The horizontal and vertical components of the velocity of the rock at time t1 calculated in part a? let v0x and v0y be in the positive x - and y -directions, respectively, the horizontal and vertical components of the velocity of the rock at time t1 are: v(t1)x = v0x and v(t1)y = 0
Calculate the horizontal and vertical components of the velocity of the rock at time t1, we need to use the equations of motion. From part a, we know that the initial velocity of the rock, v0, is equal to v0x + v0y.
Using the equation for the vertical motion of the rock, we can find the vertical component of the velocity at time t1:
y(t1) = y0 + v0y*t1 - 1/2*g*t1^2
where y0 is the initial height of the rock, g is the acceleration due to gravity, and t1 is the time elapsed.
At the highest point of the rock's trajectory, its vertical velocity will be zero, so we can set v(t1) = 0:
v(t1) = v0y - g*t1 = 0
Solving for t1, we get:
t1 = v0y/g
Substituting this value of t1 back into the equation for y(t1), we get:
y(t1) = y0 + v0y*(v0y/g) - 1/2*g*(v0y/g)^2
y(t1) = y0 + v0y^2/(2*g)
Therefore, the vertical component of the velocity at time t1 is:
v(t1)y = v0y - g*t1
v(t1)y = v0y - g*(v0y/g)
v(t1)y = v0y - v0y
v(t1)y = 0
Now, using the equation for the horizontal motion of the rock, we can find the horizontal component of the velocity at time t1:
x(t1) = x0 + v0x*t1
where x0 is the initial horizontal position of the rock.
Since there is no acceleration in the horizontal direction, the horizontal component of the velocity remains constant:
v(t1)x = v0x
Therefore, the horizontal and vertical components of the velocity of the rock at time t1 are:
v(t1)x = v0x
v(t1)y = 0
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A number with 100 digits is given. the first two digits of that number are 2 and 9 . how many digits has a square of that number?
The square of the given number will have 199 digits.
How to find the number digits in the square of the given number?A number with hundred digits is given.
The first two digits of the given number are 2 and 9.
We can use the following formula to find the total number of digits in the square of a number.
2n - 1
Where n is the total number of digits in the given number.
Let us take a number with 2 digits:
29*29 = 841 { 2*2 - 1 = 3}
We can see that the square of the 2-digit number has 3 digits in it.
Let us take a number with 3 digits:
299*299 = 89401 { 2*3 - 1 = 5}
We can see that the square of the 3-digit number has 5 digits in it.
Similarly, we can find the number of digits in the square of a 100-digit as shown below:
2n - 1 = 2*100 - 1
= 200 - 1
= 199
Therefore, we have found that the square of the given number will have 199 digits.
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What is the area of this trapezoid?
Answer:
315
Step-by-step explanation:
The function f(x) is shown in the graph.
Which type of function describes f(x)?
a) Exponential
b) Logarithmic
c) Rational
d) Polynomial
The function that describes the graph is an exponential function
How to determine the function type?From the graph, we have the following highlights:
Initially, when x increases; y seem not to increaseThen, x and y increase at the same timeFinally, y increase and x seem not to increaseThe above is the description of an exponential function
Hence, the function that describes the graph is an exponential function
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6x^2-19xy-7y^2 HELP ME PLS??
Answer:
(3x+y) (2x-7y)
Step-by-step explanation:
first write -19xy as a difference and you get 6x^2+2xy-21xy-7y^2
and then take the factor 2x from the expression that is 2x(3x+y) and do the same with the -7 that is = -7(3x+y). So this is you answer= (3x+y)(2x-7)
In 2015, around ____ percent of the world’s population had an internet connections.
(4) A taxi service charges Rs.100 as an initial fee and Rs.50 for each kilometer travelled. Write an algebraic expression for the total amount that has to be paid for a journey of x meters.
Answer:
f(x) = 50x + 100
Explanation:
The term "Rs. 100" is constant. The term "Rs. 50" keeps changing per km.
Linear equation: y = mx + b, where 'm' is rate of change, 'b' is constant
Equation built:
f(x) = 50x + 100
This will determine the cost for journey of x meters.
Which pairs of triangles appear to be congruent? Check all that apply. 2 A. Triangles 1 and 2 B. Triangles 2 and 3 C. Triangles 1 and 4 D. Triangles 1 and 3 E. Triangles 3 and 4 Triangles 2 and 4 A
Pairs of triangles appear to be congruent are :
Triangles 2 and 3. Option B
Triangles 2 and 4. Option D
Triangles 3 and 4. Option E
What are congruent triangles?Congruent triangles can be defined as the pairs of triangles with same measurement
Triangles 2 and 3 :
After observing triangles 2 and 3 it appears that triangle is congruent to triangle .
Option C
Triangles 2 and 4
After observing triangles 2 and 4 it appears that triangle 2 is congruent to triangle 4 .
Option D
E. Triangles 3 and 4
After observing triangles 3 and 4. They are congruent
Option E
Hence, Option B, D and E are correct of the triangles
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Answer:
Triangles 3 and 4
Triangles 1 and 4
Triangles 1 and 3
Step-by-step explanation:
if this is wrong tell me so i can edit the answer, but this is what i got
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
[tex]G(x) = 6-x^{4}[/tex]
Step-by-step explanation:
The red graph is the blue graph translated up 3 units, so the answer is [tex]G(x) = 6-x^{4}[/tex].
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
[tex]\textsf{2.} \quad y=\dfrac{35}{x}[/tex]
[tex]\textsf{3.} \quad y=-\dfrac{90}{x}[/tex]
[tex]\textsf{4.} \quad y=\dfrac{63}{x}[/tex]
[tex]\textsf{5.} \quad y=-\dfrac{112}{x}[/tex]
Step-by-step explanation:
If y is inversely proportional to x, then:
[tex]y \propto\dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant }k)[/tex]
Question 2
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies 7=\dfrac{k}{5}[/tex]
[tex]\implies 7 \cdot 5=\dfrac{k}{5} \cdot 5[/tex]
[tex]\implies k=35[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=\dfrac{35}{x}[/tex]
Question 3
Substitute y = -15 and x = 6 into the formula and solve for k:
[tex]\implies -15=\dfrac{k}{6}[/tex]
[tex]\implies -15 \cdot 6=\dfrac{k}{6} \cdot 6[/tex]
[tex]\implies k=-90[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given values:
[tex]\implies y=-\dfrac{90}{x}[/tex]
Question 4
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies 9=\dfrac{k}{7}[/tex]
[tex]\implies 9 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]
[tex]\implies k=63[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=\dfrac{63}{x}[/tex]
Question 5
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies -16=\dfrac{k}{7}[/tex]
[tex]\implies -16 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]
[tex]\implies k=-112[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=-\dfrac{112}{x}[/tex]
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The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph.
The slope of the graph of the function is equal to
for xxx between x=-3x=−3x, equals, minus, 3 and x=-2x=−2x, equals, minus, 2.
The slope of the graph is equal to
for xxx between x=3x=3x, equals, 3 and x=4x=4x, equals, 4.
The greatest value of yyy is y=\:y=y, equals
.
The smallest value of yyy is y=\:y=y, equals
.
By critically observing the graph shown in the image attached below, we can logically deduce that the slope of the graph of this function is equal to 0 for x, between x = -3 and x = -2.
Similarly, the slope of the graph of this function is also equal to 0 for x, between x = 3 and x = 4.
Based on the graph (see attachment), the greatest value of y is 4 while the smallest value of y is -3.
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When tariq woke up this morning, the temperature was 0 degrees. the temperature rose 23 degrees in the afternoon, the temp decreesed in the evniing. and it was 11 degrees when tariq went to bed. what integer represents the temp when tariq went to bed?
The final temperature at the time Tariq goes to bed was +12 degrees, represented as integers.
The initial temperature of the day was 0 degrees.
The temperature rose 23 degrees in the afternoon.
This implies that we move +23 on the scale, represented as an integer.
The temperature decreased 11 degrees in the evening.
This implies that we move -11 on the scale, represented as an integer.
This moves the temperature to +23 -11 = +12 degrees, represented as an integer.
Thus, the final temperature at the time Tariq goes to bed was +12 degrees, represented as integers.
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Select the correct answer. What is the approximate solution to this equation? 4lnx - 8 = 12
A. x = 148.4
B. x = 10.5
C. x = 1.61
D. x = 59,874
Answer:
Step-by-step explanation:
hello :
4lnx - 8 = 12
4lnx - 8 +8= 12+8
4lnx =20
lnx =5
coclusion : x =e^5
A. x = 148.4
If the ratio of y to x is equal to 3 and the sum of y and x is 80, what is value of y
Answer:
y = 60
Step-by-step explanation:
Step 1: Make sense of the given"The ratio of y to x is 3"
This means that, [tex]y\div x=3[/tex]
"The sum of y and x is 80"
This means, [tex]x+y=80[/tex]
Step 2: Make use of the factsIf [tex]y\div x=3[/tex], then [tex]y = (3*x)[/tex].
We can plug this into the other equation by substitution:
[tex]x + (3 * x)=80[/tex]
This simplifies to:
[tex]4x = 80[/tex]
Which we can solve out and get:
[tex]x=20[/tex].
We solved for x, but we need the value of y.
So, we go back to the equation we first derived: "[tex]y = (3*x)[/tex]".
And now we substitute the value of x, into this.
[tex]y = (3 * (20))[/tex]
By solving this out, we get:
[tex]y=60[/tex]
So, the value of y is 60.
What is the approximate number of minutes that avery spends in extra circular activities
The approximate number of minutes that Avery spends on the extra curricular activities are 122 minutes.
Given that Avery spent 10 minutes outside, 64 minutes in riding her bike, 48 minutes on the trampoline.
We have to calculate the approximate time that Avery spends on extra curricular activities.
Time spent by Avery outside=10 minutes
Time spent by Avery in riding her bike=64 minutes
Time spent by Avery on trampoline=48 minutes
Total time spent by Avery on extra curricular activities is equal to 10+64+48
=122 minutes
Hence the total time spent by Avery on extra curricular activities is 122 minutes.
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Question is incomplete as the question should include that Avery spent 10 minutes outside,64 minutes in riding her bike, 48 minutes on trampoline and rest of the time in swimming.
hi can you please help me
Answer:
See attached image
Step-by-step explanation:
I'm uncertain as to the "best statement." None seem to accurately describe the situation. I picked the one that was least incorrect (if that makes any sense).
A(n) _________is an equation satisfied by every number that is a meaningful replacement for the variable
The correct answer is identity
please help me with this im struggling
=======================================================
Explanation:
Triangle ABC is similar to triangle DEF. The order of the lettering is important because it tells us how the letters pair up.
A and D are the 1st letters, so they pair upB and E are the 2ndletters, so that's another pairC and F are the 3rd letters, which is the final pair of pointsBased on that, we can determine how the segments pair up
AB and DE correspond to each other. The segments are composed of the 1st and 2nd points.BC and EF correspond as well. The segments use the 2nd and 3rd points.AC and DF correspond also. They use the 1st and 3rd points.We want to find how long EF is, which means we'll involve BC = 17 since it is paired with it.
The diagram shows that AC = 14 and DF = 3, which is another pair we'll use
--------------------------
The key takeaway is that
AC = 14 and DF = 3 pair up togetherBC = 17 and EF also pair up togetherThose two facts lead to the steps below
[tex]\frac{AC}{DF} = \frac{BC}{EF}\\\\\frac{14}{3} = \frac{17}{EF}\\\\14*EF = 3*17\\\\14*EF = 51\\\\EF = \frac{51}{14}\\\\EF \approx 3.642857\\\\EF \approx 3.6\\\\[/tex]
The proportion in step 1 is valid due to the similar triangles, and because of the corresponding side pairs mentioned. In step 3, I cross multiplied.
Answer:
3.6 cm
Step-by-step explanation:
Similar Triangle Theorem
If two triangles are similar, the ratio of their corresponding sides is equal.
Given triangles:
ΔABC and ΔDEFTherefore the corresponding sides are:
AC and DF, BC and EF, AB and DETo find the measure of side EF, use the Similar Triangle Theorem:
[tex]\implies \sf AC:DF=BC:EF[/tex]
[tex]\implies \sf \dfrac{AC}{DF}=\dfrac{BC}{EF}[/tex]
[tex]\implies \sf \dfrac{14}{3}=\dfrac{17}{EF}[/tex]
[tex]\implies \sf EF=17 \cdot \dfrac{3}{14}[/tex]
[tex]\implies \sf EF=\dfrac{51}{14}[/tex]
[tex]\implies \sf EF=3.642857...[/tex]
[tex]\implies \sf EF=3.6\:cm\:\:(nearest\:tenth)[/tex]
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Labor productivity is normally measured by Part 2 A. the educational level of workers. B. the change in the amount of leisure. C. dividing total real domestic output by the number of workers or by the number of labor hours. D. the percentage change in GDP.
Labor productivity is normally measured by (c) dividing total real domestic output by the number of workers or by the number of labor hours.
What is Labour productivity?The total volume of production (measured in terms of Gross Domestic Product, GDP) produced per unit of labor (measured in terms of the number of employed workers or hours worked) during the course of a specific time reference period is what is referred to as labor productivity.Divide the total output by the total labor hours to find the labor productivity of a nation.What is labour productivity in India?
A measurement of labor output is labor productivity. Hourly productivity metrics are used. The actual Gross Domestic Product (GDP) produced by labor in an hour is what is referred to as labor productivity in macroeconomics. An important component of a business's overall growth is labor productivity.Learn more about labour productivity
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You have a set of 10 cards: five red and five blue. Each group of five colored cards is numbered one through five. What is the probability of drawing a red four and then a blue four, while replacing the card between the drawings?
1/100
1/10
1/20
1/90
The probability of drawing a red four and then a blue four is:
P = 1/100
How to get the probability?
We know that there are 10 cards in total, then the probability of drawing a red four (there is only one of these cards) is:
p = 1/10
Now we put the red four again, the probability of getting a red blue is computed in the same way:
q = 1/10
The probability for both events happening consecutively is:
P = p*q = (1/10)*(1/10) = 1/100
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What is the range of possible sizes for side x?
Answer:
Should be 3.9
Step-by-step explanation:
prove me wrong
There are seven roads that lead to the top of a hill. How many different ways are there to reach the top and come back ( you dont have to go on the same road there and back)?
Answer:
49 different ways
Step-by-step explanation:
If there are seven roads that lead to the top, you have seven possible choices to go to the top of the hill.
Then, to come back to the start, you also have seven possible choices (seven roads), and you can pick any road.
So, if you have seven ways to go up and seven ways to go down, the number of different ways of going to the top and coming back is the product of these numbers of possible choices.
N(total) = N(up) * N(down)
N(total) = 7 * 7
N(total) = 49 different ways
Brainliest pls and tysm!
The slope of the line is -2 use the coordinates (4,-6) to find the point-slope equation of the line
Answer: [tex]y+6=-2(x-4)[/tex]
Step-by-step explanation:
See attached image.
Can someone help me please
Answer:
The slope of the line segment CD is ( - [tex]\frac{8}{9}[/tex] )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of the midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
The slope of a line segment with coordinates of the ends
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
Point D is the midpoint of a segment AB
A ( 4 , 12 )
B ( - 6 , - 8 )
( [tex]\frac{-6+4}{2}[/tex] , [tex]\frac{-8+12}{2}[/tex] ) = ( - 1 , 2 )
D ( - 1 , 2 )
C ( 8 , - 6 )
[tex]m_{CD}[/tex] = [tex]\frac{-6-2}{8-(-1)}[/tex] = - [tex]\frac{8}{9}[/tex]
what is an equivalent expression for 3(x-9) ?
A rectangular-prism-shaped toy chest is 2 \text { m}2 m2, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text. A shipping crate is packed with 181818 of these toy chests. There is no extra space in the crate.
The volume of the shipping crate is 36 m per cube.
According to the statement
we have given that the
A rectangular-prism-shaped toy chest is 2 m by 1 m by 1 m. A shipping crate is packed with 18 of these toy chests.
And we have to find the volume of the crate.
So,
volume of toy = 2*1*1
Volume of toy = 2 meter per cube.
And Now,
The volume of shipping crate = Volume of one toy* total number of toys in crate
so, Substitute the values in the formula then
The volume of shipping crate = Volume of one toy* total number of toys in crate
The volume of shipping crate = 2*18
The volume of shipping crate = 36 m per cube.
So, The volume of the shipping crate is 36 m per cube.
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Which equation is the inverse of 5y+4= (x+3)² +?
1
6 11
10
O y = x² +/
1/2 X+
7
Oy=3± √√5x+2
O-5y-4 = -(x+3)²--1/2
7
O y=-3± √√5x+2
Answer:
-5y-4=-(x+3)2-1/(2)
Step-by-step explanation:
ANSWER: It's D
Have a great day!!!
Paul has four paper strips of the same length. He glues two of them together with 4 cm overlap, and the new strip is 36 cm long. He wants to make a 30cm long strip with the other two strips how long should the overlap be?
Answer:
maybe the answer ris 36×4 and then 30×4 and subtract the result?!?!
Consider the graph of the function f(x)=2^x which statements describe key features of function g if g(x)=3f(x)?
it's multiple choice, select all the correct answers:
y-intercept at (0,1)
y-intercept at (0,3)
horizontal asymptote of y=3
x-intercept at (3,0)
horizontal asymptote of y=0
no x-intercept
Answer:
y-intercept at (0,3)horizontal asymptote of y=0no x-interceptStep-by-step explanation:
The y-intercept of f(x) is (0,1), so the y-intercept of g(x) is (0,3).
f(x) has a horizontal asymptote at y=0. and so does g(x).
f(x) does not have an x-intercept, and neither does g(x).
Answer:
y-intercept at (0, 3)
horizontal asymptote of y = 0
no x-intercept
Step-by-step explanation:
Definitions
y-intercept: the point(s) at which the curve crosses the y-axis (when x=0).
x-intercept: the point(s) at which the curve crosses the x-axis (when y=0).
Asymptote: a line that the curve gets infinitely close to, but never touches.
Given function:
[tex]f(x)=2^x[/tex]
Properties of function f(x):
y-intercept at (0, 1)As x → -∞, y → 0 therefore there is a horizontal asymptote at y=0 and no x-intercept (since the curve never crosses the x-axis).As x → ∞, y → ∞[tex]\textsf{If }g(x)=3f(x):[/tex]
[tex]\implies g(x)=3(2)^x[/tex]
Properties of function g(x):
y-intercept at (0, 3)As x → -∞, y → 0 therefore there is a horizontal asymptote at y=0 and no x-intercept (since the curve never crosses the x-axis).As x → ∞, y → ∞Therefore the true statements are:
y-intercept at (0, 3)horizontal asymptote of y = 0no x-interceptin a recent survey,55% of cell phone owners said they text messages.what fraction of cell phone owners is this
Answer:
11/20
Step-by-step explanation:
55% = 55/100
by simplifying this fraction (divide top and bottom by 5), you get 11/20
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
The compound inequality represents the situation is r > 4 and r ≤ 4.1
Compound inequalityRadius of the gear = rr must be greater than 4 cmr > 4
r must not exceed 4.1 cmr ≤ 4.1
Therefore, r > 4 and r ≤ 4.1 is the compound inequality which represent the situation.
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Its A: r > 4 and r ≤ 4.1