The angle is changing at the rate [tex]\frac{18}{\pi }[/tex] when a is 10m from the intersection and b is 20m from the intersection.
In this problem, all three variables (x, y & z) are changing with respect to time.
x = 20 and y = 10
[tex]\frac{dx}{dt} = -1[/tex]
[tex]\frac{dy}{dt} = 2[/tex]
[tex]tan[/tex](θ)=[tex]\frac{y}{x}[/tex]
take derivative :
[tex]tan[/tex] (θ) = [tex]\frac{y}{x}[/tex]
[tex]sec^{2}[/tex](θ) [tex]\frac{d\alpha }{dt}[/tex] = [tex]\frac{x\frac{dy}{dt} - y\frac{dy}{dt} }{x^{2} }[/tex]
Substitute the values :
[tex]sec^{2} \alpha (\frac{d\alpha }{dt} ) = \frac{20 . 2 - 10. (-1)}{20^{2} }[/tex]
solve the equation :
[tex]\frac{5}{4} (\frac{d\alpha }{dt} ) = \frac{20 . 2 - 10. (-1)}{20^{2} }[/tex]
[tex]\frac{5}{4} (\frac{d\alpha }{dt} ) = \frac{50}{400 }[/tex]
[tex](\frac{d\alpha }{dt} ) = \frac{50}{400 } * \frac{4}{5}[/tex]
[tex](\frac{d\alpha }{dt} ) = \frac{1}{10 }[/tex] radian/sec
[tex](\frac{d\alpha }{dt} ) = \frac{18}{\pi } degrees/sec[/tex]
This means that the angle is increasing as a gets closer to the intersection and b gets moves away from the intersection.
So, The angle is changing at the rate [tex]\frac{18}{\pi }[/tex] when a is 10m from the intersection and b is 20m from the intersection.
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find constant rate of change
Answer: B
Step-by-step explanation:
The constant rate of change or slope is rise/run
Let's pick 2 points ( 4, 12) ( 10, 0)
We see that the y decreases by 12 and the x increase by 6, so our slope is
-12/6 = -2 hours per person
So the answer is B
draw the mail carrier's position-versus-time graph. assume that x=0m at t=0s.
The position of mailbox after 10s is equal to sum displacements is 14m.
The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).
Given velocity time graph understand in three parts.
1. first 6s mailbox have constant velocity 3m/s
the displacement covered by it = area under v-t graph(square shape)
s1=3 x 6 =18m
2. the mailbox at rest at 6-8 s.
the displacement covered by it s2=0
3. the mail returned with constant velocity 2m/s
Displacement is defined to be the change in position of an object. It can be defined mathematically with the following equation:
Displacement=Δx=[tex]x_{f} - x_{0}[/tex]
[tex]x_{f}[/tex]=refers to the value of the final position.
[tex]x_{0}[/tex]= refers to the value of the initial position.
Δx is the symbol used to represent displacement
the displacement covered by it s3 =(10-8) (-2) =-4m
the position of mailbox after 10s is equal to sum displacements=s1+s2+s3 =18+0-4=14m the displacement - time graph.
Therefore, the position of mailbox after 10s is equal to sum displacements is 14m.
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Draw the mail carrier's position-versus-time graph. Assume that x=0m at t=0s
What is the position of the mailbox?
The 130 juniors at Smithers High School are taking a class trip. Three buses will be taking the students and
chaperones to their destination, and each bus can hold up to 45 people. The first bus will be filled to capacity,
followed by the second and third buses. The function f(x) describes the total number of people on the first
bus, where x
is the number of minutes spent loading the bus.
If the first bus is boarded at a rate of 15 people per minute, what is the domain of the function?
If the first bus is boarded at a rate of 15 people per minute, the domain of the function is; (15 ≤ x ≤ 45)
How to solve Inequality word problems?We are told that;
Total number of Juniors at Smithers High School that are taking a class trip = 130
Number of buses taking each student to their destination = 3 buses
Capacity of each bus = 45 people
Now, if the function f(x) describes the total number of people on the first
bus, where x is the number of minutes spent loading the bus.
Then since the maximum number of people on the first bus is 45, then it means that the domain of the function is;
(15 ≤ x ≤ 45)
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A science museum just opened near Robert's home, and Robert bought a membership for $25. Then, he can pay just $5.75 per visit. What does it cost Robert to become a member and visit the museum 4 times?
Answer: $48.00
Step-by-step explanation:
His membership was $25.00
And EACH time he comes he pays $5.75.
so your equation is 25.00 + (5.75 x 4) = $48.00
Select all the values of x that make the equation | 3x + 4 | − 9 = 0 true.
A . 1 2/3
B. -1 2/3
C. 4 1/3
D. -4 1/3
E. 5 2/3
F. -5 2/3
[tex]|3x+4|-9=0[/tex]
Add 9 to both sides:
[tex]|3x+4|-9+9=0+9[/tex]
[tex]|3x+4|=9[/tex]
Solve the Absolute Value:
[tex]3x+4=9or3x+4=-9[/tex]
__________________________________________________________
[tex]3x+4=9[/tex]
Subtract 4 from both sides:
[tex]3x+4-4=9-4[/tex]
[tex]3x=5[/tex]
Divide both sides by 3:
[tex]\dfrac{3x}{3} =\dfrac{5}{3}[/tex]
[tex]\fbox{x = $\dfrac{5}{3} $ or 1$\dfrac{2}{3}$}[/tex]
__________________________________________________________
[tex]3x+4=-9[/tex]
Subtract 4 from both sides:
[tex]3x+4-4=-9-4[/tex]
[tex]3x=-13[/tex]
Divide both sides by 3:
[tex]\dfrac{3x}{3} =\dfrac{-13}{3}[/tex]
[tex]\fbox{x = $\dfrac{13}{3} $ or -4$\dfrac{1}{3} $}[/tex]
________________________________________________________
[tex]\fbox{Options A and D}[/tex]
-x-7y-14
-4x-14y=28 solve by elimination
Answer:
x= -28
y= 6
Step-by-step explanation:
-x-7y = -14
-4x-14y=28
Let's find x first! First, we time the first equation by -2
2x + 14y = 28
-4x -14y = 28
Add them; you will get
-2x = 56
x = -28
Then put -28 back in the x, and you will get
y= 6
What i the um of the fraction? Ue the number 18 equivalent fraction to help find the anwer -3/41/2
fractions with the same denominator added together
You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.
What are the parts of fraction?
A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.
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is it increasing or decreasing y=1/2x+2
Increasing, as the slope is positive (1/2)
Answer:
Increasing.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given linear equation:
[tex]y=\dfrac{1}{2}x+2[/tex]
Comparing the given linear equation with the slope-intercept formula, the slope of the given equation is ¹/₂.
The graph of a linear equation is increasing if its slope is positive.
(y-values increase as x-values increase).
The graph of a linear equation is decreasing if its slope is negative.
(y-values decrease as x-values increase).
Therefore, as the slope of the given linear equation is positive, its graph is increasing.
In the figure below, ⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯,
B
L
¯
,
A
M
¯
,
and ⎯⎯⎯⎯⎯⎯⎯⎯⎯
C
K
¯
are medians of △
△
A
B
C
. If AM = 21 and LO = 4, then AO =
Applying the definition of the median of a triangle, the length of AO is calculated as: 14 units.
What is the Median of a Triangle?The median of a triangle is a line segment that joins the midpoint of a side of a triangle and the opposite vertex to the side.
There are three medians in a triangle, and the three of them intersect at a point inside the triangle. This point of intersection is known as the centroid.
According to the centroid theorem of a triangle, the length from the vertex to the centroid is two-third of the length of a median.
Thus, the figure shows that triangle ABC has three medians, BL, AM, and CK, which intersect at point O. This means the centroid of the triangle is point O.
By implication, it means that:
Length of AO = 2/3 * (length of AM)
Plug in the value of AM:
Length of AO = 2/3 * (21) [centroid theorem]
AO = 2 * 7
AO = 14
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This number line models the division problem 1/4÷5 what is the quotient
15 points!
Answer: 1/20
Step-by-step explanation:
....................................
function g is a transformation of the parent exponential function which statements are true about function g if the domain of function g is x greater than zero
The correct statements are; function g is positive over (-∞, ∞), function g has a y-intercept of (0,4) and function g decreasing over the interval (-∞, 0)
What is a function?A function is defined as a relation between a set of inputs having one output each.
Given that, function g is a transformation of the parent exponential function and the domain of function g is x > 0
Studying the graph, we can conclude that,
function g is positive over (-∞, ∞)
function g has a y-intercept of (0,4)
function g decreasing over the interval (-∞, 0)
Hence, The correct statements are; function g is positive over (-∞, ∞), function g has a y-intercept of (0,4) and function g decreasing over the interval (-∞, 0)
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What is the linear regression equation for the data given? (Round to the nearest tenths place.)
the surface of an ellipsoid is intersection with a plane to form a space curve. find the vector function that represents the space curve of intersection of the ellipsoid and the plane
The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by[tex]$\mathbf{r}(t) = (x(t), y(t), z(t))$[/tex] and [tex]x(t) = a\cos(t)$ y(t) = b\sin(t)$ $z(t) = \frac{-d - ax(t) - by(t)}{c}$$[/tex]
Let [tex]$\mathbf{x} = (x, y, z)$[/tex] be the position vector of a point on the ellipsoid, and [tex]$a, b, c$[/tex] be the corresponding semi-major axes. Then the equation is
[tex]$$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1.$$[/tex]
The equation of the plane is
[tex]$$ax + by + cz + d = 0.$$[/tex]
The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by
[tex]$$\mathbf{r}(t) = (x(t), y(t), z(t)),$$[/tex]
where
[tex]$$x(t) = a\cos(t)$$$$y(t) = b\sin(t)$$$$z(t) = \frac{-d - ax(t) - by(t)}{c}$$[/tex]
The vector function that represents the space curve of intersection of the ellipsoid and the plane is given by [tex]$\mathbf{r}(t) = (x(t), y(t), z(t))$[/tex]where [tex]$x(t)$[/tex]and [tex]$y(t)$[/tex] are the coordinates of points on the ellipsoid, and [tex]$z(t)$[/tex] is determined by the equation of the plane. The vector function allows us to represent the intersection of the ellipsoid and the plane as a space curve.
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if f'(x)=cos(x^2) and f(3)=7 then f(2)=
The value of function f(2) if f'(x)= cos(x²), and f(3) = 7 is [tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{4}{\pi }}\right)+C[/tex].
What is function?The relationship between a set of potential outputs and a set of potential inputs is called a function, and it has one relationship per output between each input. This indicates that a function f will map an object x to exactly one object f(x) in the set of potential outputs if it is present in the set of inputs, also known as the domain (called the co-domain).
Given:
f'(x )= cos(x²),
f(3) = 7
Calculate the integration of the following function as shown below,
∫ f'(x) = 3∫cos(x²)
The integral is the Fresnel integral function, C(x)+C
[tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{2}{\pi }}x\right)+C[/tex]
f(3) = 7
[tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{2}{\pi }}3\right)+C[/tex]
Calculate the value of f(2) as shown below,
f(2) = [tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{2}{\pi }}\times 2\right)+C[/tex]
f(2) = [tex]\sqrt{\frac{\pi }{2}}\mathbb{C}\left(\sqrt{\frac{4}{\pi }}\right)+C[/tex]
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Smith City received 2. 45 inche of rain on Monday and 1. 72 inche of rain on Tueday. Write an equation howing a way to etimate to the nearet inch the total rainfall for the two day
an equation showing a way to estimate to the neasrt inch the total rainfall for the two day 2.45 + 1.72 ≈ 4.2 inches
1. Add the two amounts of rainfall together: 2.45 + 1.72
2. Round the answer to the nearest inch: 4.2 inches
3. The equation to estimate the total rainfall for the two days is 2.45 + 1.72 ≈ 4.2 inches.
This equation provides a simple way to estimate the total rainfall for two days. By adding the two amounts of rainfall, we can then round the answer to the nearest inch to obtain the estimated total rainfall. This equation can be used to quickly and accurately estimate rainfall totals for any two-day period.
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A study of child care enrolled 1364 infants and followed them through their sixth year in school. Later, the researchers published an article in which they stated that "the more time children spent in child care from birth to age four-and-a-half, the more adults tended to rate them, both at age four-and-a-half and at kindergarten, as less likely to get along with others, as more assertive, as disobedient, and as aggressive." $^{31}$ (a) Is this an observational study or an experiment? Justify your answer. (b) What are the explanatory and response variables? (c) Does this study show that child care causes children to be more aggressive? Explain.
(a) Is this an observational study or an experiment?
ans=Observational study – no treatment was imposed
(b) What are the explanatory and response variables?
ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior
d) Does this study show that child care causes children to be more aggressive? Explain.
No. Observational studies cannot show cause-and-effect
Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.
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find the area of the region bounded by the hyperbola 9x2 − 4y2 = 36 and the line x = 3.
Refer to the photos taken.
the number of miles mario can drive varies directly with the amount of gas that he has. he can drive 18 miles on ½ a gallon of gas. how many miles can mario drive with 9 gallons of gas?
There are 324 miles can Mario drive with 9 gallons of gas.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
He can drive 18 miles on ½ a gallon of gas.
Now,
Since, He can drive 18 miles on ½ a gallon of gas.
Let the number of miles cover with 9 gallons of gas = x
So, By definition of proportion, we get;
⇒ 18 / (1/2) = x / 9
⇒ 18 × 2 = x / 9
⇒ 36 × 9 = x
⇒ x = 324 miles
Thus, The number of miles cover with 9 gallons of gas = 324 miles
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Please help. The question and answers are in the screenshot
Answer:
D
Step-by-step explanation:
To solve for a you would need to subtract k from both sides. That would leave you with
y - k = a ([tex]x-h)^{2}[/tex] then, divide both sides by [tex](x-h)^{2}[/tex] to get letter d
a survey of 600 non-fatal accidents showed that 214 involved the use of a cell phone. find a point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone.
The population proportion of non-fatal accidents that involved the use of a cell phone is 0.03567
A population proportion is known as the share of a population that belongs to a particular group. The Confidence intervals are used to estimate population proportions.
as per given in the question,
The total number of accidents (n) are 600
The accidents involving cell phones (x) are 214
the sample proportion ([tex]\hat p[/tex]) = x/n
where
x is the count of the successes
n is the total size of the population
P is the population proportion
=> 214/600
=> 0.3567
the estimated point for population proportion is
[tex]\hat p[/tex] = 0.03567
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What is 2 to the power of three halves equal to? square root of 8 cube root of 8 cube root of 16 square root of 16
The answer to 2 to the power of three halves equal to? is square root of 8 cube root of 8 cube root of 16 square root of 16 is [tex]\sqrt{8}[/tex]
How to find the square root of a number?In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
From the question, we can simplify the question as
[tex]2^{\frac{3}{2} }[/tex]
simplifying further by simplifying the power
[tex]2^{\frac{3}{2} }[/tex] = [tex](2^{3})\frac{1}{2}[/tex]
= [tex]\sqrt{2^{3} }[/tex]
= [tex]\sqrt{8}[/tex]
hence, the solution to the problem is [tex]\sqrt{8}[/tex]
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Tarriq begins to solve the equation 50 + 2x = –190. 50 + 2x = –190 50 – 50 + 2x = –190 – 50 + 2x = –240 to finish solving the equation using the multiplication property of equality, which factor must tarriq use? a. negative 2 b. negative one-half c. one-halfd. 2
The factor which tarriq musr use if solving the equation using the multiplication property of equality to finish solving is 2.
The correct answer option is option D
How to solve equation?Tarriq solution:
50 + 2x = –190
50 + 2x = –190
50 – 50 + 2x = –190 – 50
2x = –240
Correct solution:
50 + 2x = –190
Subtract 50 from both sides
50 - 50 + 2x = -190 - 50
2x = - 240
divide both sides by 2
x = -240/2
x = -120
In conclusion, x = -120 is the solution to tarriq equation if using multiplication property of equality.
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
m=riserun=ΔyΔx
m=y2−y1x2−x1
m=0−2−2−2
m=−2−4
m=12
The answer is :
m = 0.5
Which ordered pair does NOT lie on the graph of y = x/4 + 5?
mateo is playing a word game where he's trying to make 444-letter words by rearranging the letters in the word iron. how many unique ways are there to arrange the letters in the word iron?
The word IRON can be arranged is 24 unique ways.
Given:
The word = IRON
The number of unique ways in which the letters in the word IRON can be arranged = ?
The number of letters in IRON = 4
The number of positions = 4
In the first position, any one of the 4 letters can be placed
In the second position any one of the remaining 3 letters can be placed
In the third position any one of the remaining 2 letters can be placed
The fourth position can be filled with the left over letter
So the total number arrangement in unique way
= (Number of ways to fill in 1st position)* (Number of ways to fill in 2nd position)* (Number of ways to fill in 3rd position)* (Number of ways to fill in 4th position)
=> 4 *3*2*1
= 24 ways
Hence, The word IRON can be arranged is 24 unique ways.
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If your parabola has a vertex going through the point (2,13), the axis of symmetry would be?
The axis of symmetry of the parabola would be x = 2
How to determine the axis of symmetryFrom the question, we have the following parameters that can be used in our computation:
Vertex = (2, 13)
Rewrite the vertex as follows
So, we have the following representation
(x, y) = (2, 13)
Remove the y-coordinates
This gives
x = 2
This represents the axis of symmetry
Hence, the axis of symmetry is x =2
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Jan used 22.5 gallons of water in the shower. This amount is 7.5 gallons less than the amount she used for washing clothes. Write and solve an equation to find the amount of water Jan used to wash clothes, where g is the number of gallons.
Pls show the equation
Answer: 22.5g+(22.5g-7.5g)
Step-by-step explanation: Its because its all the information combined.
The volume of a large can of tuna fish can be calculated using the formula V = πr²h. Write an equation to find the radius, r, in terms of V and H.
Answer:
[tex] r = \sqrt{\dfrac{V}{\pi h}} [/tex]
Step-by-step explanation:
V = πr²h
Switch sides.
πr²h = V
Divide both sides by πh.
r² = V/(πh)
Take the square root of both sides.
r = √[V/(πh)]
[tex] r = \sqrt{\dfrac{V}{\pi h}} [/tex]
At a real estate agency, an agent sold a house for $306,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The agency made (answers) on the house
Answer:
.......................
Answer:
$22,950, $4,590
Step-by-step explanation:
Divide 306,000 by 100. This equals 3060, or one percent of the profit.
Multiply this profit by 7.5 to get $22,950, which is the amount to agency makes.
To find what the agent makes, divide 22,950 by 10 to get 2,295, or ten percent of the agency's profits. Double it and it will 20 percent or $4,590, the amount the agent makes.
I Need help with this question
Answer:
720 / 6 = 120
120 * 4 = 480
P(1) = 120/720
P(2) = 120/720
P(3) = 120/720
P(4) = 120/720
P(5) = 120/720
P(6) = 120/720
P(1 + 2 + 3 + 4) = 480/720
C. 480 timesStep-by-step explanation:
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