The sphere's equation that passes through the given point is:
(x - 3)² + (y - 8)² + (z - 1)² = 30What is the standard equation of a sphere?A sphere's standard equation is defined by its center and radius. Remember that the radius is the distance between any two points on the sphere. The standard formula is: [tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2[/tex]To find the equation of the sphere:
The radius of a sphere is equally distant between any two points on the sphere. The sphere's center is: (3, 8, 1)So,
P = (4, 3,−1)C = (3, 8, 1)r = d(C, p)Now,
[tex]\begin{aligned}&=\sqrt{\left(x_c-x_p\right)^2+\left(y_c-y_p\right)^2+\left(z_c-z_p\right)^2} \\&=\sqrt{(3-4)^2+(8-3)^2+(1-(-1))^2} \\&=\sqrt{(-1)^2+(5)^2+(2)^2} \\&=\sqrt{1+25+4} \\\therefore r &=\sqrt{30}\end{aligned}[/tex]
Supplement the center point and radius into the standard sphere equation:
[tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2\\(x-3)^2+(y-8)^2+(z-1)^2=(\sqrt{30})^2\\(x-3)^2+(y-8)^2+(z-1)^2=30[/tex]
Therefore, the sphere's equation that passes through the given point is:
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The correct question is given below;
Find an equation of the sphere that passes through the point (4, 3,−1) and has to center (3, 8, 1).
a rectangele has and area of 48 in every dimension
f (x) = 2x² - x - 12
Find f(8)
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Answer:
f(8) = 108
Step-by-step explanation:
Hello!
Substitute 8 for x in the equation.
Evaluatef(x) = 2x² - x - 12f(8) = 2(8)² - (8) - 12f(8) = 2(64) - 8 - 12f(8) = 128 - 8 - 12f(8) = 108f(8) is 108.
Options are PR = 18, 14, 9 and 11 please help me with which it is
A bus covers a distance of 60 km in 1 hr, 56km in 2hr ,70km in 3hr, 50km in 4hr,65km in 5 hr, 60 km in 6 hr find the average speed of the bus and draw a graph for this.
A Average speed distance of 60 km in 1 hr, 56km in 2hr ,70km in 3hr, 50km in 4hr,65km in 5 hr, 60 km in 6 hr = 14.61 km/hr
Given:
Average speed=Total distance /Total time
60 km in 1 hr,
56km in 2hr ,
70km in 3hr,
50km in 4hr,
65km in 5 hr,
60 km in 6 hr
Average speed=207/21=14.61
The average speed of a body is the mean value of its speed across time. The formula for average speed is required since the speed of a moving body is not constant and fluctuates over time. Even with changing speed, the values of total time and total distance traversed may be employed, and we can get a single number to describe the complete motion using the average speed calculation.
A body's average speed is equal to the overall distance traveled divided by the entire time spent. The average speed formula is as follows:
Formula for Average Speed:
Average Speed = Total Distance Traveled / Time Spent
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the height of a frame is 2/3 times its width
The height of the frame is 1 m and the width is 1.5 meters.
The height and width are the two dimensions that are used to measure the perimeter of a rectangular frame.
The perimeter is defined as the sum of all sides of a polygon. For a rectangle it is equal to twice the sum of height and width.
Perimeter(p)=2×[height(h)+width(w)]
The given dimensions of the frame is that the height is [tex]\frac{2}{3}[/tex] the width.
Let us consider the width be x.
Hence height=[tex]\frac{2}{3} x[/tex]
Now perimeter =
[tex]2\times(x+\frac{2}{3}x) \\=\frac{10}{3} x[/tex]
But the given perimeter is 5 meter.
Therefore:
[tex]\frac{10}{3} x=5\\or,x=5\times 3\div 10\\or,x=1.5[/tex]
Therefore the width is 1.5 meters.
Height=[tex]\frac{2}{3} \times 1.5\\[/tex]=1 meter.
So we can conclude that the width is 1.5 meters and the height is 1 meter.
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A person's grade in school is generally identified by a number. give an example of a situation in which grade level is treated as categorical.
The grade level is treated as categorical when a principal wants to know the number of students from each grade will be participating in a performance.
Variables can be classified into quantitative and categorical. Quantitative variables are those which carry numerical values. Even though a person's grade in school is generally identified by a number, it is a categorical variable. Categorical variables classify data into different groups as the grade level. The grade level categorizes students into different grades and each grade level represents a particular grade only.
Any variable which is partly qualitative and represents groups of data are called categorical variables. Also grade level is ordinal. An example of a situation in which grade level is treated as categorical is when a principal wants to know how many students from each grade will be participating in a performance. Other examples of categorical variables are race, gender, age group, etc.
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Nilai dari sin 135, bantuin kakk pliss
Answer:
[tex] \frac{ \sqrt{2} }{2} \: or \: 0.7071[/tex]
Step-by-step explanation:
[tex] \sin(135) = \frac { \sqrt{2} }{2} \: or \: 0.7071 [/tex]
George wants 42 liters of a mixture of water and 15% lemon juice. he has a mixture of 5% lemon juice and a mixture of 20% lemon juice. how many liters of the 5% and 20% mixtures should he mix to get what he wants? (round you answer to the nearest tenth if necessary.)
The amount of 5% lemon juice mixture and 20% lemon juice mixture that needed to be mixed is 14 liters and 28 liters, respectively.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the amount of 5% lemon juice mixture that is needed to be mixed be represented by x, then the amount of 20% lemon juice mixture will be represented by (42-x), because the total mixture is needed to be 42 liters.
Now, given that George wants 42 liters of a mixture of water and 15% lemon juice with a mixture of 5% lemon juice, and a mixture of 20% lemon juice. Therefore, we can write,
5% of x + 20% of (42-x) = 15% of 42 liters
0.05x + 0.2(42 - x) = (0.15×42)
0.05x + 8.4 - 0.2x = 6.3
0.05x - 0.2x = 6.3 - 8.4
-0.15x = -2.1
x = -2.1 / -0.15
x = 14
Further, the amount of mixture of lemon juice that is needed to be mixed can be written as,
5% lemon juice mixture, x = 14 liters20% lemon juice mixture, (42 - x) = 28 litersHence, the amount of 5% lemon juice mixture and 20% lemon juice mixture that needed to be mixed is 14 liters and 28 liters, respectively.
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5) One band rented a van to travel to Omaha. The band started out at 9:00AM, took a break at 9:32AM, and finally arrived in Omaha at 10:04AM. How many minutes did it take the band to reach Omaha?
Answer:
1 hour and 4 minutes
Step-by-step explanation:
A rectangular field is 35 m longer than it is wide. The length of the fence around
the perimeter of the field is 290 m.
a. 1+35= w
b.
1=w+35
21+2w=290
21+2w=290
C.
1=w+35
1+w=290
d. 1=w+35
Iw=290
Answer:
length = 90
width = 55
Step-by-step explanation:
Let W = width.
Let L = length.
L = W + 35
P = 2(W + L)
290 = 2(W + W + 35)
4W + 70 = 290
4W = 220
W = 55
L = W + 35 = 55 + 35 = 90
One number is six more than the other number . thesum of their squares is 90
Answer:
the answer is 3 and 9. 9 is 6 greater than 3 and 9 squared and 3 squared added up give you 90.
Translate each phrase into an algebraic expression: Jame has 20 more dollars than 3 times the amount Brittany has.
x = 20+ 3y
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
Jame = x
Brittany = y
x = 20+ 3y
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Y varies jointly as a and n2 when s=7 and n=4, y=336. find y when s is 12 and n is 7
Y= 1764
It is given that y varies jointly as s and n2
From the given question if s = 7 and n = 4 then y =336
So,
y= k * s * n^2
Let k a constant number
336= k * 7 * 4^2
336 = k *7* 16
336 = k * 112
Therefore, k = 3
So now we get the General equation i.e
y= 3 * s * n^2
Now we have to find the value of y when s= 12 and n= 7
Y=3* 12* 7^2
= 3*12*49
=1764
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PLS ASAP AND TY IF U ANSWERED
Answer:
3.5 un
Step-by-step explanation:
to find the new length of the square using a scale factor of 1/7 you can just multiply 24.5 by 1/7
this is basically dividing 24.5 by 7
24.5 / 7 = 3.5
that is your answer
PLEASE HELP ME!
How do the graphs of y = f (x) + k, y = f(x – h), and y = -f(x) compare to the graph of the parent function f?
f(x) + k will shift the graph up k units.
For example, the notation f(x) + 5 will shift the curve up by 5
If k is negative, then the curve shifts down that amount
-------------------------
f(x-h) shifts the graph to the right h units
Example: f(x-2) shifts to the right 2 units
Another example: f(x+7) shifts left 7 units. In this case, h = -7
--------------------------
y = -f(x) is a reflection over the x axis
This is because we're multiplying each y coordinate by -1
A point like (1,2) reflects to (1,-2)
Problems.
87. the 4550 men in the arena comprised 85% of the people in
the arena. how many people were in the arena?
There are 5354 people were in the arena.
Percentage:
The term percentage is referred as a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
The formula for calculating the percentage is,
Percentage = (Actual value/Total value) x 100
Given,
Here we have that, 4550 men in the arena comprised 85% of the people in the arena.
Now we need to find how many people were in the arena.
Let p be the number of people in Arena.
So, based on the percentage formula,
It can be written as,
=> 85% = (4550 / p) x 100
=> 85/100 = 4550 /p
=> 0.85 = 4550/p
=> 4550/0.85 = p
=> p = 5354
Therefore, there are 5354 people were in the arena.
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Drama Teacher's Friend
Find the number that replaces each letter to complete the pattern in the
sequence. Use that number to replace the letter in the ordered pairs.
A =
1, 3, A, 7, 9, 11, B
3, C, 12, 24
2, 1, D, -1, -2, E, -4
F, 4, 9, 16, 25
7, 3,-1, G, -9
|||||||||||||||
E =
F =
G=
Answer:
hi 8jgvjig up uttgui86yghjSolve for x in the given equation: 1/5 x = 2/5 What would be the inverse operation you would use to solve for x?
HELP! (3x4)+ 52 MARKING BRAINLY!
Answer:
64
Step-by-step explanation:
[tex]3 \times 4\\= 12\\= 12 + 52\\= 64[/tex]
Answer:
64
Step-by-step explanation:
first 3 x 4 = 12
12+52=64
(-13,2)(-17,9) find the slope of the line through each pair of points
Work Shown:
[tex](x_1,y_1) = (-13,2) \text{ and } (x_2,y_2) = (-17,9)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{9 - 2}{-17 - (-13)}\\\\m = \frac{9 - 2}{-17 + 13}\\\\m = \frac{7}{-4}\\\\m = -\frac{7}{4}\\\\[/tex]
A slope of -7/4 means that we move down 7 and to the right 4.
Make a Prediction Predict the sum of -2 + 2. Explain
your prediction and check it using the number line.
Answer:
My prediction of the sum is 0.
Hope this helps :)
Step-by-step explanation:
It is 0 because if you owe 2 dollars and you pay it back with 2 dollars then you have 0 dollars owed.
--------------------> 2nd: 2 (positive two - move right)
<-------------------- 1st: - 2 (negative two - move left)
<----------l----------l-----------l----------l----------l--------->
-2 -1 0 1 2
j + (-6); j = -3 “evaluate each expression for the given value”
Answer:
-3+(-6)= -9
Step-by-step explanation:
Each small square in the graph paper represents 1 square unit. Find the area of each figure. Explain your reasoning.
A
B
W
the firstone is 9 the seconf one is 14
Answer:
A. 7.5
B. 10
Step-by-step explanation:
The first one is 3x2 + half of 3x1 for 6 + 0.5*3 total.
The second one is 3x2 + 4 times half a 2x1 for 6 + 4 * 0.5 * 2 = 10
Find the derivative of the function using the definition of derivative. f(x) = kx d
Derivatives are essential for solving calculus and differential equation problems then the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]
What is meant by derivatives?The rate of change of a function with respect to a variable in Mathematics. Derivatives are essential for solving calculus and differential equation problems.
Given a traditional unbent position, f(x) = kx + d, where k is the pitch and (0, d) is the y-intercept.
a) Consider our position at two distinct points first:
f(x) = kx + d
f(x + h) = k(x + h) + d = kx + kh + d
Evaluate the derivative, then
[tex]$\lim h \rightarrow x \frac{f(x+h)-f(x)}{h}[/tex]
substitute the values in the above equation, we get
[tex]$&=\lim h \rightarrow x \frac{(k x+k h+d)-(k x+d)}{h} \\[/tex]
simplifying the above equation, we get
[tex]$&=\lim h \rightarrow x \frac{k h}{h} \\[/tex]
[tex]&=\lim h \rightarrow x k \\[/tex]
= k
Therefore, the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]
b. Since the actual function is linear, its part is all real numbers by definition.
c. Since the product is a constant function, its part is all real digits by meaning.
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Which factor provides the basis for the grading of newly diagnosed malignant tumors? size of the tumor x number of metastases degree of differentiation of the cells number of lymph nodes involved
The factor that provides the basis for the grading of newly diagnosed malignant tumours is degree of differentiation.
What is the degree of differentiation?The level of differentiation impacts an individual's capacity to control their emotions, thoughts, individuality, and connections to others. The degree of any differential equation can be obtained when it is expressed as a polynomial; otherwise, the degree cannot be defined.
The mechanisms by which immature cells develop into mature cells with particular roles are described in biology. This indicates the degree to which tumour tissue resembles the healthy tissue from which it originated in the context of cancer. Compared to poorly or undifferentiated cancer cells, well-differentiated cancer cells resemble normal cells more and grow and spread more slowly. Tumour grading systems, which vary for each form of cancer, use differentiation.
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The Amari family installed an inground pool, what is the volume of the inground pool?
50 points for the answer
Answer:
154^2ft
Step-by-step explanation:
you multiply LxWxH for getting the volume
Elsa opens an account to save money for a family vacation. the account earns an annual interest rate of 4% 4 % . she earns $37 $ 37 in simple interest after 6 6 months.
Amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
As given,
Simple interest amount earned by Elsa = $37
Annual interest rate R= 4%
Time T =6 months
Let P be the principal amount she put while opening account
Simple interest = (P × R × T) / 100
⇒37 ={P × 4 × (6/12)}/100
⇒P =(37 × 100) / 2
= $1850
Therefore, amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
The complete question is:
Elsa opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in simple interest after 6 months. How much money did she put in the account when she opened it?
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f (x) = -4x² + 10x + 13
Find f(7)
Will give brainliest and 5 star rating. Thank you. :)
Answer:
f(7) = -113
Step-by-step explanation:
Hello!
Substitute 7 for x in the equation.
Evaluatef(x) = -4x² + 10x + 13f(7) = -4(7)² + 10(7) + 13f(7) = -4(49) + 70 + 13f(7) = -196 + 70 + 13f(7) = -113f(7) is -113.
Converting units is always an exercise in linear relationships. how many inches is 2.50 m? (2.54 cm=1.0 inch)
There are 98.4252 inches in 2.50m.
Unit Conversion is defined as a process that involves multiplication and division by a numerical factor or a particular conversion factor.
For Example .Convert 2m into cm.
As we know that 1m=100cm
multiplying both sides by 2 we get
2m = 200 cm.
According to the question
It is given that 2.54 cm = 1 inch
[tex]1cm = \frac{1}{2.54} inch[/tex]
[tex]100cm=\frac{100}{254} inch[/tex]
[tex]1m = \frac{100}{2.54}[/tex] ( as 100cm = 1m)
we need 2.50 m So we multiply both sides by 2.50
[tex]2.50m=\frac{2.50*100}{2.54} \\\\ 2.50m=\frac{250}{2.54}[/tex]
[tex]2.50m=98.4252 inch[/tex]
Therefore , there are 98.4252 inches in 2.50m.
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Please help loll and show your work if you can
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
10) -6(-5+r) = 102
30 -6r =102
-6r = 72
r = -12
11) -1 = x - 4 +4
x =-1
12) 0 = -6x -2x
-8x = 0
x= 0
13)5n+ 4n =9
n =1
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