Given :
Center of sphere , C( 1 , -1 , 6 ) .
To Find :
Find equations of the spheres with center (1, −1, 6) that touch the following planes.a) xy-plane b) yz-plane c) xz-plane .
Solution :
a)
Distance of the point from xy-plane is :
d = 6 units .
So , equation of circle with center C and radius 6 units is :
[tex](x-1)^2+(y-(-1))^2+(z-6)^2=6^2\\\\(x-1)^2+(y+1)^2+(z-6)^2=36[/tex]
b)
Distance of point from yz-plane is :
d = 1 unit .
So , equation of circle with center C and radius 1 units is :
[tex](x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1[/tex]
c)
Distance of point from xz-plane is :
d = 1 unit .
So , equation of circle with center C and radius 1 units is :
[tex](x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1[/tex]
Hence , this is the required solution .
4.5 and 5 are respectively the average of 2sets of number 3, 4, x, y and 2x, y, 4, 3, find the value of x, y
Step-by-step explanation:
4.5 * 4 = 18.
3 + 4 + x + y = 18, x + y = 11.
5 * 4 = 20
2x + y + 4 + 3 = 20, 2x + y = 13
Hence, x = 2 and y = 9.
use rounding to estimate the product of 198 and 42 round to nearest 10
Answer:
≈ 8000
Step-by-step explanation:
Step 1: Round 198
198 ≈ 200
Step 2: Round 42
42 ≈ 40
Step 3: Multiply
200(40) = 8000
Real answer is 8316.
PLEASE HELP!! WILL GIVE BRAINLIEST TO THE FIRST PERSON
Answer:
x=10
Step-by-step explanation:
I believe if you're trying to solve for x and the two lines are the same length, you just have to set the values equal to each other and solve.
Step-by-step explanation:
12 =x+3
x=9
3x -11
3(9) - 11
27-11
=16
The toy horse collection contains 10 horses. You purchase the set and then sell 3 horses to Kate. If you only charge the exact price (no tax involved), how much does Kate pay you?
Answer:
three tenths of the original amount
Let's start.
There are 10 horses.
(Buying the set is not important, since it does not affect this scenario.)
You sell three horses to Kate, and you expect her to give you the exact price.
Let's say that 10 horses cost the total (unknown).
10 horses equal the total amount, or 1
10 to 1
Now, you sell 3 of these horses. You must multiply 10 and n to make 3.
10 x n = 3
10x 3/10 = 3
Do the same to the other side.
1 x 3/10 = 3/10
3 to 3/10
can someone help with this please!! 2f^0p^3×5g^2
Answer:
Step-by-step
Rank Topic Problem Formatted Problem
77201 Solve for g 4g=24
4
g
=
24
4
g
=
24
77202 Solve for g 4g-2=22-8g
4
g
−
2
=
22
−
8
g
4
g
-
2
=
22
-
8
g
77203 Solve for g -4gh-8gi-2g+1=6h-6
−
4
g
h
−
8
g
i
−
2
g
+
1
=
6
h
−
6
-
4
g
h
-
8
g
i
-
2
g
+
1
=
6
h
-
6
77204 Solve for g 5g+2=3g+12
5
g
+
2
=
3
g
+
12
5
g
+
2
=
3
g
+
12
77205 Solve for g 5g=W
5
g
=
W
5
g
=
W
77206 Solve for g 5g-3g+g+8=2g+1+g+g
5
g
−
3
g
+
g
+
8
=
2
g
+
1
+
g
+
g
5
g
-
3
g
+
g
+
8
=
2
g
+
1
+
g
+
g
77207 Solve for g 6=-3/7g
6
=
−
3
7
g
6
=
-
3
7
g
77208 Solve for g -6g+36=12
−
6
g
+
36
=
12
-
6
g
+
36
=
12
77209 Solve for g 6g=100
6
g
=
100
6
g
=
100
77210 Solve for g 6g-3.5=8.5
6
g
−
3.5
=
8.5
6
g
-
3.5
=
8.5
77211 Solve for g 7(g-2)=5(g+4)
7
(
g
−
2
)
=
5
(
g
+
4
)
7
(
g
-
2
)
=
5
(
g
+
4
)
77212 Solve for g 7+(5g)/2=-13
7
+
5
g
2
=
−
13
7
+
5
g
2
=
-
13
77213 Solve for g 7200mg=g
7200
mg
=
g
7200
mg
=
g
77214 Solve for g 7800g=kg
7800
g
=
kg
7800
g
=
kg
77215 Solve for g 18-2g=4g
18
−
2
g
=
4
g
18
-
2
g
=
4
g
77216 Solve for g 18g+11=22g+27
18
g
+
11
=
22
g
+
27
18
g
+
11
=
22
g
+
27
77217 Solve for g 19*23=17g
19
⋅
23
=
17
g
19
⋅
23
=
17
g
77218 Solve for g 2.5g=17.5
2.5
g
=
17.5
2.5
g
=
17.5
77219 Solve for g 2|g+1|=14
2
|
g
+
1
|
=
14
2
|
g
+
1
|
=
14
77220 Solve for g 20+5g=10
20
+
5
g
=
10
20
+
5
g
=
10
77221 Solve for g g(x)=(x+6)/(x^2+2x-35)
g
(
x
)
=
x
+
6
x
2
+
2
x
−
35
g
(
x
)
=
x
+
6
x
2
+
2
x
-
35
77222 Solve for g 21.26=4g+3.54
21.26
=
4
g
+
3.54
21.26
=
4
g
+
3.54
77223 Solve for g 219÷104=2*(pv(1.34g))
219
÷
104
=
2
⋅
(
p
v
(
1.34
g
)
)
state the solutions for the quadratic equation depicted in the graph.
Answer:
(-4,0), (-3,0)
Step-by-step explanation:
The solution of a quadratic equation is simply when the graph crosses the x-axis. This is because at that point, the function will equal 0.
From the graph, we can see that the graph touches the x-axis at x=-4 and x=-3.
Therefore, our solutions for the graphed quadratic is x=-4 and x=-3.
And we're done!
Evaluate the expression 2*2^3*5-3
Answer:
77 would be the right answer
Help me with this one too
Answer:
2 + 8 -7 = 3
Hope it helps.......
-ayuda ¡¡¡ Se tiene previsto implantar un proyecto de "Caucho sintético" cuya inversión sería de S/ 2 500 000, para un tamaño de planta de 12 000 toneladas anuales. Luego de estudiar el proyecto, los promotores estiman que es más conveniente un tamaño de 19 200 toneladas por año. ¿A cuánto ascenderá la inversión total, si el exponente del factor de escala es α=0,63? ayuda !!!!!
Answer:
En caso de un tamaño de producción de 19,200 toneladas anuales, el costo de inversión total ascenderá a $3,999,936.
Step-by-step explanation:
Dado que la inversión inicial será de $ 2,500,000 para un tamaño de planta de 12,000 toneladas anuales, se estima que cada tonelada requiere una inversión de $208.33 (2,500,000 / 12,000).
Por lo tanto, en caso de una producción anual de 19,200 toneladas, el costo de inversión aumentará según lo establecido en la siguiente multiplicación:
208.33 x 19,200 = X
3,999,936 = X
Por lo tanto, en caso de un tamaño de producción de 19,200 toneladas anuales, el costo de inversión total ascenderá a $3,999,936.
A figure was created using a triangle and a semicircle. Use the ruler provided to measure the dimensions of the triangle and the semicircle to the nearest centimeter.
Which measurement is closest to the area of the figure in square centimeters?
A.
78 cm2
B.
81 cm2
C.
106 cm2
D.
53 cm2
Answer: D
Step-by-step explanation:
f(x) = 6x2 + 2 what is the domain
Answer:
All Real Numbers
Step-by-step explanation:
[tex]f(x)=6x^2+2[/tex]
To find the domain of a quadratic function, we can make a table.
x y f(x)=6x^2+2
-1 8 6(-1)^2+2
0 2 6(0)^2+2
1 8 6(1)^2+2
You can keep going and identity that all the x values/ domains are real numbers.
10- (6m + 7) what is this
Answer:
3 + 6m
Step-by-step explanation:
If you are just trying to get a simplified term, then follow these steps.
10 - (6m + 7)
10 - 7 + 6m
3 + 6m
Given the function k(t)=2t−1: a. Evaluate k(2). b. Solve(k)=7.
Answer:
[tex]k(2) = 3[/tex]
[tex]t = 4[/tex]
Step-by-step explanation:
Given
[tex]k(t) = 2t - 1[/tex]
Solving (1): k(2)
Take t as 2 such that t = 2
This gives
[tex]k(2) = 2 * 2 - 1[/tex]
[tex]k(2) = 4 - 1[/tex]
[tex]k(2) = 3[/tex]
Solving (2): k(t) = 7
Substitute 7 for k(t)
[tex]7 = 2t - 1[/tex]
Add 1 to both sides
[tex]7 + 1 = 2t - 1 + 1[/tex]
[tex]2t = 8[/tex]
Divide both sides by 2
[tex]t = \frac{8}{2}[/tex]
[tex]t = 4[/tex]
What is absolute value ?
Answer:
the magnitude of a real number without regard to its sign.
Step-by-step explanation:
Solving Absolute Value is just asking you how far away -4 is from zero. Since distance is always a positive number (you can't travel "negative" steps, just steps in a different direction), the result of absolute value is always positive. Make the number in the absolute value sign positive.
A certain triangle has perimeter of 3080 mi. The shortest side measures 78 mi less than the middle side, and the longest side measures 377 mi more than the middle side. Find the lengths of the three sides.
Answer:
Smallest=849mi
Middle=927mi
Largest=1304mi
Step-by-step explanation:
My work is in the attachment but here are some notes:
Draw a diagram and use the given info to label itSet up an equation which relates all the sides (in this case they add up to the perimeter) using a variable (I picked m because each side is based off of the middle distance)Solve for your variable and plug it back into the original equation to find your values(4.5 x 104) + (300) =
Answer:
768
Step-by-step explanation:
1.6=Y/1.5 WHAT IS THE ANSWER
Isolate the variable Y by multiplying 1.5 on both sides.
[tex]Y=1.6*1.5[/tex]
[tex]Y=2.4[/tex]
Hope this helps.
頑張って!
Answer:
y=2.4
Step-by-step explanation:
You need to get Y alone so just multiply it with the reciprocal: 1.5/1 on both sides. This cancells out the denominator and just multiplies 1.6 with 1.5 to get 2.4
Write 1/10 as a decimal number
Answer:
0.1
Step-by-step explanation:
hope this helps
A media personality argues that global temperatures are not rising, because every year an increase is reported such as 0.08 degrees C. The difference from the previous year is less than the margin of error of about 0.15 degrees C, so that difference should be ignored. What is a strong counterargument?
Answer
:we are told that every year the temperature rises by 0.08degrees Centigrade,
So the difference between margin of error and the increase is much higher
That is
0.15-0.08=0.07
But remember Margin of error=Critical value *Standard deviation of population
And it is a quantity that measures accuracy
So the counter argument is that this is still an increase and it should be considered.
.
Answer:
The difference with any previous decade is much greater than the margin of error
Step-by-step explanation:
show that the sequence with sum of the first n term sn=3n²+5n is an arithmetic sequence.
Answer:
The formula says that the sum of the first n terms of our arithmetic sequence is equal to n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.
what value of x makes the equation 7x-2(3x+1)=4x-(3-x)-19 true?
Answer:
X=5
Step-by-step explanation:
HELP ME!!
The square of the sum of seven times a number and
seven
7(n+7)^2
seven times the number and seven squared
If fx) = 3x - 2 and g(x) = 2x + 1, find (f+g)(x).
A.5x-3
B.5x-1
C.x-1
D.x-3
Look at the graph. On a coordinate plane, a graph increases through (negative 1, 4), levels off at (0, negative 3), and then increases up through (2, 5). Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction = StartFraction 1 Over 1 EndFraction = 1. and the rate of change between the points (0, -3) and (2, 5) to be StartFraction 5 minus (negative 3) Over 2 minus 0 EndFraction = StartFraction 8 Over 2 EndFraction = 4. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong? The points (–1, –4), (0, –3), and (2, 5) are not all on the graph. The expressions StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction and StartFraction negative 3 minus (negative 5) Over 2 minus 0 EndFraction both equal 1. She miscalculated the rates of change. Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.
Answer:
Answer is A
explanation:
there is no point (0.-3) on the graph.
Answer:
it's D edg 2020
Step-by-step explanation:
What is the area of this figure?
Answer:
44 cm^2
Step-by-step explanation:
You can separate this figure into three rectangles. The area of the first rectangle is 20. The area of the second rectangle is 6. And the area of the third is 18. If you add those all together you get 44 cm^2
An explorer is climbing up and rappelling down a series of cliffs and drop-offs. She starts at her base camp, which is on the middle of a mountain. She begins by rappelling down an 82.5-foot drop-off and then climbs a cliff of 30.4 feet. Next she rappels down a 45.5-foot drop-off and then climbs a 25.2-foot cliff.Finally she makes two 45.4-foot climbs. Part A: How far above or below her base camp is the explorer now?
Answer:
162.8 above her camp site she starts at the middle and drops 82.5 and then climbs 30.4 which puts her at 52.1 then by her repelling down another 45.5 drop she then proceeds to climb 25.2 which puts her at 72.4 and if you multiplie 45.4 by 2 it counts for the extra 90.4 drop which then concludes her climb to be bellow her site by 162.8 and the 1st word is supposed to be bellow my bad.
Step-by-step explanation:
step by step is above
60) 786
Long division?
Answer:
This image will help!
Thanks and have a good day.
The table shows four members numerous expressions which expression is an integer when it evaluated?
Answer:
could you include the table?
Step-by-step explanation:
Examples: Determine if the graph is a function. If it is, state the domain and range.
Answer:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.Jan 8, 2019
Step-by-step explanation:
Ten people ordered calculators. The least expensive was $29.95 and the most expensive was $89.95. Half of them ordered a $69.95 calculator. Select the best
estimate of the amount spent on calculators.
$490
$660
$550
$805
Choose the best estimate for the total amount spent for all 10 calculators.
O A. $805
OB. $490
OC. $550
OD. $660
Answer:
310
Step-by-step explanation:
least money 19.95
Most money = 39.95
Mean = (least+most)/2 = 29.95
money for half people = 5 × (mean) 29.95
Amount of money for half people = 149.75
Lower limit for amount of the other half = 19.95 × 5 = 99.75
The Upper limit for the amount of the other half = 39.95 × 5 = 199.75
Mean = (99.75 + 199.75)/2 = 149.75
Total money spent (Mean) = 149.75 + 149.75 = 299.5
The Best estimate is B) 310 because it is closest to 295.5
A mean is an arithmetic average of a set of observations. The correct option is D.
What is Mean?A mean is an arithmetic average of a set of observations. It is given by the formula,
Mean = (Sum of observations)/Number of observations
To make the calculations easy let's round off the given numbers. Therefore, we can write the values as,
Least expensive A=30Most expensive B=90half of order C=70Now, the mean and the money for half the people can be written as,
Mean = (least + most)/2 = 60
money for half people = 5 × 60
Therefore, the amount of money for half people will be,
Amount of money for half people = 300
Lower limit for amount of the other half = 29.95 × 5 = 149.5
The Upper limit for the amount of the other half = 89.95 × 5 = 449.75
Mean = (149.75 + 449.75)/2 = 299.6
Total money spent (Mean) = 299.6 + 299.6 = 599.25
Hence, The Best estimate is $660. This is because it is closest to 599.25.
Learn more about Mean here:
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