -16 * (7/8)^2 + 28 * (7/8) + 5 = 9.375 + 21 + 5 = 35.375 ft
Therefore, The ball reaches a maximum height of 35.375 ft.
Learn more about height here: brainly.com/question/28122539
#SPJ1
In base ten, 67.315 is exactly 6.7315 tens, is exactly __________ ones, is exactly __________ tenths, is exactly __________ hundredths, is exactly __________thousandths and is exactly __________hundreds.
In base ten, 67.315 is exactly 6.7315 tens, is exactly 7 ones, is exactly 3 tenths, is exactly 5 hundredths, is exactly 1 thousandths and is exactly 6 hundreds.
When we break down 67.315 in base ten, we can see that it is composed of:
6 tens because 6*10 = 60
7 ones because 7*1 = 7
3 tenths because 3*0.1 = 0.3
5 hundredths because 5*0.01 = 0.05
1 thousandths because 1*0.001 = 0.001
So, 67.315 is exactly 6.7315 tens, is exactly 7 ones, is exactly 3 tenths, is exactly 5 hundredths, is exactly 1 thousandths and is exactly 6 hundreds.
Express each of the following events in terms of the events A, B and C as well as the operations of complementation, union and intersection: (a) at least one of the events A, B, C occurs: (b) at most one of the events A, B, C occurs: (c) none of the events A, B, C occurs; (d) all three events A, B, C occur; (e) exactly one of the events A, B, C occurs: (f) events A and B occur, but not C; (g) either event A occurs or, if not, then B also does not occur. In each case draw the corresponding Venn diagrams.
Here we will have to use the set theory to understand where intersection and union can be used to obtain the results.
a)
Here we need to write an expression for the event that at least one of the events A, B, and C occurs. Hence the event will be of occurrence of
A or B or C
We know that or implies a union of sets hence it will be
(A U B U C)
b)
Here we need to find the occurrence at most one of the events hence we get
[not A and not B and not C] or [A and not B and not C] or [not A and B and not C] or [not A and not B and C]
the word and implies an intersection hence we get
[not A ∩ not B ∩ not C] U [A ∩ not B ∩ not C] or [not A ∩ B ∩ not C] U [not A ∩ not B ∩ C]
c)
None of the event occurs will imply
[not A ∩ not B ∩ noy C]
d)
This will simply be the opposite of c) hence we will get
A ∩ B ∩ C
e)
Here we will just remove the possibility of non-occurrence of any event from option b) to get
[A ∩ not B ∩ not C] U [not A ∩ B ∩ not C] U [not A ∩ not B ∩ C]
f)
Here we will get
A ∩ B ∩ not C
g)
Here there will be 2 possibilities A occurs and does not occur.
[A ∩ B ∩ C] U [not A ∩ not B ∩ C]
To learn more about Set Theory visit
https://brainly.com/question/28278437
#SPJ4
Fabiana is making a sandbox for her children. She has made a wooden frame for her backyard that is 4 feet long, 4 feet wide, and 2 feet deep. She can purchase sand for the sandbox for $20 per cubic meter. How much will it cost Fabiana to purchase sand? (Hint: 1 foot = 0.3048 meters.)
(Round your answer to the nearest dollar.)
Answer:
$195
Step-by-step explanation:
First, we need to know the volume of the box, that way we can know how much sand we need to buy.
l x w x h = v
4 x 4 x 2 = 32
Now we have the volume in feet but we need to convert it into meters.
32 x 0.3048 = 9.7536
Next, we'll multiply the meters by the price so that we'll have the total cost.
9.7536 x 20 = 195.072
A model of DNA is shown.
Structure 1
MMM
Which label identifies a hydrogen bond?
A. Structure 1
B. Structure 2
C. Structure 3
Structure 4
D. Structure 4
Structure 2
3
5%
Structure 3
K
A hydrogen donor and acceptor must both be present for a hydrogen bond to form.
How do you tell if a bond is a hydrogen bond?The key concepts in hydrogen bonding are;
The Hydrogen Bond Acceptor is the electronegative atom containing the lone pair electrons.The Hydrogen Bond Donor is the electronegative atom that is joined to the hydrogen.The Hydrogen Bond Donor and the Hydrogen Bond Donor must be 180 degrees apart.Typically, a strongly electronegative element like N, O, that is covalently connected to a hydrogen bond serves as the donor in a hydrogen bond.
Given that the information is incomplete, the above information shows adequate information about hydrogen bonds.
Read more about hydrogen bond here:
https://brainly.com/question/1420470
#SPJ1
students deliver newspapers and magazines to houses.
One day, they have to deliver 875 newspapers and 1200 magazines.
Each student can deliver either 35 newspapers or 50 magazines in 1 hour.
Each student can only work for 8 hours.
Work out the minimum number of students needed
Answer:
Step-by-step explanation:
To determine the minimum number of students needed, we need to first determine how many newspapers and magazines each student can deliver in total (over 8 hours).
Each student can deliver 35 newspapers + 50 magazines = 85 newspapers + magazines per hour.
In 8 hours, each student can deliver 85 newspapers + magazines/hour * 8 hours = 680 newspapers + magazines.
Now, we can divide the total number of newspapers and magazines to be delivered by the number of newspapers and magazines each student can deliver in 8 hours:
875 newspapers + 1200 magazines = 2075 newspapers + magazines
2075 newspapers + magazines / 680 newspapers + magazines/student = 3 students.
Therefore, the minimum number of students needed to deliver 875 newspapers and 1200 magazines is 3 students.
Round 36 to the nearest tenth
given m<1=65 degree, what is m<7?
Based on the Alternate Exterior Angles Theorem, the measure of angle 7 is 65 degrees.
What is the Alternate Exterior Angles Theorem?The Alternate Exterior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent (equal in measure). In other words, the angles on the outside of the lines, on opposite sides of the transversal, have the same measure
Angles 1 and 7 are exterior angles, therefore:
m<7 = m<1
Substitute
m<7 = 65 degrees.
Learn more about the alternate exterior angles theorem on:
https://brainly.com/question/24839702
#SPJ1
A boat sailed 25 miles south and then 15 miles East. About how many miles is it from where it started
Answer:
below
Step-by-step explanation:
The direct distance, d, from starting point is the hypotenuse of a right triangle with two legs of 25 mi and 15 mi
Pythagorean Theorem
d^2 = 25^2 + 15^2
show d = sqrt(850) = 29.15 mi
Julius and Isaiah share a reward of 440 in a ratio of 2:3 . How much does Isaiah get?
Answer: if Isaiah gets two thirds than he'll get 293.333333334 but if he gets one third than he will get 146.666666667
Step-by-step explanation:
describe the end behaviors of the polynomial 8x^7-2x^5-4x^4+2x^3+7x^2
The end behavior of the polynomial 8x^{7}-2x^{5}-4x^{4}+2x^{3}+7x^{2}
is given in graph.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.
Now,
Given polynomial is 8x^{7}-2x^{5}-4x^{4}+2x^{3}+7x^{2}.
So, the graph will be dominated by x^7 because it is the highest power.
Hence,
the end behavior of the function is as shown in graph.
To know more about polynomials visit the link
https://brainly.com/question/11536910?referrer=searchResults
#SPJ1
HELP PLEASE
-0.9p+3.2=-1.7p
Answer:
p = - 4
Step-by-step explanation:
- 0.9p + 3.2 = - 1.7p ( add 1.7 to both sides )
0.8p + 3.2 = 0 ( subtract 3.2 from both sides )
0.8p = - 3.2 ( divide both sides by 0.8 )
p = [tex]\frac{-3.2}{0.8}[/tex] = - 4
Answer: p=-4
Step-by-step explanation:
-0.9p+3.2=-1.7p
+0.9p +0.9p
3.2=-0.8p
32=-8p
p=-4
According to current prices 1.7 grams of gold is worth the same amount as 130 grams of
silver. How much gold would 1000 grams of silver be worth? How much silver would 10
grams of gold be worth?
Answer:
Below
Step-by-step explanation:
1.7 / 130 go/si
1000 si * 1.7 /130 go/si = 13.08 gm of gold
10 go / ( 1.7/130 go/si) = 764.7 gm of silver
Find the equation of the line that passes through the given point and has the given slope. (Use x as your variable.
(0, 8), m= 4
The equation of the line passing through the point (0, 8), and having a slope of m = 4 is y = 4x + 8.
What is equation of a line?The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
The equation of the line passing through the points (x1, y1), with a slope of m is given by the formula:
(y - y1) = m (x - x1)
Given that the point is (0, 8) and the slope, m = 4.
Substituting the values we have:
(y - y1) = m (x - x1)
y - 8 = 4 (x - 0)
y - 8 = 4x
y = 4x + 8
Hence, the equation of the line passing through the point (0, 8), and having a slope of m = 4 is y = 4x + 8.
Learn more about equation of line here:
https://brainly.com/question/21511618
#SPJ1
The area of a rectangle parking lot is 6016m^2. If the length of the parking lot is 94m what is the width
Answer:
21 IAMOOOOOOOO
Step-by-step explanation:
Answer:
w = 64
Step-by-step explanation:
A = 6016[tex]m^2[/tex]
l = 94m
A = lw
Sub in all the known values
6016 = (94)(w)
w = [tex]\frac{6016}{94}[/tex]
w = 64
What is the equation of a line with slope 1/4 which passes through the point (0,7)?
Write the equation in slope-intercept form, y = mx + b.
Answer:
y=1/4x+7
Step-by-step explanation:
If the y-intercept is (0,7), then the b is +7
the slope is 1/4 which is equal to m
your equation is y=1/4x+7
Hillary
earns $17.92 weeding gardens for 3.2 hours.
She is paid the same hourly rate to mow lawns.
Hillary mows lawns for 2.875 hours. How much
does Hillary earn mowing lawns?
Find the equation for the function described below. (Let x be the independent variable and ybe the dependent variable.) The linear function whose graph has slope −4 and passes through the point (5,2)
The linear function whose graph has slope -4 and passes through the point (5, 2) is f(x) = -4x + 22
Let us assume that f(x) be a required linear function.
We know that an equation of the line passing through point (x₀, y₀) and having slope m is:
(y - y₀) = m(x - x₀)
Let (x₀, y₀) = (5, 2) and slope m = -4
So, the equation of the line would be,
(y - y₀) = m(x - x₀)
(y - 2) = -4(x - 5)
y - 2 = -4x + 20
y -2 + 2 = -4x + 20 + 2
y = -4x + 22
Let y = f(x)
f(x) = -4x + 22
So, the linear function is: f(x) = -4x + 22
Learn more about linear function here:
https://brainly.com/question/27749345
#SPJ4
a bernoulli differential equation is one of the form observe that, if or , the bernoulli equation is linear. for other values of , the substitution transforms the bernoulli equation into the linear equation consider the initial value problem (a) this differential equation can be written in the form with 1/x , 5 , and 2 . (b) the substitution y^-1 will transform it into the linear equation -1/x -5 . (c) using the substitution in part (b), we rewrite the initial condition in terms of and : 1/5 . (d) now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).
The Bernoulli differential equation is a nonlinear ordinary differential equation of the form:
dy/dx + P(x)y = Q(x)y^n, where n ≠ 0, 1.
For n = 0 or n = 1, the equation is linear. For other values of n, a common technique to linearize the equation is to make the substitution y = v^(-1/n-1). The resulting equation is:
dv/dx + (P(x) + Q(x)/v^(1/n-1)) * (1/n-1) * v^(1/n-2) * dv/dx = 0.
For the initial value problem given, we have P(x) = -1/x, Q(x) = -5, and n = 2.
We make the substitution y = v^(-1), so v = y^(-1), and dv/dx = -y^(-2)dy/dx. The equation becomes:
-y^(-2)dy/dx + (-1/x - 5y^2) = 0.
We have the initial condition y(1) = 1/5. In terms of v, the initial condition becomes v(1) = 1/(1/5)^2 = 25.
Now, the differential equation is linear, and we can solve it using standard methods, such as separation of variables. To find the solution that satisfies the initial condition, we may use numerical methods such as the Euler method or Runge-Kutta method.
To Know more about Bernoulli equation
https://brainly.com/question/15396422
#SPJ4
