find y ″ by implicit differentiation. simplify where possible. x2 9y2 = 9
Answers
y" by implicit differentiation of x² + 9y² = 9 is y" = -( x²+ 9y²)/ y.
Implicit differentiation is referred to the procedure where differentiation of an implicit equation is done with respect to the desired variable, say x while treating the other variables as unspecified functions of the desired variable (say x).
x² + 9y² = 9
⇒ 9y² = 9 - x²
⇒ 9y²/ 9= (9- x²)/ 9
⇒ y²= 1- x²/9
First order differentiation of implicit function y²= 1- x²/9 is termed as y'. Here y²= 1- x²/9 is differentiated with respect to x,
That is,
(d/dx) y²= (d/dx)(1- x²/9)
2y (dy/dx) = 0 - 1/9( 2x dx/dx)
2yy' = - 2x/9
yy'= -x/9
y' = - x/9y
Second order differentiation of the implicit function y²= 1- x²/9 is termed as y''. Here y' = - x/9y is differentiated with respect to x,
That is,
(d/dx)y' = (d/dx)(-x/9y)
y" = (-1/9)( - xy'/ y² + 1/y)
y"= (xy' -y )/ 9y²
y" = {x(-x/9y) - y}/ 9y²
y" = -( x²+ 9y²)/ y
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Related Questions
Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each person? Define a variable, write an equation, solve the equation, and answer in a complete sentence. (Remember to clearly show your work on your work page.)
Answers
Answer:
Juan = 93 years.
Gabe = 31 years.
Catherine = 25 years.
Step-by-step explanation:
Let the age of Juan = J
Let the age of Gabe = G
Let the age of Catherine = C
Translating the word problem into an algebraic equation, we have;
\( J = 3G\) ..........equation 1
\( G = C + 6 \) ........equation 2
\( J + G + C = 149 \) ........equation 3
We would solve the linear equations by using the substitution method;
Substituting equation 2 into equation 1;
\( J = 3(C + 6)\)
\( J = 3C + 18\) ........equation 4
Substituting equation 2 and equation 4 into equation 3;
\( (3C + 18) + (C + 6) + C = 149 \)
Simplifying the equation, we have;
\( 5C + 24 = 149\)
\( 5C = 149 - 24\)
\( 5C = 125\)
\( C = \frac {125}{5}\)
C = 25 years.
To find G; from equation 2
\( G = C + 6\)
Substituting the value of "C" into equation 2, we have;
\( G = 25 + 6\)
G = 31 years.
To find J; from equation 1
\( J = 3G \)
Substituting the value of "G" into equation 1, we have;
\( J = 3 * 31\)
J = 93 years.
Therefore, Juan is 93 years old, Gabe is 31 years old and Catherine is 25 years old.
need to pass this class!
Answers
4w=90-5-33
4w=52
w=13
Which angle is supplementary to ∠1?
Answers
 I REALLY NEED HELP WITH THIS!!
Determine the angles of a rotation
A) 90º clockwise
B) 90º counterclockwise
C) 180º
D) 270º clockwise
E) 270º counterclockwise
is 2 correct answers ❗️ 
Answers
An angle of rotation is the measure of the amount that a figure is rotated about a fixed point called a point of rotation.
Explain the angles of a rotation?Movement in circles is rotation. The daily rotation of the Earth about its axis is an example of a rotation, which is the movement of something through one full circle. [ + of] Alternative Words: wheel, revolving, revolution more words for rotationAngle of rotation =m = m is the product of the number of central angles and the measure of a single central angle to get the angle of rotation between two points or vertices.The definition of the direction of a rotation in a plane in terms of the rotation's angle. The rotation will move counterclockwise if the angle of rotation is positive. The rotation will move counterclockwise if the angle of rotation is negativeThe angle of a rotation is 90 clockwise
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BP has a bond outstanding with 15 years to maturity, a $1,000 par value, a coupon rate of 6.9%, with coupons paid semiannually, and a price of 98.17 (percent of par) 18 | Attempt 1/10 for 10 pts. Part 1 What is the cost of debt?
Answers
There is an outstanding bond from BP with a 15-year maturity, a $1,000 par value, a 6.9% coupon rate that is paid semi-annually, and a price of 98.17. As a result, the annual cost of debt for this bond is roughly 8.5 percent.
To calculate the cost of debt, we need to determine the yield to maturity (YTM) of the bond. The YTM is the rate of return an investor would earn by purchasing the bond and holding it until maturity. We can use the bond pricing formula to calculate the YTM.
The bond pricing formula is as follows:
\(\text{Bond Price} = \frac{{C \times (1 - (1 + r)^{-n})}}{{r}} + \frac{{M}}{{(1 + r)^n}}\)
Where:
C = Coupon payment
r = Yield to maturity (YTM)
n = Number of periods
M = Par value
Given information:
Coupon payment (C) = \(\$1,000 \times \frac{6.1\%}{2} = \$30.50\)
Par value (M) = $1,000
Bond price = $1,000 × 83.57% = $835.70
We know the bond has 15 years to maturity, and coupons are paid semiannually. So, the number of periods (n) is 15 years × 2 = 30.
Using the bond pricing formula, we can rearrange it to solve for the YTM:
\(Bond Price = \frac{{C \times (1 - (1 + r)^{-n})}}{{r}} + \frac{{M}}{{(1 + r)^n}}\)
Substituting the given values:
\($835.70 = \left(\frac{{\$30.50 \times (1 - (1 + r)^{-30})}}{{r}}\right) + \left(\frac{{\$1,000}}{{(1 + r)^{30}}}\right)\)
To find the YTM, we need to solve this equation either algebraically or using numerical methods like trial and error or using financial calculators/spreadsheets.
By using a financial calculator or spreadsheet, we find that the YTM is approximately 8.5%. Therefore, the cost of debt for this bond is approximately 8.5% per year.
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Complete question :
Problem 17 Intro BP has a bond outstanding with 15 years to maturity, a $1,000 par value, a coupon rate of 6.1%, with coupons paid semiannually, and a price of 83.57 (percent of par). | Attempt 1/10 for 10 pts. Part 1 What is the cost of debt? B+ decimals Submit
Please help NEEDED ASAP!!!!
taxi cab tariffs in London, England, are as follows.
For the first 234.8 metres or 50.4 seconds (whichever is reached first)
there is a minimum charge of 2.60 GBP.
For each additional 117.4 metres or 25.2 seconds (whichever is reached first), if the distance travelled is less than 9656.1 metres there is a charge of 0.20 GBP.
Once the distance has reached 9656.1 metres then there is a charge of 0.20 GBP for each additional 86.9 metres or 18.7 seconds (whichever is reached first)
1. Develop a piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in metres.
2. Find the cost of 0.2 km, 5 km, and 15 km rides.
3. Develop a piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance.
4. Find the cost of 0.5 minute, 5 minute, and 15 minute rides.
5. Given that the actual taxi fare is always the greater of the two models, find:
(i) the cost of a ride that takes 10 minutes to go 4 km (if) the cost of a ride that takes 5 minutes to go 4 km
Answers
Answer:
1. A piecewise linear model for the cost, C, of a taxi ride based on the distance travelled, m, in meters can be represented as:
C = 2.60 (m<234.8)
C = 2.60 + 0.20(m-234.8) (234.8<=m<9656.1)
C = 2.60 + 0.20(9656.1-234.8) + 0.20(m-9656.1) (m>=9656.1)
2.To find the cost of 0.2 km, 5 km, and 15 km rides:
0.2 km = 200 m, the cost would be 2.60 GBP
5 km = 5000 m, the cost would be 2.60 + (0.20 * (5000-234.8)) GBP = 2.60 + 858 GBP = 1118 GBP
15 km = 15,000 m, the cost would be 2.60 + (0.20 * (9656.1-234.8)) + 0.20(15,000-9656.1) GBP = 2.60 + (0.20 * 9656.1-234.8) + 0.20(15,000-9656.1) = 2.60 + 1712.2 + 2040 = 3964.8 GBP
3. A piecewise linear model for the cost, D, of a taxi ride based on the time taken, t, in seconds, ignoring distance can be represented as:
D = 2.60 (t<50.4)
D = 2.60 + 0.20(t-50.4) (50.4<=t<1260)
D = 2.60 + 0.20(1260-50.4) + 0.20(t-1260) (t>=1260)
4. To find the cost of 0.5 minute, 5 minute, and 15 minute rides:
0.5 minute = 30 seconds, the cost would be 2.60 GBP
5 minutes = 300 seconds, the cost would be 2.60 + (0.20 * (300-50.4)) GBP = 2.60 + 44 GBP = 2.60+44 = 3.04 GBP
15 minutes = 900 seconds, the cost would be 2.60 + (0.20 * (1260-50.4)) + 0.20(900-1260) GBP = 2.60 + (0.20 * 1260-50.4) + 0.20(900-1260) = 2.60 + 252 + -12 GBP = 2.48 GBP
5. Given that the actual taxi fare is always the greater of the two models, find:
(i) the cost of a ride that takes 10 minutes to go 4 km is 1118 GBP (by distance model)
(ii) the cost of a ride that takes 5 minutes to go 4 km is 3.04 GBP (by time model)
It is important to
Solve -4(3x – 7) = 40 for x.
Answers
I NEED THIS ASAP ILL GIVE YPU BRAINLIST!
Answers
Answer:
3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
So what I did was divided the seconds by ounces and got 3 for each so...
3 is the constant of proportionality.
BAM!
Question 3 of 10
In the diagram below, Ed is parallel to Xy. What is the value of x?
Answers
The value of y will be 75°. The correct option is C.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines.
A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.
Given that the two parallel lines are DE and XY. The angle y will be calculated as,
y = 180 - 105
y = 75°
Hence, the measure of the angle y is 75°
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Write this expression using exponents
34
Answers
Answer: 17²
Step-by-step explanation:
Two families have been out on dinner.at the end of the night they pay their 100 pound bill they use a 50 percent of coupon which halves their bill then they split their remaining amount equally between the two families
Answers
The amount that one family paid is 25 pound
Here two families had dinner and bill was 100 pound
They used the coupon on which they got 50% off
To find the percentage we have to use percentage formula:
\(=\frac{Value}{Total \ Value} *100\)
\(=\frac{50}{100} *100\)
\(= 50 \ Pounds\)
The remaining bill was 50 pound
Now this amount is divided between the 2 families
\(=\frac{50}{2}\)
\(= 25 \ pound\)
So one family has to pay 25 pounds
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Factor the expression.
24 + 7x − 5x2
Answers
Answer:
-(5x+8)(x - 3)
Step-by-step explanation:
add and subtract second term to expression and factor using grouping
A random sample of 155 observations results in 62 successes. [You may find it useful to reference the z table.]a. Construct the a 90% confidence interval for the population proportion of successes. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)b. Construct the a 90% confidence interval for the population proportion of failures. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)
Answers
For a random sample of 155 observations results in 62 successes.
a) A 90% confidence interval for the population proportion of successes is equals to the (0.335 , 0.465).
b) A 90% confidence interval for the population proportion of failure is equals to the (0.535 , 0.665).
We have a random sample of 155 observations results in 62 successes. So,
Observed value, x = 62
Sample size,n = 155
Population Proportion, p = x/n
= 62/155
= 0.4
a) We have to determine 90% confidence interval for the population proportion of successes. Using the distribution table, for 90% confidence interval, z-score value is equals to 1.6. Consider Confidence interval formula with proportion, CI \(= p ± z×\sqrt\frac{p(1-p)}{n}\)
substitute all known values in above formula, \(= 0.4 ± 1.64\sqrt\frac{0.4(1- 0.4)}{155}\)
= 0.4 ± 0.0645
= (0.4 - 0.0645 , 0.4 + 0.0645)
= (0.335 , 0.465)
b) Now, we have to determine a 90% confidence interval for the population proportion of failures.
Now consider, here failure observed values, x = 155 - 62
= 93
proportion, p = x/n
= 93/155 = 0.6
Consider the confidence interval formula, CI \(= p ± z×\sqrt\frac{p(1-p)}{n}\)
substitute values, \(= 0.6 ±1.64×\sqrt\frac{0.6(1-0.6)}{155}\)
= 0.6 ± 0.0645
= (0.6 - 0.0645 , 0.6 + 0.0645)
= (0.535 , 0.665)
Hence, required value is (0.535 , 0.665).
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A clothesline rope is 8 feet long. Which of these is another way to express 8 feet?answer choicesA/FB/GC/HD/J
Answers
As per the concept of fraction, we can express 8 feet as 2 ²/₃ yards.
The term fraction refers to the numerical values which are a part of the whole.
8 feet can be expressed in another way.
In order to convert to a yard measurement, we divide the length by the conversion ratio.
Here we know that 1 yard = 3 feet
=> yards = feet ÷ 3
Here we have calculated the measurement of 8 feet.
So, the equivalent yard measurement is expressed as,
=> yards = 8/3
When we convert it into mixed fraction form, we get,
=> 2 ²/₃ yards.
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The complete question is:
F) 2*1/3 yards G) 2*1/2 yards H )2*2/3 yards J )2*3/4 yards. A clothesline rope is 8 feet long. Which of these is another way to express 8 feet? answer choices -A/FB/GC/HD/J
Find the simplified product:
3/2x^5*3/64x^9
Answers
Answer: The answer is 4x^4 to the cube root of 2x^2
Brainliest plss!
Which equation represents 95% of 200?
OA n =200(95%)
OB n = 95. 200
OC n = 200 - 0.95
OD n = 0.95 - 200
Answers
Answer:
The answer is A. n=200(95%)
What is the value of this product
Answers
Answer:
The value of the product is 2²
The line L1, is y= 5x+1
The line L2, is 2y-10 +3=0
Show how these 2 lines are parallel
Answers
Answer:
Step-by-step explanation:
L₁: y = 5x + 1
Slope of L₁ = 5
L₂: Did you mean 2y - 10x +3 = 0 ?
2y = 10x - 3
y = 5x - 1.5
Slope of L₂ = 5
L₁ and L₂ have the same slope, so the lines are parallel.
determine an expression that represents:
perimeter:
area:
3x+8;5x+2
Answers
Answer:
........................
Step-by-step explanation:
the precent chaance a certain door is locked is 70%. the key to unlock the door is one of ten keys hanging on a key rack. you get to pick two keys before walking to the door. what is the probability that you will get through the door without returning for more keys?
Answers
The required probability for the given event is given as 0.5.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
The probability of a door being locked is 70% = 0.7
Total number of keys is 10.
The number of keys being carried is 2.
Thus, there can be two cases for getting through the door.
Case 1: The door is locked.
The probability to open the door by 1 key is 1/10.
Then, the probability to open the door by 2 keys is 2/10 = 1/5.
Case 2: The door is open.
In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,
1 - 0.7 = 0.3.
Now, the overall probability should consider both the cases as,
P(getting through the door) = P(Door is closed and keys open it)
+ P(The door is open)
= 0.3 + 1/5
= 0.3 + 0.2
= 0.5.
Hence, the probability to get through the door without returning for more keys is 0.5.
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Suppose that a researcher thinks that female college basketball players can run a farther distance in nine minutes than the national average nine-minute run for female college students. The Health-Related Physical Fitness test is a standardized fitness test that includes a nine-minute run where researchers measure the distance (in yards) that a person can run in nine minutes. The national average nine-minute run for female college-aged students is 1960 yards with a standard deviation of 348. The researcher tests 16 female college basketball players and finds that the average nine-minute run for the basketball players is 2150 yards. Calculate the z test. Round the answer to two decimal places.
Answers
The correct answer is: z-test value is approximately 2.18
To calculate the z-test, we need to compare the sample mean (X) of the basketball players to the population mean (μ) of the national average nine-minute run for female college-aged students. The formula for the z-test is:
z = (X- μ) / (σ / √n)
Where:
- X is the sample mean (2150 yards)
- μ is the population mean (1960 yards)
- σ is the population standard deviation (348 yards)
- n is the sample size (16 basketball players)
Substituting the values into the formula, we get:
z = (2150 - 1960) / (348 / √16)
= (190) / (348 / 4)
= 190 / 87
≈ 2.18
Rounded to two decimal places, the z-test value is approximately 2.18.
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Given f(x)=3x2−5x−2.
What is the value of f(−2/3)?
Answers
Answer:
\(2\frac23\)
Step-by-step explanation:
Hello!
Evaluate the function for -2/3, by plugging it in for x in the equation.
Evaluate\(f(x) = 3x^2 - 5x - 2\)\(f(-\frac23) = 3(-\frac23)^2-5(-\frac23)-2\)\(f(-\frac23) = 3(\frac49) + \frac{10}{3} - 2\)\(f(-\frac23) = \frac{4}3 + \frac{10}3 - 2\)\(f(-\frac23) = 4 \frac23 - 2\)\(f(-\frac23) = 2\frac23\)The evaluated value is \(2\frac23\).
Answer:
Step-by-step explanation:
The absolute value of negative two third is really 2/3 but if your trying to reduce it to the lowest term its 0.66 or 0.67 However I would just put only 2/3 in the box, confidently knowing it would be scored correct.
Solve the equation: 7M - 1 = 6
Answers
Answer:
M=1
Step-by-step explanation:
7M-1=6
7M=6+1
7M=7
M=7/7
M=1
will mark brainliest and rate 5/5
Answers
Answer:
its c
Step-by-step explanation:
because i multuply
Answer:
320 cubic centimeters
Step-by-step explanation:
Multiply.
--
20 x 4 x 4 = 320
--
Finding Volume
Length x Width x Height = Volume
--
The masses or the apples in a crop being sent to market are normally distributed with a mean mass of 200 g and a standard deviation of 30 g. If there are 130 apples in a basket, how many apples will be more than 135 g and less than 230 g ? Include a diagram to explain your answer. Show all your work.
Answers
1. The number of apples that will be more than 135 g and less than 230 g is approximately 115 apples.
To determine the number of apples that fall within the given mass range, we need to calculate the z-scores corresponding to the lower and upper limits of the range and use the standard normal distribution table.
Given:
Mean mass of apples = 200 g
Standard deviation = 30 g
Number of apples = 130
First, we calculate the z-score for the lower limit (135 g):
z1 = (135 - 200) / 30 = -2.17
Next, we calculate the z-score for the upper limit (230 g):
z2 = (230 - 200) / 30 = 1
Using the standard normal distribution table, we find the cumulative probability corresponding to these z-scores:
P(Z < -2.17) ≈ 0.0146 (probability of being less than -2.17)
P(Z < 1) = 0.8413 (probability of being less than 1)
To find the probability of the mass falling within the given range, we subtract the lower probability from the upper probability:
P(-2.17 < Z < 1) = P(Z < 1) - P(Z < -2.17) ≈ 0.8413 - 0.0146 ≈ 0.8267
Finally, we multiply this probability by the total number of apples to find the expected number of apples within the given range:
Number of apples within the range = 0.8267 * 130 ≈ 107.67
Rounding this to the nearest whole number, we find that approximately 108 apples will fall within the given mass range.
Therefore, the number of apples that will be more than 135 g and less than 230 g is approximately 108 apples.
To visualize the mass range of the apples, we can draw a normal distribution curve with the mean and standard deviation given. The x-axis represents the mass of the apples, and the y-axis represents the probability density.
The range of interest, from 135 g to 230 g, can be marked on the x-axis. We calculate the corresponding z-scores for the lower and upper limits as mentioned earlier. The area under the curve between these z-scores represents the probability of the mass falling within the range.
Using the standard normal distribution table, we find the cumulative probabilities corresponding to the z-scores and calculate the difference to obtain the probability of the mass falling within the range.
Multiplying this probability by the total number of apples gives us the expected number of apples within the range.
In this case, the expected number is approximately 108 apples.
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What is the complete factorization of the polynomial below?
O A. (x+2)(x+)(**)
OB. (x-2)(x+)(x-)
C. (x-2)(x+)(x+1)
OD. (x+2)(x+1)(x-1)
Answers
The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)
What is an equation?
An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
A polynomial is an expression consisting of coefficients and variables forming an equation.
Given the polynomial:
x³ + 2x² -x - 2
Factorizing:
= (x + 2)(x² - 1)
= (x + 2)(x + 1)(x - 1)
The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)
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An equilateral triangle shares a single side with a kite to form a new
quadrilateral, as shown below.
Calculate the size of angle p.
Give your answer in degrees (°).
Answers
Answer:
<P = 41
Step-by-step explanation:
we can consider this first figure as a quadrilateral and the trianlgle attached to be is equilateral triangle (as it is already shown in the figure that sides are equal)
we know that each angle of equalateral triangle is 60°
we can see that angle 79° is attached to it and even other angle is also attached
let the other angle be x
we can notice that x and the angle of equi triangle make a linear pair
so 180 - 60
= 120°
the opposite angle to the angle x will be also equal as angles on the same side of qual sides will be equal
now we know that total angle sum of quadrilateral is 360°
so
79 + 120 + 120 + <P = 360
319 + <P = 360
<P = 360 - 319
<P = 41
A small can of beans is 3 in. high with a 1 in. radius and sells for $1.49. Which can of beans is a better deal?
a. 9 in. high; 3 in. radius; sells for $39.95
b. 3 in. high; 2 in. radius; sells for $5.96
c. 3 in. high; 3 in. radius; sells for $13.41
Answers
Therefore, the can of beans that is the best deal is option b, which has the lowest price per unit volume.
What is volume?Volume is a measure of the amount of space occupied by an object or a substance. It is often measured in cubic units such as cubic centimeters, cubic inches, or cubic meters. The formula for finding the volume of different objects may vary based on their shape and size, but it typically involves measuring the length, width, and height of the object and multiplying them together.
Here,
To determine which can of beans is the better deal, we need to compare their volumes and prices per unit volume.
The volume of the small can of beans is:
V₁ = πr₁²h₁
= π*(1)²*(3)
= 3π
The price per unit volume of the small can is:
P₁ = $1.49 / 3π
≈ $0.157 per cubic inch
For the other cans of beans, we can calculate their volumes and prices per unit volume:
a. V₂ = πr₂²h₂
= π*(3)²*(9)
= 81π
P₂ = $39.95 / 81π
≈ $0.155 per cubic inch
b. V₃ = πr₃²h₃
= π*(2)²*(3)
= 12π
P₃ = $5.96 / 12π
≈ $0.132 per cubic inch
c. V₄ = πr₄²h₄
= π*(3)²*(3)
=27π
P₄ = $13.41 / 27π
≈ $0.165 per cubic inch
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Find An Equaton Of The Plane. The Plane That Passes Through The Point (−2,3,2) And Contains The Fine Of Intersection Of The Planes X+Y−Z=2 And 2x−Y+5z=4
Answers
The equation of the plane that passes through the point (-2, 3, 2) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 5z = 4 is: 6x - 7y - 3z + 39 = 0.
To find an equation of the plane that passes through the point (-2, 3, 2) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 5z = 4, we need to find the direction vector of the line of intersection and use it to form the equation of the plane.
(A) The equation of a plane is given by Ax + By + Cz = D, where A, B, and C are the coefficients of the normal vector to the plane.
(B) To find the direction vector of the line of intersection, we can take the cross product of the normal vectors of the two given planes.
Find the normal vectors of the two planes. For the first plane x + y - z = 2, the normal vector is ⟨1, 1, -1⟩. For the second plane 2x - y + 5z = 4, the normal vector is ⟨2, -1, 5⟩.
Take the cross product of the normal vectors to find the direction vector of the line of intersection:
Direction vector = ⟨1, 1, -1⟩ × ⟨2, -1, 5⟩
Calculate the cross product:
Direction vector = ⟨6, -7, -3⟩
Now that we have the direction vector, we can use it along with the given point (-2, 3, 2) to write the equation of the plane. The equation will be in the form Ax + By + Cz = D, where A, B, and C are the components of the direction vector, and D is found by substituting the coordinates of the given point:
6(x + 2) - 7(y - 3) - 3(z - 2) = 0
Simplify the equation:
6x + 12 - 7y + 21 - 3z + 6 = 0
6x - 7y - 3z + 39 = 0
The equation of the plane that passes through the point (-2, 3, 2) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 5z = 4 is:
6x - 7y - 3z + 39 = 0
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1.
A bucket is put under a leaking ceiling. The amount of water in the bucket doubles every minute. After 8 minutes,
the bucket is full. After how many minutes is the bucket half-full?
I
Answers
Answer:
4min
Step-by-step explanation:
half full = 4min. disregard the doubles every min.
Answer:
7 minutes
Step-by-step explanation: