Answer:
The equation is:
(1/a)x + (1/b)y + (1/c)z = 1
Step-by-step explanation:
The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:
<0 - a, b - 0, 0 - 0>
<-a, b, 0> .....................(1)
The direction vector between (0, 0, c) and (0, b, 0) is given as:
<0 - 0, b - 0, 0 - c>
= <0, b, -c> .....................(2)
To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).
Doing this, we have:
<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>
To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:
(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0
(bc)x + (ac)y + (ab)z = (ac)b
Dividing both sides by abc, we have:
(1/a)x + (1/b)y + (1/c)z = 1
We will call π, the plane with points P, Q, R ( the intercepts )
The solution is:
π : -bc×x + ac×y -ab×z - bac = 0
c) d = | bac|/√ ( -bc)² + (-ac)² + ( -ab)²
The intercepts P Q R are three points of the plane, according to that
P ( 0, b, 0 ) intercept with y-axis
Q ( a, 0, 0 ) intercept with x-axis
R ( 0, 0, c ) intercept with z-axis
We will find the vectors PQ and PR both are on the plane
PQ = [ a, 0, 0 ] - [ 0, b, 0 ] ⇒ PQ = ( a , -b, 0 )
PR = [ 0, 0, c ] - [ 0, b, 0 ] ⇒ PR = ( 0, -b c )
The vectorial product of these two vector will give us, one normal vector to the plane.
i j k
PQ * PR = a -b 0 = i (-bc) - j ( ac - 0 ) + k ( -ab - 0)
0 -b c
PQ * PR = [ -bc, -ac, -ab ]
we call this vector n = [ -bc, -ac, -ab ]
Let´s now find a vector between P, and a general point T ( x , y , z ) on the plane.
PT = [ x, y, z ] - [ 0, b, 0 ] ⇒ PT = [ x-0 , y - b , z - 0 ]
PT = [ x, y-b, z ]
Vector PT is perpendicular to vector n, then their dot product must be 0
Then:
PT × n = 0
[ x, y-b, z ] × [ -bc, -ac, -ab ] = 0
x × (-bc) + ( y - b )× (ac) + z × (- ab) = 0
-bc×x + ac×y -bac - ab×z = 0
-bc×x + ac×y -ab×z = bac (1)
Finally, we got the implicit equation for plane π as:
π : -bc×x + ac×y -ab×z - bac
c) The distance (d) between the plane and the origin is:
d = | D | / | n |
| n | = √ ( -bc)² + (-ac)² + ( -ab)²
|D| = | bac| the right side of the equation (1)
Then
d = | bac|/√ ( -bc)² + (-ac)² + ( -ab)²
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X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 51, σ = 10, find P(36 ≤ X ≤ 56)
Answer:
0.6247
Step-by-step explanation:
The formula for calculating a Z-score is Z = (X - μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question,
μ = 51, σ = 10. We are to find P(36 ≤ X ≤ 56)
Step 1
Find the Probability of X ≤ 36
μ = 51, σ = 10
Z = (X - μ)/σ
Z = 36 - 51/ 10
Z = -15/10
Z = -1.5
We find the Probability of Z = -1.5 from Z-Table
P(X <36) = P(X = 36) = P(Z = -1.5)
= 0.066807
Step 2
Find the Probability of X ≤ 56
μ = 51, σ = 10
Z = (X - μ)/σ
Z = 56 - 51/ 10
Z = 5/10
Z = 0.5
We find the Probability of Z = 0.5 from Z-Table:
P(X < 56) = P(X = 56) = P(Z = 0.5)= 0.69146
Step 3
Find P(36 ≤ X ≤ 56)
P(36 ≤ X ≤ 56) = P(X ≤ 56) - P(X ≤ 36)
= P( Z = 0.5) - P(Z = -1.5)
= 0.69146 - 0.066807
= 0.624653
Approximately to 4 decimal places , P(36 ≤ X ≤ 56) = 0.6247
Describe how to determine the average change between x=3 and x=5 forbthe function f(x)=3x^3+2
Answer:
147
Step-by-step explanation:
f(3)=83
f(5)=377
377-83=294
5-3=2
294/2=147
To find the average rate of change, we divide the change in the output value by the change in the input value.
Use the distributive property to simplify the expression 3(4x + 9).
Answer:
12x+27
Step-by-step explanation:
The solution is A = 12x + 27
The value of the equation is A = 12x + 27
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
A = 3 ( 4x + 9 )
Now , on simplifying the equation , we get
By using the distributive property in the equation
Multiplying by 3 on both the values in the brackets , we get
A = 3 ( 4x ) + 3 ( 9 )
On further simplification of the equation ,
The value of A = 12x + 27
Therefore , the value of A is 12x + 27
Hence , the value of the equation is A = 12x + 27
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3lbs of sour candies cost 4.50. what is the unit price
Answer:
$1.50
Step-by-step explanation:
1.50 x 3 = 4.50
Answer:
1.50$ per pound
Step-by-step explanation:
Step 1: State what is known
They tell us that 3 pounds cost 4.50$
Step 2: Find how much 1 pound cost
We divide 4.50$ by 3 to find out how much 1 pound costs
4.5/3 = 1.5
Therefore 1 pound of sour candies cost 1.50$
Convert the equation:
[tex]6x ^{2} - 3y ^{2} + 12x - 18y - 3 = 0[/tex]
to the standard form of a hyperbola.
Answer:
(x+1)²/6 - (y+3)²/12 = 1
Step-by-step explanation:
The standard form of writing the equation of an hyperbola is expressed as;
(x-h)²/a² - (y-b)²/b² = 1 where (h,k) is the centre of the hyperbola.
Given the equation:
6x²-3y²+12x-18y-3 = 0
We are to convert it to the standard form of writing the equation of a hyperbola.
Collecting the like terms will give;
(6x²+12x)-(3y²+18y)-3 = 0
Divide through by 3
(2x²+4x)-(y²+6y)-1 = 0
Completing the square of the equation in parenthesis and adding the constants to the other side of the equation:
(2x²+4x)-(y²+6y+(6/2)²)-1 = 0+(6/2)²
(2x²+4x)-(y²+6y+9)-1 = 9
2x²+4x -{(y+3)²} = 9+1
2x²+4x - (y+3)² = 10
Divide through by 2
x²+2x -(y+3)²/2 = 5
(x²+2x+(2/2)²)-(y+3)²/2 = 5+(2/2)²
(x²+2x+1) - (y+3)²/2 = 5+1
(x+1)²-(y+3)²/2 = 6
Divide through by 6
(x+1)²/6 - (y+3)²/12 = 1
The resulting equation is the required standard form of a hyperbola with centre at (-1, -3)
Use compatable numbers, then divide. 448 ÷ 8 a. 450 ÷ 10 = 45 b. 500 ÷ 10 = 50
Answer: B
Step-by-step explanation: I think thats right
What percent of the cube of 5 is 5?
Answer:
4%.
Step-by-step explanation:
The cube of 5 is 125.
So the required percentage is (5 * 100) / 125
= 500/125
= 4%.
Prove using the trigonometric identities the following equation
Answer:
Step-by-step explanation:
[tex]\frac{(1-cosA)^2+sin^2A}{sinA(1-cosA) }=\frac{1-2cosA+cos^2A+sin^2 A}{sinA(1-cos A)}[/tex]
[tex]=\frac{2-2cos A}{sinA(1-cosA)}[/tex]
[tex]=\frac{2(1-cosA)}{sinA(1-cosA)}=\frac{2}{sinA}=2cscA[/tex]
what is the definition of addition
Answer:
the difinition of addition is adding two things together
Step-by-step explanation:
Answer: Hi!
The definition of addition is when you add two or more more numbers (positive or negative.)
Hope this helps!
Cubes are to be stacked in perfectly square layers that can be 5x5 (25 cubes), 4x4 (16 cubes), 3x3 (9 cubes), 2x2 (4 cubes), and 1x1 (1 cube). Each layer above the bottom one must have fewer cubes in it than the layer below it. If you have 54 cubes, and all of them must be stacked, what is the smallest bottom layer you can possibly have?
Answer:
25 cubes
Step-by-step explanation:
Conditions are:
Each layer must be a perfect squareThe layers must be smaller starting from the bottom layerThere are 54 cubes and all of them must be stackedThen the the option is:
5*5 + 4*4 + 3*3 + 2*2 = 25 + 16 + 9 + 4 =54So the smallest bottom layer is 5*5 = 25 cubes and the layers from the bottom are:
25, 16, 9, 4 cubesDoes a regular pentagon tessellate? if yes, why and if no, why?
Answer:
No.
Step-by-step explanation:
A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 108°, is not a divisor of 360°.
1-1 Relations and Functions Marcus drives 32 miles to work each day. He records the number of minutes it takes him to drive and writes his average speed as the input and the number of minutes as the output. He recorded his information in a table, like the one shown below. Speed (mph) Time (minutes) 60 32 45 43 55 35 50 38 62 31 If Marcus drives no faster than 65 miles per hour, what is the domain that includes all possible average speeds using interval notation? O A. [0, 65] B. [65,-) O C. (0, 65) D. (65,-)
Answer:
A. [0, 65]
Step-by-step explanation:
Given that
Distance that Marcus drives every day = 32 miles.
The table having average speed as input and time taken as output is shown below in the table format:
[tex]\begin{center}\begin{tabular}{ c c}Speed(mph) & Time(minutes) \\ 60 & 32 \\ 45 & 43 \\ 55 & 35 \\ 50 & 38 \\ 62 & 31 \\\end{tabular}\end{center}[/tex]
To find:
The domain that includes all possible average speeds using interval notation = ?
Solution:
First of all, let us understand what is a domain of a function.
Domain of a function is set of valid input values that can be provided to the function so that it has a valid output.
If a function is written as:
[tex]y=f(x)[/tex] then values of [tex]x[/tex] are the input given to the function.
In the given question statement, we are given that maximum Average speed attained by Marcus is 65 miles per hour.
That means domain has a maximum value of 65.
Let us learn something about interval notation.
( or ) means the value is not inclusive.
[ or ] means the value is inclusive.
Here 65 will be inclusive.
On the left side of comma, lower value is written and on the right side of comma, larger value is written.
So, domain for the current situation will be:
[0, 65]
0 is taken as the minimum value of domain here, because average speed value can not be negative.
This interval will contain all the possible values of input (average speed) as shown in the above table of values.
if the farm needs to pack 12,70,224 litchis in boxes that hold 144 litchis ,how many boxes would be required .
For this, we will divide 1,270,224 by 144.
1,270,224 ÷ 144 = 8,821.
For this result, we can conclude that the number of boxes required to pack 1,270,224 litchis is 8,821 boxes.
Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME
Answer:
The answer is A. CommutativeStep-by-step explanation:
What is cumulative property?
In mathematics it has to do with movement of digits/factors without affecting the overall outcome of an operation
in addition of numbers, commutative explains that
A+B= B+A which ever way it must give the same outcome
example say A= 2
and B= 3 then
2+3= 3+2
5= 5
In multiplication
A*B= B*A as we can see
2*3= 3*2
6=6
Both figures in the equal signs are same
A dataset from a government survey contains variables for 87 adults age from 18 to 85. The variables include iron level ( µ g/dL), cholesterol level (mg/dL), and systolic blood pressure (mmHg). The researchers built a multiple regression to predict the mean iron level based on 2 variables, cholesterol level and systolic blood pressure.A partial regression ANOVA table is provided. Complete the ANOVA table aning. Use a significance level of a 0.05. Regression ANOVA Table Source df SSMSF Statistic p-value regression104535226.5 error 84 53813 640.6 Give the degrees of freedom as a whole number, the value of F to at least two decimals, the the p-value to at least three decimals. Then form the conclusion based on your results
Answer:
Step-by-step explanation:
The complete question tells us that;
A dataset from a government survey contains variables for 87 adults age from 18 to 85. The variables include iron level ( µ g/dL), cholesterol level (mg/dL), and systolic blood pressure (mmHg). The researchers built a multiple regression to predict the mean iron level based on 2 variables, cholesterol level and systolic blood pressure.A partial regression ANOVA table is provided. Complete the ANOVA table aning. Use a significance level of a 0.05. Regression ANOVA Table Source df SSMSF Statistic p-value regression104535226.5 error 84 53813 640.6 Give the degrees of freedom as a whole number, the value of F to at least two decimals, the the p-value to at least three decimals. Then form the conclusion based on your results.
NOTE: the attached minilab worksheet calculates this problem.
below is the attached image.
A number N is greater than 3. Which of the following best represents the location of 3N
on a number line?
Answer:
The second number line represent the location of 3N values.
Step-by-step explanation:
The first number line represent the inequality N > 3.
Now, the new number is 3N.
Consider the second number line values:
3N = {12, 15, 18, 21, ....}
The second number line represent the location of 3N values.
Answer:
d
Step-by-step explanation:
HEEEELP ME PLEASEEEE :(
(The problem is in the picture)
Solve for R: 16 + 8(R-6) = 5R + 50.
Answer:
82/3
Step-by-step explanation:
Hi! I'm back!
16+8r-48=5r+50
8r-32=5r+50
3r=82
r=82/3
Answer:
R = 82/3
Step-by-step explanation:
16 + 8(R - 6) = 5R + 50.
16 + 8 × R - 8 × 6 = 5R + 50
16 + 8R - 48 = 5R + 50
8R - 5R = 50 + 48 - 16
3R = 82
R = 82/3
R = 82/3
Thus, the value of R is 82/3
9000 is 10 times as much as?
Answer:
900
Step-by-step explanation:
What is the equation of the line given the two points
(-1,-6) and (-3, -8)
Answer:
y=x-5
Step-by-step explanation:
First we need to find the slope.
(-8+6)/(-3+1)
-2/-2
So the slope is 1
Using -1,-6 because we know the slope is 1, if we add 1 to x, we add 1 to y
So the y intercept is 0,-5
The equation is y=x-5
First find the gradient
[tex] \frac{y2 - y1}{x2 - x1} = \frac{( - 8) - ( - 6)}{( - 3) - ( - 1)} = \frac{5}{2} [/tex]
then using the formula y-y1 = m(x-x1)
y - (-6) = 5/2(x-(-1))
y + 6 = 5/2 (x+1)
2y + 12 = 5x + 5
2y - 5x = 5-12
2y - 5x = -7
5x - 2y = 7
so equation of the line is 5x -2y = 7
Sorry if im wrong
(x+3)/(x-5)=(19-3x)/(x-5)
Answer: 4
Step-by-step explanation:
(x+3)/(x-5)=(19-3x)/(x-5)
x+3=19-3x
4x=16
x=4
Which expression is the radical form of
Answer:
see below
Step-by-step explanation:
You know that the denominator of a fractional exponent is the same as a root index, so ...
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}\\\\\boxed{x^{\frac{2}{7}}=\sqrt[7]{x^2}}[/tex]
Graph the inequality. y>|x+5|-3
Answer:
Step-by-step explanation:
Which equation represents the function represented by the table? 17 POINTS!!!
Answer:
f(x) = -x -1
Step-by-step explanation:
You can make the correct choice by seeing which equation works for the first line of the table.
f(-1) = -(-1) -1 = 0 . . . . . the first equation works
f(-1) = -(-1) +1 = 2 . . . not zero
f(-1) = -1 -1 = -2 . . . not zero
f(-1) = 1 -(-1) = 2 . . . not zero (same as second equation)
Answer:
f (x)= -x-1
Step-by-step explanation:
Suzanne is cooking a roast. The table at the right gives the temperature F(1). in degrees Fahrenheit, of the roast at several times (in minutes) after she removes the roast from the oven Calculate the average rate of change for the temperature from 10 to 20 minutes. Include units in your answer!
Answer:
I use celcius so can u convert if I were to answer ?
ASAP! equation of the line in slope-intercept form
Line through (2,6) and perpendicular to y+4=3x
Answer:
y = -1/3x + 6[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First, change the original equation to slope intercept form:
y + 4 = 3x
y = 3x - 4
Now, find the slope of the perpendicular line. It will be the opposite reciprocal:
The opposite reciprocal of 3 is -1/3.
Next, plug this into the slope intercept equation along with the given point, so we can solve for b:
y = mx + b
6 = -1/3(2) + b
6 = -2/3 + b
6.67 = b
So, the equation will be y = -1/3x + 6[tex]\frac{2}{3}[/tex]
Which expression is the simplest form -(4x^3+x^2)+2(x^3-3x^2)
Answer:
6x^3-5x^2
Step-by-step explanation:
(4x^3+x^2)+2(x^3-3x^2)
4x^3+x^2+2x^3-6x^2
4x^3+2x^3+x^2-6x^2
6x^3+x^2-6x^2
6x^3-5x^2
The simplest form of the given expression [tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )[/tex] is,
[tex]6x^{3} - 5x^{2}[/tex].
Here, given expression is,
[tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )[/tex]
What is simplest form of equation?
The simplest form is the smallest possible equivalent fraction of the number.
Now,
Simplest form of expression,
[tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )\\4x^{3} +x^{2} +2 x^{3} -6x^{2} \\6x^{3} - 5x^{2}[/tex]
Hence, The simplest form of the given expression [tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )[/tex] is, [tex]6x^{3} - 5x^{2}[/tex].
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what divides a two dimensional shape into two congruent shapes
Answer:
Rectangle is a 2dimensional shape so, let me explain using it
The diagonal of a rectangle divides the rectangle into two triangles that are congruent and they are the same size and shape.
Another example is parallelogram
The diagonal of a parallelogram also divides the figure into two triangles that are congruent.
Step-by-step explanation:
David washes all 24 windows in his house he washed 6 windows each mr big and 2 windows each afternoon
How many days did it take him to wash all of his windows?
Answer:
3 days
Step-by-step explanation:
6 in the morning and 2 at the afternoon which mean David washed 8 windows a day.
24/8=3
So it took him 3 days
Hope this helps! :)
(pls mark brainliest)
Answer:
3 days
Step-by-step explanation:
when you divide 24 by 8 you get 3
Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets
an average of 150,000 new views. The average ratio of likes-to-views of Dagogo's videos is 1 : 5. Dagogo
wants to reach a total of 9,000,000 views on his channel.
Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he
uploads?
Answer:
2,000
Step-by-step explanation:
I just completed it on Khan Academy and it was right. I hope this helps!
Answer:
2000 likes per minute
Step-by-step explanation:
thats the answer on khan