Answer:
C, E
Step-by-step explanation:
Here, we want to change the equation of a circle from general form to standard form. This is done by making the leading coefficients 1, completing the squares, and then rewriting the equation in standard form.
The leading coefficients of the given equation are 2, so we first want to divide by 2. This gives ...
x² +y² -4x -6y +8 = 0
Subtracting 8 puts us in better position to complete the squares.
x² +y² -4x -6y = -8
Now, we can add the squares of half the coefficients of the linear terms.
(x² -4x +4) +(y² -6x +9) = -8 +13 . . . . . . matches C
And we can simplify this to the standard form equation:
(x -2)² +(y -3)² = 5 . . . . . matches E
NO LINKS PLEASE
I NEED THEM TODAY
NO LINKS!!!
Answer:
13. True, False, True
14. False, True, True
15. All true
What is the diameter of a hemisphere with the volume of 74466
[tex]\textit{volume of a hemisphere}\\\\ V=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=74466 \end{cases}\implies 74466=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3} \\\\\\ 74466=\cfrac{2\pi r^3}{3}\implies 223398=2\pi r^3\implies \cfrac{22398}{2\pi }=r^3\implies \cfrac{111699}{\pi }=r^3 \\\\\\ \sqrt[3]{\cfrac{111699}{\pi }}=r~\hfill \stackrel{\textit{diameter = 2r}}{2\sqrt[3]{\cfrac{111699}{\pi }}\implies \sqrt[3]{\cfrac{893592}{\pi }}}~~ \boxed{\approx~~65.77}[/tex]
Maryan harvested a total of 22.69 t of rice and sold it in 100 kg bags. how many full bags did she sell
Answer:
1t = 1000kg
22.69 x 1000= 22690 kg
22690 kg ÷ 100 = 226.9
I would usually round it to 227 but I would say 226, since they are asking how many full bags she sold.
4x+y=2 solve for y algebra 2
Answer:
Step-by-step explanation:
4x + y = 2
y = -4x + 2
A cyclist travels a distance of 837 1/2 feet in 25 seconds. The cyclist travels at a constant rate. What is the unit rate, in feet per second, at which the cyclist travels?
PLEASE
Answer:
[tex]\boxed{33.5 \ \text{feet/second}}[/tex]
Step-by-step explanation:
To find the unit rate, we need to find out how much distance does the cyclist travel in 1 second. For that, we need to use the unitary method. A unitary method is a method that determines the unit rate of an object.
Note: Since the cyclist travels at a constant rate, unitary method can be used.
[tex]\rightarrow 837 \dfrac{1}{2} \ \text{feet in 25 seconds}[/tex]
[tex]\rightarrow 837.5 \ \text{feet} = 25 \ \text{seconds}[/tex]
Divide both sides by 25:
[tex]\rightarrow \dfrac{837.5}{25} \ \text{feet} = \dfrac{25}{25} \ \text{seconds}[/tex]
[tex]\rightarrow 33.5 \ \text{feet} = 1 \ \text{seconds}[/tex]
[tex]\rightarrow \boxed{33.5 \ \text{feet/second}}[/tex]
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Donald said that the median is 2. What did he do wrong?
8,13,2,4,48
Answer:
He did not put the numbers in order.
Explanation:
The numbers need to be in order from smallest to largest before you find the median.
Solve for b
SOLVE ASAP!!
Answer:
Step-by-step explanation:
<A and <B are alternate interior angles. That means they are in the interior of the parallel lines and they are on opposite sides of the transversal.
When that happens <A = <B
8x + 78 = 2x + 114 Subtract 2x from both sides.
8x - 2x + 78 = 2x - 2x + 114 Combine
6x + 78 = 114 Subtract 78 from both sides
6x + 78 - 78 = 114 - 78
6x = 36 Divide by 6
6x/6 = 36/6
x = 6
I think you are asked for B
<B = 2x + 114
<B = 2*6 + 114
<B = 12 + 114
<B = 126
[tex] \sf \large \: find \: \frac{dy}{dx} \: if \: x=a ( \Theta + sin \Theta ) , y= a (1- Cos \Theta ) \: at \: \Theta = \frac{π}{2} \\ \\ \\ \\ \\ [/tex]
Kindly Don't Spàm!
Thanks!!!!
Given :
[tex] \: \: \: [/tex]
[tex] \rm \large \: x = a ( \Theta + Sin \Theta )[/tex][tex] \: \: \: [/tex]
[tex] \rm \large y = a ( 1 - cos \: \Theta )[/tex][tex] \: \: [/tex]
Now , x = a ( θ + sin θ )
[tex] \: \: [/tex]
Diff w.r.t " θ "
[tex] \: \: \: [/tex]
[tex] \rm \large\frac{dx}{dθ } = a \: \frac{d}{dθ} (θ + \sin\theta )[/tex][tex] \: \: [/tex]
[tex] \boxed{ \rm \large\underline{ \frac{dx}{d \theta} = a(1 + \cos \theta ) }}[/tex][tex] \: \: [/tex]
Now y = a ( 1-cosθ)
[tex] \: \: [/tex]
Diff w.r.t " θ " we get .
[tex] \: \: [/tex]
[tex] \rm \large \frac{dy}{d \theta} = a \frac{d}{d \theta} (1 - cos \theta) [/tex][tex] \: \: \: [/tex]
[tex] \boxed{ \rm \large \underline{ \frac{dy}{d \theta} = a \sin \theta}}[/tex][tex] \: \: \: [/tex]
From eqn ( 1 ) & ( 2 )
[tex] \: \: [/tex]
[tex] \rm \large \frac{dy}{dx} = \frac{ \frac{dy}{d \theta} }{\frac{dx}{d \theta}} [/tex][tex] \: \: \: [/tex]
[tex] \: \: \: \rm \large = \frac{ \cancel{a} \: sin \theta}{ \cancel a \: (1 + cos \theta)} [/tex][tex] \: \: [/tex]
[tex] \rm \large \: = \frac{sin \theta}{1 + \cos \theta } [/tex][tex] \: \: \: [/tex]
[tex] \rm \large \: \frac{2 \sin( \frac{\theta }{2} ) cos\frac{\theta }{2} }{2 \: cos ^{2} \frac{\theta }{2}} \: \: ......(sin \: a \: = 2 \: sin \frac{a}{2} \: cos \frac{a}{2} 1 + \: cos \: a \: = 2cos ^{2} \frac{a}{2} )[/tex][tex] \: \: [/tex]
[tex] \rm \large \: \frac{dy}{dx} = \frac{sin \frac{ \theta}{2} }{cos \frac{ \theta}{2} } [/tex][tex] \: \: [/tex]
[tex] \rm \large \: \frac{dy}{dx} = tan \frac{ \theta}{2} [/tex][tex] \: \: [/tex]
[tex] \rm \large \: ( \frac{dy}{dx} ) = tan \frac{ \frac{ \theta}{2} }{2} [/tex][tex] \: \: [/tex]
[tex] \rm \large \: = tan( \frac{ \theta}{4} )[/tex][tex] \: \: [/tex]
[tex] \boxed{ \rm \large \underline{ ( \frac{dy}{dx} ) = \frac{\pi}{2} = 1}}[/tex][tex] \: \: [/tex]
Hope Helps!:)
Given the function h of x equals 2 times the cube root of x minus 10 end root plus 4, what is the x-intercept of the function?
–10
–4
2
8
Step-by-step explanation:
if I understand correctly, then we have
h(x) = 2 × cubic root(x - 10) + 4
the x-intercept is the x value where y or h(x) = 0.
0 = 2 × cubic root(x - 10) + 4
0 = cubic root(x - 10) + 2
-2 = cubic root(x - 10)
-8 = x - 10
x = 2
The intercept is the point where a line or curve crosses the axis. The x-intercept of the function is (2,0)
Intercept of a functionThe intercept is the point where a line or curve crosses the axis. Given the function below:
h(x) = 2(∛x-10) + 4
For the x-intercept, it is the point where h(x) = 0.
Substitute
2(∛x-10) + 4 = 0
2(∛x-10) = -4
(∛x-10) = -2
Take the cube of both sides
x-10 = (-2)^3
x -10 = -8
x = -8 + 10
x = 2
Hence the x-intercept of the function is (2,0)
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I hate these types of problems
I was never taught this stuff
The value of stock changes from $22 on Monday to $30 on Tuesday. Calculate the percent increase.
22 + 22 x r = 30
22 x r = 30 - 22
r = 8 : 22
r = +36,36%
r = increase rate
Evaluate the triple integral. X dv, where e is bounded by the paraboloid x = 4y2 4z2 and the plane x = 4. E
The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]
The second integral using limits a and b
[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
What is integration?Integration is defined as adding small parts to form a new significant part.
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral
0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2\pi\int_0^1\int_b^axydx[/tex]
The second integral using limits a and b
[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]
[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]
[tex]16\pi\int_0^1[r-r^5]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
Read more on Triple integral here:
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please help asap
For each relation, decide whether or not it is a function.
Answer:
Step-by-step explanation:
Refer to the definition of a function. I'll just give you a layman's definition to be concise.
For something to be a function, there needs to be exactly 1 output for every input. You cannot have a case where you input 1 value, and get 2 or more values as an output.
In math we call all the possible input values the domain, and we call all the possible output values the range.
Let's take a look at each situation on your worksheet.
1. Is a function. This is because only one arrow stems from each input value. There are cases where the different input values give the same output, sure, but each input returns 1 discrete thing, not an array of things.
(Think of it this way, if i had a machine that could answer any question I had with yes, no or maybe. I wouldn't want the machine to give me "yes and maybe" or "yes and no" as the result when I ask it a question. That doesn't make sense and I would think the machine is broken. What could happen, is that I ask the machine different questions, and for those different questions, it gave me the same answer, like "yes" and "yes" respectively. in that case, it would be acceptable, because it isn't contradicting itself for any individual question.)
2. Not a function. There are 2 different output values for b.
(Refer back to my machine analogy. The "machine" in this question is contradicting itself. I gave the machine one input, and the machine is telling me, "it's this and actually it's this other thing too")
3. Is a function for the same reasons as 1.
4. Isn't a function.
(It's basically telling you, the machine reads -6 as -4, but it also reads -6 as 0, and also 2. And it also tells you the machine reads -4 as -3, but it also reads it as 8. Again, the machine should only read 1 input in 1 way and not contradict itself. )
Please help! I don't know what answer b is, but i know a, thank you.
They are corresponding angles
Step-by-step explanation:
We know that x=75⁰ because
[tex]180 - 105 = 75[/tex]
75⁰ is angle EFB
Since we know this, and because we know that AD//EH,
We can conclude that x=75⁰(AD is parallel to EH and angle CBA or x and angle EFB are corresponding angles)