Reduce the power by applying the identity,
[tex]\sin^2x+\cos^2x=1[/tex]
[tex]\implies\displaystyle\int\sin^3x\,\mathrm dx=\int\sin x(1-\cos^2x)\,\mathrm dx[/tex]
Let [tex]u=\cos x\implies\mathrm du=-\sin x\,\mathrm dx[/tex]:
[tex]\implies\displaystyle\int\sin^3x\,\mathrm dx=-\int(1-u^2)\,\mathrm du[/tex]
[tex]=\dfrac{u^3}3-u+C=\boxed{\dfrac{\cos^3x}3-\cos x+C}[/tex]
Rope: 15 feet, cut 4 sections how long is each section of rope?
To calculate the length of each section when dividing a rope into 4 parts, the total length of the rope is divided by 4. For a 15-foot rope, each section is 3.75 feet long. If a 30-foot rope is used, each section would be 7.5 feet long.
Explanation:To find out the length of each section of rope when a 15-foot rope is cut into 4 equal sections, we simply divide the total length of the rope by the number of sections.
Therefore, each section would be: 15 feet ÷ 4 = 3.75 feet long.
Now, if twice the length of this nylon rope is used, that means we would have a 30-foot rope instead of a 15-foot rope. Again, if we cut this 30-foot rope into 4 equal sections, each section would then be: 30 feet ÷ 4 = 7.5 feet long.
A triangle with coordinates A(1, 1), B(4, 2), C(3, 5) is translated three units down and five units to the left. What are the coordinates of the new triangle
Answer:
[tex]A' = (-4,-2)\\B'=(-1,-1)\\C'=(-2, 2)[/tex]
Step-by-step explanation:
Given:
[tex]A = (1,1)\\B=(4,2)\\C=(3,5)[/tex]
A translation upward or downward affects the [tex]y[/tex] value of a coordinate while a translation left or right affects the [tex]x[/tex] value of a coordinate.
We are translating the whole triangle down three units, so we subtract all the[tex]y[/tex] values by 3.
We are also translating the whole triangle to left left five units, so we will subtract all the [tex]x[/tex] values by 5.
[tex]A = (1-5,1-3)\\B=(4-5,2-3)\\C=(3-5,5-3)[/tex]
New Coordinates:
[tex]A' = (-4,-2)\\B'=(-1,-1)\\C'=(-2, 2)[/tex]
Answer:
I've actually know the answer, its easy it's simple it's completely easy like it's so easy like its extremely easy. Okay the answer to this written question will be 78
Step-by-step xplanation:
because
Anna is 26 ft. high on a rock-climbing wall. She descends to the 15-foot mark, rests, and then climbs down until she reaches her friend, who is 8 feet from the ground. How many feet has Anna descended?
Answer:
She has descended a total of 18 feet from the top to her friend.
Step-by-step explanation:
Anna is 26 ft. high on a rock-climbing wall.
She descends to the 15-foot mark,means she come to a height of [tex]26-15=11[/tex] feet and rests.
Then climbs down until she reaches her friend, who is 8 feet from the ground.
So, she climbs down [tex]15-8=7[/tex] feet more.
Hence, in total Anna has descended [tex]11+7=18[/tex] feet
The answer : She has descended a total of 18 feet from the top to her friend.
Mary and tom park their cars in an empty parking lot with n ≥ 2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). mary and tom pick parking spaces at random. (all pairs of distinct parking spaces are equally likely.) what is the probability that there is at most one empty parking space between them?
Answer:
p(at most one space between) = (4n-6)/(n(n-1))
Step-by-step explanation:
There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...
(n -1) +(n -2) = 2n-3
The number of ways that 2 cars can be parked in n spaces is ...
(n)(n -1)/2
So, the probability is ...
(2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))
___
If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.
__
Check
For n=2 or 3, p=1 as you expect.
For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
We have,
To find the probability that there is at most one empty parking space between Mary and Tom's cars, we need to consider two scenarios:
Mary and Tom park their cars in adjacent spaces.
Mary and Tom park their cars in spaces with one empty space in between them.
Scenario 1: Mary and Tom park their cars in adjacent spaces.
In this case, there are (n - 1) ways for them to pick adjacent spaces out of the n spaces. Since there are n spaces to choose from initially, the probability for this scenario is (n - 1) / n.
Scenario 2: Mary and Tom park their cars with one empty space between them.
In this case, there are (n - 2) ways to pick two parking spaces with one empty space in between them. Again, since there are n spaces to choose from initially, the probability for this scenario is (n - 2) / n.
Now, we add up the probabilities of both scenarios because they are mutually exclusive:
Total Probability = Probability of Scenario 1 + Probability of Scenario 2
Total Probability = [(n - 1) / n] + [(n - 2) / n]
To make these fractions have a common denominator, we can rewrite them as:
Total Probability = [(n - 1) + (n - 2)] / n
Total Probability = [2n - 3] / n
Thus,
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
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A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?
A. 0.1654
B. 0.1982
C. 0.1827
D. 0.1346
Answer:
A. 0.1654
Step-by-step explanation:
Let's call :
D: The event in which a person has a disease
ND: The event in which a person doesn't have a disease
TD: The event in which the test result is positive
Therefore, the probability that a person has the disease given that his test result is positive is calculated as:
P(D/TD) =P(D∩TD)/P(TD)
Where P(D∩TD) is the probability that a person has a disease and the test result is positive and P(TD) is the probability that the test result is positive.
So, The probability P(D∩TD) is calculated as a multiplication of:
P(D∩TD)=0.1% * 99% = 0.099%
Because 0.1% is the percentage of population that actually has the disease and 99% is the probability that the test detect the disease when it is present.
Then, for calculate the probability P(TD) we need to sum the probability of the following cases:
The probability that a person has a disease and the test result is positive, that is P(D∩TD) and it is equal to 0.099%The probability that a person doesn't have a disease and the test result is positive, that is P(ND∩TD) and it is calculated as:P(ND∩TD)= (100%-0.1%)*0.5%=0.4995%
Because (100%-0.1%) is the percentage of population that doesn't have the disease and 0.5% is the probability that the test imply that a person has the disease when it is not present.
So, P(TD) is calculated as:
P(TD) = P(D∩TD) + P(ND∩TD)
P(TD) = 0.099% + 0.4995%
P(TD) = 0.5985%
Finally, P(D/TD) is:
[tex]P(D/TD) =\frac{0.099%}{0.5985%}=0.1654[/tex]
How do you do this equation Laura's paper airplane flew 8 1/6 feet. That was 2 3/4 feet farther than Max's plane flew. Write and solve an equation to show how far Max's paper airplane flew.
Answer:
laura's distance = max's distance + 2 3/4 feetmax's distance = 5 feet 5 inchesStep-by-step explanation:
If you consider the English-language meaning of the description of the distances, you can see there might be several ways you could write an equation that says the same thing. Some of them are ...
laura's distance = max's distance + 2 3/4 feet
laura's distance - max's distance = 2 3/4 feet
laura's distance - 2 3/4 feet = max's distance
The first of these equations is shown as an answer above. The last of these equations gives max's distance directly, so is the most useful for finding that value.
laura's distance - 2 3/4 feet = max's distance
8 1/6 feet - 2 3/4 feet = max's distance
5 5/12 feet = max's distance . . . . . . do the arithmetic
_____
Describing addition and subtraction of mixed numbers is beyond the scope of this answer. Many calculators can work with fractions directly, in case you cannot do it by hand.
Max's paper airplane flew 65/12 feet.
To solve this problem,
we need to set up an equation to represent the relationship between Laura's paper airplane and Max's paper airplane. Let's use the variable 'x' to represent the distance Max's paper airplane flew.
We know that Laura's airplane flew 8 1/6 feet and that was 2 3/4 feet farther than Max's airplane.
So the equation is: x + 2 3/4 = 8 1/6. To solve the equation, we need to subtract 2 3/4 from both sides: x = 8 1/6 - 2 3/4.
Now, let's convert the mixed numbers to improper fractions. 8 1/6 = 49/6 and 2 3/4 = 11/4.
So the equation becomes: x = 49/6 - 11/4.
To subtract fractions, we need a common denominator, which in this case is 12. Multiplying the fractions,
we get x = 98/12 - 33/12. Subtracting the numerators, we have x = 65/12.
Therefore, Max's paper airplane flew 65/12 feet.
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I don't know how to solve this:
In a pair of complementary angles, one angle measures 18* less than three times the other angle. Find the measure of each angle.
Answer:
18, 72
Step-by-step explanation:
Two angles are complementary if they sum up to 90°. Call them [tex] x, (90-x) [/tex]. From the second part,
[tex]
3 x = 90-x+18 \\
4x = 72 \\
x= 18 [/tex]
The second angle is [tex] 90-18 = 72 [/tex]
The graph displays a proportional relationship. What is the unit rate shown by the graph?
Answer:
Step-by-step explanation: Im pretty sure they are asking you for the slope so it would be y = 0.5x
Answer:
0.5
Step-by-step explanation:
The unit rate is the number of units obtained in the "y" variable per unit obtained in the "x" variable. This behavior is observed in proportional relationships. For example: imagine that we know that the price for 5 pencils is $2.5. Since this is a proportional relationship, the unit rate will be the price of 1 single pencil, that is obtained by dividing 2.5 / 5 = 0.5.
In this case we also know that the graph passes through the point (1, 0.5), so the unit rate is given in that point. :)
Can someone step by step help me answer the ones that aren’t done
Number 6
Answer:
y = (c - ax)/b
Step-by-step explanation:
ax + by = c
by = c - ax
y = (c - ax)/b
I answered number 5 in your last question.
Step-by-step explanation:
5) C=5(F-32)
9
Multiply both sides by 9
9C=5(F-32)
Divide both sides by 5
9C=F-32
5
Add 32 to both sides
9C+32=F
5
Deshawn fuels 2 yachts and 6 barges. Each boat gets 126 gallons of fuel. To find out how much fuel he needs for all boats, deshawn first finds the number of boats, then he uses an algorithm to multiply. Which are the three partial products deshawn could add to find the final product?
which of the following functions is graphed below?
Answer:
A . You may have noticed that the difference between all the answers is that at the end of the problems there are the greater then and less then symbols. You may have noticed as well that in the graph, the points shown have an open point, or a filled in point. The filled in points are only applied if the symbol is ≤ or ≥. The open points are used when the symbol is the less then or greater then symbol without the line under it. Hope this helps!
Upon joining the Girl Scouts a member receives 4 patches. Karen has been in the girls scouts for quite awhile and has a total of 70 patches. If Karen earns 3 patches each month,how many months has Karen been a member of the girls scouts?
Answer:
Karen has been a member of Girl Scouts for 22 months
Step-by-step explanation:
Let
x -----> the time in months
we know that
The total number of patches must be equal to the number of months multiplied by 3 patches each month plus 4 patches
so
[tex]70=3x+4[/tex]
Solve for x
Subtract 4 both sides
[tex]70-4=3x\\66=3x[/tex]
Divide by 3 both sides
[tex]22=x[/tex]
Rewrite
[tex]x=22\ months[/tex]
therefore
Karen has been a member of Girl Scouts for 22 months
Karen has been a member of the Girl Scouts for 22 months.
Explanation:To determine the number of months Karen has been a member of the Girl Scouts, we can set up an equation using the information given.
Let's assume that Karen has been a member for x months.
Since she earns 3 patches each month, the total number of patches she has earned is 3x.
Adding the initial 4 patches she received upon joining, we have the equation 3x + 4 = 70.
To solve for x, we can subtract 4 from both sides of the equation: 3x + 4 - 4 = 70 - 4, which simplifies to 3x = 66.
Finally, we can divide both sides of the equation by 3 to solve for x: x = 66 ÷ 3 = 22.
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Which is the graph of f(x)=1/4(4)^x
Answer: the 3rd one
Step-by-step explanation: you can type it into a graphing calculator and get the answer
wants the perimeter of his rectangular garden to be, at most, 60 feet. He plans on making the length 19 feet. what is the maximum width of his garden , Solving Equations Word problems geometry and angles
Answer:
width = 11 feet
Step-by-step explanation:
The perimeter of a rectangle is 2 times length + width.
He already decided that the perimeter is at most 60 feet and the length is 19 feet. Then replacing in the formula for perimeter you have:
60 = 2 ( 19 + width)
30 = 19 + width
11 = width
Therefore the maximum width is 11 feet
Which could be the entire interval over which the function,
f(x), is positive?
(00, 1)
(-2, 1)
• 60,0)
(1.4)
Answer:
(-2, 1)
Step-by-step explanation:
Hi Juliadayx! How are you?
Well, maybe you already heard about the domain and the range of a function.
The domain is the set of values that the independent variable can take (usually referred to as the letter "x"), while the range is the set of values that the dependent variable takes, which is called f(x) or function of x.
In this case, the exercise asks you to evaluate for which values of “x” (right column of the table), the function “f(x)” takes positive values (left column of the table), the positive values also include zero. And in this case you can see that the function f(x) is only positive for the values of "x": -2, -1, 0 and 1. Therefore, the answer is the entire interval (-2, 1).
I hope I've been helpful!
Regards!
The process of manipulating one or more independent variables and measuring their effect on one or more dependent variables while controlling for the extraneous variables is called an experiment. a. True b. False
Answer: Ok, let's think our dependent variable like the position of a car with velocity of 50km/h, and our independent variable the time.
so, you can choose any time you want, and for each time, the car will be in a different position, so the position is a variable dependent of the time.
let's suppose you don't know the velocity of the car.
first you see the position at a time t₁ and the position is r₁.
then you see the position at time t₂, and the result is r₂.
here you changed the independent variable and observed how the dependent variable changed. And in this case, with the 4 numbers you observed you can obtain the velocity of the car.
So yes, you can call it an experiment.
A local Computer City sells batteries ($3) and small boxes of pens ($5). In August, total sales were $960. Customers bought 5 times as many batteries as boxes of pens. How many of each did Computer City sell?
Answer:
The number of batteries sold was 240 and the number of small boxes of pens sold was 48
Step-by-step explanation:
Let
x -----> the number of batteries sold
y ----> the number of small boxes of pens sold
we know that
[tex]3x+5y=960[/tex] -----> equation A
[tex]x=5y[/tex] ----> equation B
substitute equation B in equation A
[tex]3(5y)+5y=960\\15y+5y=960\\20y=960\\y=48\ boxes\ of \ pens[/tex]
Find the value of x
[tex]x=5(48)=240\ batteries[/tex]
therefore
The number of batteries sold was 240 and the number of small boxes of pens sold was 48
how do you find a regression equation
Answer:
A regression coefficient is the same thing as the slope of the line of the regression equation.
Step-by-step explanation:
The equation for the regression coefficient that you'll find on the AP Statistics test is: B1 = b1 = Σ [ (xi – x)(yi – y) ] / Σ [ (xi – x)2].
To find a regression equation, you plot the data on a scatter plot, draw an approximate line of best fit, calculate its slope and y-intercept, and then write the equation. Alternatively, you can use statistical software or a calculator's regression function to find the most accurate equation.
Explanation:To find a regression equation, one can follow these steps:
Collect a set of data with two variables; for instance, pinky finger length as the independent variable, x, and height as the dependent variable, y.Plot the data points on a scatter plot to visually assess the relationship.Draw a line that seems to best fit the data points. This is often done by eye, aiming to minimize the distance of all points from the line, leading to the least-squares regression line.Identify two points on the line to calculate the slope (rise over run).Determine the y-intercept by extending the line to where it crosses the y-axis.Combine the slope and y-intercept into the equation of the line, which typically has the form y=mx+b, where m is the slope and b is the y-intercept.Use statistics software or a calculator's regression function to find a more accurate regression equation.An example regression equation from sample data might look like this: ŷ = 173.51 + 4.83x, where x is the independent variable and ŷ is the predicted value of the dependent variable, y.
It is crucial to remember that regression equations predict outcomes for the variables within the given data set, but they should not be extrapolated beyond the scope of the available data. Variability in real data means that different samples might yield different regression equations, which is why it is important to consider the goodness of fit, such as the correlation coefficient or the coefficient of determination (r2).
Find the midpoint of a line segment
When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 54s to walk from your gate to the baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 83s to travel the same distance. How long will it take you to travel from the gate to baggage claim if you walk while riding of the moving sidewalk?
Answer:
Your travel time will be 32.71 secs.
Step-by-step explanation:
Let the total distance be x feet.
Speed while walking = [tex]\frac{x}{54}[/tex] feet per second
Speed on the sidewalk = [tex]\frac{x}{83}[/tex] feet per second
Therefore, total speed while walking on moving sidewalk =
[tex]\frac{x}{54} +\frac{x}{83y}[/tex]
= [tex]\frac{83x+54x}{54\times83}[/tex]
= [tex]\frac{137x}{4482}[/tex]
= [tex]\frac{x}{32.71}[/tex]
Hence, your travel time will be 32.71 secs.
A town uses positive numbers to track incresses in population and negitive numbers to track decresses in population. The population had decressed by 300 residents over the past 5 years. The same numbers of residents left each year. What was the change in towns population each year?
Answer:
60 people left each year so -60
Step-by-step explanation:
-300 is the total population change over the past 5 years
The population decreased.
Divide 300/5 to find the amount of people who left each year
300/5= 60
60 people left each year.
The change in the towns population is (-60)
Find the area of this irregular polygon.
Answer:
970m^{2}
Step-by-step explanation:
This polygon can be divided in two figures: one is a triangle, an the other one is a square.
We'll begin calculating the triangle's area, using the following formula:
[tex]At= \frac{b.h}{2}[/tex]
Where:
[tex]H= height = 30 m[/tex]
[tex]B = 9 m + 9 m + 20 m = 38 m[/tex]
As you can see, I added both sides of the triangle that measure 9 m and also the lenght of the square that measures 20 m! This added up is what the base of the triangle measures on total.
[tex]At= \frac{38 m .30 m}{2}[/tex]
[tex]At= \frac{1140 m^{2} }{2}[/tex]
[tex]At= 570 m^{2} [/tex]
Now we are going to calculate the square's area, that is much more simple:
[tex]As= L^{2} [/tex]
Where:
[tex]L=20 m [/tex]
[tex]As= (20 m)^{2} = 400m^{2} [/tex]
To know the whole figure's area, we add up both areas:
[tex]A = At+As = 570m^{2} +400m^{2}=970m^{2} [/tex]
What is the exact distance from the mother fox to her kit
The exact distance from the mother fox to her kid fox is option (B) √221 is the correct answer.
What is distance between two points?It is the length of the straight line connecting these points in the coordinate plane. This distance can never be negative, therefore we take the absolute value while finding the distance between two given points. The distance formula is an application of the Pythagorean theorem.
For the given situation,
The mother fox is at (x₁, y₁) = (-7,7)
The kid fox is at (x₂, y₂) = (7,2)
The formula of distance between two points is
[tex]d=\sqrt{(x_{2} -x_{1} )^{2} +{(y_{2}-y_{1})^{2}}[/tex]
⇒ [tex]d=\sqrt{(7-(-7) )^{2} +{(2-7)^{2}}[/tex]
⇒ [tex]d=\sqrt{(7+7)^{2} +{(2-7)^{2}}[/tex]
⇒ [tex]d=\sqrt{(14)^{2} +{(-5)^{2}}[/tex]
⇒ [tex]d=\sqrt{196+25}[/tex]
⇒ [tex]d=\sqrt{221}[/tex]
Hence we can conclude that the exact distance from the mother fox to her kid fox is option (B) √221 is the correct answer.
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The question's subject is ambiguous but appears to be about wildlife biology, focusing on the relationship between mother foxes and their kits or chimpanzee social behavior. The exact distance between a mother fox and her offspring is not provided and would vary in the wild, but close proximity is typical for maternal care.
Explanation:It seems there might be some confusion in the question as it refers to a 'mother fox' but the given information relates to chimpanzees and red foxes in different contexts. If the question pertains to the actual distance a mother fox might maintain from her kit (assuming 'kit' is used to mean 'offspring'), it is not specified in the provided information. The exact distance would depend on numerous factors including the age of the kit and the environmental circumstances. However, in the natural setting, foxes, which are eutherian mammals, may stay close to their offspring to provide nourishment and protection. In the case of chimpanzees, mothers and offspring maintain close physical proximity especially in the juvenile years, as offspring are dependent on the mother for care and learning social skills.
You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to reach your destination.
Answer:
3 hours
Step-by-step explanation:
275+55 t=440
55 t=440-275
or 55 t=165
t=165/55=3
Blossom Company began the year with retained earnings of $390000. During the year, the company recorded revenues of $489000, expenses of $379000, and paid dividends of $44500. What was Blossom retained earnings at the end of the year?
a) 489000
b) 455500
c) 533500
d) 833500
Answer:
b) $455,500
Step-by-step explanation:
We have been given that Blossom Company began the year with retained earnings of $390000. During the year, the company recorded revenues of $489000, expenses of $379000, and paid dividends of $44500.
To find the retained earnings, we will use following formula.
[tex]\text{Retained earnings}=\text{Retained earnings (Previous)+Revenue}-\text{Expenses}-\text{Dividends}[/tex]
Upon substituting our given values, we will get:
[tex]\text{Retained earnings}=\$390,000+\$489,000-\$379,000-\$44,500[/tex]
[tex]\text{Retained earnings}=\$879000-\$423,500[/tex]
[tex]\text{Retained earnings}=\$455,500[/tex]
Therefore, the retained earnings at the end of the year was $455,500.
Can someone help me with the ones that aren’t done
5:
C = 5/9(F - 32)
C = 5/9(F) - 17.777
-5/9(F) + C = -17.777
-5/9(F) = -C - 17.777
F = 5/9(C) + 32.0306
Answer:
[tex]5.\, F=\frac{9C}{5}+32\\6.\,y=\frac{c-ax}{b}\\7.\,p=\frac{mq}{n}\\8.\,t=\frac{A-P}{Pr}\\9.\,y=\frac{12-6x}{5}\\10.\,y=\frac{9x-6}{3}\\12. x=\frac{9+5y}{6}\\13.\,\pi=\frac{c}{d}\\14.\,A=\frac{s^2}{R}\\15.\,w=\frac{P-2l}{2}\\16.\,y=\frac{3x-2}{5}\\17.,x=\frac{6-3by}{2a}\\18.\,w=\frac{V}{lh}[/tex]
Step-by-step explanation:
We need to solve following equations in terms of indicated variable:
[tex]5.C=\frac{5}{9}\left ( F-32 \right ):F\\6.ax+by=c;y\\7.\frac{m}{n}=\frac{p}{q};p\\8.A=P+Prt;t\\9.6x+5y=12;y\\10.3y+2=9x-4;y\\12.6x-5y=9;x\\13.C=\pi d\\14.R=\frac{s^2}{A};A\\15.P=2l+2w;w\\16.3x-5y=2;y\\17.2ax+3by=6;x\\18.V=lwh;w[/tex]
Solution:
[tex]5.\, F=\frac{9C}{5}+32\\6.\,y=\frac{c-ax}{b}\\7.\,p=\frac{mq}{n}\\8.\,t=\frac{A-P}{Pr}\\9.\,y=\frac{12-6x}{5}\\10.\,y=\frac{9x-6}{3}\\12. x=\frac{9+5y}{6}\\13.\,\pi=\frac{c}{d}\\14.\,A=\frac{s^2}{R}\\15.\,w=\frac{P-2l}{2}\\16.\,y=\frac{3x-2}{5}\\17.,x=\frac{6-3by}{2a}\\18.\,w=\frac{V}{lh}[/tex]
For what values of y : is the value of the binomial 5y−1 greater than the value of the fraction 3y−1/4
PLEASE HELP ASAP
Answer:
y>0.375
Step-by-step explanation:
Answer:
For the values of y greater than [tex]\frac{3}{17}[/tex]
Step-by-step explanation:
Suppose 5y-1 greater than the value of the fraction [tex]\frac{3y-1}{4}[/tex]
That is,
[tex]5y - 1 > \frac{3y-1}{4}[/tex]
[tex]4(5y - 1) > 3y - 1[/tex]
[tex]20y - 4 > 3y - 1[/tex]
[tex]20y - 3y > -1 + 4[/tex]
[tex]17y > 3[/tex]
[tex]\implies y>\frac{3}{17}[/tex] ( a > b ⇒ [tex]\frac{a}{d} > \frac{b}{d}[/tex] where, d > 0 )
Hence, for the values of y greater than [tex]\frac{3}{17}[/tex] the value of the binomial 5y-1 greater than the value of the fraction [tex]\frac{3y-1}{4}[/tex].
20 POINTS AND BRAINLIEST PLZ HELP
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.
A. −5
B. -1/5
C. 1/5
D. 5
Answer:
Step-by-step explanation:
B or C is your answer
Pelomyxa palustris is an amoeba with a length of 4.9 mm.Amoeba proteus has a length of 0.7 mm.How many amoeba proteus would you have to line up to equal the length of three pelomyxa palustris?
Answer:
21
Step-by-step explanation:
Let n represent the number we're looking for. Then ...
n × (proteus length) = 3 × (palustris length)
n × 0.7 mm = 3 × 4.9 mm
n = (3 × 4.9 mm)/(0.7 mm) = 3 × 49/7 = 3 × 7
n = 21
You would have to line up 21 amoeba proteus to equal the length of three pelomyxa palustris.
Answer:
21
Step-by-step explanation:
1. 49
x 3 1
14.7.
21 _=period move
2. 0.7./14.7.
-14
07
-7
0
check your answer:
21
x0.7. 1
14.7.
When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel:
F=kR4(This is known as Poiseuille’s Law;) A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. Show that the relative change in F is about four times the relative change in R. How will a 5% increase in the radius affect the flow of blood?
Answer:
[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]
So a 5% relative increase in R would mean a 20% relative increase in F
Step-by-step explanation:
First we need to remind the definition of relative increase of a variable.
For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].
Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].
Let's then start by deriving F with respect to R:
[tex]\frac{dF}{dR}=4kR^3[/tex]
thus
[tex]dF=4kR^3dR[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]
[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].
If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get
[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]
According to Poiseuille's Law, the flux of blood through a blood vessel is proportional to the fourth power of the vessel's radius. By differentiating both sides of the equation, it can be shown that a small relative change in radius corresponds to four times that change in flux. Therefore, a 5% increase in radius results in a 20% increase in blood flow.
Explanation:Poiseuille’s Law states that the flux (F), which is the volume of blood flowing per unit time through a given point in a blood vessel, is proportional to the fourth power of the blood vessel's radius, R. In terms of an equation, F = kR4, where k is a constant of proportionality.
To show that the relative change in F is approximately four times the relative change in R, consider a small change in R (expressed as ΔR), and the corresponding change in F (ΔF). The relative change in F is ΔF/F and the relative change in R is ΔR/R.
By differentiating both sides of the equation, you get ΔF/ΔR = 4kR3. Therefore, ΔF/F = 4(ΔR/R), proving the statement. A 5% increase in the radius would therefore result in a 20% increase in the flux, or the blood flow rate.
Learn more about Poiseuille’s Law here:https://brainly.com/question/31595067
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