Solution
we are given the two linear equations
First Equation
[tex]\begin{gathered} -2x+y=3 \\ \\ y=2x+3 \end{gathered}[/tex]Second Equation
[tex]y=-\frac{1}{2}x-2[/tex]Let mA and mB denotes the gradient of the first and second equation respectively written as
[tex]m_A\text{ and }m_B[/tex]Using the slope - intercepty form, one can see that
[tex]\begin{gathered} m_A=2 \\ \\ m_B=-\frac{1}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} m_A\times m_B=2\times-\frac{1}{2} \\ \\ m_A\times m_B=-1 \end{gathered}[/tex]Therefore, the lines are Perpendicular
Option B
adratic Equations to Fi... m You Try! As a Visual Example C: A rectangle has a length that is 3 meters more than twice the width. The area of the rectangle is 44 square meters. Find the dimensions of the rectangle. Sketch a visual of this problem below. 1
Let l be the length and w be the width of the rectangle.
Then the statement: "length that is 3m more than twice the width" becomes
l = 2w + 3
The area of a rectangle is length times width
Therefore
[tex]\begin{gathered} l\times w=44m^2 \\ \Rightarrow w(2w+3)=44 \\ \Rightarrow2w^2+3w-44=0 \\ \end{gathered}[/tex]Factorising the quadratic equation, we have:
[tex]\begin{gathered} 2w^2+11w-8w-44=0 \\ \Rightarrow w(2w+11)-4(2w+11)=0 \\ \Rightarrow(w-4)(2w+11)=0 \\ \Rightarrow w=4\text{ or -5.5} \end{gathered}[/tex]Since w cannot be negative, then the only possibility is:
w=4
since l = 2w+3, then
l=2(4)+3=8+3=11
Hence the length is 11m and the width is 4m
5. The following data set is given:766870717273686974657169746473Construct a dot plot:6465666768697071727374757612Clear All Draw: Dot
To construct the data plot, count how many times each number appears in the table. This is the same as the frequency of each number in the table:
[tex]\begin{gathered} 64\rightarrow1 \\ 65\rightarrow1 \\ 68\rightarrow2 \\ 69\rightarrow2 \\ 70\rightarrow1 \\ 71\rightarrow2 \\ 72\rightarrow1 \\ 73\rightarrow2 \\ 74\rightarrow2 \\ 76\rightarrow1 \end{gathered}[/tex]Draw a dot on each number with the same height as the corresponding frequency:
Please help me with the question below (also please explain).
To find the surface area of the given figure identify all the faces on the figure, calculate the area of each face and then sum the areas:
Measures in red
Number of faces in green, total faces 9
Area of a triangle:
[tex]A=\frac{1}{2}bh[/tex]Area of a rectangle:
[tex]A=bh[/tex]Area of faces 1 and 2(rectangles):
[tex]\begin{gathered} A_1=A_2=20in*11in \\ A_1=A_2=220in^2 \end{gathered}[/tex]Area of faces 3 and 4 (triangles):
[tex]\begin{gathered} A_3=A_4=\frac{1}{2}(12in)(9in) \\ \\ A_3=A_4=54in^2 \end{gathered}[/tex]Area of faces 5 and 6 (rectangles):
[tex]\begin{gathered} A_5=A_6=12in*5in \\ A_5=A_6=60in^2 \end{gathered}[/tex]Area of faces 7 and 8 (rectangles):
[tex]\begin{gathered} A_7=A_8=20in*5in \\ A_7=A_8=100in^2 \end{gathered}[/tex]Are of face 9 (rectangle):
[tex]\begin{gathered} A_9=20in*12in \\ A_9=240in^2 \end{gathered}[/tex]Total surface area:
[tex]\begin{gathered} SA=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8+A_9 \\ \\ SA=220in^2+220in^2+54in^2+54in^2+60in^2+60in^2+100in^2+100in^2+240in^2 \\ \\ SA=1108in^2 \end{gathered}[/tex]Then, the surface area of the given figure is 1108 square inches) From the example below, choose the Independent quantity and dependent quantity. An increase in cardio exercise results in a decrease in weight. independent quantity dependent quantity
In order to identiy which is the dependet quantity and independent quantity, you consider that an independent quanity is that quantity does not depend of any other. Insteas of that, dependent quantity depends of the values of other quantity.
In the given case, you have that an increase in cardio exercise results in a decrease in weight. In this case you can notice that the weight depends of the cardio exercide. Hence, cardio exercise is the independent quantity, and weitgh is the dependent quantity.
5. (a) The bar graph below shows the favourite colour by a class of students. Favourite Colour 5 Number of Students 1 GA Yal Calour (1) Given that twice as many students like blue than red, how many students like blue? [1] Using the information found in part (a) (1), complete the bar graph above. [1] (iii) Calculate the number of students in the class. (iv) What percentage of students like pink? [1]
ANSWER
8 students like the blue color
we have a total number of 30 students in the class
The percentage of students who like pink is 16.67%
STEP-BY-STEP EXPLANATION:
Given information
From the graph provided, we can deduce the below information
4 students like red
7 students like green
6 students like yellow
5 students like pink
Step 1: Find the number of students who like the blue color?
Let the number of students that like blue be b
Since twice as many students like blue than red, then we can determine the number of students who like blue color using the below expression.
b = 2r
Red = r = 4 students
b = 2 x 4
b = 8 students
Hence, 8 students like the blue color
Part C: Find the total number of students in class
The total number of students can be calculated by summing all the students that love the different colors
Total students in the class = 4 + 7 + 6 + 5 + 8
Total students in the class = 30 students
Hence, we have a total number of 30 students in the class
Part D: What percentage of students like pink
We can calculate the number of students that like pink using the below formula
[tex]\text{ \% of students that like pink = }\frac{\text{ number of students that like pink color}}{\text{total numebr of the students}}\times\text{ 100\%}[/tex]Recall, the number of students who like pink is 5, and the total number of students is 30
[tex]\begin{gathered} \text{ \% of students who like pink = }\frac{5}{30}\times100\text{ \%} \\ \text{ \% of students who like pink = 0.166667 }\times100\text{ \%} \\ \text{ \% of students who like pink = 16.67 \%} \end{gathered}[/tex]Hence, the percentage of students who like pink is 16.67%
8) M is the midpoint of LN LM = 5x+4 and MN = 12x-24. What is the value of x?What is the length of LN?MNLN
Solution
For this case we know that M is the midpointof the line LN
And we also know that:
LM= 5x+4 , MN= 12x-24
Then we can find the value of x using this equation:
LM = MN (By definition of midpoint)
Replacing we got:
5x+4= 12x-24
Solving we have:
4+24 = 12x -5x
28 = 7x
x= 28/7= 4
And solving for LN we got:
LN= LM + MN
LM= 5*4+4= 24
MN= 12*4 -24=24
Then:
LN= 24+24= 48
I just wanted to make sure that my answer is correct.I have to find the reference angle given the degree.
Answer:
[tex]\text{ 80}\degree[/tex]Explanation:
Here, we want to get the reference angle of the angle given
The reference angle is simply the acute angle that corresponds to the given angle
Since the angle is negative, we have to add multiples of 360 degrees until we get an acute angle
Mathematically, we have this as:
[tex]\text{ -13600 + 360(38) = 80}\degree\text{ }[/tex]fill in the blanks of the x and y chart using the equation : 8x -4y=16chart x: _,0,3,_y: 0,_,_,2
Chart x: 2,0,3,3
Chart y: 0,-4,2,2
24) A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population, p, grows as a linear function of time t, where t is the number of years after 2003. Part B: Find a linear function that relates the student population to the time.
The population of the student is a linear function with respect to time.
Let population be "p" and time be "t", thus we can write general form of the equation as:
[tex]p=mt+b[/tex]Where
m is the slope
b is the y-intercept
of the line...
Let's take the year 2003 at t = 0.
So,
2004 would be t = 1
2005 would be t = 2
2006 woud be t = 3
We have population of 1200 at the base year 2003, thus a coordinate pair of point (t, p) will be (0, 1200).
We have a population of 1500 in 2006, thus a coordinate pair of point (t, p) will be (3, 1500).
We have two points:
(0, 1200)
(3, 1500)
Let's calculate the slope, which is the rate of change of p with respect to t.
Change in p = 1500 - 1200 = 300
Change in t = 3 - 0 = 3
Rate of Change = 300/3 = 100
This is the slope, or m.
Thus, the equation will be:
[tex]p=100t+b[/tex]To find b, we can use the point (t,p) = (0, 1200). So,
[tex]\begin{gathered} p=100t+b \\ 1200=100(0)+b \\ b=1200 \end{gathered}[/tex]The correct equation will be:
[tex]p=100t+1200[/tex]Matching with answer choices, it is First Option, f(x) = 100x + 1200
I need help with this, it’s from my trig prep guide.It asks to answer (a) and (b) But please put these ^ separately so I know which is which
Part (a).
Sigma notation (or summation notation) of binomial expansion is the following:
[tex](w+z)^n=\sum ^n_{k\mathop=0}\binom{n}{k}w^{n-k}\cdot z^k[/tex]where
[tex]\binom{n}{k}[/tex]denotes the binomial coefficient.
In our case, n is 4 and
[tex]\begin{gathered} w=3x^5 \\ z=-\frac{1}{9}y^3 \end{gathered}[/tex]So by substituting these terms into the sigma expantion, we have
[tex](3x^5+(-\frac{1}{9}y^3))^4=\sum ^4_{k\mathop{=}0}\binom{4}{k}(3x^5)^{4-k}\cdot(-\frac{1}{9}y^3)^k[/tex]So, the sum in summation notation is:
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}\binom{4}{k}(3x^5)^{4-k}\cdot(-\frac{1}{9}y^3)^k[/tex]Part b.
By expanding the above sum, we have
[tex]\begin{gathered} (3x^5-\frac{1}{9}y^3)^4=\binom{4}{0}(3x^5)^4\cdot(-\frac{1}{9}y^3)^0+\binom{4}{1}(3x^5)^3\cdot(-\frac{1}{9}y^3)^1+\binom{4}{2}(3x^5)^2\cdot(-\frac{1}{9}y^3)^2+ \\ \binom{4}{3}(3x^5)^1\cdot(-\frac{1}{9}y^3)^3+\binom{4}{4}(3x^5)^0\cdot(-\frac{1}{9}y^3)^4 \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \binom{4}{0}=1 \\ \binom{4}{1}=4 \\ \binom{4}{2}=6 \\ \binom{4}{3}=4 \\ \binom{4}{4}=1 \end{gathered}[/tex]we have
[tex](3x^5-\frac{1}{9}y^3)^4=(3x^5)^4+4(3x^5)^3\cdot(-\frac{1}{9}y^3)^{}+6(3x^5)^2\cdot(-\frac{1}{9}y^3)^2+4(3x^5)^1\cdot(-\frac{1}{9}y^3)^3+(-\frac{1}{9}y^3)^4[/tex]which gives
[tex](3x^5-\frac{1}{9}y^3)^4=81x^{20}-12x^{15}\cdot y^3+\frac{6}{9}x^{10}\cdot y^6-\frac{12}{729}x^5\cdot y^9+\frac{1}{6561}y^{12}[/tex]Therefore, the simplified expansion is given by:
[tex](3x^5-\frac{1}{9}y^3)^4=81x^{20}-12x^{15}\cdot y^3+\frac{2}{3}x^{10}\cdot y^6-\frac{4}{243}x^5\cdot y^9+\frac{1}{6561}y^{12}[/tex]entsDrag the slider to 3 centimeters.The ratio of centimeters to inches is 3 centimeters toinches.
So, 3 cm corresponds to 1.81 inches
1) Considering that
1 inch ----- 2. 54 cm
2) Let's make this conversion by a simple Rule of three
1 inch ------ 2.54 cm
i -------- 3 cm
2.54i=3*1
Divide both sides by 2.54
[tex]\begin{gathered} i=\frac{3}{2.54}\text{ } \\ i\text{ =1}.81 \end{gathered}[/tex]3) So, 3 cm corresponds to 1.81 inches
O 12 Ms. Ruby has 1 beanbag chair in her room. She lets 4 students take equal turns sitting in the chair during a 38-minute reading period. How long is each student's turn in the beanbag? * O 1/4 minutes O 4/1 minutes 4/28 minutes O 38/4 minutes
The number of students allowed to sit, N=4.
The total number of minutes, T=38 minutes.
Let x be the number of minutes for a student
[tex]\begin{gathered} 4\text{ students-}\longrightarrow38\text{ minutes} \\ 1\text{ student--x} \\ \text{Cross multiplying,} \\ x=\frac{38\text{ minutes}}{4\text{ students}}\times1\text{ students} \\ =\frac{38}{4\text{ }}\text{minutes} \end{gathered}[/tex]can someone explain to me how to solve -8+(-4)
when you have an opperation as:
[tex]-a+(-b)[/tex]You have to use the next statments:
[tex]+(+b)=+b[/tex][tex]+(-b)=-b[/tex][tex]-(-b)=+b[/tex]You can follow the next image:
Then the answer will be:
[tex]-8+(-4)=-8-4=-12[/tex]The result is - 12
12. Graph the function. Label the vertex and axis of symmetry. State the domainand range. Then describe where the function is increasing and decreasing. *f(x) = {(x – 1)2 +3
we have
f(x)=(1/2)(x-1)^2+3
this is a vertical parabola open upward
the vertex is a minimum
the vertex is the point (1,3)
the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
the axis of symmetry is x=1
The domain of any parabola is all real numbers
Domain (-infinire, infinite)
The range is the interval {3, infinite)
The function is increasing at the interval (1, infinite)
The function is decreasing at the interval (-infinite, 1)
see the attached figure to better understand the problem
please wait a minute
what number is halfway between 82 and 28 on the number line?
To find the number that is in the halfway between two numbers, we just need to find the average of the two numbers, that is, we sum the numbers and divide by two.
For example, we know that the number halfway between 1 and 3 is the number 2, so we would have:
[tex]\text{halfway number = }\frac{(1+3){}}{2}=\frac{4}{2}=2[/tex]So, if we want to find the halfway number between the numbers 82 and 28, we have that:
[tex]\text{halfway number = }\frac{(82+28){}}{2}=\frac{110}{2}=55[/tex]So the answer is 55.
Hope it helps!
data =(type an integer or a decimal. use a comma to separate answers as needed )
From the following picture:
we can find the values for the trigonometric functions for values as 30 and 60 degrees.
For instance, tan 30 is equal to
[tex]\tan 30=\frac{1}{\sqrt[]{3}}[/tex]Since
[tex]\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}[/tex]then,
[tex]\tan 30=\frac{\sqrt[]{3}}{3}[/tex]However, we have a minus sign, this imply the angle is negative. In other words,
[tex]\tan -30=-\frac{\sqrt[]{3}}{3}[/tex]Now, since -30 = 330, then we have
[tex]\tan 330=-\frac{\sqrt[]{3}}{3}[/tex]so the answer is
[tex]\theta=330\text{ }[/tex]does (-43, 4) make the equation y = -43 true?
No, (-43, 4) does not make the equation
What is the slope of the of the linerepresented by y = 6x - 7?
The line is represented by the equation
y = 6x - 7
The equation has been presented in the slope-intercept form and that is expressed as
y = mx + b
Where the value of m is the slope of the line.
The value of m in the above equation is 6. The slope of the line is 6. Or better expressed as follows;
The slope is m = 6
Match the given slope (m) and y-intercept (b) with the equation of the line in slope-Intercept form.Slope, m = 2. y-intercept, b = 5DRAG & DROP THE ANSWERSlope, m = 3, y-intercept, b = 5y = 50 +3Slope, m = 5, y-intercept, b = 4y = 2r + 5y = 5x + 2y = 3x + 5y = 5x +4
We have the following:
We have that an equation in the form the slope-intercept has the following form
[tex]y=mx+b[/tex]where, m is the slope and b is the intersect
Therefore,
1.
Slope, m = 2. y-intercept, b = 5
The equation is:
[tex]y=2x+5[/tex]2.
Slope, m = 3, y-intercept, b = 5
The equation is:
[tex]y=3x+5[/tex]3.
Slope, m = 5, y-intercept, b = 4
The equation is:
[tex]y=5x+4[/tex]I need help pls help
Multiply both sides by w:
[tex]8=(\frac{56}{105})w[/tex]multiply both sides by 105:
[tex]\begin{gathered} 8\cdot105=56w \\ 840=56w \end{gathered}[/tex]Divide both sides by 56:
[tex]\begin{gathered} w=\frac{840}{56} \\ w=15 \end{gathered}[/tex]Engine Size: The size of an engine is a measure of volume. To calculate the size of an engine is to find the volume of a cylinder and multiply by the number of cylinders. The size of a cylinder is given as a bore size, or diameter, and a stroke size, or height, of the cylinder.
Hello there.
To answer this question, we'll use the information given by the question: the size of the cylinder given by the bore measure, the height given by the stroke size and the volume of the engine will be found multiplying that measure by the number of cylinders;
First, we'll find the size of a cylinder:
Given the bore size and the height, we can calculate the volume of just one cylinder, using the formula: pi * r^2 * h or pi * (d/2)^2 * h.
In this case, knowing that the bore size is equal to the diameter, we'll use the second formula:
pi * (4.25/2)^2 * 3.76
Using the approximation for pi, we get: 53,313275 in³
Now, multiplying by the number of cylinders, we get: 426,5062 in³.
Rounding up to the nearest hundreth, we may get 426.50 in³.
How do I graph a polar equation for r^2=4cos3theta and find the points for it ? my teacher said i got this question wrong and i want to understand, thank you.
We have the followiing:
[tex]\begin{gathered} r^2=4\sin 3\theta \\ r=-\sqrt[]{4\sin3\theta}=-2\sqrt[]{\sin 3\theta} \\ r=\sqrt[]{4\sin 3\theta}=2\sqrt[]{\sin3\theta} \end{gathered}[/tex]Part BSales associates at an electronics store eam different commissionpercentages based on the items they sell. The table shows the totalsales and commission earnings for four sales associates at theelectronics store last month.Electronics Store Sales and CommissionsTotal SalesCommissionEarnings5673$22$1.298$37$3,277S101$5.180$150The table below shows the total sales of two sales associates at theelectronics store last month.Electronics Store SalesSales TotalAssociate SalesJon $2,881Tia $4,163Use the model you created in Part A to estimate how much moremoney, in dollars, Tia eamed in commission than Jon. Show orexplain your workEnter your answer and your work or explanation in the boxprovided
From the table shown:
we need to find the relationship between the commission earnings and the total sales
John's sales = $2881
Tia's sales = $4163
Note that:
$2881 falls between $1298 and $3277
Using the extrapolation formula:
[tex]\begin{gathered} Y(x)\text{ = Y(1) + }\frac{x-x(1)}{x(2)-x(1)}\times\text{ \lbrack{}Y(2)-Y(1)\rbrack} \\ 2881\text{ = 1298 + }\frac{x-37}{101-37}\times\lbrack3277-1298\rbrack \\ 51.2\text{ = x - 37} \\ x\text{ = 51.2 + 37} \\ x\text{ = 88.2} \end{gathered}[/tex]Jon's commission = $88.2
For Tia's commission:
How many 1 × 2 shelf cleats 8″ a 1 × 2 board 16′ long can be cut from long? How much is left? (Disregard waste in saw cut.)
Using simple mathematical operations, 2 (1 × 2, 8in long) shelves can be obtained from (1 × 2, 16in long) with no cleats being left.
In this question, we need to find the number of 1 × 2 shelf cleats 8″ a 1 × 2 board 16′ long can be cut from long.
A number of shelves that can be cut:
Shelf size that needs to be obtained: 1 × 2, 8in long
Shelf size from which to obtain: 1 × 2, 16in long
Now, calculate as follows:
16/8 = 2
and the remainder = 0
Since, the remainder is 0, then no cleat is left over.
Therefore, using simple mathematical operations, 2 (1 × 2, 8in long) shelves can be obtained from (1 × 2, 16in long) with no cleats being left.
Know more about mathematical operations here:
https://brainly.com/question/8959976
#SPJ1
Graph using the slope intercept formula 4y+x=12
Graph using the slope intercept formula 4y+x=12
we know that
the equation of the line in slope intercept form is equal to
y=mx+b
so
isoalte the variable y in the given equation
4y=-x+12
divide by 4 both sides
y=(-1/4)x+12/4
y=(-1/4)x+3+
To graph the line, we need two points
Find the intercepts
Y- intercept (value of y when the value of x is equal to zero)
this value is given
b=3
y-intercept is (0,3)
X-intercept (value of x when the value of y is equal to zero)
For y=0
0=(-1/4)x+3
(1/4)x=3
x=12
the x-intercept is (12,0)
we have the points (0,3) and (12,0)
using a graphing tool, plot the points, join them and graph the line
see the attached figure
please wait a minute
using a graphingor
vo zequa
What is the surface area of the cone to the nearest tenth? The figure is not drawn to scale.thank you ! :)
To calculate the surface area of a cone we can use the following formula:
[tex]S=\pi r^2+\pi Lr[/tex]where r represents the radius of the base and L represents the slant height.
The radius of our cone is 7cm and the slant height 19cm, using those values on the formula we have our answer:
[tex]S=\pi(7)^2+\pi(19)(7)=49\pi+133\pi=182\pi\approx571.8[/tex]The surface area of this cone is 571.8 cm².
Bisector / Midpoint/Vertex on DiagramJol 28, 10:36:34 AM?Which of the following statements must be true based on the diagram below?(Diagram is not to scale.)PRRS is a segment bisector.ORS is a perpendicular bisector.oS is the vertex of a pair of congruent angles in the diagram.o R is the midpoint of a segment in the diagram.S is the midpoint of a segment in the diagram.None of the above.
From the figure in the question,
Since PR = RQ, Then
The line RS divides the line segment PQ into two equal halves
Hence
[tex]\bar{RS}\text{ is a segment bisector}[/tex]Also, the angle at R is 90 degree
Therefore line RS is perpendicular to line PQ
Hence
[tex]\bar{RS}\text{ is a perpendicular bisector}[/tex]Also,
since PR = RQ
Then, R is the mid-point of PQ
Hence
[tex]R\text{ is the midpoint of a segment in the diagram}[/tex]Therefore
The following are the corrcet answers
1. Line RS is a segment bisector
2. Line RS is a perpendicular bisector
3. R is the midpoint of a segment in the diagram
Find the slope of the line that passes through the pair of points listed below.(1, 0) , (-4, 2)
Answer:
[tex]m\text{ = -}\frac{2}{5}[/tex]Explanation:
Here, we want to calculate the slope of the line that passes through the given points
Mathematically, we have that as:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]where:
(x1,y1) = (1,0)
(x2,y2) = (-4,2)
Substituting the values, we have:
[tex]m\text{ = }\frac{2-0}{-4-1}\text{ = -}\frac{2}{5}[/tex]Ariella is a full-time sales associate at a clothing store. She earns a weekly salary of $275 and earns 15% commission on all of her sales. Create a model of this situation to represent the amount of money Ariella makes after x dollars in sales.Step 1 of 3 : What is the y-intercept and what does the y-coordinate of the y-intercept represent?Step 2 of 3 : What is the slope and what does this value represent?Step 3 of 3 : Write an equation in slope-intercept form to model this situation.
Since x represents the total amount of dollars in Ariella's sales, and she earns a commission of 15% over her sales, then multiply x by 15/100 to find the commision that Ariella earns:
[tex]\frac{15}{100}x=0.15x[/tex]She earns a salary of $275 additional to the comission for her sales. Then, the model that represents the amount of money that Ariella makes after x dollars in sales is:
[tex]y=0.15x+275[/tex]Step 1:
The y-intercept is the value of y when x=0. It can be identified in the equation as the constant term, in this case, 275. The ordered pair (0,275) represents the point in the coordinate plane where the graph of y=0.15x+275 intercepts the Y-axis.
Therefore, the y-intercept is (0,275) and the y-coordinate represents Ariella's base weekly salary.
Step 2:
The slope is the coefficient of the variable x. In general, it represents the rate of change of the variable y with respect to x, i.e. the amount by which the variable y increases when x increases 1 unit. In the context of the problem, we can see that it represents the commission rate.
Therefore, the slope is 0.15 and it represents the commission rate that Ariella gets for her sales.
Step 3:
The equation of a line with slope m and y-intercept b in slope-intercept form is:
[tex]y=mx+b[/tex]As explained above, the slope for this model is 0.15 and the y-intercept is 275.
The equation shown in the beginning of the explanation was already written in slope-intercept form.
Therefore, the quation in slope-intercept form that models this situation is:
[tex]y=0.15x+275[/tex]
Calculate the volume of water in the cup when it is full
To find:
The volume of the water in the cup when it is full.
Solution:
The volume of the water is equal to the difference of the volume of the small cone and the larger cone.
Here, the ratio of the radius of both cones is equal to the ratio of their heights. SO,
[tex]\begin{gathered} \frac{r}{2.7}=\frac{20}{20-8} \\ \frac{r}{2.7}=\frac{20}{12} \\ \frac{r}{2.7}=\frac{5}{3} \\ r=4.5 \end{gathered}[/tex]The radius of the larger cone is 4.5 cm.
So, the volume of the water is:
[tex]\begin{gathered} V=\frac{1}{3}\pi R^2H-\frac{1}{3}\pi r^2h \\ =\frac{1}{3}\pi(R^2H-r^2h) \\ =\frac{1}{3}\pi((4.5)^2(20)-(2.7)^2(12)) \\ =\frac{1}{3}\cdot\frac{22}{7}(405-87.48) \\ =\frac{22}{21}(317.52) \\ =332.64cm^2 \end{gathered}[/tex]The volume of water when the cup is full is 332.64 cm^2.