Answer:
The equation of the sphere with center (-3, 2 , 5) and radius 4 is [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
The intersection of the sphere with the yz- plane gave the equation [tex](y-2)^{2} + (z-5)^{2} = 7[/tex] which is a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex].
Step-by-step explanation:
The equation of a sphere of radius r, with center (a,b,c) is given by
[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]
where, [tex]x,[/tex] [tex]y,[/tex] and [tex]z[/tex] are the coordinates of the points on the surface of the sphere.
Hence, the equation of the sphere with center, (-3, 2 , 5) and radius 4 becomes
[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]
[tex](x-(-3))^{2} +(y-(2))^{2} + (z-(5))^{2} = 4^{2}[/tex]
Then,
[tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
This is the equation of the sphere with center (-3, 2 , 5) and radius 4,
Now, for the intersection of this sphere with the yz- plane,
The [tex]yz -[/tex]plane is where [tex]x = 0[/tex], then we set [tex]x = 0[/tex]
Them the equation [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex] becomes
[tex](0+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
[tex](3)^{2} +(y-2)^{2} + (z-5)^{2} = 16\\9 +(y-2)^{2} + (z-5)^{2} = 16\\(y-2)^{2} + (z-5)^{2} = 16 - 9\\(y-2)^{2} + (z-5)^{2} = 7[/tex]
This equation is the equation of a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex]
This is the part of the sphere that intersects with the yz-plane.
3y^2+y^- 5+ 4y+2y^3+8
Answer:
9y+3
Step-by-step explanation:
you add all the common numbers and you end up with:
9y^6+3+y^-5
then you put the y^-5 under the other numbers and make it positive so it becomes:
9y^6+3/y^5, then you subtract the exponents of y: 6-5, so that cancels out the y on the bottom making it:
9y+3
What is the y-intercept of the linear equation x-3y=-6?
To find the y-intercept, let x = 0.
0 - 3y = -6
-3y = -6
y = 2
The y-intercept of the equation is the point (0, 2).
Answer:
2
Step-by-step explanation:
Solve the equation for y. First subtract x from both sides then divide by -3. The result is y=1/3x+2 with the number "2" representing the y-intercept.
In a triangle, the measure of one angle is five more than the first and the third angle is one more than four times the first.
Answer:
A= 29
B=34
C=117
Step-by-step explanation:
A triangle has three sides and a triangle always adds up to be 180
A + B + C = 180
B = A + 5
C = 4A + 1
Plug in.
A + A + 5 + 4A + 1 = 180
6A + 6 = 180
6A = 174
A = 29
Now since you found A, find the other two by plugging A in!
C = 4(29) + 1
C = 117
Plug in the B equation
B = 29 + 5
B=34
Check your answers
29 + 117 + 34 = 180
Consider the sequences of numbers.
5, 10, 15, 20, 25, 30, 35, 40, 45, . . .
10, 20, 30, 40, 50, . . .
Which statements are true regarding the patterns of the sequences? Check all that apply.
The first pattern involves repeated addition by 5.
The second pattern involves repeated addition by 10.
The first pattern involves multiplication by 2.
If a number is in the first pattern, then it is also in the second pattern.
The second pattern can be created by multiplying each number in the first pattern by 2.
Answer:
1,2,5
Step-by-step explanation:
The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1 so options (A),(B), and (E) will be correct.
What is the pattern?A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.
The hint which is present in a given pattern hides in the pattern only.
For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.
Another example is 2,4,16,256 in this pattern each term is the square of the previous term and this will become its specific pattern.
Given the two patterns.
In the first pattern, each term become by adding 5 so option (A) is correct.
In the second pattern, each term become by adding 10 so option (B) is correct.
The term in the second pattern becomes by multiplying 2 in pattern 1
For example 5× 2 = 10 and 10 × 2 = 20 so option (E) will be correct.
Hence "The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1".
For more information about the pattern,
brainly.com/question/14013716
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what is 95.85 estimated to
Answer:
96
Step-by-step explanation:
Answer:
96
Step-by-step explanation:
95.85≅96, because 8>5.
20% of ___= 100 Find the answer
Answer:
500
Step-by-step explanation:
20% of x = 100
Write 20% as a decimal - - > 0.2(x) = 100
Isolate and solve for x - - > x = 100/0.2
Therefore, x = 500
Answer:
500
Step-by-step explanation:
Let the no. be x
20% of x = [tex]\frac{20}{100} x[/tex]
And ,
[tex]\frac{20}{100} x = 100\\=> 20x = 10000\\ => x = \frac{10000}{20} = 500[/tex]
I’m having trouble solving this question can someone please help me out!!!
Answer:
Step-by-step explanation:
The answer is A
Which of the following is NOT equivalent to 60/80?
A.)3/4 B.)75% C.)7.5 D.)0.750
Answer:
C
Step-by-step explanation:
Everything else is equivalent.
Hope this helps!
Answer:
C. 7.5
Step-by-step explanation:
60/80 = 3/4 = 75% = 0.75
Everything is equal except for 7.5 because 7.5 = 750%
Hope This Helps :)
x + y = -50
y = 4x
Answer (x,y)
Answer:
x = -10 ; y = -40
Step-by-step explanation:
Note:
y = 4x.
Plug in 4x for y in the first equation:
x + y = -50
x + (4x) = -50
Solve for x. First, simplify, then isolate the variable, x.
x + 4x = -50
5x = -50
Divide 5 from both sides of the equation.
(5x)/5 = (-50)/5
x = -50/5
x = -10
Plug in -10 for x in one of the equations:
y = 4x
y = 4(-10)
y = -40
x = -10 ; y = -40 is your answer.
~
2^20-2^1)=2^x. Solve for x
Answer:
x=19
Step-by-step explanation:
2^20-2^1=2^x(since they have the same base we can remove the bases)20-1=xx=19y=x^-5 A) translate 5 units down B) translate 5 units up C) translate 5 units left D translate 5 units right
Answer:
B a translation 5 units to the left
Step-by-step explanation:
Edge 2021
Look at the arrows in the following drawings
Answer:
a) perpendicular b) parallel c) perpendicular d) neither
Step-by-step explanation:
Perpendicular means that the lines will intersect/cross and create a 90 degree angle
Parallel lines will never intersect/cross because they are going the same way.
What is this simplifided 54123×54÷2=
Answer:
1461321
Step-by-step explanation:
Of 57 cars making up a freight train, 23 are boxcar. What fraction of the cars are not boxcars?
Answer:
total no of cars =57
Cars which are not boxcars =57-23=34
23/34×57=1339/34
Suppose we want to know whether students who study more (hours per week) have a higher grade point average. What kind of question is this? *
Answer:
See who studies and who doesnt then compare
Step-by-step explanation:
See who studies and who doesn't
take the assignment
ask for the score of the people who did and for who didn't
collect the data and organize it
Simplify the following expression.
-21 - (-11)
Answer:
-10
Step-by-step explanation:
well you know that
[tex](-)(-)=(+)[/tex]
so we have
[tex]-21-(-11)\\\\=-21+11\\\\=-10[/tex]
The measure of an angle is 2°. What is the measure of its complementary angle?
Answer:
88°
Step-by-step explanation:
Complementary angles have a sum of 90°, just do 90 - 2 and there's your answer.
4x + 16 - x= 22 + 6
O A. x = 3
O B. x= 2
O C. x = 4
D. x = 11
Answer:
The Answer is C
Step-by-step explanation:
22+6= 28
4(4)+16-4=28
Thus, the answer is C, X=4.
Answer:
C. x=4
Step-by-step explanation:
4x-x=22+6-16
3x=12
x=12÷3
x=4
what is 17492/15098.766= i dont have brain
The answer is 1.158505
Simplify the expression. -/4/
helppppp i dont know pslßss
Answer:
width=3
Step-by-step explanation:
area=length X width
length=4 X width
=>area=4 X width X width
=>area=(2 X width)^2
=>36=(2 X width)^2
=>6=2 X width
=>width=3
the area of a rectangle is length times width
A = L times W
A = 26. so 36 = L times W
The length is 4 times the width
L = 4W
Thus, we can switch L to 4W in the area equation
36 = 4W ×W = 4W²
36 ÷ 4
=√9
=3cm
whats 48 divided by 2
Answer:
My answer to the question is 24.
Find the unknown length y in the following pair of similar triangles.
which of the following sets of numbers could represent the three sides of a triangle
A 6,20,28
b 4,11,15
c 9,19,30
d 5,15,19
Answer:
d 5,15,19
Step-by-step explanation:
The sum of the shortest two sides must be longer than the longest side. That is only the case for selection D.
__
If the sum is equal to the longest side, the segment ends will meet, but the "triangle" will look like a line segment. Many authors do not allow such a thing to be called a triangle. Hence, 'b' is not an answer to this question.
(Some authors do allow such a triangle, in which case, there would be two answers here: B and D.)
please help its multiplying rational numbers
-3.2(-5.6)(4)
= -3.2 - 5.6 x 4
= -3.2 - 22.4
= -25.6
Consider the point. (1, 4, 5) What is the projection of the point on the xy-plane?
Given :
A point ( 1 ,4 ,5 ).
To Find :
The projection of the point on the xy-plane .
Solution :
Now , to find projection of a point in a plane in a plane we need to replace the coordinate of that remaining axis which is not in the plane .
Here , the plane given is xy-plane . So , remaining axis is z .
So , we replace coordinate of z =0 .
Therefore , the projection of the point ( 1 ,4 ,5 ) on the xy-plane is ( 1 ,4 ,0 ) .
Hence , this is the required solution .
find the area of the region enclosed by the curves y=x and y=(x-2)^2
Answer:
Step-by-step explanation:
14.5845842 518.5874 funny
Answer:
Step-by-step explanation:
Gummi bears come in twelve flavors, and you have one of each flavor. Suppose you split your gummi bears among three people (Adam, Beth, Charlie) by randomly selecting a person to receive each gummi bear. Each person is equally likely to be chosen for each gummi bear.
(a) What is the probability that Adam gets exactly three gummi bears?
(b) If you know that each person recieved at least one gummi bear, what is the probability that Adam gets exactly three gummi bears?
(c) What is the expected number of gummi bears that Adam gets?
(d) If you know that each person recieved at least one gummi bear, what is the expected number of gummi bears that Adam gets?
(e) Is there more variance in the number of gummi bears that Adam gets with or without knowing that everyone gets at least one gummi bear? Explain your answer without calculations.
Step-by-step explanation:
From the given gummi bear, the chance that Adam is selected for any draw is 1/3 as well as the chance he is not selected at any draw is 2/3.
a). The probability of Adam getting exactly three gummi bears = P(Adam gets selected at 3 draws and not selected at the remaining 9 draws)
= [tex]$ (\frac{1}{3})^3 (\frac{2}{3})^9 = \frac{2^9}{3^{12}} $[/tex]
Now, the 3 draws where Adam gets selected can be any 3 out of 12 draws in [tex]$ {\overset{12}C}_3 $[/tex] = 220
Thus, probability of Adam getting three gummi bears = [tex]$ 220 \times \frac{2^9}{3^{12}} $[/tex]
= 0.21186
b). Probability that Adam will get the three gummi bears given each person will received at the most 1 gummi bear
= P(of the remaining 9 draws after assigning one gummi bear to each one, Adam gets selected at 2 draws and not selected at 7 draws) = [tex]$ {\overset{9}C}_2 (\frac{1}{3})^2 (\frac{2}{3})^7 $[/tex]
= 0.23411
c). Let X = Number of the gummi bears which Adam will get. Then, X = number of draws out of 12 draws Adam gets selected and X ~ B(12, 1/3). So, Adam will get gummi bears= mean of B(12, 1/3) = 12 x (1/3) = 4
d). Let Y = Number of the gummi bears that Adam will get, given each person will received at the most 1 gummi bear Then, Y = number of draws Adam gets selected in the remaining 9 draws and Y ~ B(9, 1/3). So, the expected number of bears that Adam gets given each person received at least 1 gummi bear
= 1 + mean of B(9, 1/3) = 4
e). When every one gets atleast one gummi bear, the new sample size will be 9 and so we can say that there is a reduction in variance.
what does x = in this equation? 7x-2+2x+14=33
Answer:
x = 7/3
Step-by-step explanation:
First, combine like terms:
7x + 2x - 2 + 14 = 33
(7x + 2x) + (14 - 2) = 33
9x + 12 = 33
Isolate the variable, note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 12 from both sides:
9x + 12 (-12) = 33 (-12)
9x = 33 - 12
9x = 21
Next, divide 9 from both sides:
(9x)/9 = (21)/9
Simplify. Divide common factors:
x = (21/9)/(3/3) = 7/3
x = 7/3
what are the domain and range of the function represented by the set of order pairs? {(-12,-5),(-10,5),(10,-5),(12,5)}
Answer:
Domain: -12, -10, 10, 12
Range: -5, 5
Step-by-step explanation:
The Domain is the first coordinate which is x.
The Range is the second coordinate which is y.
Hope This Helps :)