The equation of tangent to the curve y = 8√x at the point (4,16) is y = 2x + 8 .
We have to find equation of tangent line to the curve y = 8√x at the point (4, 16), we first find the slope ;
So , slope of the tangent line is derivative of function y = 8√x at point (4, 16).
which means : y' = 4[tex]x^{-\frac{1}{2} }[/tex] ;
At the point (4, 16), the value of x is 4.
So , y' = 4 × [tex]4^{-\frac{1}{2} }[/tex] = 2 .
By Using the point slope form, the equation of the tangent line is ;
⇒ y - 16 = (2)(x - 4) ;
Simplifying this equation, we get:
⇒ y - 16 = 2x - 8
⇒ y = 2x + (16 - 8)
⇒ y = 2x + 8 .
Therefore, the equation of the tangent line to the curve is y = 2x + 8 .
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The given question is incomplete , the complete question is
Find an equation for the tangent to the curve y = 8√x at the point (4,16) .
The tension T at each end of a chain has magnitude 25 N (see the figure). What is the weight of the chain?
As per the tension the weight of the chain is 2.55 kg
The tension is the force exerted by a rope, cable, or chain on an object to which it is attached.
To solve this problem, we need to understand the relationship between tension and weight. The weight of an object is the force with which it is attracted towards the earth due to gravity.
Using the given magnitude of tension (25 N) for each end, we can rewrite this equation as:
25 N - 25 N = Weight of the section
Simplifying this, we get:
Weight of the section = 0 N
This means that the weight of a small section of the chain is negligible compared to the tension at each end. However, if we consider the entire length of the chain, the weight cannot be ignored.
To calculate the weight of the chain, we need to find its mass. We can do this using the formula:
Mass = (weight of the chain) / (gravitational acceleration)
We know that the tension at each end of the chain has a magnitude of 25 N. Since the chain is in equilibrium, the net force on the chain must be zero. This means that the weight of the chain must be equal to the tension at each end.
Therefore, we can write:
Weight of the chain = 25 N
Now we can use the formula for mass:
Mass = (25 N) / (9.8 m/s²)
Using a calculator, we get:
Mass = 2.55 kg
This confirms that the weight of the chain is indeed equal to the tension at each end, as expected.
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Complete Question:
The tension T at each end of the chain has magnitude 25 N (see the figure). What is the weight of the chain?
The historical returns on a balanced portfolio have had an average return of 5% and a standard deviation of 14%, Assume that returns on this portfolio follow a normal distribution. (You may find it useful to reference the z table.) a. What percentage of returns were greater than 33%? (Round your final answer to 2 decimal places.) Percentage of returns = %
b. What percentage of returns were below -37%? (Round your final answer to 2 decimal places.) Percentage of returns %
The percentages of returns are given as follows:
a. Greater than 33%: 2.28%.
b. Below -37%: 0.13%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for this problem are given as follows:
[tex]\mu = 5, \sigma = 14[/tex]
The proportion above 33% is the one subtracted by the p-value of Z when X = 33, hence:
Z = (33 - 5)/14
Z = 2.
Z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228 = 2.28%.
The proportion below -37% is the p-value of Z when X = -37, hence:
Z = (-37 - 5)/14
Z = -3.
Z = -3 has a p-value of 0.0013.
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4,400 is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 22 years to the nearest cent
After 22 years the amount in the account will be 12,386.
What is simple interest?Simple interest is an interest amount calculated on the principal amount with certain interest rate. It is given by the formula,
[tex]S.I.=\frac{P*n*r}{100}[/tex]
Where P is the principal amount, n is the number of years, r is the rate of interest.
4,400 is placed in an account i.e., Principal amount, P=4400
With an annual interest rate, r=8.25%
Number of years, n=22 years.
Amount in the account after 12 years will be,
By using simple interest formula,
[tex]S.I.=\frac{P*n*r}{100}[/tex]
= [tex]\frac{4400*8.25*22}{100}[/tex]
=7,986
Interest amount = 7,896.
Total amount after 22 years= interest amount + principal amount
= 7896+4400
= 12,386.
Hence, after 22 years the amount in the account will be 12,386.
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Which of the equations below could be the equation of this parabola? ASAP
The Equation of Parabola shown in the graph is y=2x².
What is Equation of Parabola?The general equation of a parabola is given by
y = a(x – h)² + k or x = a(y – k)² +h.
Here (h, k) denotes the vertex. y = a(x – h)² + k is the regular form. x = a(y – k)²+h is the sidewise form.
Given:
We have vertex (0, 0).
As, from the Graph the parabola is open up.
So, it is of the form y= ax², a>0.
Thus, the Equation of parabola is y=2x².
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Evaluate the following expression by drawing the unit circle and the appropriate right triangle. The angle is in radians.
cos(5π/3)
The answer for the angle cos (5π/3) is 1/2.
We know that in the polar coordinate system,
x = r cosθ ; y = r sinθ
Since, we are approximating using a unit circle, therefore, r = 1
As we can see in the graph of unit circle, we take the angle in radians anti-clockwise as 5π/3.
As we want the value of cos(5π/3), we look for the x coordinate.
We get this from the end point of the angle that we have drawn on the unit circle in anti-clockwise motion.
The x co-ordinate is 1/2, hence we get the value of cos(5π/3) as 1/2.
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(true/false) suppose the first column of a is three times of the second column. then the homogeneous equation ax
The statement that " Homogeneous equation Ax = 0 has trivial solution if it has at least 1 free variable" is FALSE .
For a system of Linear Equations, a free variable is a variable which can take any value, whereas
the Leading Variable is a variable which is determined by the values of the free variables.
The presence of a free variable means that existence of a non trivial solution to Ax = 0 because a free variable corresponds to a column of A that does not contain a pivot position in the corresponding row of [A|0].
So , the corresponding variable can be set to any non zero value, which gives a non trivial solution to Ax = 0.
Therefore, we can conclude that the homogeneous equation Ax = 0 has the trivial solution if and only if the equation has no free variables.
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The given question is incomplete , the complete question is
The homogeneous equation Ax = 0 has the trivial solution if and only if the equation has at least one free variable. True or False ?
If two medians of a triangle are congruent, then what is the triangle?
IV. Long Answer and Analysis (20 points) Do a simple Price Elasticity of Demand Calculation: ; A. If an original price was $5.00 and the amount bought (purchased) was an amount of 50 units (say of good like McDonalds Big Macs). What is the Revenue the producer receives at this point: $________ B. Now the price is lowered to $4.00 and now 200 Big Macs are purchased. What is the new revenue at this point: has it gone up or down?
C. using the formula for Price elasticity of Demand, calculate the actual fraction value of the change In price
If the quantity of big macs demanded falls from 2.0 million to 1.6 million as the price of whoppers falls from $1.40 to $.80, the cross-price elasticity of demand for big macs is 0.4.
What is cross-price elasticity?Cross-price elasticity quantifies how responsive a product's demand is to changes in a related product price. Some products on the market frequently have connections to one another.
This could imply that the demand for a product can be favourably or negatively impacted by a product's price change. The cross elasticity of demand, also known as the cross-price elasticity of demand, in economics quantifies the relationship between the percentage change in the quantity of a commodity sought and the percentage change in the price of another good, ceteris paribus. The cost of milk is one such example. People might switch to 2% milk if full milk prices rise. Similar to how whole milk gets more popular as 2% milk prices go up.
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The qualitative characteristic that means there is agreement between a measure and a real-world phenomenon is:
A) Verifiability.
B) Representational faithfulness.
C) Neutrality.
D) Materiality.
Verifiability is the ability to demonstrate that a measure is in agreement with a real-world phenomenon. It is an important qualitative characteristic of financial reporting.
Verifiability is a qualitative characteristic of financial reporting that refers to the ability to demonstrate that a measure is in agreement with a real-world phenomenon. This means that the financial information presented is accurate and reliable, and that it faithfully reflects the underlying transactions or events that it is supposed to represent. Verifiability is important because it ensures that users of financial statements, such as investors and creditors, are able to make informed and accurate decisions based on the information contained in the statements. This is achieved through the use of external auditors to objectively verify the integrity of financial statements and disclosures. If a measure is not verifiable, it is not considered to be a reliable source of information and should not be used for decision-making. Verifiability is essential for reliable financial reporting.
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according to a recent pew research center survey, 23% of us adults say they have not read a book in any format in the past 12 months. assume the stated rate of 23% is indeed the correct population proportion value.
This means that out of every 100 US adults, 23 of them have not read a book in the past year. This rate is quite high, considering the vast number of books available to read.
To calculate the number of US adults who have not read a book in the past year, we can use the following equation:
Number of US Adults Who Have Not Read a Book in the Past Year = Total Number of US Adults x Proportion of US Adults Who Have Not Read a Book in the Past Year
First, determine the total number of US adults. For example, let's say that there are 80 million US adults.
Next, multiply the total number of US adults by the proportion of US adults who have not read a book in the past year (0.23). Therefore, 80 million x 0.23 = 18.4 million US adults who have not read a book in the past year.
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A car drove at 65 miles per
hour for 7 hours. How
many miles are left if the
entire trip is 540 miles?
Answer: 85 miles left
Step-by-step explanation:
65 miles x 7 hours = 455 miles
540 miles - 455 miles = 85 miles
The radius of a circle is 17 meters. What is the circle's circumference?
Answer:[tex]34\pi[/tex]
Step-by-step explanation:
c=[tex]2\pi R=2*17\pi =34\pi[/tex]
Answer:
43.98 meters
Step-by-step explanation:
classify the following set of measurements as accurate, precise, both, or neither. checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g
The dimensions listed above are thus neither exact nor precise.
In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.
It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.
The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.
The dimensions listed above are thus neither exact nor precise.
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Tamika and Li are painting a mural. Tamika has painted 1/3 of the mural and Li has painted 1/6 of it. What part of the mural have they painted in all?
Answer:
Tamika has painted 1/3 of the mural, and Li has painted 1/6 of it. To find the total part of the mural that they have painted together, we need to add these fractions:
1/3 + 1/6
We need to find a common denominator to add these fractions. The smallest common multiple of 3 and 6 is 6. We can convert 1/3 to 2/6 by multiplying the numerator and denominator by 2:
2/6 + 1/6 = 3/6
So, Tamika and Li have painted 3/6 of the mural in all. We can simplify this fraction by dividing both the numerator and denominator by 3:
3/6 ÷ 3/3 = 1/2
Therefore, Tamika and Li have painted 1/2 of the mural in all
(4a-5)-(-2a-3) find the difference
Answer: [tex]6a-2[/tex]
Step-by-step explanation:
[tex](4a-5)-(-2a-3)\\=4a-5+2a+3\\=6a-2[/tex]
The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5
Apply the product rule to 4a^5:
⇒ 4^3(a^5)^3
Raise 4 to the power of 3:
⇒ 64(a^5)^3
Apply the power rule and multiply exponents, (a^m)^n = a^mn:
⇒ 64a^5*3
Multiply 5 by 3:
64a^15
⇒ (4a-5)⇒ = 9a⇒ (-2a-3)⇒ = 5Therefore, The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5
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assume that water is poured into a spherical bottle at a constant rate. which of the following graphs best represents the height of water in the bottle as a function of the amount of water in the bottle?
A graph that shows a slow and steady increase at first, followed by a steeper increase as the bottle approaches full capacity, would be the most accurate representation. Without seeing the available graphs, it's difficult to say which one is the best representation.
The best graph to represent the height of water in a spherical bottle as a function of the amount of water in the bottle is a non-linear graph that has a curved shape.
As the volume of water in the bottle increases, the height of the water will also increase, but not at a constant rate. The curve will become steeper as the bottle fills up, because the same amount of water will fill less and less of the remaining space in the bottle. Therefore, a graph that shows a slow and steady increase at first, followed by a steeper increase as the bottle approaches full capacity, would be the most accurate representation.
The height of water in a spherical bottle as a function of the amount of water in the bottle would be represented by a non-linear graph that has a curved shape. As the volume of water in the bottle increases, the height of the water will also increase, but not at a constant rate. The curve will become steeper as the bottle fills up, because the same amount of water will fill less and less of the remaining space in the bottle.
The most correct illustration would be a graph showing a gradual increase at initially, followed by a sharper increase as the bottle nears capacity. It's challenging to determine which graph is the best depiction without seeing the available graphs.
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Question 5 (1 point)
When budgeting for savings, you should wait until you pay all your bills and
discretionary expenses and then see if you have money left.
True
False
The adage "You should wait until after paying all of your bills and discretionary expenses before budgeting for savings" is accurate.
How do you determine discretionary spending?Consider your disposable income, or the amount of money that remains in your paycheck after taxes. Your discretionary income is the amount that remains after deducting all of your expenses, such as rent or mortgage payments, student loans, utilities, and food. Spending that are not necessary to run a household are categorized as discretionary expenses, including travel and luxury purchases. In other words, the income-earner has the option of paying for these items or services.Think about whether it's a want or a need before deciding whether it's a discretionary spend. Food is necessary, but it doesn't have to come from a restaurant.To learn more about discretionary expense, refer to:
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What are the coordinates of R' for the Dilation D(0,5 P) (PQRS)?
The coordinate of R' after dilation of (0.5, P) is at R(- 1.5, - 1.5).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, The coordinate point of R is (1, 1).
Now, After a dilation of 0.5 it would be (1×0.5, 1×05) ⇒ (0.5, 0.5).
Again a dilatation of P(- 3, - 3) would be, - 3[(0.5, 0.5)] ⇒ (- 1.5, - 1.5)
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PLEASE HELP ASAP DUE SOON!
The domain of the function g(x) is given as follows:
x ≥ -1.
How to obtain the domain of the function?The domain of a function is composed by the set that contains all possible input values for the function.
The square root function is defined only for non-negative values, hence the domain is obtained as follows:
6x + 6 ≥ 0
6x ≥ -6
x ≥ -6/6
x ≥ -1.
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find an equation of the line with the given slope and containing the given point. write the equation using function notation. slope -7 through (-5,9)
The equation of line with slope as "-7" and passes through point (5,9) in function notation is f(x) = -7x - 26 .
We know that the equation of the line with slope "m = -7" passing through the point (-5, 9) can be found using the point-slope form of the equation of a line : which is ⇒ y - y₁ = m(x - x₁)
where (x₁, y₁) = (-5, 9) is the point and m = -7 is the slope.
On Substituting the values of point and slope , in the equation ,
⇒ y - 9 = -7(x - (-5)) ;
Simplifying the expression further ;
⇒ y - 9 = -7(x + 5) ;
⇒ y - 9 = -7x - 35 ;
Adding 9 to both sides,
⇒ y = -7x - 26
In function notation is f(x) = -7x - 26 .
Therefore, the required equation of the line is f(x) = -7x - 26 .
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the charged balloon in (figure 1) expands as it is blown up, increasing in size from the initial to final diameters shown.
The size of a balloon increases as it is blown up because of the pressure of the air inside the balloon is greater than the atmospheric pressure outside.
The change in size of the balloon is determined by the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume (PV = nRT). Therefore, when air is added to the balloon and the pressure inside the balloon increases, its volume decreases. We can calculate the final diameter of the balloon, given the initial diameter and the change in pressure. For example, if the initial diameter of the balloon is 10 cm and the change in pressure is 0.5 atmospheres, then the final diameter of the balloon is[tex](10 cm) x [(1 + 0.5)⁰’⁵] = 10.63 cm.[/tex]
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Help pls!! I’ll give points and brainliest!!!
Please help solve for nmber 4
The requried a measure of the exterior angle ∠4 = 63°.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
As we know that for a triangle, the sum of the remote interior angle is equal to the measure of the exterior angle.
So, from the figure.
31 + 32 = ∠4
∠4 = 63°
Thus, the requried measure of the exterior angle ∠4 = 63°.
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i need help with this problem lol
Answer:15
Step-by-step explanation:
We know this figure's all angles sum is equal to 180*(n-2)=180*3=540
so,
112+7x+5+6x+2+10x-8+4x+24=540
27x+135=540
27x=405
x=15
1. Cuando Raúl y Esperanza llegaron a una fiesta quedaban 3/10 del pastel, así que se dividieron esa porción en partes iguales. ¿Qué parte del pastel completo le tocó a cada uno?
Answer:
13
Step-by-step explanation:
first multiply then divide and subtract
The above PPF of producing mountain bikes to racing bikes.
The factory is currently producing 250 mountain bikes and 100 racing bikes per week (point A). If they wanted to produce 50 more racing bikes per week (point B), what would be there opportunity cost?
A. 100 racing bikes
B. 250 mountain bikes
C. 50 mountain bikes
D. There is no opportunity cost.
They wanted to produce 50 more racing bikes per week (point B), what would be there opportunity cost There is no opportunity cost.
What is meant by speed?
the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. The speed of sound and light both represent quickness in movement, going, traveling, proceeding, or performance.Full speed ahead. relative quickness in action, advancement, etc. complete, maximum, or ideal rate of motion: Nine seconds are all it takes for the car to reach speed.An object's speed can be determined by calculating the distance it covers in a given amount of time. For instance, an automobile is moving at 70 miles per hour if it covers 70 miles in an hour (miles per hour).The opportunity cost of producing 50 more racing bikes per week (moving from point A to point B) would be the amount of mountain bikes that the factory would have to give up producing in order to allocate resources to producing more racing bikes.
From the PPF, we can see that in order to produce an additional 50 racing bikes per week, the factory would have to decrease its production of mountain bikes by 50 (moving from 250 to 200). Therefore, the opportunity cost of producing 50 more racing bikes per week is 50 mountain bikes (option C).
So the answer is C. 50 mountain bikes.
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decide whether the function could be linear, exponential, or neither. linear exponential neither correct: your answer is correct. if the function could be linear or exponential, write a possible equation for the function. (if the function is neither, enter neither.) f(x)
Since the ratio of consecutive outputs is not constant, the function is not an exponential function. Hence the function is neither linear nor exponential.
To determine whether the given function is linear, exponential, or neither, first compute the average rate of change of with respect to and then compute the ratio of the consecutive outputs.
If the average rate of change is constant, then the function is linear.
If the ratio of consecutive outputs is constant, then the function is exponential.
x y Average rate of change ratio of consecutive outputs
-1 3 [tex]\frac{\delta y}{\delta x}=[/tex](6-3)/0-(-1)=3 6/3=2
0 6 (12-6)/(1-0)=6 12/6=2
1 12 (18-12)(2-1)=6 3/2
2 18 (30-18)/(3-2)=12 5/3
3 30 - -
Observe the above table, for the given function, the average rate of change from to is , and from to is .
Since the average rate of change is not constant, the function is not a linear function.
Observe the above table, for the given function, the ratio of consecutive outputs from -1 to 0 is 2 from 0 to 1 is 2, and from 2 to 1 is3/2
Since the ratio of consecutive outputs is not constant, the function is not an exponential function.
Hence the function is neither linear nor exponential.
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Find the average number from the following numbers. 13, 33, 2, 10, 3.
Answer: 12.2
Step-by-step explanation:=
61/5=12.2
The expected value of an unbiased estimator is equal to the parameter whose value is being estimated. A) True B) False
The expected value of an unbiased estimator is equal to the parameter whose value is being estimated. A) True B) False . the answer is false
g consider the following sets of vectors. show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. then find a basis for each set and give the dimension.
(i) A basis for the set is {(2, 3, 4), (3, -2, 1)} and the dimension is 2.
(ii) A basis for the set is {(1, 1, 1, 1), (2, 0, 0, -1)} and the dimension is 2.
(i) {(2, 3, 4), (3, -2, 1)}
(i) The set contains the zero vector (0, 0, 0). It is closed under addition because for any two vectors in the set, the sum of the two vectors is also in the set. It is closed under scalar multiplication because for any vector in the set and any scalar, the scalar multiplied by the vector is also in the set.
A basis for the set is {(2, 3, 4), (3, -2, 1)} and the dimension is 2.
(ii) {(1, 1, 1, 1), (2, 0, 0, -1)}
(ii) The set contains the zero vector (0, 0, 0, 0). It is closed under addition because for any two vectors in the set, the sum of the two vectors is also in the set. It is closed under scalar multiplication because for any vector in the set and any scalar, the scalar multiplied by the vector is also in the set.
A basis for the set is {(1, 1, 1, 1), (2, 0, 0, -1)} and the dimension is 2.
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The complete question is:
Consider the following sets of vectors. show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. then find a basis for each set and give the dimension.
(i) {(2, 3, 4), (3, -2, 1)}
(ii) {(1, 1, 1, 1), (2, 0, 0, -1)}