The mistake of Derek is that 72 divided by 8 is 9, not 8.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
Given is an equation that Derek is trying to solve.
The equation is 8d = 72.
8d = 72
In the first step, Derek divided both sides of the equation by 8, which is a correct way to solve the problem.
We have to divide both sides of the equation by 8.
8d / 8 = 72 / 8
This step is correct.
After dividing, in the left hand side, there will be only 'd' remaining and in the right hand side, 27/8 = 9.
d = 9
But Derek got 8 instead of 9 in the right hand side.
Hence the value of d is 9 and not 8, which is the mistake of Derek.
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Please help! Systems of equation/matrix problem
5. TELEVISION During t
ring the summer, Manuel watches television M hours per day, Monday through Friday. Harry watches television H hours per day, Friday and Saturday. Ellen watches television E hours per day, Friday through
Sunday. Altogether, they watch television 37 hours each week. On Fridays, they watch a total of 11 hours of television.
If the number of hours Ellen spends watching television on any given day is twice the number of hours that Manuel
spends watching television on any given day, how many hours of television does each of them watch each day?
Answer:
see attached
Step-by-step explanation:
two expressions that are equivalent to 3f
The two expressions are written as :
3f + 2f + 4s 5f + 4sHow to solve for the expressions that are equivalent to 3f+4s+2f3f+4s+2f this expression that we have here is a mathematical expression that we can combine by making use of the commutative addition.
We would have the first expression when we write the equation as:
3f+4s+2f = 3f + 2f + 4s
We would have the second expression when we write the equation as
5f + 4s
This is the solution of the expression.
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two expressions that are equivalent to 3f+4s+2f ?
A marble statue of height h1metres is mounted on a pedestal. The angles of elevation of the top and bottom of the statue from a point h2metres above the ground level are αandβrespectively. Show that the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.
So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.
To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.
From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.
We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.
Let's call the height of the pedestal as "h3"
So we can write the following equations:
h1/((h3+h1)-h2)= tan(α)
h1/((h3)-h2)= tan(β)
By solving the above equations we can get the value of h3 which is the height of the pedestal.
((h1−h2)tanβ+h2tanα)/tanα−tanβ
This is the final equation which gives the height of the pedestal.
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State the critical values for a one-sample t test given the following conditions:
1. Two-tailed test, a = .05, n = 12
2. One-tailed test, lower-tail critical, a = .01, df = 15
3. Two-tailed test, a = .01, df = 26
4. One-tailed test, upper-tail critical, a = .05, n = 30
Use the values listed in the table; do not round. Be sure to include the appropriate signs in your answers:
• if positive --> + and the value
. if negative --> - and the value
if both --> +/- and the value
(Privitera, 2019, p. 250, #14)
The critical values for a one-sample t test given the following conditions are +1.796, -1.796 2. -2.60 3. +2.576, -2.576 4. +1.729.
What is value?Value is a term used in many different contexts to refer to the worth or importance of something. It is used to describe the worth of an item or service in terms of its utility, its ability to satisfy a need or desire, or its usefulness in exchange. Value can also refer to the worth of an individual or group in terms of their contribution to society or their inherent worth. Value is subjective and can vary greatly from one person or group to another.
1. +1.796, -1.796
2. -2.60
3. +2.576, -2.576
4. +1.729
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which of the following is an integral element that defines sport and therefore distinguishes it from play and dramatic spectacle?
One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.
In sports, there are typically opponents or teams competing against each other to achieve a goal or win a match.
This competitive aspect is not present in play or dramatic spectacles, where the focus is typically on individual or group performance rather than competition against others.
Sports are defined as physical activities that involve a set of rules and are typically competitive in nature. They are typically organized and played by people in order to achieve a goal or win a match. Examples of sports include football, basketball, soccer, tennis, baseball, and golf.
Sports are also a form of recreation, entertainment, and physical activity. They can be played individually or in teams. They help to improve physical fitness, and mental health and also promote teamwork and social interaction.
Therefore, One integral element that defines sport and distinguishes it from play and dramatic spectacle is the concept of competition.
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Jupiter has a radius of 44 ,423 miles. As the planet rotates on its axis, a point on its equator travels at 669,883 miles per day.
(a) Find the angular speed of a point on its equator in radians per day.
(b) Find the number of rotations the planet makes per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
Hey there!
Answers;
(a) 15 radians/day(b) Number of rotations = 2| Explanation |
For part (a):
[tex]v=669,883[/tex] [tex]miles/day[/tex]
[tex]r=44,423[/tex] [tex]miles[/tex]
[tex](a)V=rw[/tex]
[tex]w=\frac{v}{r}[/tex] [tex]=\frac{669883}{44423}[/tex][tex]=15.0796[/tex] [tex]radians/day[/tex]
[tex]15[/tex] [tex]radians/day[/tex]
For part (b):
[tex]Circumference=2\pi r[/tex]
[tex]2*3.14*44423[/tex]
[tex]278976*44[/tex]
Number of rotations = [tex]\frac{669883}{278976*44}[/tex] = [tex]2*40[/tex] ⊥ ≈ [tex]2[/tex]
Hence:
(a) [tex]15[/tex] [tex]radiations/day[/tex]
(b) Number of rotations = [tex]2[/tex]
___________________________________________
Hope this helps! If you mark Brainliest, TYSM! :D
What is the measure of n?
28
m
7
n = [?]
Give your answer in simplest form.
The measure of the side length n is equal to 14 for the right triangle.
How to evaluate the length of n in the right triangleConsidering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent m and hypotenuse 28+7= 35;
cosθ = m/35
for the smaller right triangle with adjacent 7 and hypotenuse m
cosθ = 7/m
m/35 = 7/m
m² = 245 {cross multiplication}
m = √245 = 7√5 {take square root of both sides}
(√245)² = 7² + n² {by Pythagoras rule for the smaller right triangle}
245 = 49 + n²
n² = 245 - 49 {collect like terms}
n² = 196
n = √196 {take square root of both sides}
n = 14
Therefore, the measure of the side length n is equal to 14 for the right triangle
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I NEED HELP ASAP, I PROMISE WHOEVER IS CORRECT IS GOING TO GET BRAINLIST!
The numbers that correctly complete the two-way table are 100,70, 170, 80, 130, 210, 180,200, and 380 as shown in the attached chart.
How to calculate the number of sweatshirts per color and style?Total of sweatshirts= 380
Total with no hood= 210
Green sweatshirts= 180
Purple sweatshirts with no hood= 70
Based on this information we can conclude:
There are 170 sweatshirts with no hood (380-210= 170)There are 200 purple sweatshirts (380 - 180 = 200)There are 130 purple sweatshirts (200-70 = 130)There are 100 green sweatshirts with hood (170-70= 100)There are 80 green sweatshirts with hood (180-100 = 80)Learn more about two-way tables in https://brainly.com/question/29766382
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X^2 - y^2
—————-
3x - Зу
Step-by-step explanation:
x² - y² = (x + y)(x - y)
3x - 3y = 3(x - y)
(x + y)(x - y) / (3(x - y)) = (x + y)/3
Answer:
x^2 - y^2
_______
3x - 3y
(x+y) (x-y)
_______ { (x-y) (x-y) cancels out}
3(x-y)
(x+y)
____
3
Hope this will help you...!!!!
6= 1/v+2
Solve for V
simplify your answer as much as possible
Answer:
your question is 6=1/v+2
Step-by-step explanation:
6-2=1/v
4v=1
v=1/4
The compound figure shown is composed of a
semicircle and a rectangle.
Which best represents the area of the composite
figure
A) 88ft2
B) 108 ft2
C) 75 ft2
D) 100ft2
Answer:
A
Step-by-step explanation:
this is a college level question ? oh my ...
to get the total area we need to add the area of the rectangle and the area of the half-circle.
the area of the rectangle is
length × width = 15 × 5 = 75 ft²
the area of the half-circle is
pi×r² / 2
how do we get r (radius) ?
we know, both lengths of the rectangle must be equally long. so, 15 ft.
we see that the remaining length after the half-circle is 9 ft.
so, the diameter of the half-circle is 15 - 9 = 6 ft.
the radius is half the diameter, so r = 6/2 = 3 ft.
the area is therefore
pi×3² / 2 = 9pi /2 = 14.13716694... ft²
in total that makes
75 + 14.13716694... = 89.13716694... ft²
the closest of your answer options is A : 88 ft²
If angle A=−170∘, what is the radian measure of A? Enter an exact fraction that contains the π symbol.
The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π
How to convert degrees to radians?When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Thus, since we want to find the radian measure of 170 degrees, it means that;
If 180° = π radians,
then; 170° = (170 * π)/180
= ¹⁷/₁₈π
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The top selling brand of vape machines sold 10000 units at $89 per unit in 2018. what is their market share if the vape machine market had sales of $1.4M?
The market share of the vape machine market had sales of $1.4M is given as 63.57%.
How to solve for the market share of the vape machineTo calculate the brand's market share, you would need to divide the brand's sales by the total sales of the market and then multiply by 100 to get the percentage.
In this case, the brand's sales are 10000 units x $89/unit = $890,000.
So the market share would be:
$890,000 / $1,400,000 x 100 = 63.57%.
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i need help 10 divided by 75.10
quotient.
After divide, the value of quotient is 0.133.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
⇒ 10 divided by 75.10.
Now, We get;
⇒ 10 divided by 75.10
⇒ 10 ÷ 75.10
⇒ 0.133
Thus, The value of quotient after divide = 0.133
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In 2015, as part of its 10th high school reunion, the class of 2005 held a reception at the high school. In an informal survey, the principal of the high school asked 50 of the attendees about their income. The principal computed the mean income of the 50 attendees to be $148,535. In an article published by the local newspaper, the principal was quoted as stating, "The members of our class of 2005 enjoyed resounding success. Last year, they had a mean income of $148,535!"
Part A: What is a statistical advantage of using the median of the reported incomes, rather than the mean, as the estimate of the typical income? (4 points)
Part B: The principal felt the individuals who attended the reception may be different from the class as a whole. A more detailed survey of the class was planned to determine a better estimate of income. The staff developed two methods based on the available funds to carry out the survey.
Method 1: Send out an e-mail to all 2,476 members of the class and ask them to complete an online form. The staff estimates that at least 500 members will respond.
Method 2: Select a simple random sample of members of the class and contact the selected members directly by phone. Follow up to ensure all responses are obtained. Because method 2 requires more time than method 1, the staff estimates only 100 members of the class can be contacted using method 2.
Which of the two methods would you select for estimating the average yearly income of all 2,476 members of the class of 2005? Explain your reasoning by comparing the two methods and by describing the effect of each method on the estimate.
Method 2 is the best option for estimating the average yearly income of the class of 2005.
What type of sampling technique is used?I would select Method 2 for estimating the average yearly income of all 2,476 members of the class of 2005. Method 2 involves selecting a simple random sample of members of the class and contacting them directly by phone. This method guarantees that the sample will be representative of the entire population and thus provides the best estimate of the average income of the class. By randomly selecting the sample, we can be sure that the sample will be unbiased and the results will be more reliable. Method 1, on the other hand, involves sending an e-mail to all 2,476 members of the class and asking them to complete an online form. Although this method is easier and less time-consuming, it does not guarantee a representative sample. If only 500 people respond, it is possible that the sample will not be representative of the entire population and thus, the results will not be accurate. Overall, It will ensure that the sample is representative of the entire population and that the results are unbiased and reliable.To learn more about the sampling theory refer to:
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For each description below, identify each underlined number as a parameter or statistic. Use appropriate notation to describe each number, e.g., .(a) Nationwide, 84% of people are living in the same house they were living in one year ago. The town council of Pleasant Valley surveys 100 residents and find that 75% of them have not moved in the past year.(b) The mean birthweight of infants in the United States in 2006 was 3.3 kg with a standard deviation of 0.57 kg. An obstetrician determines that among her own patients, the mean birthweight was 3.6 kg.
The mean birthweight of the obstetrician's own patients is higher than the national mean.
In the first description, 84% is a parameter, since it describes the population as a whole. The survey of 100 residents in Pleasant Valley yields a statistic of 75%, since it is a sample of the population.
In the second description, the mean birthweight of infants in the United States in 2006 of 3.3 kg and the standard deviation of 0.57 kg are both parameters. The mean birthweight of the obstetrician's own patients of 3.6 kg is a statistic. To calculate the difference between the two means, we can subtract the two values: 3.6 kg - 3.3 kg = 0.3 kg. This 0.3 kg difference indicates that the mean birthweight of the obstetrician's own patients is higher than the national mean.
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Debbie shipped 2 packagesone weighed 2 pounds10 ounces the other weighed 4 pounds and12 ounces what is the total weight of The 2 packages
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
what is unitary method ?The unit tactic is a strategy for addressing issues that entails first figuring out the value of a particular unit, then increasing that value to figure out the needed value. Simply put, the unit method is employed to obtain a minimum unit value from a multiple that is supplied. For example, 40 pens may cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its homologue and reciprocal are equal in terms of mathematics, algebra, linear algebra, applied mathematics, or mathematics for matrices or operators.
given
1 pound = 16 ounces
for 2 packages
2 pounds 10 ounces + 4 pounds 12 ounces
6 pounds and 22 ounces
= 7 pounds 10 pounces
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
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Can anyone help??
Which line is parallel to y=-4x+11 and goes through (2,1)? Hint: use point slope form
A)y-1=-4x(x-2)
B)y-1=-1/4(x-2)
C)y-1=4(x-2)
D)y-2=-4(x-1)
(I’m trying to do test corrections :c )
A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).
What is the point-slope form?Mathematically, the point-slope form of a line is modeled by this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the given linear equation y = -4x + 11, the slope is given by:
y = -4x + 11
m₁ = -4
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ (m represents the slope.)
At point (2, 1), an equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -4(x - 2)
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determine if one of the given vectors is in the span of the other vectors. (hint: check to see if the vectors are linearly dependent, and then appeal to this theorem.) u=[1,7,8,3] v=[-1,3,5,3]
w=[4,8,6,0]
a. None of the vectors is in the span of the other vector.
b. One of the vectors is in the span of the other vector
Out of the given vectors is in the span of the other vectors, b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.
If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.
To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent. We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.
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show 2/3 of 4 on the number line.
The position of the value is shown on the number line attached to this answer.
What is a number line?A number line is a ray which extends from -∞ to +∞ as its two extreme ends. Thus all number fall within this range such that all directed numbers can be located on the number line.
A directed number is a any number which has either a positive or negative sign. This implies that the position of all numbers can be shown on the line.
Thus, from the question to show 2/3 of 4 on the number line;
2/3 of 4 = 2/3 x 4
= 8/ 3
= 2 2/3
The position of 2 2/3 is shown on the number line attached to this answer.
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suppose that sum a n and sum b n are series with positive terms. prove that if lim n -> infty a n/b n does not exist, and sum b n diverges, then sum a n also diverges
The comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.
Suppose that [tex]$\sum_{n=1}^{\infty} a_{n}$ and $\sum_{n=1}^{\infty} b_{n}$[/tex] are series with positive terms. We assume that does not exist and that [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex]diverges.
To prove that [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] also diverges, we will use the comparison test. Since [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex] diverges, we can find a number M such that [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges. Since [tex]$\lim_{n\rightarrow \infty} \frac{a_{n}}{b_{n}}$[/tex] does not exist, we can find a number N such that for all [tex]$n \geq N$, $\frac{a_{n}}{b_{n}} > 1$[/tex].
Now, for any [tex]$n \geq \max \{M,N\}$[/tex], we have [tex]$\frac{a_{n}}{b_{n}} > 1$[/tex]. Thus, [tex]$a_{n} > b_{n}$[/tex]. By the comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.If the ratio of two series with positive terms,[tex]$\sum_{n=1}^{\infty}a_n$[/tex] and [tex]$\sum_{n=1}^{\infty}b_n$[/tex], does not converge to a limit as n approaches infinity and [tex]$\sum_{n=1}^{\infty}b_n$[/tex] diverges, then [tex]$\sum_{n=1}^{\infty}a_n$[/tex] must also diverge.
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2. Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00. Carnuba's Car
Rental charges $.15 per mile and has a service of twenty dollars. At how many miles will the
charge for each company be the same?
The charge of each company will be the same at 40 miles.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let us suppose the miles travelled as x.
Given that:
Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:
C = 0.10(x) + 40
Carnuba's Car rental charges $.15 per mile and has a service of $20.
D = 0.15(x) + 20
The charge of both the companies would be equal when C = D:
0.10(x) + 40 = 0.15(x) + 20
40 -20 = 0.15x = 0.10x
20 = 0.5x
x = 20/ 0.5
x = 40
Hence, the charge of each company will be the same at 40 miles.
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State if the three numbers can be the measures of the sides of a triangle. 7, 10, 10
Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.
Can be the measures of the sides of a triangle?Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:
A + B > C
A + C > B
C + B > A
As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.
if we use:
A = 7
B = 10
C = 10
Then we get:
7 + 10 > 10 ---> 17 > 10
7 + 10 > 10 ---> 17 > 10
10 + 10 > 7 ---> 20 > 7
All the ienqualities are true, thus, these can be the measures of the sides of a triangle.
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a flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m. the sheet is immersed in a uniform electric field of magnitude that is directed at from the plane of the sheet (fig. e22.2). find the magnitude of the electric flux through the sheet
The magnitude of the electric flux through the sheet will be 6.1 N.m²/C.
What is Electric flux?
The amount of electric lines of force (or electric field lines), which cross a specific area, is referred to as electric flux, a feature of an electric field. According to this theory, electric field lines begin with positive electric charges and end with negative charges.
The following formula can be used to get the electric flux:
∅ = EAcosФ
where,
∅ = Electric flux
E is the Electric field which is 73.9 N/C.
A is Area of the plate which is = (0.4 m)(0.6 m) = 0.24 m²
θ is the angle between normal to the area and electric field lines = 90° - 20° = 70°.
Putting these values in our formula, we get:
∅ = (73.9)(0.24)cos(70°)
∅ = 6.1 N.[tex]m^{2}[/tex]/c.
Therefore the Magnitude of the electric flux through the sheet is 6.1 N.m²/C.
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Area:
10
Area:
?
Area:
40
Answer: THE CORRECT ANSWER IS 30
Step-by-step explanation:
Find the line passing through the point of intersection of the lines xâ3y+1=0,2x+5y=9
and
(i) parallel to yâ2x=0
(ii) perpendicular to 2x+yâ5
the equation of the required line is 3xâ2y+1=3x1â2y1+1.
(i) We are given the parallel line of the given equation, that is yâ2x=0.
So, the equation of the required line will be yâ2x=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get
y1â2x1=c
or, c=y1â2x1
Hence, the equation of the required line is yâ2x=y1â2x1.
(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.
So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get
3x1â2y1+1=c
or, c=3x1â2y1+1
Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.
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is 5 a quartly number
Answer:
Step-by-step explanation:
Quarter implies 4. If there were 20 items, and you broke them into quarters, each quarter would have 5 items.
The table shows the number of smartphones sold at an electronics store each day. A 2-column table with 5 rows. Column 1 is labeled Day with entries Monday, Tuesday, Wednesday, Thursday, Friday. Column 2 is labeled Smartphones sold with entries 8, 13, 12, 10, 15. To the nearest tenth, what is the standard deviation of the data? Use this formula: s = StartRoot StartFraction Sigma-summation (x Subscript I Baseline minus x Overbar) squared Over n minus 1 EndFraction EndRoot 1.5 smartphones 1.9 smartphones 2.1 smartphones 2.7 smartphones
The standard deviation of the data is 2.41 smartphones.
What are the types of representing data?Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.
Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.
Given, The number of smartphones sold at an electronic store each day
is represented by the table with two columns and 5 rows.
The mean of the data set is,
= (8 + 13 + 12 + 10 + 15)/5.
= 11.6.
We know the formula for the standard deviation of a data set is,
= [tex]\frac{1}{\sqrt{n}}\sqrt{\sum_{i =1}^{n} (x_i - \overline{x}{}})^2[/tex].
= (1/√5)×√[(-3.6)² + (-1.4)² + (-0.4)² + (-1.6)² +(-3.4)²].
= (1/√5)×[√29.2].
= 2.41.
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Answer:
2.7 Smartphones
Step-by-step explanation: Just did it
If a rock is thrown upward on the planet Mars with a velocity 16 m/s, its height in meters t seconds later is given by y = 16t − 1.86t2. (Round your answers to two decimal places.)
(a)Find the average velocity (in m/s) over the given time intervals:
A. [1,2]
B. [1,1.5]
C. [1,1.1]
D. [1,1.01]
E. [1,1.001]
The average velocity (in m/s) over the given time intervals is [1,2]
Part A.
Keep in mind that the formula for average velocity is
(Y2 - Y1)/V avg = displacement/time interval (t2 - t1)
Given that the rock's position at time t is determined by:
y = 16t - 1.86*t^2
Part 1
for the time period [1, 2]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*2 - 1.86*22 = 24.56 m when t2 = 2 sec.
So
average Velocity = (24.56 - 14.14)/(2 - 1) (2 - 1) = 10.42 m/s V avg
Part 2.
for the time period [1, 2]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.5 - 1.86*1.52 = 19.815 m when t2 = 1.5 sec.
So,
average Velocity = (19.815 - 14.14)/(1.5 - 1) (1.5 - 1) = 11.35 m/s V avg
Part 3.
During the period [1, 1] .1]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.1 - 1.86*1.12 = 15.3494 m when t2 = 1.1 sec.
So,
average Velocity = (15.3494 - 14.14)/(1.1 - 1) (1.1 - 1)
average Velocity = 12.094 m/s and equals 12.09 m/s (In two decimal places)
Part 4.
During the period [1, 1] .01]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.01 - 1.86*1.012 = 14.262614 m when t2 = 1.01 sec.
So,
average Velocity = (14.262614 - 14.14)/(1.01 - 1) (1.01 - 1)
12.26 m/s and V avg = 12.2614 m/s (In two decimal places)
Part 5.
During the period [1, 1] .001]
Y1 = 16*1 - 1.86*12 = 14.14 m when t1 = 1 sec.
Y2 = 16*1.001 - 1.86*1.0012 = 14.15227814 m when t2 = 1.001 sec.
So,
average Velocity = (14.15227814 - 14.14)/(1.001 - 1) (1.001 - 1)
12.28 m/s V avg = 12.27814 m/s (In two decimal places)
Part B.
Rock's immediate velocity will be determined by:
d[16t - 1.86t2]/dt = V= dy/dt
Velocity = 16*1 - 2*1.86*t
time = 1 second,
Velocity = 16 - 2*1.86*1
average velocity at time t is equal to V = 12.28 m/s.
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solve for an unknown quantity in a two-variable linear equation, given one of the values. determine a two-variable linear equation that represents a scenario, identifying constraints on the variables in terms of the context.
A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.
If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.
2x+5y = 19
The x intercept is when y=0,
then, 2x+ (5×0) = 20
2x = 20, x=10
y intercept is when x=0, then
2×0 + 5y = 20
5y = 20, y= 20/5 =4
So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.
If one the values are given , we can substitute it in the equation to calculate the other variable.
In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.
2x + (3×2) = 12
2x = 12-6
2x = 6
x =3
So when y=2 then x=3.
Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.
So, we can solve a two variable linear equation through different ways.
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