Taylor and Miranda are performing on a magic dimension-changing
stage that is 20 feet long by 15 feet width. The length is
decreasing linearly with time at a rate of 2 feet per hour and
width is incre
Answers
- The stage will have the maximum area after 2.5 hours.
- The stage will disappear after 10 hours.
To determine when the stage will have the maximum area, we can calculate the rate of change of the area with respect to time. The area of the stage is given by the product of its length and width:
Area = Length * Width
Let's denote the length of the stage as L(t) and the width as W(t), where t represents time in hours. Given that the length is decreasing at a rate of 2 feet per hour and the width is increasing at a rate of 3 feet per hour, we can express L(t) and W(t) as:
L(t) = 20 - 2t
W(t) = 15 + 3t
Now, we can express the area A(t) as a function of time:
A(t) = L(t) * W(t) = (20 - 2t) * (15 + 3t)
To find the time when the stage has the maximum area, we can differentiate A(t) with respect to time and set it to zero:
dA(t)/dt = 0
Let's differentiate A(t) and solve for t:
dA(t)/dt = (20 - 2t) * 3 + (15 + 3t) * (-2) = 0
60 - 6t - 30 - 6t = 0
-12t = -30
t = 2.5
So, the stage will have the maximum area after 2.5 hours.
To determine when the stage will disappear, we need to find the time at which the area becomes zero. Setting A(t) to zero, we have:
A(t) = (20 - 2t) * (15 + 3t) = 0
This equation will be true when either (20 - 2t) or (15 + 3t) is zero. Solving each equation separately:
20 - 2t = 0
-2t = -20
t = 10
15 + 3t = 0
3t = -15
t = -5
Since time cannot be negative, we discard t = -5. Therefore, the stage will disappear after 10 hours.
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The complete question is:
Taylor and Miranda are performing on a magic dimension-changing stage that is 20 feet long by 15 feet width. The length is decreasing linearly with time at a rate of 2 feet per hour and width is increasing linearly with time at a rate of 3 feet per hour. When will the stage have the maximum area, and when will the stage disappear (has 0 square feet)?
Related Questions
You are working with a satellite image of Anchorage, AK (∼150
∘
W) with the time stamp 0300Z, Dec. 3 2011. This means that it was 3AM on Dec. 3 at the Prime Meridian when the image was taken. What was the local time and day in Anchorage when the image was taken?
Answers
the local time in Anchorage when the image was taken was 5:00 PM, and the local day was Dec. 2, 2011.
To determine the local time and day in Anchorage when the satellite image was taken, we need to consider the time difference between the Prime Meridian (0 degrees longitude) and Anchorage, Alaska (approximately 150 degrees west longitude).
Each time zone is approximately 15 degrees wide, representing a one-hour difference in local time. Anchorage is in the Alaska Standard Time (AKST) zone, which is typically UTC-9 (nine hours behind UTC) during standard time.
Given that Anchorage is about 150 degrees west of the Prime Meridian, we can calculate the time difference as follows:
150 degrees / 15 degrees per hour = 10 hours
Therefore, when the image was taken at 0300Z (3:00 AM), Dec. 3, 2011, at the Prime Meridian, the local time and day in Anchorage were:
3:00 AM - 10 hours = 5:00 PM, Dec. 2, 2011
So, the local time in Anchorage when the image was taken was 5:00 PM, and the local day was Dec. 2, 2011.
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Consider the equation - 3x2 + 27x - 63 = 0.
What is the discriminant of the equation?
Answers
Answer:
answer is 19/9.
Step-by-step explanation:
give me brielient.
why the absolute value of a number will never be negitve
Answers
True because if a number is negative 4 the absolute value will be 4
find the surface area of a cuboid
Answers
Answer:
143.52 cm^2Solution,
Length(l)=7.2 cm
Breadth(b)=3.1 cm
Height(h)=4.8 cm
Now,
\(surface \: area \: of \: cuboid \\ = 2(l \times b + b \times h + h \times l) \\ = 2(7.2 \times 3.1 + 3.1 \times 4.8 + 4.8 \times 7.2) \\ = 2(22.32 + 14.88 + 34.56) \\ = 2(71.76) \\ = 143.52 \: {cm}^{2} \)
hope this helps...
Good luck on your assignment..
The surface area of cuboid is 143.52 square centimeters whose length is 7.2cm, width is 3.1 cm and height is 4.8 cm.
The formula for surface area of cuboid:
Surface area = 2(l×w + w×h + h×l).
Where l is length,
w is width,
h is height,
l=7.2 cm, w = 3.1cm and h=4.8 cm.
Plug in these values in above formula:
Surface area = 2(7.2×3.1 + 3.1×4.8 + 4.8×7.2)
=2(22.32 + 14.88 + 34.56)
=2(71.76)
=143.52
Hence, the surface area of cuboid is 143.52 square centimeters.
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A Businessman exchange Nepali currency rupees 660000 INR to US Dollar at the rate of Dollar 1 is equal to INR rupees 110 after 4 days Nepali currency is revaluated by 10% and he has changed the dollars INR to Nepali currency again what is his gain or loss find it
Answers
Answer:
Gain = $666.67
Step-by-step explanation:
The businessman exchanged 660000 INR to US Dollar using the exchange rate of $1 = INR 110
Value of the money in dollars is;
(660000 × 1)/110 = $6000
Now, Nepali currency is reevaluated by 10%. This means it's value has gone up by 10%.
Thus, exchange rate of $1 is now;
110 - 10%(110) = INR 99
Thus, 660000 INR to US Dollar using this new exchange rate gives;
(660000 × 1)/99 = $6666.67
Therefore he made a gain.
Gain = 6666.67 - 6000
Gain = $666.67
a traffic light is red for 25 seconds, yellow for 5 seconds, and green for 55 seconds. what is the probability that when you reach the light, a) the light is green b) the light is yellow c) the light is not red d) the light is not green
Answers
The probability of light being green ,yellow, not red ,and not green are 11/17, 1/17, 12/17 and 6/17 respectively.
Traffic light is red for 25 sec
Traffic light is yellow for 5 sec
Traffic light is green for 55 sec
Total of 85 seconds
The probability of the light being yellow when you reach it, all other things being equal, is 5 / 85 = 1/17
The probability of the light being green when you reach it, all other things being equal, is 55/ 85 = 11/17
The probability of the light being not red when you reach it, all other things being equal, is 5+55/ 85 = 60/85 = 12/17
The probability of the light being not green when you reach it, all other things being equal, is 5+25/ 85 = 30/85 = 6/17
As a result, the odds of a light being green, yellow, not red, or not green are respectively 11/17, 1/17, 12/17, and 6/17.
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Calculate the area of triangle abc with altitude bd, given a (−6, 0), b (0, 0), c (0, 6), and d (−3, 3). 18 square units 9 square units 18.5 square units 21 square units
Answers
Answer: 18 unit²
If BD is altitude, then AC is the base.
AC = BD =
The area is: A = 1/2bh
A = 1/2 * = 18 unit²
Step-by-step explanation:
Determine whether or not the following variable is a rank and give the units. Student ratings of a course on a 5-point Likert scale
B. The ratings are not ranks and have no units
C. The ratings are not ranks and the units are Likerts
D. The ratings are ranks and have no units
Answers
C. The ratings are not ranks and the units are Likerts.
In the context of student ratings of a course on a 5-point Likert scale, let's analyze the options further:
A. The ratings are ranks and have no units: In a ranking system, the responses would be ordered or ranked in a specific sequence. For example, if the students were asked to rank the course from best to worst, their responses would be assigned specific positions or ranks. However, in a Likert scale, the responses are not based on relative ranking but rather on levels of agreement or disagreement. Therefore, the ratings in this case are not ranks.
B. The ratings are not ranks and have no units: This option is accurate. The responses on a Likert scale do not represent ranks because they do not indicate a specific ordering or hierarchy. Each response on the 5-point Likert scale represents a different level of agreement or disagreement, rather than a rank.
C. The ratings are not ranks and the units are Likerts: This option is the most appropriate choice. Likert scales use response categories (e.g., strongly agree, agree, neutral, disagree, strongly disagree) instead of ranks. The units associated with this variable would be "Likerts" to indicate the scale used.
D. The ratings are ranks and have no units: This option is not applicable since the ratings on a 5-point Likert scale are not considered ranks.
Therefore, option C is the correct answer. The ratings on a 5-point Likert scale are not ranks, and the units associated with this variable are "Likerts" to represent the scale used.
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Find the difference quotient for the function f(x)=−3x3.
Answers
The difference quotient for the function f(x) = -3x^3 is -3(h + x)^3 - (-3x^3) / h.
In other words, we substitute (h + x) into the function f(x) in place of x, and subtract the original function f(x) from this new expression. Finally, we divide the result by h.
To calculate the difference quotient, let's substitute (h + x) into the function:
f(h + x) = -3(h + x)^3
Now, we subtract the original function f(x) = -3x^3 from f(h + x):
f(h + x) - f(x) = -3(h + x)^3 - (-3x^3)
= -3(h^3 + 3h^2x + 3hx^2 + x^3) + 3x^3
= -3h^3 - 9h^2x - 9hx^2 - 3x^3 + 3x^3
= -3h^3 - 9h^2x - 9hx^2
Finally, we divide the result by h:
(-3h^3 - 9h^2x - 9hx^2) / h
Simplifying the expression, we get:
-3h^2 - 9hx - 9x^2
Therefore, the difference quotient for the function f(x) = -3x^3 is -3h^2 - 9hx - 9x^2. This expression represents the average rate of change of the function f(x) as x varies by a small amount h. It provides an approximation of the instantaneous rate of change at a specific point on the curve.
By taking the limit as h approaches 0, we can obtain the derivative of the function f(x) at a particular point.
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Prompt: It's 5:30 AM, and as a helicopter pilot you've just been told there's an injured man on a boat you need to get to a hospital . The boat is going towards where you are a at 10 mph, but is currently 400 miles away. You need to get him as soon as possible, but you only have 6600 lbs of fuel in your helicopter, which burns 1200 lbs per hour and always travels at 150 mph. Also, you need to account for 30 min of fuel spent hovering over the boat to get the man into the helicopter and 1 extra hour of fuel due to helicopter standards. Therefore, when can you depart your station to get the man as soon as possible?
Answers
Answer:
leave at 1:30 PM
Step-by-step explanation:
10 mph 40 hours 6600/1200 5.5 hr 40/15 2 hr 40 mins 5.5 -.5 =
After two hours there at the meeting place, the helicopter must depart at 1:30 pm to join the boat.
What is Speed ?Speed is the rate an object travels in a predetermined period of time.
Its speed is expressed in km/h.
As per the given information in the question,
If the boat goes to the station ,
Speed of the boat = 10mph
it will take 400/10 = 40 hours.
The helicopter has, 6600 lbs of fuel.
It will take 30 minutes to clean the fisherman and an additional hour to get enough fuel.
1.5 × 1200 = 1800 lbs of fuel.
So, the amount of fuel helicopter now has
6600 - 1800
= 4800 lbs of fuel.
This will allow it to fly for 4 hours as:
4800 lbs/1200 lbs per hour, It can only travel at 150 mph for two hours one way.
= 300 miles distance from the station.
The boat is available at 400 miles, and its maximum flight time at 150 mph is two hours going one way, which is 100 miles from where it is now,
So,
100/10 = 10 hours, the journey to the meeting location will take the boat ten hours.
To reach the boat, which will require 10 hours, the chopper must take off after 8 hours since it will take 2 hours.
So 8 hours of time from 5:30 am will be equal to 1:30 pm.
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Your question seems incomplete, probably the complete question is:
A crewman on a fishing boat was injured and needs to be treated in a hospital right away. You are with a Coast Guard station nearest to the boat, but you are 400 miles away. The boat travels at a rate of 10 mph. It is 5:30 A.M. You have a helicopter that can hold 6600 lbs. of fuel, consumes 1200 pounds of fuel an hour, and travels 150 mph. However, you need to save a minimum of 1 hour worth of fuel for landing problems at the Coast Guard station, and you need to have 30 minutes’ worth of fuel to remove the crewman from the boat. You have to create a plan for extracting the crew member. When would you leave and why? Fully explain your answer.
Help with please question
Answers
The most appropriate choice for parallelogram will be given by
\(\Delta ABD \cong \Delta CDB\) has been proved
What is a parallelogram?
Parallelogram is a quadrilateral in which each pair of opposite sides are parallel and equal.
There are different properties of parallelogram-
Opposite sides of a parallelogram are equal
Opposite angles of a parallelogram are equal
Diagonals of a parallelogram bisect each other
Here,
AD || BC [Definition of Parallelogram]
\(\angle ADB \cong \angle CBD\) [Alternate interior angle theorem]
AB || CD [Definition of Parallelogram]
\(\angle ABD \cong \angle CDB\) [Alternate interior angle theorem]
\(DB \cong DB\) [DB is the common side]
\(\Delta ABD \cong \Delta CDB\) [ASA axiom]
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Tonya wants to estimate what proportion of her school's seniors plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom. Identify the population and parameter of interest.
Answers
If Tonya interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to prom, the population and the parameter of interest are 750 and 36/750 respectively.
To find the population and the parameter of interest:
Tonya wants to estimate what proportion of her school's seniors plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom. In this problem, the population is the group of seniors in Tonya's school. There are 750 seniors in her school, but only 50 were interviewed. Therefore, the population is all 750 seniors in the school. The parameter of interest is the proportion of all seniors in the school that plan to attend the prom. We are given that Tonya found 36 seniors in her SRS of 50 who plan to go to the prom. Therefore, the proportion of all seniors in the school that plan to attend the prom is 36/750.Hence, the population and the parameter of interest are 750 and 36/750 respectively.
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use cylindrical coordinates. evaluate x2 dv, e where e is the solid that lies within the cylinder x2 y2 = 4, above the plane z = 0, and below the cone z2 = 36x2 36y2.
Answers
Using cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).
To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.
In cylindrical coordinates, the solid e can be defined as follows:
Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).
Angle: θ ranges from 0 to 2π (full revolution around the z-axis).
Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.
To convert the integral, we need to express x^2 in terms of cylindrical coordinates:
x^2 = (rcosθ)^2 = r^2cos^2θ
The integral in cylindrical coordinates becomes:
∫∫∫ (r^2cos^2θ) r dz dr dθ
Now we can determine the bounds for the variables:
r ranges from 0 to 2.
θ ranges from 0 to 2π.
z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.
Substituting the bounds and integrating, we can evaluate the integral to find the desired result.
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can anyone help me with this?
Answers
Note that based on the quartiles the estimated number of rides less that 6.5 minutes long is about about 5 rides.
How is this so ?To estimate the number of rides that would be less than 6.5 minutes long, we can make use of the interquartile range (IQR).
Assumption - Data is Symmetrically distributed.
Recall that IQR is the variance between the first quartile (Q1) and the third quartile (Q3).
So IQR = Q3 - Q1
= 10 minutes - 6.5 minutes
= 3.5 minutes
Based on the assumption above we can consider Q2 as the 50th percentile.
Thus, to estimate the number of rides that would be less than 6.5 minutes long, use the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the Z-score,
X is the value we want to estimate (6.5 minutes),
μ is the mean of the data (which we assume to be Q2),
σ is the standard deviation of the data (which we assume to be IQR / 1.35).
NOte: The factor 1.35 is an approximation for converting the IQR to the standard deviation of a normal distribution
Z = (6.5 -8) / (3.5 /1.35)
= - 0.5 / 2.59
= -0.57857142857
≈ - 0.58
Based on statistical calculator, the proportion of data that falls below a Z-score o - 0.58, which represents the expected number of rides that would be less than 6.5 minutes long, is
= 0.2787.
Thus, te estimated number of rides less than 6.5 minutes long ≈ 0.2787 * 16
= 4.4592
≈ 4.5 rides
Thus we can expect the 4 or 5 rides to be less than 6.5 minutes long.
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If a dilation is applied to a triangle, then the image must be
O a congruent triangle.
O a triangle that is flipped over a line of symmetry.
a triangle that is rotated about a given point
O a larger or smaller triangle.
Answers
Answer: it would be a congruent triangle
Step-by-step explanation:
i have no idea but i got it right :)
Please answer Thank you please answer hurry PLease
Answers
Answer:
$(80.5x + 69)
Step-by-step Explanation:
Recall, distributive property of multiplication can simply be expressed as follows, x(y + z) = xy + xz or x(y - z). Where x, y, and z could be any number.
Now, let's use the distributive property to show the total costs of plants Gloria decides to buy as an expression and also simplify it.
Thus, Gloria buys:
4 ferns = 4(0.5x - 3) = 4(0.5x) - 4(3) = $(2x - 12)
2 palms = 2(10x - 2.50) = 2(10x) - 2(2.50) = $(20x - 5.00)
10 lilies = 10(5 + 0.25x) = 10(5) + 10(0.25x) = $(50 + 2.5x)
8 shrubs = 8(4.50 + 7x) = 8(4.50) + 8(7x) = $(36 + 56x)
Total cost of the plants = (2x - 12) + (20x - 5) + (50 + 2.5x) + (36+ 56x)
Open the parentheses and then simplify:
Total cost = 2x - 12 + 20x - 5 + 50 + 2.5x + 36 + 56x
= 2x + 20x + 2.5x + 56x - 12 - 5 + 50 + 36
Total cost = $(80.5x + 69)
the ratio of men to women working for a company is 3 to 5. if there are 216 employees total, how many men work for the company?
Answers
Answer:
\(81\:\text{men}\)
Step-by-step explanation:
Since there are 3 men for every 5 women in the company, for each women there will be \(\frac{3}{5}\) men.
Therefore, we can write the following system of equations:
\(\begin{cases}\frac{3}{5}w=m,\\w+m=216\end{cases}\)
Solving, we get:
\(w+\frac{3}{5}w=216,\\\frac{8}{5}w=216,\\w=216\cdot \frac{5}{8}=135\:\text{women}\)
Therefore, there are \(216-135=\boxed{81\:\text{men}}\) in the company.
What fraction is shown on the ruler below?
Correct answer pls!
Answers
Answer:
The last one, I think
Step-by-step explanation:
Answer: 4 5/16
Step-by-step explanation: becuase i got 100 on quiz
sec(pi/2 -x) =csc x true or false
Answers
Answer:
true
Step-by-step explanation:
if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:
\(sec\left(\frac{\pi }{2}\:-x\right)\) \(=\frac{1}{\sin \left(x\right)}\)
\(\frac{1}{\sin \left(x\right)}\) \(=\csc \left(x\right)\)
so, yes, \(sec\left(\frac{\pi }{2}\:-x\right)\) \(=\csc \left(x\right)\)
hope this helps!!
While online last week, you saw the following advertisement:
Shop at Impressive lonics!
The ions in our jewelry will balance your energy
and improve your health. Nine out of ten people
report significant improvement in the way they
feel within one week of wearing our jewelry.
SALE ENDS SATURDAY!
Which of the following is the most likely scientific explanation for why so
many people report improvement after wearing this jewelry?
A. The company paid actors to answer questions about the jewelry.
B. The ions in the jewelry change the electric field around the body,
improving blood flow.
OC. The ions in the jewelry improve energy flow through the body.
OD. Some people may feel improvement after a week because their
body is healing naturally, without help from the ions.
Answers
The most likely scientific explanation for improvement after wearing this jewelry was D. Some people may feel improvement after a week because their body is healing naturally, without help from the ions.
How to explain the improvement ?The placebo effect is the best scientific explanation for why so many people experience better after donning a particular piece of jewelry.
The placebo effect happens when users of a product claim to be experiencing physical or mental changes as a result of using it, despite the fact that the product itself lacks the ingredients necessary to produce these effects. The jewelry is acting as a placebo in this scenario.
After a week, some people may experience improvement as their bodies begin to recover on their own, without the aid of the ions.
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You are on a 4.7 mile run and have already 1.97 miles. How many more miles do you need to run?
Answers
Answer:
2.73
Step-by-step explanation:
You would need to run 2.73 miles to have ran 4.7 miles in all.
4.7 - 1.97
Seth earns $20 a day and $2 for each ticket he sells at the local theatre. Write and solve an inequality that can be used to find how many tickets he must sell in a day to earn at least $85.
write an inequality
Answers
Answer:
43
Step-by-step explanation:
divide 85 then add 1
explanation: from here, you would solve to find the value of x. to do this, you subtract 20 from each side of the equation, leaving you with the new equation: 2x = 65. From here, divide both sides by 2. This leaves you with the final answer being x = 32.5. since you can’t sell half a ticket, you would need to round up to get the full number of tickets to be 33. Therefore, Seth would need to sell 33 tickets to make at LEAST $85
for exercise, mae jogs miles then walks an additional to cool down. if her jogging speed is miles per hour faster than her walking speed and her total exercise time is , what is her walking speed?
Answers
Mae's walking speed is 10 miles per hour. This is calculated by considering the given information.
Let's assume Mae's walking speed is represented by the variable "x" (in miles per hour). According to the given information, her jogging speed would then be "x + 12.5" miles per hour.
To calculate Mae's exercise time, we can use the formula: time = distance / speed.
Mae jogs 27 miles at a speed of "x + 12.5" miles per hour, so her jogging time can be calculated as:
jogging time = 27 / (x + 12.5)
Mae walks an additional 3 miles at a speed of "x" miles per hour, so her walking time can be calculated as:
walking time = 3 / x
The total exercise time is given as 3 hours. Therefore, we can set up the equation:
jogging time + walking time = 3
Substituting the calculated values, we get:
27 / (x + 12.5) + 3 / x = 3
To solve this equation, we can start by multiplying all terms by x(x + 12.5) to eliminate the denominators:
27x + 27 * 12.5 + 3(x + 12.5) = 3x(x + 12.5)
Simplifying the equation:
\(27x + 337.5 + 3x + 37.5 = 3x^2 + 37.5x\)
Combining like terms:
\(30x + 375 = 3x^2 + 37.5x\)
Rearranging the terms to set the equation equal to zero:
\(3x^2 + 7.5x - 375 = 0\)
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(\(b^2\) - 4ac)) / (2a)
In this case, a = 3, b = 7.5, and c = -375. Substituting these values into the quadratic formula:
x = (-7.5 ± √(\(7.5^2\) - 4 * 3 * -375)) / (2 * 3)
x = (-7.5 ± √(56.25 + 4500)) / 6
x = (-7.5 ± √(4556.25)) / 6
Calculating the square root:
x = (-7.5 ± 67.5) / 6
Simplifying further:
x = (60 / 6) or x = (-75 / 6)
Since Mae's walking speed cannot be negative, the solution is x = 10.
Therefore, Mae's walking speed is 10 miles per hour.
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The complete question is:
For exercise, Mae jogs 27 miles then walks an additional 3 miles to cool down. If her jogging speed is 12.5 miles per hour faster than her walking speed and her total exercise time is 3 hours, what is her walking speed? The athlete's walking speed is
Find the missing terms in each geometric sequence.
1. 256, ___, ___, -32, -64
2. 27, 9, ___, ___, 1/3
3. 5x^2, ___, 5x^6, 5x^8, ___, ...
Answers
Answer:
1) 256, -128, 64, -32
2) 27, 9, 3, 1, 1/3
3) 5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰,
Step-by-step explanation:
1. In this geometric series each term is obtained by multiplying the previous term by (-1/2) or dividing by (-2).
256 ÷ (-2) = - 128
-128 ÷ (-2) = 64
64 ÷ (-2) = (-32)
The geometric series is:
256, -128, 64, -32...
We can find the common ratio by dividing the second term by first term.
2) 27, 9, ___, _________, 1/3
\(\sf \boxed{\bf common \ ratio= \dfrac{second \ term}{first \ term}}\)
\(\sf = \dfrac{9}{27}\\\\ = \dfrac{1}{3}\)
\(\sf 9*\dfrac{1}{3}=3\\\\3*\dfrac{1}{3}=1\)
The geometric series is:
27, 9, 3, 1, 1/3....
3) 5x², _____, 5x⁶, 5x⁸, _____, ....
Here, we can take 3rd term and 4th term to find the common ratio.
\(\sf common \ ratio = \dfrac{5x^8}{5x^6}\\\\\)
\(\s = x^{8-6}\\\\=x^2\)
5x² * x² = 5x⁴
8x⁸ * x² = 8x¹⁰
The geometric serious is:
5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰, ...
\(\sf 1.) \ 256, -128, 64, -32,..\\ \\ 2.) \ 27, 9, 3, 1, 1/3,... \\ \\3.) \ 5x^2, 5x^4, 5x^6, 5x^8,5x^{10} , ...\)
\(\sf Geometric \ formula: ar^{n-1}\)
where 'a' is first term, 'r' is common ratio.1)Find the common ratio:
next term ÷ previous term32 ÷ -64 = -1/2Equation: \(256(-\frac{1}{2} )^{n-1}\)
2nd term: \(256(-\frac{1}{2} )^{2-1}=-128\)
3rd term: \(256(-\frac{1}{2} )^{3-1}=64\)
2)Find common ratio:
next term ÷ previous term9 ÷ 27 = 1/3Equation: \(27(\frac{1}{3} )^{n-1}\)
3rd term: \(27(\frac{1}{3} )^{3-1}=3\)
4th term: \(27(\frac{1}{3} )^{4-1}=1\)
3)Find the common ratio:
next term ÷ previous term5x^8 ÷ 5x^6 = x^2Equation: \(5x^2 (x^2)^{n-1}\)
2nd term: \(5x^2 (x^2)^{2-1} = 5x^2 (x^2) = 5x^{4}\)
5ht term: \(5x^2 (x^2)^{5-1} = 5x^2 (x^8) = 5x^{10}\)
6.1 true or false: points that minimize a nonlinear function are inherently less accu- rately determined than points for which a non- linear function has a zero value.
Answers
The given statement, points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value is FALSE.
What is a nonlinear function?In mathematics, a nonlinear function is a function that is not linear, i.e. a function whose graph is not a straight line. Simplest non-linear functions are quadratic function, exponential function and logarithmic functions. Nonlinear functions do not follow the superposition principle, which is fundamental to linear systems, which states that if the input is scaled by any factor, then the output will also be scaled by that factor.
Points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value. The above statement is false because the points that minimize a nonlinear function can be determined more accurately than the points where the nonlinear function has zero value.
Also, there is no such rule that the points that minimize a nonlinear function are less accurate than points for which a nonlinear function has a zero value.
To know more about nonlinear function, refer here:
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Round 259.98991 to the nearest hundredth.
259.99
259.990
259.9899
260.00001
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HTU.TH
(hundreds, tens, units . tenths, hundredths)
Find the midpoint of these 2 points
Answers
Answer:
(3.9,4.45)
Hope this helps.
Which of the binomials below is a factor of this trinomial?
6x2 - 6x - 72
Answers
\(6 {x}^{2} - 6x - 72 = \)
\(6( {x}^{2} - x - 12) = \)
\(6(x - 4)(x + 3)\)
Math Math help help help ASAP please
Answers
Answer:
a.) 10,000
b.) 512
Step-by-step explanation:
which statement accurately describes how to reflect point A (3,-1) over the y axis
Answers
The reflection over the y-axis only changes the sign of the x-component so the reflected point is A' (-3, -1)
How to reflect point A over the y-axis?Here we can't see the options, so I will teach you how to reflect any point over the y-axis.
Any point on the X-Y plane is defined by its coordinates (x, y).
If we reflect this point over the y-plane, we only change the sign of the x-component of the point.
So after the reflection, we get the point (-x, y).
Then if we apply that reflection to point A (3, -1). We will get the reflected point:
A' (-3, -1)
If you want to learn more about reflections:
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