how to graph y=-8/3x+9
Answers
2.000
5.333
=−2.667
x−intercept=
8
27
=3.37500
y−intercept=
3
27
=9
Step-by-step explanation:
this is the equation for a line in slope-intercept form
the y-intercept is 9, so find (0,9) on the graph
then, the slope is -8/3 (think "rise" over "run"), so from the point (0,9) you have to count down 8 (for -8) and then to the right 3 (for +3). from this point, you can now repeat the pattern of counting down 8 and right 3 and making points to connect.
when at least two points are connected, you have a line and that is your graph
Related Questions
The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface area generated is
A=8/3π√a[(h+a)³/²-a³/2]
Use the result to find the value of h if the parabola y²=36x when revolved about the x-axis is to have surface area 1000.
Answers
Answer:
See below for Part A.
Part B)
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
Step-by-step explanation:
Part A)
The parabola given by the equation:
[tex]y^2=4ax[/tex]
From 0 to h is revolved about the x-axis.
We can take the principal square root of both sides to acquire our function:
[tex]y=f(x)=\sqrt{4ax}[/tex]
Please refer to the attachment below for the sketch.
The area of a surface of revolution is given by:
[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]
Where r(x) is the distance between f and the axis of revolution.
From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:
[tex]r(x)=y(x)=\sqrt{4ax}[/tex]
Now, we will need to find f’(x). We know that:
[tex]f(x)=\sqrt{4ax}[/tex]
Then by the chain rule, f’(x) is:
[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]
For our limits of integration, we are going from 0 to h.
Hence, our integral becomes:
[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]
Combine roots;
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]
Integrate. We can consider using u-substitution. We will let:
[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]
We also need to change our limits of integration. So:
[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]
Hence, our new integral is:
[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]
Simplify and integrate:
[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
FTC:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]
Simplify each term. For the first term, we have:
[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]
We can factor out the 4a:
[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
For the second term, we have:
[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =(2a)^3[/tex]
Hence:
[tex]\displaystyle =8a^3[/tex]
Thus, our equation becomes:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]
We can factor out an 8a^(3/2). Hence:
[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Hence, we have verified the surface area generated by the function.
Part B)
We have:
[tex]y^2=36x[/tex]
We can rewrite this as:
[tex]y^2=4(9)x[/tex]
Hence, a=9.
The surface area is 1000. So, S=1000.
Therefore, with our equation:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
We can write:
[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]
Solve for h. Simplify:
[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]
Divide both sides by 8π:
[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]
Isolate term:
[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]
Raise both sides to 2/3:
[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]
Hence, the value of h is:
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
You seem to have left out that 0 ≤ x ≤ h.
From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is
[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]
We have
y(x) = 2√(ax) → y'(x) = 2 • a/(2√(ax)) = √(a/x)
so the integral is
[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]
[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]
[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]
[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]
Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :
[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]
[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]
[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]
[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]
[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]
PLease im almost out of time
Answers
There is no question so currently, I am unable to help you.
Question 3 of 5
Which fraction and decimal forms match the long division problem?
SO
tele
OAS 0.50
OR S and 0.58
OGS and 0.58
OS and 0.58
I NEES HELP plz
Answers
Answer:
8/15= 0.533
Step-by-step explanation:
8 divided by 15 isn't possible so according to the rules of division we introduce a (0.) then we add a (0) to the back of (8) to make it (80) which is bigger than (15) so we now have (80/15) which is (5) remaining (5) then we add the back of the (0.) it then becomes (0.5) we then step down the remaining (5) and also add a (0) at the back to make it (50) which is also bigger than (15) (50/15) which gives us (3) and a remaining (5) add (3) to the back of (0.5) to become (0.53) also still step down the remaining (5) add a zero to it to become (50) still divide by (15) gives (3) and remains (5) and it gives the same answer so it is a reoccurring decimal.
Thank you hope I was of help!!
Drag the missing word into place
swhen they enter the balls throw
Or you run real quick to get home
Solar
ENGTE
Kinetic
Answers
Answer:
kinetic energy
Step-by-step explanation:
When a person runs, their body must convert potential energy into kinetic energy.
Buster needs to find x and y in the following system.
Equation A: - 8x + 14y = 10
Equation B: 4x + 3y = 25
Buster decided to use elimination to solve this system. Do you agree or disagree? Why
Answers
Answer:
U GO TO DHS
Step-by-step explanation:
Bags of pretzels are sampled to ensure proper weight. The overall average for the samples is 9 ounces. Each sample contains 25 bags. The standard deviation is estimated to be 3 ounces. The upper control chart limit (for 99.7% confidence) for the average would be ________ ounces.
Answers
Answer:
The value is [tex]UCL = 10.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 9 \ ounce[/tex]
The sample size is n = 25
The standard deviation is [tex]\sigma = 3 \ ounce[/tex]
Given that the sample size is not large enough i.e n< 30 we will make use of the student t distribution table
From the question we are told the confidence level is 99.7% , hence the level of significance is
[tex]\alpha = (100 -99.7 ) \%[/tex]
=> [tex]\alpha = 0.003[/tex]
Generally the degree of freedom is [tex]df = n- 1[/tex]
=> [tex]df = 25 - 1[/tex]
=> [tex]df = 24[/tex]
Generally from the student t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24[/tex] is
[tex]t_{\frac{\alpha }{2} , 24 } = 3.0 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 24} * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 3.0 * \frac{3 }{\sqrt{25} }[/tex]
=> [tex]E =1.8 [/tex]
Gnerally the upper control chart limit for 99.7% confidence is mathematically represented as
[tex]UCL = \= x + E[/tex]
=> [tex]UCL = 9 + 1.8[/tex]
=> [tex]UCL = 10.8[/tex]
Find the 5th term of the following sequence:
f(n) = 3(-2)"
Answers
Answer:
42
Step-by-step explanation:
uih
|7-8| • 4 + 3 (-1) ???????
Answers
Answer:
1
Step-by-step explanation:
|7-8| • 4 + 3 (-1) =
= |-1| • 4 + (-3)
= 1 • 4 - 3
= 4 - 3
= 1
What is the slope of a line that passes through the following points (4, 6) and (2, 0)?
Answers
Answer:
3
Step-by-step explanation:
Step-by-step explanation:
formula to fine slope
m=tan()=y2-y1/x2-x1
3. To make purple frosting, you start with white frosting.
Then you add 2 drops of red food coloring and 3 drops of
blue food coloring. If 4 red drops come out with the first
squeeze, how many blue drops should you add?
Answers
==================================================
Explanation:
We basically mix red and blue to get purple. The ratio needed is 2 parts red, and 3 parts blue. We can shorten this by writing 2:3
Note how we can double both parts of the ratio to get 4:6, showing that 4 drops of red correspond to 6 drops of blue, which is the answer we want.
------------------
Another approach:
x = some positive real number
(2 parts red)/(3 parts blue) = (4 parts red)/(x parts blue)
2/3 = 4/x
2x = 3*4 .... cross multiply
2x = 12
x = 12/2 .... divide both sides by 2
x = 6
So 6 drops of blue go with 4 drops of red.
Use the Distributive Property to expand the expression -3(6.3x + 1.5y)
Answers
Answer:
(-3*6.3x)+(-3*1.5y)
(-18.9x)+(-4.5y)
You need to purchase supplies for an employee appreciation picnic. Your boss gives you the shopping list below and asks that you get the best deal by buying from one grocer, either Quality Groceries or Fresh Market. You call both grocers, and they provide the price information that you put into the table. Which grocer will provide all these picnic supplies for the lowest cost, and what is that cost without sales tax?
Hamburger Patties 50
Hot Dogs 2 dozen
Hamburger Buns 50
Hot Dog Buns 2 dozen
Potato Salad 2 gallons
Ice Cream 5 gallons
Product Quality Groceries Unit Quality Groceries Price per Unit Fresh Market Unit Fresh Market Price per Unit
Hamburger Patties Package of 10 $15.50 Package of 8 $12.40
Hot Dogs Package of 12 $6.23 Package of 10 $4.99
Hamburger Buns Package of 8 $3.79 Package of 8 $3.55
Hot Dog Buns Package of 12 $2.75 Package of 8 $2.55
Potato Salad Gallon $4.33 Gallon $5.55
Ice Cream Gallon $7.55 Gallon $6.99
Answers
Answer:
this doesnt make sense is there any type of picture or more explanation on the question? i'll still help :)
Step-by-step explanation:
6.2x1015 (the 15 is above the 10)
Answers
Answer:
9.3
Step-by-step explanation:
6.2 x 15/10= 9.3
Answer:
Scientific notation is 1.6 x 10^16 and in regular format is:
160000000000000000
How much simple interest does $5,000 earn in 4 years at an interest rate of 5%. Round to
the nearest cent.
Answers
Answer:
1000
Step-by-step explanation:
A rhombus is not a
a. polygon. c. trapezoid.
b. parallelogram. d. quadrilateral.
Answers
Answer:
polygon
Step-by-step explanation:
A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. A rhombus has 4 sides.
Hope this helps:) Have a great day!
Need help asap in a hurry, please. Doing a budget The gross income is $54,000.
Answers
This package of sliced cheese costs $2.97, How much would a package with 18 slices cost at the same price per slice
Answers
Answer:
Cant you just type that in the calculator 18 times lol
Step-by-step explanation:
use a calculator
The mass of a textbook is 1.25 kg about how many pounds is this
Answers
Answer:
2.755778
Step-by-step explanation:
Just search how much pounds is 1.25 kg?
0 = 4 + n/5 two step equations
Answers
Answer: n= -20?
Step-by-step:
Simplify both sides of the equation
1/5n+4=0
Then subtract 4 from both sides
1/5n + 4 - 4 = 0 - 4
1/5n= -4
Then multiply both sides by 5
5*(1/5n)=5*(-4)
Answer:
0=n
Step-by-step explanation:
1. 0=4+n/5
add 4 and n
2. 0=4n/5
×5. ×5
3. 0=4n
-- --
4 4
4. 0=n
Look at the picture for a more detailed steps
please answer 44 mins remaining
Answers
Answer:
y=x-2
Hope this helps.
hope you get it right.
Which of the following numbers is closest to 11?
O A. 7123
B. V115
O c. 118
O D. 120
Answers
Answer:
the answer is D
Step-by-step explanation:
A. √123 = 11.09
11.09-11 = 0.09
B. √115 = 10.72
11-10.72 = 0.28
C. √118 = 10.86
11-10.86 = 0.14
D. √120 = 10.95
11-10.95 = 0.05 ( the smallest difference )
Carmen quiere invertir 700 dólares, de tal forma que en
90 días le produzca 63 dólares de interés simple.
¿Que tasa de interés debe elegir?
Answers
La fórmula de interés simple, nos permite calcular I, que es el interés ganado o pagado de un préstamo. Según esta fórmula, la cantidad de interés está dada por I = C·i·t, donde C es el capital, i es la tasa de interés anual en forma decimal, y t es el período de tiempo expresado en años Tenemos que:
C = 700 dólares
i = ???
t = 90/360 = 0.25 (Expresado en años)
I = C*i * t
i = I / C*t
i = 63/ (0.25*700)
i = 0.36
R/ Debe elegir una tasa de interés de 36% anual.
The interest on the amount invested for 90days given $63 as interest is 36.5%
Simple interest is the amount of money added to money invested. It is calculated as:
[tex]SI = \frac{PRT}{100}[/tex]
P is the amount invested (principal) = $700
R is the rate
T is the time (in years) = 90/365
SI is the interest = $63
Substitute the given values into the formula
[tex]63=\frac{700 \times R \times 90}{365 \times 100}\\63=\frac{63000R}{36500}\\63= 1.72602R\\R=36.5\%[/tex]
This shows that the interest on the amount invested for 90days given $63 as interest is 36.5%
Learn more here: https://brainly.com/question/21640787
How can this expression be written another way?
Apply the distributive property and the greatest common factor to write an equivalent expression.
Enter your answer by filling in the boxes.
105 + 35m = __ (__)
Answers
Answer:
(105 x 30) + (105 x 5) + m
Step-by-step explanation:
Answer:
(105 x 30) + (105 x 5) + m
Step-by-step explanation:
Hope this helped have an amazing day!
What is the zero of 4x - 3y = -24?
Answers
solve the equations 7(x+4)=21
iready
Answers
Step-by-step explanation:
[tex]\bullet\hookrightarrow\sf 7 (x+4)=21 [/tex]
[tex]\bullet\Rrightarrow\sf 7x+28=21 [/tex]
[tex]\bullet\rightarrowtail\sf 7x=21-28 [/tex]
[tex]\bullet\twoheadrightarrow\sf 7x=-7 [/tex]
[tex]\bullet\looparrowright\sf x=\dfrac{-7}{7}[/tex]
[tex]\bullet\rightharpoonup\sf x=-1 [/tex]
HELPPPPPPPP PLZZZZZZX
Answers
Answer:
ur answer should be BStep-by-step explanation:
Please help don’t pass this question please help me out !
Answers
Answer: I think it is (D)
Step-by-step explanation: Its hard to explain but I hope this helps anyways!
Answer:
I think its D to so I would go with that
x2 + kx + (k + 3) is tangent to x-axis. Find the value
of k.
Answers
Step-by-step explanation:
Since x² + kx + (k + 3) is tangent to the x-axis, the quadratic function has a repeated root.
The discriminant is zero, so b² - 4ac = 0.
=> k² - 4(1)(k + 3) = 0
=> k² - 4k - 12 = 0
=> (k - 6)(k + 2) = 0
Hence k = 6 or k = -2.
The value of k is -2 and 6.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + kx + (k + 3) is tangent to the x-axis.
This means,
The equation has roots.
Now,
The determinant of the equation is equal to zero.
D = b² - 4ac
x² + kx + (k + 3) is in the form of ax² + bx + c.
a = 1
b = k
c = k + 3
Now,
D = 0
k² - 4(k + 3) = 0
k² - 4k - 12 = 0
k² - (6 - 2)k - 12 = 0
k² - 6k + 2k - 12 = 0
k(k - 6) + 2(k - 6) = 0
(k + 2) (k - 6) = 0
k + 2 = 0
k = -2
k - 6 = 0
k = 6
Thus,
k = -2 and 6.
Learn more about equations here:
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24 is what percent of 12?
need help? anyone know this?
Answers
Answer:
200
Step-by-step explanation:
Evaluate 3 + (a + 4)(8 - b) when a = 5 and b = 6.
The value of the expression is
Answers
Answer:
21
Step-by-step explanation:
you plug in 5 for a and 6 for b and solve.
The value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21
How to evaluate an expression?3 + (a + 4)(8 - b)
when,
a = 5 and b = 6
substitute into the expression= 3 + (5 + 4) (8 - 6)
= 3 + 9 (2)
= 3 + 18
= 21
Therefore, the value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21
Learn more about evaluation:
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