The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
A=12h
sin54°= h/5
ℎ= 5 / sin54°
h= sin54° / 5
Therefore: A=12 * sin54° / 5
74.164 feet2
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
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Use spherical coordinates to show that the triple integral from negative infinity to infinity of the (sqrt of x^2+y^2+z^2 * e^-(x^2+y^2+z^2)) dxdydz = 2pi
The improper triple integral is defines as the limit of a triple integral over a solid sphere as the radius of the sphere goes to infinity. (Hint: write inequalities for a solid sphere of radius p, and then let p -> infinity)
We have used spherical coordinates to show that the triple integral from negative infinity to infinity of the [tex]\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]
What is meant by triple integral?Triple integrals, as their name suggests, are three sequential integrations that can be used to determine a volume or to integrate in a fourth dimension over three other independent dimensions.
The total amount of heat in the three-dimensional room can be calculated using this triple integral.
We understand that triple integrals have several uses if "dimension" can refer to something other than a spatial dimension. We could determine a 3-D object's overall inertia or the gravitational attraction on a basketball.
The sum of an infinite number of rectangular prisms across a bounded region in three-space is a double integral, which represents the volume beneath the surface above the xy-plane.
[tex]$$To show that $\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$, begin by converting the integral into spherical coordinates. Recall that $\rho^2=x^2+y^2+z^2$ and $d V=\rho^2 \sin \phi d \rho d \phi d \theta$. To convert the bounds, notice that as $x, y$, and $z$ expand infinitely in both directions, this can be modeled to a sphere of an infinite radius.\\$$[/tex]
[tex]$$This means that the new bounds become $0 \leq \rho \leq \infty, 0 \leq \phi \leq \pi$, and $0 \leq \theta \leq 2 \pi$. Because the integral is infinite, let the upper limit of $\rho$ be $R$ and take the limit as $R$ goes to infinity. To evaluate with respect to $\rho$, first use $u$ substitution by letting $u=\rho^2$ and then integrating by parts$$[/tex]
[tex]$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z$[/tex]
[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0 \int_0^R \sqrt{\rho^2} e^{-\left(\rho^2\right)} \rho^2 \sin \phi d \rho d \phi d \theta \\& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^\pi \int_0^R e^{-\rho^2} \rho^3 \sin \phi d \rho d \phi d \theta \\[/tex]
[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^2 \sin \phi\left[\frac{1}{2}\left(-e^{-\rho^2}\left(1+\rho^2\right)\right)\right]_{\rho=0}^{\rho-R} d \phi d \theta \\& =\frac{1}{2} \lim _{R \rightarrow \infty} \int_0^{2 \pi \pi} \int_0^\pi \sin \phi\left[-e^{-R^2}\left(1+R^2\right)+e^{-0^2}\left(1+0^2\right)\right] d \phi d \theta\end{aligned}$$[/tex]
[tex]$$\\\text{Use L' Hospital's Rule to simplify the limit}$$\begin{aligned}& \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z \\& =2 \pi(1)-2 \pi \lim _{R \rightarrow \infty}\left(\frac{2 R}{2 R e^{R^2}}\right) \\& =2 \pi-\lim _{R \rightarrow \infty} \frac{1}{e^{R^2}} \\& =2 \pi-0 \quad \text { As } \lim _{x \rightarrow \infty} \frac{1}{e^x}=0 . \\& =2 \pi\end{aligned}$$[/tex]
[tex]$$Therefore,$$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]
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50 POINTS + BRAINLIEST
Answer:
I believe the answer may be 31.5cm.
Step-by-step explanation:
I first found the area of the total region which was 70cm. From there I found the area of the triangle to the left of the region by doing 6x7 which is 42, and multiplied by 1/2 because it is a triangle. I did the same to the triangle on the right, doing 5x7 which is 35, and multiplied by 1/2 since this is also a triangle. Finally, I subtracted both totals of 21, and 17.5 from the 70, getting a grand total of 31.5cm.
Answer:
31.5 cm²
Step-by-step explanation:
To find the area of the crossed region, subtract the areas of the two triangles from the area of the rectangle.
Formulae:
Area of a rectangle = length × widthArea of a triangle = ¹/₂ × base × heightArea of the rectangle
⇒ A = (4 + 6) × 7
⇒ A = 10 × 7
⇒ A = 70 cm²
Area of triangle 1
⇒ A = ¹/₂ × 6 × 7
⇒ A = 3 × 7
⇒ A = 21 cm²
Area of triangle 2
⇒ A = ¹/₂ × 5 × 7
⇒ A = 2.5 × 7
⇒ A = 17.5 cm²
Area of the crossed region
⇒ A = 70 - 21 - 17.5
⇒ A = 49 - 17.5
⇒ A = 31.5 cm²
please someone help me with this escape room question! i’ve been stuck on this problem for so long now
Answer:
Q1 - 7910
Q2 - 9710
Q3 - 1097
Q4 - 7190
I don't know what these mean, but here you go..?
if Q(x)=8x^2+10 find Q(1/4)
The value of Q (1/4) as required to be determined in the task content is; 10 ½.
What is the value of the function instance Q (1/4)?It follows from the task content that the value of the function instance Q (1/4) is to be determined based on the given function definition; Q(x)=8x^2+10.
Hence, since the given function is; Q (x) = 8x² + 10.
The function instance Q (1/4) can be evaluated as follows;
Q (1/4) = 8 ( 1/4 )² + 10
= 8 • 1/16 + 10
= 1/2 + 10
= 10 ½.
Ultimately, the value of the function instance Q (1/4) is; 10 ½.
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finance the median player salary for the new york yankees was $1.6 million in 2001 and $5.2 million in 2009. write a linear equation giving the median salary y in terms of the year x. then use the equation to predict the median salary in 2017.
The median salary in 2048 will be 2.853 million
What is meant by equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. A condition on a variable (or variables) that ensures that two expressions in the variable (or variables) have the same value is known as an equation. An equation remains the same if the LHS and the RHS are switched; this value of the variable is referred to as the solution or root of the equation.A general linear equation is given by:
y=a × x + b
Where the slope is a and the y-intercept is b.
We shall discover that the linear equation for this scenario is
y = 0.033 × x + 1.269
And we may anticipate that in 2048, the median salary will be 2.853 million.
The slope can be expressed as if the line passes through the points (x1, y1) and (x2, y2).:
[tex]$a=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, we know that whereas the median player pay in 2007 (x = 7) was y = 1.5 million, it was y = 1.7 million in 2013 (x = 13).
The following two points can be written as follows:
(7,1.5)
(13,1.7)
Note that the y-value is in millions.
Then the slope of the linear equation will be:
[tex]$a=\frac{1.7-1.5}{13-7}=0.033[/tex]
So the linear equation is something like:
y=0.033 × x + b
Remember the point (7,1.5), which indicates that for x=7, we also get y=1.5, so we can substitute these in the equation above:
1.5=0.033 × 7+b
1.5-0.033 × 7 = b = 1.269
Then the linear equation is:
y=0.033 × x+1.269
b) Now we want to predict the median salary in 2048 . For 2048 the
x-value is x=48
So we just need to evaluate this in the linear equation:
y = 0.033 × 48 + 1.269 = 2.853
Then the median salary in 2048 will be 2.853 million
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Write an equation of the line containing the given point and parallel to the given line.
(7.-5); 4x - 5y = 2
The equation of the line containing point (7, -5) and having slope 4/5 is found as y = 4/5x - 3/5.
Explain the term slope intercept form?A line's equation of the type y = mx + b can be written in slope intercept form. The m stands for the line's slope, and the b for the y-intercept. When you need to find a point on the a line or solve for y given x, you utilise the slope intercept form.The given data:
Passing points (x1, y1) = (7, -5)Parallel line's equation: 4x - 5y = 2Comparing eq with standard form:
5y = 4x - 2
y = 4/5 x - 2/5
slope m = 4/5
As both lines are parallel, the slope of both lines will be equal.
Thus, using slope intercept form
y - y1 = m(x - x1)
y + 5 = 4/5 (x - 7)
y + 5 = 4/5x - 28/5
y = 4/5x - 3/5
Thus, the equation of the line containing point (7, -5) and having slope 4/5 is found as y = 4/5x - 3/5.
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The principal of a large high school is concerned about the number of absences for students at his school. to investigate, he prints a list showing the number of absences during the last month for each of the 2500 students at the school. for this population of students, the distribution of absences last month is skewed to the right with a mean of 1.1 and a standard deviation of (1.4). suppose that a random sample of 50 students is selected from the list printed by the principal and the sample mean number of absences is calculated.
a.) What is the shape of the sampling distribution of the sample mean? Explain
b.) What are the mean and standard deviation of the sampling distribution of the sampling mean?
c.) What is the probability that the mean number of absences in a random sample of 50 students is less than 1?
d.) Because the population distribution is skewed, the principal is considering using the median number of absences last month instead of the mean number of absences to summarize the distribution. Describe how the principal could use a simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50.
The shape of the sampling distribution of the sample mean is approximately normal because the sample size is greater than 3.
Why do we use sampling distribution?The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution. The frequency distribution of a variety of possible outcomes for a population statistic makes up the sampling distribution of a specific population.The probability distribution of a statistic that is produced by taking numerous samples from a certain population is known as the sampling distribution. To make the process of statistical inference simpler, researchers utilize sample distributions.When you repeat your survey or poll for all potential samples of the population, you get the sampling distribution of a proportion. For instance, you may conduct many polls rather than asking 1000 cat owners which cat food they prefer.Given data :
a ) Approximately normal because the sample size is greater than 3.
b ) b ) ux = 1.1 and Jx = [tex]\frac{1.4}{\sqrt{40} }[/tex]= 0.198
c ) c ) P ( ux ∠ 1 ) = normal cdf ( lower : 1000, upper : 1, u : 1.1 , J : 0.198 ) = 0.3068
d ) The principal could pick 50 students may times and find the median and repeat several times until he has every possible sampling distribution.
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PLEASE WHAT IS THIS?!!? WHATS THE ANSWER?
Answer: bottom right
Complex numbers are used to describe current, I, voltage, E, and impedance, Z. These three quantities are related by the equation EIZ. Given two of these quantities, solve the equation EIZ for the missing variable. I=5+2i, Z=9+6i
The value of the voltage (E) is given as 33 + 48i
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equation:
E = IZ
Where E is the voltage, I is the current and Z is the impedance.
But I = 5 + 2i, Z = 9 + 6i, substituting the values gives:
E = IZ
E = (5 + 2i)(9 + 6i)
E = 45 + 30i + 18i - 12
E = 33 + 48i
The value of E is 33 + 48i
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Solve the following linear equation.
4x+8=4(x+4)−8
The equation 4x+8=4(x+4)−8 can be simplified by distributing the 4 on the right side of the equation:
4x+8=4x+16-8
Subtracting 4x from both sides:
8=16-8+8
Which simplifies to:
8=8
This is a true statement, so x could be any real number. The solution to the equation is x is any real number or x∈R.
the first pentagon is dilated to form the second pentagon. drag and drop the answer to correctly complete the statement. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. the scale factor is response area. a pentagon with a side length of 5. an arrow points to a smaller pentagon with a side length of 1
The scale factor of the dilated pentagon is the ratio of the side length of the original pentagon to the side length of the dilated pentagon.
In this case, the side length of the original pentagon is 5 and the side length of the dilated pentagon is 1. Therefore, the scale factor is 5:1 or 5/1. To calculate the scale factor, divide the side length of the original pentagon by the side length of the dilated pentagon. In this case, the calculation would be 5 / 1 = 5. The scale factor of the dilated pentagon is 5.
We can also use the formula for finding the scale factor of two figures: Scale Factor = Length of figure 1 / Length of figure 2. In this case, the length of figure 1 is 5 and the length of figure 2 is 1. So, the scale factor is 5.
Therefore, the scale factor of the first pentagon to the second pentagon is 5.
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If a company has issued 2 million shares, the share price is $125 per share, and the company has generated $18 million in earnings, calculate the PE ratio. Give your answer to 2 decimal places.
Answer:
P/E = 125/9= 13.89:1
Step-by-step explanation:
2mm shares at $ 125/share
18mm earnings so earnings per share EPS = 18/2 =9
The P/E ratio is calculated by dividing the stock's current price by its latest earnings per share.
P/E = 125/9= 13.89:1
Answer:
Step-by-step explanation:
The earnings per share can be calculated as
Earnings per Share =Total EarningsTotal Shares=$18,000,0002,000,000=$9.
Therefore the PE ratio is
PE Ratio =$125$9≈13.89.
DUE SOON PLEASE HELP SUPER CONFUSED
Answer: mean would be d or 998.67 wouldn't it
Step-by-step explanation:
because mean 998.67 median 1100 and mode 1500
i think that is right but i am not 100% sure
Suppose that a firm produces 275,000 units a year and sells them all for $8 each. The explicit costs of production are $1,800,000 and the implicit costs of production are $400,000. The firm earns an accounting profit of
The firm's accounting profit earnings as required to be determined in the task content is; $0.
What is the firm's accounting profit earnings?As evident in the task content, the firm produces 275,000 units a year and sells them all for $8 each.
Therefore, the total revenue generated from sales is; 275,000 × $8 = $2,200,000.
Hence, since the total cost is the sum of $1,800,000 and $400,000 which is; $400,000 + $1,800,000 = $2,200,000.
Ultimately, the total accounting profit earned is; Revenue generated - Expenses = $2,200,000 - $2,200,000 = $0.
Therefore, the total accounting profit earned is; $0.
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PLEASE HELP!
Q: Match the key aspect of a function's graph with its meaning.
x-intercept
f(x) < 0
y-intercept
f(x) > 0
Matching the Meaning of Key Featu
Intro
↑
↑
intervals of the domain where the
graph is below the x-axis
location on graph where output is
zero
intervals of the domain where the
graph is above the x-axis
location on graph where input is zero
Done
Question
Answered step-by-step
"Match the key aspect of a function's graph with its meaning. f(x) > 0 intervals of the domain where the graph is above the x-axis f(x) < 0 location on graph where input is zero x-intercept location on graph where output is zero y-intercept intervals of the domain where the graph is below the x-axis Common Core Algebra 'httpsinIscorekam edgenuftycomPlayer Common Core Algebra /- MAJIO9 / AcR 7haijliy Giapiij Instruction Active of a Graph the Meaning of Key Features Matching of a function $ graph with its meaning Match the key aspect intervals of Ihe domain where the graph. IS above the x-axis flx) > E Iocation on graph where input IS zero fix) < 0 Iocation on graph where output IS x-Intercepi zero Intervals Of the domain where the y-intercept graph Is below the x-axis Untto Done PrevousAaml Type here i0 search"
PLEASE HELP WITH 6 THANKS SO MUCH ILY I WILL DO ANYTHING U WANT
Answer:
A=22 dots
B=51 squares
C=number of squares = the number of squares times 2, plus 2
Step-by-step explanation:
A-
10*2=20
20+2=22
B-
104-2=102
102/2=51
C-
there is only one row so that adds 2 dots and then you multiply the number of squares by 2 then add 2 to the product
Answer:
a) 22 dots
b) 51 squares
c) Number of dots = 4 + 2 x (number of squares - 1)
Step-by-step explanation:
Actually, in this question you are better off solving c) first for the formula and then using it to solve a) and b)
Let's look at the relationship between squares and dots:
Number of squares Number of dots
1 4
2 6
3 8
You can see that as the number of squares increases by 1, the number of dots increases by 2 with 4 dots as the starting point
We can easily come up with a formula by treating this as an arithmetic sequence.
The number of dots represents the term # and the number of dots the actual term value
The difference between consecutive terms is 2 and is called the common difference (d)
The nth term will be referred to using aₙ
So we have
a₁ = 4
a₂ = 6
a₃ = 8
The nth term of any arithmetic sequence is
aₙ = a₁ + d(n-1) where d is the common difference
This is the answer to c). Translating to dots and squares we get
Number of dots = 4 + 2 x (number of squares - 1)
a) Use the formula
a₁₀ = 4 + 2(10-1) = 4 + 2 x9 = 4 + 18 = 22 dots
b) Here we are given the value of term = 104
Substituting we get
104 = 4 + 2(n-1)
104-4 = 2(n-1)
100 = 2(n-1)
n-1 = 100/2 = 50
n = 51
That means the there are 51 squares in the diagram which has 104 dots
Eric fell asleep at 3:15 pm he woke up after 2 hours and 35 minutes what time did eric wake up
A professor wants to randomly select 4 students to go to the board. She decides to randomly select the fifthstudent who enters the classroom and every sixth student after that. Determine the students who will be going to the board.Write down the student numbers.
The randomly number of the students who got selected are 4,5,6,7,.......
Professor randomly select the fourth and every student after that
Now by using the next term formula which is
=>a + d(n-1)
The next student is the 2nd student.
=>4 + 1*(2-1)
=>4 + (1)
=>4 + 1
=> 5
The 3rd student will be
=>4 + 1(3-1)
=>4 + 1(2)
=>4 + 2
=> 6
The 4th student will be
=>4 + 1(4-1)
=>4 + 1(3)
=> 4+ 3
=> 7
students numbers are 4,5,6,7......
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jan is laying her tile in the kitchen. the rectangular floor dimensions are 12 ft by 16 ft. it's costs $3.25 per square foot for installation. How much will jan's remodel cost?
The amount of money which Jan's remodel would cost is equal to $624.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 12 × 16
Area of rectangle = 192 square feet.
For the total cost, we have the following;
Total cost = Area of remodel × cost per square foot.
Total cost = 192 × 3.25.
Total cost = $624.
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A sphere of radius r is cut by a plane h units above the equator, where h < r. Find the volume of solid (spherical segment) above the plane.____A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. Find the volume of the resulting ring.____
The volume of the spherical segment above the plane is[tex](1/3) *\pi * (r^2 - (r-h)^2) * h[/tex] and the volume of the ring resulting from drilling a hole through the center of a sphere is [tex]\pi * (R^2 - r^2) * R.[/tex].
A sphere of radius "r" is cut by a plane "h" units above the equator. To find the volume of the solid (spherical segment) above the plane, we first need to find the height of the segment, which is (r - h). Then, we can use the formula for the volume of a spherical segment: [tex](1/3) * \pi * (r^2 - (r-h)^2) * h.[/tex]
A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. To find the volume of the resulting ring, we can use the formula for the volume of a cylindrical ring: [tex]\pi * (R^2 - r^2) * h[/tex], where h is the height of the ring. Since the hole goes all the way through the sphere, the height of the ring is equal to the radius of the sphere, R. So the volume of the ring is [tex]\pi * (R^2 - r^2) * R[/tex].
In the first problem, the volume of the solid (spherical segment) above the plane is [tex](1/3) * \pi * (r^2 - (r-h)^2) * h[/tex]. In the second problem, the volume of the resulting ring is [tex]\pi * (R^2 - r^2) * R.[/tex]
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Can someone help with this?
The value of f(x) . g(x) is 3x² + 5x - 2 two linear functions multiplied together to form a quadratic function.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, Are two function f(x) 3x - 1 and g(x) = x + 2.
Now, f(x) . g(x) is nothing but multiplication of f(x) and g(x).
Therefore,
f(x) . g(x) = (3x - 1)(x + 2).
f(x) . g(x) = 3x² + 6x - x - 2.
f(x) . g(x) = 3x² + 5x - 2.
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I NEED HELPPPPP PLS HELP
A cube is a three-dimensional shape with all sides of equal length, width, and height. If the length of the packaging box is 4xy, then all the sides of the cube have the same length 4xy.
What is the straightforward meaning of volume?
The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.
To find the volume of a cube, we use the formula: volume = side x side x side = (side)^3
Therefore, the volume of the packaging box in terms of x and y is (4xy)^3 = (4xy)(4xy)(4xy) = (4xy)^3 = (4x)^3 * y^3 = 64x^3 * y^3
So the volume of the packaging box is 64x^3 * y^3 cubic units.
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what is the average class score ? round your answer to the nearest whole number
Divide the following and then check by multiplying.
7)84
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
OA. The quotient does not have a remainder. The quotient is
B. The quotient has a remainder not equal to 0. The quotient is
OC. The quotient is undefined.
help!
How do you determine the value(s) of k such that the system of linear equations has the indicated number of solutions: no solutions for x + 2y + kz = 6 and 3x + 6y + 8z = 4?
4/3 is the value of k that makes the system of linear equations has no solutions .To determine the value(s) of k such that the system of linear equations has no solutions, we need to use the concept of consistency and consistency of a system of linear equations, which is the property that a system of equations has exactly one solution or no solution.
A system of linear equations is consistent if it has exactly one solution and inconsistent if it has no solution. We can use the concept of determinant of a matrix to check the consistency of the system of linear equations. The determinant of a matrix is a scalar value that can be calculated from the elements of a matrix and it tells us whether a matrix is invertible or not. An invertible matrix corresponds to a consistent system of linear equations and a non-invertible matrix corresponds to an inconsistent system of linear equations. To check the consistency of the system of linear equations, we can use Cramer's Rule, which states that the determinant of the coefficient matrix must be non-zero for the system to have a unique solution.
The coefficient matrix of the given system of equations is:
| 1 2 k |
| 3 6 8 |
The determinant of the coefficient matrix is:
|1 2 k|
|3 6 8| = (18) - (26) + (k*3) = 8 - 12 + 3k
If the determinant of the coefficient matrix is non-zero, the system of equations will have a unique solution, if the determinant of the coefficient matrix is zero, the system of equations will have no solution.
So for the system of linear equations to have no solution, the determinant of the coefficient matrix must be zero.
8 - 12 + 3k = 0
3k = 4
k = 4/3
So the value of k that makes the system of linear equations has no solutions is 4/3.
It is worth noting that if there are infinite solutions, the determinant of the matrix is zero but the rank of the matrix (the number of linearly independent rows or columns) is smaller than the number of variables
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Kent completed his homework in 52.752 minutes. What is this number rounded to the nearest tenth? Explain how you decided.
Answer:52.8
Step-by-step explanation:
52.752
in 752 is more than 5 so it gets rounded to 8so it = 52.8
question if s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of nst ?
If s and t are integers greater than 1 and each is a factor of the integer n, then the product nst must be divisible by both s and t. This is because s and t are factors of n, which means that n is divisible by s and t.
The product of two integers is divisible by the factors of each of those integers. Therefore, since n is divisible by s and t, and nst is the product of n, s, and t, nst must also be divisible by s and t. This can be proven by the definition of divisibility: if a number, in this case n, is divisible by an integer, in this case s or t, then the product of that number and another integer, in this case t or s, is also divisible by the initial integer.
For example, if n = 24, s = 4, and t = 3, we can see that 4 and 3 are factors of 24, since 24 is divisible by 4 and 3. The product of 24, 4 and 3 is 2443 = 288. 288 is also divisible by 4 and 3.
In summary, if s and t are integers greater than 1 and each is a factor of the integer n, then s and t must be factors of nst.
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Kazuko says the expressions 5x and 6 - x are equivalent expressions, because you
can substitute 1 for x in both expressions and get the same result. Is Kazuko's
reasoning correct? Explain.
Answer:
Yes, Kazuko's reasoning is correct
Step-by-step explanation:
If u substitute 1 in place of x in both expressions, they both equal 5 when solved
Let D(p) be the number of iced cappuccinos sold each week by a coffeehouse when the price is p cents.
a) What does the expression D(225) represent?
b) Do you think that D(p) is an increasing function or a decreasing function? Why?
c) What does the following equation tell you about p? D(p)=180
d) The coffeehouse sells n iced cappuccinos when they charge the average price in their area,
t cents. Thus, D(t)=n . What is the meaning of the following expressions: D(1.5t), 1.5D(t), D(t+50), D(t)+50?
a) The expression D(225) represents the number of iced cappuccinos sold each week by a coffeehouse when the price is 225 cents.
b) Whether D(p) is an increasing or decreasing function depends on the relationship between the price of iced cappuccinos and the number sold. If the price of iced cappuccinos increases, the number sold may decrease (decreasing function) or if the price of iced cappuccinos decreases, the number sold may increase (increasing function) . It's possible that the coffeehouse has made a market research and they know what is the best price for their iced cappuccinos.
c) The equation D(p) = 180 tells you that the coffeehouse sells 180 iced cappuccinos each week when the price is p cents.
d) D(1.5t) represents the number of iced cappuccinos sold each week when the price is 1.5t (1.5 times the average price in the area). 1.5D(t) represents the number of iced cappuccinos sold each week when the price is the average price in the area multiplied by 1.5. D(t+50) represents the number of iced cappuccinos sold each week when the price is t+50 (50 cents more than the average price in the area). D(t)+50 represents the number of iced cappuccinos sold each week when the price is the average price in the area plus 50.
It's important to note that all these expressions doesn't give us any information about the relation between price and quantity sold, they just give us the value of the function for specific values of p.
Write one and four hundredths in standard form.
Answer:
The answer is 1.04
Step-by-step explanation
For 1.04, 4 is in the hundredths place, and 0 is in the tenths place.
