(a) x² + y² + z² + 18(x - y + z) + 218 = 0
(b) (x + 9)² + (y - 9)² + 56 = 0
Step-by-step explanation:
The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;
(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ------------------(i)
From the question:
The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.
Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;
(x - (-9))² + (y - 9)² + (z - (-9))² = 5²
(x + 9)² + (y - 9)² + (z + 9)² = 25 ------------------(ii)
Open the brackets and have the following:
(x + 9)² + (y - 9)² + (z + 9)² = 25
(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25
x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25
x² + y² + z² + 18(x - y + z) + 243 = 25
x² + y² + z² + 18(x - y + z) + 218 = 0 [equation has already been normalized since the coefficient of x² is 1]
Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:
x² + y² + z² + 18(x - y + z) + 218 = 0
(2) To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;
(x + 9)² + (y - 9)² + (0 + 9)² = 25
(x + 9)² + (y - 9)² + (9)² = 25
(x + 9)² + (y - 9)² + 81 = 25 [subtract 25 from both sides]
(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25
(x + 9)² + (y - 9)² + 56 = 0
The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0
Find the solution for the following: Three backpackers cooked rice for dinner. The first one gave 400g of rice and the second 200g of rice. The third one did not have any rice so he gave $6 to the other two. How should they divide the $6 in a fair way ( assume they equally shared the dinner) ?
Answer:
First backpacker should receive $4 and the second one $2
Step-by-step explanation:
notice that the total amount of rice for the three is 600 g.
Then, the first one that gave 400 g contributed 400 out of 600, that is 400/600 = 2/3
The second one contributed 200 out of 600, that is 200/600 = 1/3
then the first one should receive 2/3 of the $6 = (2/3) x 6 = $4
and the second one should receive 1/3 of the %6 = (1/3) x 6 = $2
what is the answer for -8=-16+n
Answer:
n=8
Step-by-step explanation:
[tex]-8=-16+n\\\\-8+16=-16+16+n\\\\8=0+n\\\\n=8[/tex]
Answer:
Step-by-step explanation:
-8=-16+n
-8(+16)=-16(+16)+n get "n" by itself by adding 16 to both sides.
negative eight plus sixteen is positive eight. on the right side the sixteens cancel eachother out, so you are left with just "n".
Therefore...,
8=n
Calculus Ch. 1.2 Classwork Problems Evaluating limits Graphically
Answer:
16) 2
17) -5
18) doesn't exist
19) doesn't exist
20) doesn't exist
21) 3
22) 4
23) 6
Step-by-step explanation:
16) as you move towards -9, the function adopts the value 2
17) as one moves towards x = -6 , from both sides (right and left) the function goes to the value -5
18) As one moves towards x = -4 (from the right and from the left, the functions seems to diverge towards + ∞. So normally the convention for limits stipulates: Undefined or Doesn't exist
19) f(-4) doesn't exist (for same reasons as above (there is a singularity here)
20) As one moves towards 2 from the right, the function gets towards the value 3, while approaching from the left the function goes towards the value 5. So formally we say that the limit doesn't exist (from the left and from the right limits don't agree)
21) f(2) is the well defined value of 3
22) approaching x= 4 from the right and from the left both lead towards the value 4.
23) f(4) is 6
5g + 18-7g + 4g = 8
Answer:
Step-by-step explanation:
9g - 7g + 18 = 8
2g + 18 = 8
2g = -10
g = -5
what is a positive and a negative number between 1 and -1 ?
Answer:
The answer is 0
Step-by-step explanation:
It's between -1 and 1 and it's not positive only and it's not negative only
Find the midpoint of the segment joining X(5,6) and Y(9,2).
Answer:
(7,4)
Step-by-step explanation:
The midpoint formula is:
[tex]M=(\frac{x_1+x_1}{2},\frac{y_1+y_2}{2})[/tex]
Let (5,6) be x₁ and y₁ and let's let (9,2) be x₂ and y₂. Thus, the midpoint is:
[tex]M=(\frac{5+9}{2},\frac{6+2}{2})[/tex]
Add:
[tex]M=(\frac{14}{2},\frac{8}{2})[/tex]
Divide by 2:
[tex]M=(7,4)[/tex]
So, our midpoint is (7,4).
And we're done!
y = mx + c
5.
Use the grid below to answer these questions.
a) Draw and label the graph of y = 3x + 1.
15
[
10
5
b) Draw a line parallel to y = 3x + 1 and
passing through the point (0, -3).
o
2
3
4
5
c) Write down the equation of this line.
Answer:
Step-by-step explanation:
graph cannot be drawed
I need help please no one helps me
Answer:
the first blank is 9 and the second is 8. when you switch the numbers in the equation the answer will still be the same. hope this was helpful!
Answer:72 is 8 times as many as 9 and 9 times as many as 8
Step-by-step explanation:
(6 + 7) + 8 = 6 + (7 + 8)
which property of addition shows
Answer: Associative Property of Addition
Step-by-step explanation: The problem (6 + 7) + 8 = 6 + (7 + 8)
demonstrates the associative property of addition.
Notice that the addends, or the number we're adding,
are the same on both sides of the equals sign, 6 + 7 + 8.
The associative property of addition tells us that when we're adding more
than two numbers, the grouping of addends does not change the sum.
For example here, (6 + 7) gives us 13, and 14 + 8 gives us 21.
On the right side, (7 + 8) gives us 15, and 6 + 15 gives us 21.
So the sum is the same, regardless of which way we group the addends.
The absolute value of some number x is 17, and the number y is 23. How much is
sum x + y? How many different results do you get?
Answer:
we get only one solution that is 23 + 17 = 40
Hope it helps
f(-1/2)=1/2x +3/2 what is the answer to this?
Answer:
5/4, just sub in x
Step-by-step explanation:
How many bricks each 0.16m2 are required for paving a courtyard of 5.5m long and 4.8m wide?
Under which conditions does the commutative property apply to compositions of f(x) and g(x)? A- When they are inverse functions B- when they are equal for at least one value of x C- when they are equal for all values of x D- when they are not inverse functions
Answer:
A- When they are inverse functions
C- when they are equal for all values of x
Step-by-step explanation:
The order of function application in a composition can be reversed if ...
the functions are inverses of each otherthe functions are identical (equal for all values of x)_____
In the first case, the composition gives an output equal to its input for the functions in either order.
In the second case, you cannot tell the functions apart, since they produce the same output for the same input. Hence, you can't tell if they are reordered or not.
Assume the triangle has given measurements. solve for the remaining sides and angles.
Answer:
Step-by-step explanation:
You can calculate the length of side a using the Cosine Rule:
a^2 = 32.6^2 + 41.4^2 - 2.32.6.42.4 cos pi/6
a^2 = 456.01
a = √456.01
a = 21.35
By the Sine Rule:
32.6 / sin B = 21.35 / sin pi/6
sin B = (32.6 * sin pi/6) / 21.35
sin B = 0.76347
B = 0.869 radians.
C = pi - pi/6 - 0.869 = 1.749 radians.
- 17 RATIONAL OR IRRATIONA
Answer: All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. So its Rational.
:)
Answer:
17 is an irrational number.
Step-by-step explanation:
17 is a prime number with no factors other than itself and 1 therefore minus square root of 17 is an irrational number.
Type the integer that makes the following multiplication sentence true: –3 × = 9
Answer:-3
-3
Step-by-step explanation:
You are allowed to multiply as many 2's and/or as many 5's as
you want. What can be the last digit of your result?
If 5 's multiplied many times then always unit digit will be 5.
If power of 2 is divide by 4 then , if remainder is zero then unit digit will be 6 and if remainder is 1 then unit digit will be 2 , if remainder is 2 then unit digit will be 4 and if remainder is 3 then unit digit will be 8.
First here we analyse when many of 2's is multiplied.
[tex]2^{1} =2\\2^{2} =4\\2^{3}=8\\2^{4} =16\\2^{5} =32\\2^{6}=64[/tex]
Here , we observed that after [tex]2^{4} =16[/tex] , unit digit will be repeat.
So, If power of 2 is divide by 4 then , if remainder is zero then unit digit will be 6 and if remainder is 1 then unit digit will be 2 , if remainder is 2 then unit digit will be 4 and if remainder is 3 then unit digit will be 8.
Now, analyse when many of 5's multiplied.
[tex]5^{1}=5 \\5^{2}=25\\5^{3}=125[/tex]
So, When 5 's multiplied many times then always unit digit will be 5.
Learn more:
https://brainly.com/question/23558983
Consider xưy" – 14xy' + 56y = 0. Find all values of r such that y=x" satisfies the differential equation for x > 0. Enter as a comma separated list: r= 7,8 help (numbers) Enter two linearly independent solutions of the form above: y1 = x7 help (formulas) y2 = 48 help (formulas) Now find a solution satisfying the initial values y(1) = 4, y'(1) = 3: y= 29x? – 25,28 help (formulas)
I bet the ODE is supposed to read
[tex]x^2y''-14xy'+56y=0[/tex]
Then if [tex]y=x^r[/tex], we have [tex]y'=rx^{r-1}[/tex] and [tex]y''=r(r-1)x^{r-2}[/tex], and substituting these into the ODE gives
[tex]r(r-1)x^r-14rx^r+56x^r=0\implies r(r-1)-14r+56=r^2-15r+56=0[/tex]
Solving for r, we find
[tex]r^2-15r+56=(r-8)(r-7)=0\implies \boxed{r=8\text{ or }r=7}[/tex]
so that [tex]y_1=x^8[/tex] and [tex]y_2=x^7[/tex] are two fundamental solutions to the ODE. Thus the general solution is
[tex]\boxed{y(x)=C_1x^8+C_2x^7}[/tex]
Given that [tex]y(1)=4[/tex] and [tex]y'(1)=3[/tex], we get
[tex]\begin{cases}4=C_1+C_2\\3=8C_1+7C_2\end{cases}\implies C_1=-25\text{ and }C_2=29[/tex]
So the particular solution is
[tex]\boxed{y(x)=29x^7-25x^8}[/tex]
How do you do this question?
Answer:
240 ft
Step-by-step explanation:
When she stops, her velocity is 0. The first time that happens is at t = 3 minutes. Her position at that time is equal to the area under the curve.
You can use area of a trapezoid, or you can split the shape into two triangles and a rectangle. Watch your units! Speed is given in ft/s, and time is given in minutes.
Using trapezoid area:
A = ½ (1 min + 3 min) (2 ft/s)
A = ½ (60 s + 180 s) (2 ft/s)
A = 240 ft
What is the sum of 637,391+372,088
the result of this problem is 1009.479
Which expression is a factor of 21x2 + 13x – 20?
A. 3x – 4
B. 7x - 5
C. 7x + 4
D. 3x + 5
Answer:c
Step-by-step explanation:
7x - 5 is the factor of 21x²+13x-2.Option B is correct.
What is the equation?An equation is a statement indicating the equality of two expressions that contain variables and/or numbers. In essence, equations are questions, and the pursuit of methodically resolving these questions has been the impetus for the development of mathematics.
It is given that, the expression is 21x²+13x-2.
We have to find the factor of the expression.
Algebraic expression factorization is the process of identifying two or more expressions whose product equals the given expression. Algebraic expression factorization is hence the multiplication procedure in reverse.
[tex]=21x^2+13x-20 \\\\ =\left(21x^2-15x\right)+\left(28x-20\right) \\\\ =3x\left(7x-5\right)+4\left(7x-5\right) \\\\ =\left(7x-5\right)\left(3x+4\right)[/tex]
The factors of the expression are (7x-5) and (3x-4).
Thu option B is correct.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
Would like an answer for this question. Which represents 7(45) using the distributive property to simplify? SELECT THE TWO THAT APPLY. 1# 7 (40 - 5) 2# 7 (4) + 7 (5) 3# 7 (40 +5) 4# 7 (40) + 7(5)
Answer:
7(45)=7(40)+7(5)
Step-by-step explanation:
We need to represent 7(45) using the distributive property to simplify.
We can write 45 as 40+5
So it becomes,
7(45) = 7(40+5)
Distributive property is : a(b+c)=ab+ac
a=7, b = 40 and c = 5
7(40+5)=7(40)+7(5)
So, the correct option is (4).
Help me please!!! :(
Answer:
the greatest common factor is 5^2 * 7^3
(I think!!!)
Help with algebra homework please...with work shown to explain
Answer:
C: -3/7
Step-by-step explanation:
Put an extended line over each direct point you see and then count the graph it takes to reach the nearest point.
Here is a picture to better explain it!
I need help ASAP!! 1+(x-4)=-(3x+6)+1
Answer: x= -2
Step-by-step explanation: 1.) use PEMDAS
2.) distribute the 1 and -1 to (x+4) and (3x+6) --> 1+x+4 = -3x-6+1
3.) Put common terms on the same side (so x's together and the numbers together) so you will add 3 to the right side and add 3x to the left side
4.) that will get you 4x = -8 so then you will divide 4 to both sides to get x by itself
5.) Answer: x=-2
5.)
Find the distance between the pair of points and then round your answer to the nearest tenth.
(-4,5) and (4.0)
d=(22 – 21) + (92 – 41)?
Answer:
[tex] d = 9.4 units [/tex] (nearest tenth)
Step-by-step explanation:
Given the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], distance between (-4, 5) and (4, 0) is calculated as follows:
Let [tex] (-4, 5) = (x_1, y_1) [/tex]
[tex] (4, 0) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(4 - (-4))^2 + (0 - 5)^2} [/tex]
[tex] d = \sqrt{(8)^2 + (- 5)^2} [/tex]
[tex] d = \sqrt{64 + 25} [/tex]
[tex] d = \sqrt{89} [/tex]
[tex] d = 9.4 units [/tex] (nearest tenth)
How do you find the area?
Answer:
• First attachment's graph is correct
• Second attachment, the area is approximately 8.6
Step-by-step explanation:
Remember that the area between two curves is defined as the following:
[tex]\mathrm{The\:area\:between\:curves\:is\:the\:area\:between\:curve\:f(x)\:and\:curve\:g(x)\:on\:interval\:[a,b]} :\\A=\int _a^b|f\left(x\right)-g\left(x\right)|dx[/tex]
We are given the curves y = 7cos(2x), and y = 7 - 7cos(2x) on interval [0, π/2]. Therefore, applying the area formula, we have the solve the following integral:
[tex]\int _0^{\frac{\pi }{2}}\left|7\cos \left(2x\right)-\left(7-7\cos \left(2x\right)\right)\right|dx[/tex]
From now on take a look at the attachment. It shows how to solve the integral, and it's exact value. The area is not 9.727 as you entered, it is approximately 8.6. Your graph however was accurate, but there can be no work shown for that as it's much easier to use a graphing calculator.
Solve for x
4( 3x - 5) = -2(-x + 8) - 6x
Answer:
Step-by-step explanation:
12x - 20 = 2x -16 - 6x
12x - 20 = -4x - 16
16x - 20 = -4x
20x = 20
x = 1
y+1 = 1/2 (x-6) solve for y in simplest form
Answer:
y = 1/2x -4
Step-by-step explanation:
Subtract 1 from both sides of the equation and simplify.
y = 1/2(x -6) -1
y = 1/2x -3 -1
y = 1/2x -4
Answer:
y=1/2x-4
Step-by-step explanation:
y+1=1/2(x-6)
y=1/2(x-6)-1
y=1/2x-6/2-1
y=1/2x-3-1
y=1/2x-4
The density of a certain material is such that it weighs 10 ounces per gallon of volume. Express this density in pounds per pint. Round your answer to the nearest hundredth.
Answer:
0.08 pounds per pint.
Step-by-step explanation:
Given: The density of a certain material is such that it weighs 10 ounces per gallon.
We are to express this density in pounds per pint.
1 gallon ⇒ 10 ounces
1 pound = 16 ounces
How many pounds? = 10 ounces.
Cross-multiplying gives;
[tex]\frac{10 * 1}{16} = 0.625[/tex] pounds
1 gallon = 8 pints
The density in pounds per pint is;
0.625 pounds ÷ 8 pints = 0.078125 pounds per pint = 0.08 pounds per pint (answer rounded up to the nearest hundredth).