The question seems to be incomplete. I assume that we have the equation of a sphere, and we want to define equations of the intersection between that sphere and some given planes.
A general sphere of radius R centered at the point (a, b, c) is written as:
(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2
Each of the planes will have a fixed value, to find the intersection, we just need to "fix" that fixed value in the equation above.
a) Intersection with xy-plane
The xy-plane has a z-value of 0 (the x and y values are free) so to write the intersection we only need to fixate z = 0.
Using the general sphere we get:
(x - a)^2 + (y - b)^2 + (0 - c)^2 = R^2
(x - a)^2 + (y - b)^2 + c^2 = R^2
(x - a)^2 + (y - b)^2 = R^2 - c^2
This is a circle, centered at (a, b) in the xy-plane, and with a radius of:
√(R^2 - c^2)
Similarly:
b) intersection with xz-plane
Here we have y = 0, then the equation becomes:
(x - a)^2 + (0 - b)^2 + (z - c)^2 = R^2
(x - a)^2 + b^2 + (z - c)^2 = R^2
(x - a)^2 + (z - c)^2 = R^2 - b^2
c) intersection with yz-plane
Here we have x = 0
(0 - a)^2 + (y - b)^2 + (z - c)^2 = R^2
a^2 + (y - b)^2 + (z - c)^2 = R^2
(y - b)^2 + (z - c)^2 = R^2 - a^2
Finally, in which cases we would write DNE?
Only if the expression at the right (the radius of the circle) are smaller than zero.
For example, if R^2 - a^2 < 0, then the sphere does not intersect the yz-plane.
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HELP PLS!!!
Use a calculator to find the measure of angle(theta). Round answer to the nearest degree.
5. sin(theta) = 0.7264
7. cos(theta) = 0.5674
9. tan(theta) = 8.235
Answer:
5.) 0.01267773206
6.) 9.902836313×10-3
7.)0.1449606409
There are 32 desks in a room.
If x represents the number of rows of desks, which expression would equal the number of desks in each row?
the function that represents the graph in the image is
Write an input and output pair that is a function and stays a function when you switch the input and output
9514 1404 393
Answer:
{(1, 2), (3, 4)}
Step-by-step explanation:
If you want both the relation and its inverse to be functions, there can be no repeated x-values, and no repeated y-values.
In the above pair of points, I have avoided duplicates by making all of the values different. That is not necessary, but it satisfies this problem easily.
What factors of 54 have the sum of -15
Answer:
-9 and -6
Step-by-step explanation:
-9 x -6 = 54
-9 - 6 = -15
What is m∠A? ???????
Answer:
A=124°
Step-by-step explanation:
5x - 5 = 180
5x = 185
x = 37
A=124
Guided Practice
Find the balance in the account.
$4000 principal earning 6% compounded annually, after 5 years
A.
$5352.90
B.
$6872.20
C.
$4240
Answer:
A.
$5352.90
Step-by-step explanation:
A=p(1+r)^t
A=4,000×(1+0.06)^(5)
A=5,352.90
.........................................................
Answer:
The Final Investment Value is
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Is this unsolvable?
Answer:
[tex]sum \: angle \: of \: a \: triangle \: = 180 \\ here \: 90 + x + y = 180 ....(1)\\ but \: given \: that \: x = \frac{y}{5} \\ y = 5x .....(2)\\ put \: (2) \: in \: (1) \\ = > 90 + x + 5x = 180 \\ 90 + 6x = 180 \\ 6x = 180 - 90 = 90 \\ 6x = 90 \\ x = \frac{90}{6} = 15 \: degree \\ angle \: for \: a \: stright \: \: line \: = 180 \\ x + unknown = 180 \\ 15 + unknown = 180 \\ unknown = 180 - 15 = 165 \: degree \\ thank \: you[/tex]
Every problem has a solution .Lets solve it .
Here given that
[tex]\\ \sf\longmapsto x=\dfrac{y}{5}[/tex]
Use cross multiplication[tex]\\ \sf\longmapsto y=5x\dots(1)[/tex]
Now
As its a triangle
[tex]\\ \sf\longmapsto 90+x+y=180[/tex]
Put y=5x[tex]\\ \sf\longmapsto 90+x+5x=180[/tex]
[tex]\\ \sf\longmapsto 6x+90=180[/tex]
[tex]\\ \sf\longmapsto 6x=180-90[/tex]
[tex]\\ \sf\longmapsto 6x=90[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{90}{6}[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
We need not to find y
See the marked angle and x are supplementary angles hence there sum will be 180
[tex]\\ \sf\longmapsto x+15=180[/tex]
[tex]\\ \sf\longmapsto x=180-15[/tex]
[tex]\\ \sf\longmapsto x=165[/tex]
The required angle is 165°.
The lions baseball team scored 8 runs their first game. The tigers baseball team scored 2 runs. How many times as many runs did the lions score as the tigers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Determine what value(s) for the variable would make each algebraic
equation a true number sentence.
�2 = 81 is true for ____________________.
6� = 3� + 2� + � is true for ____________________.
� + 74 = � − 74 is true for ____________________.
Answer:
k calculate it how u see it
Jonathan is solving this 3 variable system by hand.
What should be the entries for row 3 in step 3 (list them in order)? A) 0, -1, -2, 1 B) 0, 1, 3, 1 C) 0, 1, -2, 3 D) 3, 2, 1, 1
The entries for Row 3 in step 3 are : 0, -1, -2, 1
R_{1} = Row1
R_{2} = Row 2
R_{3} = Row 3
For the third step, STEP 3 :
THE VALUE OF Row 3 is obtained thus :
[tex]R_{3} = R_{3} - 3R_{1}[/tex]
[tex]From \: step \: 1 : R_{1} = [1 1 1 0][/tex]
[tex]R_{1} = [1 1 1 0] \\ \\
[tex]R_{3} = [3 2 1 1] \\
\\ 3R_{1} = 3(1 1 1 0) = [3 3 3 0][/tex]
[tex]R_{3} - 3R_{1} \: =
(3 - 3), (2 - 3), (1 - 3), (1 - 0) = (0, -1, -2, 1)[/tex]
Hence, the entry for Row 3 in step 3 will be :
(0, - 1, - 2, 1)
Learn more on linear algebra : https://brainly.com/question/13284369
What is 2/3 divided by 4 in the Simplest form?
Answer:
2/3 divided by 4 = .16
Step-by-step explanation:
This problem is pretty simple. Since we cannot divide this we can change the division sign into a multiplication, but to do this we need to also take the reciprocal of 2/3, which means we flip th number so it becomes 3/2. Now we can simply multiply. (1/4)*(3/2) which should give you 3/8
What are the factors of 36?
And is it prime or composite
Answer:
Step-by-step explanation:
Notice that
[tex]96 = 9 \times 4\\= 3^2 \times 2^2\\[/tex]
So the factors of 36 are all of the form [tex]3^a\times 2^b[\tex] where [tex]0\leq a,b\leq 2[/tex].
If we list all of them we have
Answer:
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18 and 36 and it is composite
Step-by-step explanation:
hope it helps
HELP PLEASE
here’s the picture
Answer:
True
Step-by-step explanation:
x(a+4)
Combine terms
ax+4x
Tell me step-by-step how to convert 0.15 repeating 15 to a fraction
Answer:
7/45
Step-by-step explanation:
If you can use your calculator*
Just press 0.1555555555555555555555555555 repeatedly
If you cant:
I dont know sorry
A flower bed has the shape of a rectangle 15 feet long and 12 feet wide. What is its area in square yards? Be sure to include the correct unit in your answer.
Answer:
[tex]180 ft.^2[/tex]
Step-by-step explanation:
[tex]15 ft.[/tex] × [tex]12 ft.= 180 ft.^2[/tex]
ebjkesjkbjbsjkjkdbvbjbkjsz
Answer:
jhk
Step-by-step explanation:
Rewrite the expression by factoring out the coefficient of the variable.
Answer:
[tex] - \frac{1}{2} x + 6[/tex]
by factorising out -½ :
[tex]{ \boxed{ \boxed{ = - \frac{1}{2} (x - 12)}}}[/tex]
a book bought for $20 was sold at a loss of 15%. What is the selling price?
Step-by-step explanation:
SP=?
L%=15%
CP=$20
WE KNOW,
L= L%/100×CP
L= 15/100×20
L= 15/5
L= 3
NOW,
L = CP-SP
Or, 3 = 20 - SP
Or,SP= 20 -3
SP=RS 17
Answer:
book price= $2015% of $20= $3$20 -$3 = $17sold book price = $17describe the cross section
Answer:
In Geometry, the cross-section is defined as the shape obtained by the intersection of solid by a plane. The cross-section of three-dimensional shape is a two-dimensional geometric shape. In other words, the shape obtained by cutting a solid parallel to the base is known as a cross-section.
Step-by-step explanation:
Complete the ordered pair for the equation y = 3x + 5.
( ,-16)
Complete the ordered pair.
0.-16)
Answer:
I agree with them thx plan nbj
if i pour 1/4 gallon of tea in each of the 4 pitchers. how many gallon in each pitcher
a community center is trying to raise $1680 to purchase exercise equipment. the center is hoping to receive equal contributions from members of the community. write and algebraic expression to determine how much will be needed from each person if n people contribute. Then evaluate the expression for 10, 12, 14, or 16 people.
Lets find f(n) formula
[tex]\boxed{\sf f(n)=\dfrac{1680}{n}}[/tex]
Now
[tex]\\ \sf\longmapsto f(10)=\dfrac{1680}{10}=168[/tex]
[tex]\\ \sf\longmapsto f(12)=\dfrac{1680}{12}=140[/tex]
[tex]\\ \sf\longmapsto f(16)=\dfrac{1680}{16}=105[/tex]
[tex]\\ \sf\longmapsto f(14)=\dfrac{1680}{14}=120[/tex]
in this problem x needs to be solved.
Answer:
Step-by-step explanation:
4x-7 = 7x-61
-7+61 = 7x-4x
54 = 3x
x = 18
Help fast pls will do your question in exchange ( if you have it )
Find the point on the y-axis that is 7 units from the point
(−7, −4).
(x, y) =
Answer:
-7,3
Step-by-step explanation:
The point on y - axis has coordinates = (0, -4)
We have a point whose coordinates are - P(-7, -4)
We have to find the point on the y-axis that is 7 units from the point.
What is the formula to find the distance between the two points on Cartesian plane ?The distance between two points -
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
According to the question, we have -
Coordinates of Point : P(-7, -4)
Since the other point is on y - axis, therefore its x - coordinate will be 0.
Let the point on y - axis have coordinates as - (0, k).
Using the formula discussed above -
7 = [tex]\sqrt {\left( {-7- 0} \right)^2 + \left( {-4 - k } \right)^2 }[/tex]
49 = [tex](-7)^{2}[/tex] + [tex](-4-k)^{2}[/tex]
[tex](-4-k)^{2}[/tex] = 0
[tex](k + 4)^{2}[/tex] = 0
Solve the quadratic equation, you will get -
k = -4
Hence, the point on y - axis has coordinates = (0, -4)
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pls help! will do brainliest
Answer:
Answer: (√3)/2
Step-by-step explanation:
[tex] \sin(35 \degree) \cos(25\degree) + \cos(35\degree) \sin(25\degree) \\ [/tex]
from trigonometry identities:
[tex] \sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b) \\ [/tex]
a » 35°
b » 25°
Therefore;
[tex] = \sin(35\degree + 25\degree) \\ = \sin(60\degree) \\ \\ = \frac{ \sqrt{3} }{2} [/tex]
Question: If m<4 = 6x - 16 and m<8 = 2x + 4, then m<4 = _____
Pls show how you got it cause it’s confusing me a lot
Answer:
m<4 = 14
Step-by-step explanation:
m<4 = m<8
6x - 16 = 2x + 4
+16 +16
-----------------------
6x = 2x + 20
-2x -2x
-----------------------
4x = 20
/4 /4
-----------------------
x = 5
m<4 = 6x - 16
= 6(5) - 16
= 30 - 16
= 14
Thus, m<4 = 14
Answer:
m<4 = 14 --> final answer
HELP PLEASE 15 POINTS
Answer:
5200mlStep-by-step explanation:
As we know:-1000ml = 1L
Hence,
5090ml = 5.09L
5200ml = 5.2L
5L
Here,
5.2L is the greatest amount.
Answer: 5,200 ml
Step-by-step explanation:
1 L = 1,000 ml
5 L = 5,000 ml
1. Lựa chọn yêu cầu cần đạt trong Chương trình Giáo dục phổ thông môn Toán 2018 lớp 3, xây dựng một công cụ sử dụng trong đánh giá thường xuyên. Trình bày định hướng sử dụng công cụ đánh giá đã xây dựng trong dạy học môn Toán lớp 3 theo hướng hình thành, phát triển năng lực, phẩm chất của học sinh.
Answer:
So basically you add x with 9 and you get 9x
