Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.
What is the area of a square?The area of the square is defined as the square of its sides.
Let the side of the square is a then its area will be a².
Area of square figure = Side².
Let the side of the square is x= 29cm.
It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.
And the rate of change in side of square dx/dt = 1.625 cm/hour
We have to calculate the rate of change in an area of the square (A).
hen, area A = x²
On differentiating A with respect to time(t) we get a rate of change in area
dA/dt = d(x²)/dt
= 2x dx/dt
= 2×29×1.625
= 94.25 cm²/hour
Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.
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6) Complete the equation so that it has infinitely many solutions.
12x-x+8+ 3x =__x+__
The simplified equation is 14x+8 which has infinitely many solutions as given in the question.
What does the equation mean?Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.How do you solve an equation?1.Remove parenthesis and combine like terms to simplify either side of the equation.
2.Isolate the variable term on one side of the equation using addition or subtraction.
3.To find the variable, use multiplication or division.
Given equation is:
12x-x+8+ 3x
= 11x+3x+8
=14x+8
Therefore, the simplified equation is 14x+8 which has infinitely many solutions.
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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
PLEASE I NEED HELP!!
the cost of a taxi ride consist of a flat fee plus a cost per mile. if 30 miles cost $20 and 50 miles cost $30, write a linear function that describes the cost of a trip, c, in terms of the number of miles, n. what is the cost per mile and what is the flat fee?
A linear function that describes the cost of a trip, c, in terms of the number of miles, n will be "c=0.60n+0.67n" and cost per mile is $0.6 and $0.67 and the flat fee is $50.
What is cost per mile?Once you are aware of your mileage and total expenses, calculating cost per mile becomes a straightforward equation. Your cost per mile is calculated by dividing your total expenses by the total number of miles you have driven. Your expenses per mile are influenced by your variable and fixed costs, so you should probably pay closer attention to how much you're shelling out for each mile your drivers cover. You can better understand your primary costs and produce more accurate bids for new contracts by knowing your expenses at this specific level.
Here,
cost per mile,
20/30=$0.67/mile
30/50=$0.60/mile
c=0.60n+0.67n
flat fee,
=$30+$20
=$50
The cost per mile is $0.6 and $0.67, and the flat rate is $50. A linear function that expresses the cost of a trip, c, in terms of the number of miles, n, will be "c=0.60n+0.67n".
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Jade ha 28 triangle card. He ha 4 time a many trading card a jordan. How many trading card do they have altogether
Jade and Jordan both have a total of 35 trading cards altogether.
Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.
As, Jade has 28 trading cards
Let Jordan has 'x' trading cards.
Now, as Jade has 4 times as many trading cards as Jordan.
So, 28 = 4x
4x = 28
x = 7
So, Jordan has 7 trading cards.
Now, they both have a total of 35 trading cards altogether.
Hence, Jade and Jordan both have a total of 35 trading cards altogether.
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a question posted on the lycos web site on june 18, 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes. what is the most likely issue with the sample they collected?
The most likely problem with the sample they gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".
Defined the term biased survey?This phrase describes the different factors and biases that may affect survey results. Either biased responses are deliberate or unintentional, they make survey results less valuable because they are erroneous.With participant surveys that ask for self-reporting, this might become a specific problem.Any survey's bias response is crucial since it determines the validity of the data, so preventing bias is absolutely necessary if you want insightful survey responses.Among the most prevalent types is leading bias. As an illustration, consider the scenario in which your question concerns customer happiness and the response alternatives are Very Satisfied, Satisfied, and Dissatisfied. Results in this case may be affected by bias.Thus, the most likely problem with the sample lycos web site gathered to determine whether they believed marijuana should be lawfully available for medical uses has to do with the survey's likelihood of being "biased".
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth
Step-by-step explanation:
imagine a circle with the center at the vertex of the angle x, and the radius 72 ft.
cos(x) = 28/72 = 7/18 = 0.388888888...
x = 67.11461952...° ≈ 67.1°
length of 3 feet, a width of 2 feet, and a height of 5 feet. What is the volume of the refrigerator?
Answer:
30 feet^3
Step-by-step explanation:
length x width x height
3 x 2 x 5
=30
Beginning with the equation 3m=7 write the new equation produced by multiplying both sides by 3/8
Answer:
9/8 m = 21/8
or
9m/8 = 21/8
Step-by-step explanation:
3m = 7
3/8 × 3m = 3/8 × 7
9/8 m = 21/8
Caina earned a scholarship of $6,000 next year. She also expects to receive a grant of $3,200 next year and will make another $400 per month working a part-time job. How much does she anticipate in income next year?
Caina anticipate in income next year $14000.
What is an income?
The amount of money, property, and other value transfers received over a predetermined period of time in return for goods or services is often referred to as income.
We have,
A scholarship of $6000 and a grant of $3200 together are $9200
6000 + 3200 = 9200.
She will make another $400 per month working a part-time job, so for 12 months she will make $400 × 12 = $4800.
All together will be $9200 + $4800 = $14000.
Therefore, She anticipate in income next year $14000.
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please hep me asap!!!
Write the converse, inverse, and contrapositive of the following conditional statement.
"If I eat too much candy, I will get sick."
Converse: If I get sick, I ate too much candy.
Inverse: If I don't eat too much candy, then I will not get sick
Contrapositive: If I do not get sick, I did not eat too much candy.
What is the conditional statement?
'If p, then q's statements are examples of conditional statements. In this case, "p" stands for "hypothesis" and "q" for "conclusion."
A converse statement is one that is produced by flipping a conditional statement's hypothesis and conclusion.
So, Converse: If I get sick, I ate too much candy.
An inverse assertion presupposes that each of the original claims is true.
So, Inverse: If I don't eat too much candy, then I will not get sick.
When you reverse the hypothesis and the conclusion in a statement, you have a contrapositive statement that refutes both propositions.
So, Contrapositive: If I do not get sick, I did not eat too much candy.
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The altitude of a triangular sign is 18 inches less than 3 times its base. Define the functions that describe the altitude and base of the triangle, and then use these functions to build an area function of the triangle
Functions to build an area function of the triangle , A = b2 + 2b.
What Altitude of a Triangle?A perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude. A triangle can be drawn with three altitudes because it has three sides. There are various types of elevations in triangles. When computing the area of a triangle, the altitude, also known as its height, is indicated by the letter.The section of a perpendicular line traced from a triangle's vertex to the side directly across from it is the triangle's altitude. The base of the triangle that the altitude touches forms a straight angle. It is often referred to as a triangle's height and is represented by the letter "h." The distance between the vertex and its opposing side can be calculated to determine its size. It should be remembered that every triangle has three altitudes that can be drawn from each of the vertices. See the intersection of the triangle's three elevations by paying attention to the triangle in the illustration below. The "Orthocenter" is this location.According to our question-
Let b = the base
altitude = 2b + 4
A = b(2b+ 4)/2
A = b(b + 2)
A = b2 + 2b
Hence, Functions to build an area function of the triangle , A = b2 + 2b.
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a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 l/min, the well mixed solution is pumped out at a rate of 6 l/min. find the number a(t) of grams of salt in the tank at time t.
The number of grams of salt in the tank at time t is given by the differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
What is rate?The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.
An equation with a function and one or more of its derivatives is referred to as a differential equation:
At the start, the tank contains A(0) = 30 g of salt.
Salt flows in at a rate of
(1 g/L) * (4 L/min) = 4 g/min
and flows out at a rate of
(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min
so that the amount of salt in the tank at time t changes according to
A'(t) = 4 - A(t)/50
So,
[tex]A'(t) = 4 - \frac{A(t)}{50}[/tex]
The solution of linear differential equation y' + ay = g(x) is in the form,
[tex]e^{ax}y=\int {e^{ax}g(x)} \, dx +c[/tex]
Now, putting the values,
[tex]a=\frac{1}{50} \\g(x)=4[/tex]
[tex]e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\[/tex]
Now,
[tex]A(t)=200+Ce^{-\frac{1}{50}t}\\[/tex]
Putting the initial value,
[tex]30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170[/tex]
So, the function will be [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
Therefore, the number of grams of salt in tank at time t is given by differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].
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Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
The cars are 315 miles apart 1.5 hours after they start moving. Use the answer
from part (c) to write an equation.
Which expression is equivalent to 3x5y?
Answer:
15y
Step-by-step explanation:
3 times 5 is 15 with the variable
1. Given that p=5xy + q, express y in terms of p,q and x.
2.Given that p=7x +4q, express x in terms of p and q.
[tex]\huge\mathcal{♨Answer♥}[/tex]
Answer is on the attachment...
☆...hope this helps...☆
_♡_mashi_♡_
The equation p=5xy+q can be expressed in terms of p,q, and x as y = (p-q)/5x.
The equation p=7x+4q can be expressed in terms of p and q as x = (p-4q)/7x.
Given in the first equation, p = 5xy+q
p-q=5xy
y=(p-q)/5x
Here we need to express y in terms of p,q, and x so we need all these three variables on one side of the equation and y on the other side. Initially we more q to the left-hand side of the equation which makes it p-q=5xy. Now we divide the left-hand side and the right-hand side by 5x making the equation y = (p-q)/5x.
Similarly in the second equation, p = 7x+4q
p-4q = 7x
x = (p-4q)/7
Here we need to express x in terms of p and q so we need all these two variables on one side of the equation and the term x on the other side. First, we will move 4q to the left-hand side of the equation which will make it p-4q=7x. Now, we will divide the whole equation by 7 which will make the equation x = (p-4q) / 7.
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Translation rule:
(x, y) (x + 2, y – 4)
Either draw in the translated image or write down the new coordinates for the translated image
Step-by-step explanation:
it is really simple :
every x is increased by 2, every y is decreased by 4.
C = (-4, 2) -> C' = (-2, -2)
R = (-5, -1) -> R' = (-3, -5)
T = (-1, 1) -> T' = (1, -3)
The dot plot shows 20 students' scores on a quiz
in English class.
Quiz Scores
If one student from the class is chosen at
random, what is the probability that he or she
scored MORE than 15 points on the quiz?
Answer:
Probability = A. 2 / 5
Step-by-step explanation:
Probability = ( Number of Favorable Outcomes ) / (Total Number of Outcomes )
So the Total Number of Students = 20
Number of Students ( Dots ) scored more than 15 = 3+2+1+2 = 8
Probability = 8 / 20 = 2 / 5
Glad to Help
Answer: 12/20= 3/5
Step-by-step explanation:
you have to count all the dots on the dot plot to find your denominator which is 20.
then you count all the dots that are fifteen or more and there are 12 so 12/20 is the probability which is simplified into 3/5.
given that 3p = 2m - 5q, express m in terms of p and q
Answer:
Step-by-step explanation:
3p. = 2m - 5q
-2m. = -3p - 5q
Divide through by -2
m. = (3p + 5q) \2
The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.
Given equation 3p = 2m - 5q
3p + 5q = 2m
(3p + 5q) / 2 =m
Hence, m = (3p+5q) / 2
To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.
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50 POINTS
You are looking at starting a summer business mowing lawns to get started. You already need to purchase some items investing in your business. You already have a lawnmower, but below are the items you still need to purchase.
what is the total amount you plan to invest in your lawn mowing business? [__]
1. You just determined how much you are willing to invest to get your summer job started. Write an inequality to represent when you start making a profit if you charge $15 to mow one lawn.
2. at the end of the summer, you have mowed a total of 16 lawns right in equation that represents your total earnings. How much did you earn? [Show your work]
with investment costs taken into account, did you:
a. lose money
b. make money
Regarding the situation described, it is found that:
The total amount invested is of $25.
1. You start making a profit when 15x - 25 > 0.
2. You earned $215 with this work.
With the investment, you made money (option b).
What is the total amount investment?The investment was as follows:
Pack of 50 lawn bags for $10.Eye protecting glasses for $15.Hence the total amount invested was of:
10 + 15 = $25.
What is the profit inequality?The profit is given by revenue subtracted by costs.
In the context of this problem, the revenue and the cost functions are given as follows:
Revenue: R(x) = 15x (as you charge $15 to mow one lawn).Cost: C(x) = 25. (investment).Hence the profit function is:
P(x) = R(x) - C(x)
P(x) = 15x - 25.
You start making a profit when:
P(x) > 0.
15x - 25 > 0.
The amount you earned mowing 16 lawns is of:
P(16) = 15(16) - 25 = $215.
(positive profit, hence you made money).
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Determine whether the relation is a function.
(0, 1) (5, 6) (7, 9) (8, 9)
A. Not a function, there is not a unique y-value for each x-value
B. Not a function, there is not a unique x-value for each y-value
C. Function, there is a unique x-value for each y-value
D. Function, there is a unique y-value for each x-value
Answer:
C. Function, there is a unique x-value for each y-value
Solve the following proportion for u. 7/u=3/11 Round to the nearest tenth.
The solution for u in the expression given as 7/u = 3/11 is u = 25.7
How to determine the solution to the variable u in the expression?From the question, the algebraic expression is given as
7/u = 3/11
There is no constant to add to or subtract from the expression
So, the equation remains the same
7/u = 3/11
Multiply both sides of the equation by u
This gives
u * 7/u = 3/11 * u
Evaluate the products
So, we have the following equation
7 = 3/11u
Multiply both sides of the equation by 11/3
This gives
11/3 * 7 = 3/11u * 11/3
Evaluate the products in the above expression
77/3 = u
So, we have
25.6667 = u
Approximate
25.7 = u
Rewrite as
u = 25.7
Hence, the solution is u = 25.7
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Cesium-137 has a half-life of about 30 years. if we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?
For 200mg of Cesium-137, it will be 229 years which is less than 230 years until only 1 milligram remains.
The amount of time a radioactive item takes to decay is known as the material's half-life.
The first-order kinetics for a half-life is given as 0.693 / k.
Given half-life = 30 years,
k = rate-constant =?
30 = 0.693 / k
k = 0.0231 years ⁻¹
The integrated rate law for first-order kinetics is given as follows:
A = A₀[tex]e^{-kt}[/tex]
k = rate constant of the reaction
A₀ = Concentration of reactant initially = 200 mg
A = t = 1 mg
Putting all values in the equation will give,
t = 229 years.
Thus, Cesium takes 229 years to decay to reach from 200milligram to 1 milligram in weight.
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What happens if the slope is undefined? Provide an example of two points that would be on a line with an undefined slope.
What happens when the slope of a line is undefined is that, the line is a vertical line that crosses the x-axis.
The points could be (1, 5) and (1, 10)
How to explain the undefined slope?It is known that linear equations have slopes
These slopes are the average rate of change of the function
The values of these slopes can be
ZeroPositive or negativeUndefinedWhen the slope is undefined, it means that the line is a vertical line
An example of the vertices on such line is (x, y) and (x, y + n)
See that the x coordinate remains constant, while the y coordinate changed
Take for instance, a line that passes through (1, 5) and (1, 10) would have an undefined slope
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assuming that earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 1046 kilometers due north of the other?
The difference between the distance between the two cities if of 14.842 latitudes.
The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.
Therefore, the earth has 181 latitudes.
Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.
Hence the distance covered by all 181 latitudes = 2 X radius of the Earth
= 2 X 6378 km
= 12756
Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be
12756/181
= 70.475 km
Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.
Therefore the difference in latitudes between the two cities is
1046/70.475
= 14.842 latitudes
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what does the adjusted r squared tell us about the relationship between sales, price, and advertising? the model explains about 90% of the variance in sales. the model explains about 60% of the variance in sales. the model explains about 80% of the variance in sales. the model explains about 70% of the variance in sales.
The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
Define the term adjusted r squared?R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.
R-squared describes how much the variance with one variable describes the variance of the other. So, if a model's R2 is 0.50, the model's inputs can explain roughly half of a observed variation.A score of 70 to 100 shows that a specific portfolio closely reflects the underlying stock index, whereas a score of 0 to 40 indicates a relatively poor correlation the with index.Higher R-squared scores also suggest that beta measurements are more reliable. The volatility of either a security or portfolio is measured by beta.Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
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if a fair die is rolled, what is the probability of landing on an even number or a number greater than 2
The probability of landing on an even number or a number greater than two is 5/6.
A fair die is rolled. We need to find out the probability of landing on an even number or a number greater than two.
Let the event of landing on an even number be denoted by the variable E1. Let the event of landing on a number greater than two be denoted by the variable E2. We need to calculate P(E1 ∪ E2).
P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)
P(E1 ∪ E2) = (3/6) + (4/6) - (2/6)
P(E1 ∪ E2) = 5/6
Hence, the probability of landing on an even number or a number greater than two is 5/6.
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Determine the distance between the points (−2, −3) and (2, 0). 2 units 4 units 5 units 10 units
The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x 2 - x 1) 2 + (y 2 - y 1) 2. where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The order of the points does not matter for the formula as long as the points chosen are consistent.
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Answer:
it is 5 units!
6 groups of what tenths is 4.2
The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.
What is Decimals?
Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
6 groups of ____ tenths is 4.2
4.2 ÷ 6 = 0.7
Hence, 6 groups of 0.7 tenths is 4.2
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simplify by using order of operations 22 - (8 x 1) divided by (6 - 4) - 2
The value of the expression 22 - (8 x 1) divided by (6 - 4) - 2 is 0.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
The expression given is:
22 - (8 x 1) divided by (6 - 4) - 2
= 22 - (8 x 1) ÷ (6 - 4) - 2
= [22 - 8] ÷ [2 - 2]
= 14 ÷ 0
= 0
The value is 0.
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