The motion of the arrow, described by the kinematic equation for the height, h(t) = 60·t - 0.8·t² are as follows;
(a) The velocity after 1 second is 58.4 m/s
(b) The arrow hits the moon after 75 seconds
(c) The velocity of the arrow when it hits the moon is 60 m/s
(d) The arrow reaches the maximum height in37.5 seconds.
What is a kinematic equation?A kinematic equation is an equation that describes the motion of an object moving under constant acceleration.
The kinematic (equation) function for the height of the arrow is; h(t) = 60·t - 0.8·t²
The initial velocity of the arrow = 60 m/s
(a) The velocity of the arrow = The rate of change of the height, therefore;
v = h'(t) = 60 - 2 × 0.8·t = 60 - 1.6·t
The velocity after 1 second = h'(1) = 60 - 1.6 × 1 = 58.4
The velocity of the arrow after 1 second is 58.4 m/s
(b) When the arrow hits the moon, we get;
h(t) = 0, therefore;
h(t) = 60·t - 0.8·t² = 0
( 60 - 0.8·t)·t = 0
t = 0 or 60 - 0.8·t = 0
t = 60/0.8 = 75
The time the arrow hit the moon is 75 seconds after being shot
(c) The velocity of the arrow when it hits the moon is found using the equation;
h'(37.5) = 1.6 × 37.5 = 60
The velocity when it hits the moon, the velocity is 60 m/s
(d) The motion of the arrow is symmetrical, therefore, the time it takes the arrow to reach the the maximal height is the time it takes the arrow to reach back to the moon surface, which indicates;
The time it takes the arrow to reach maximum height is half the time it takes the arrow to hit the moon after being shot = 75/2 seconds = 37.5 seconds
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DETAILS LARCPALGFL2 10.1.100.
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The amount A in an account after 2 years when a principal of P dollars is invested at annual interest rate r (in decimal form) compounded annually is given by A = P(1 + r). Find r.
P= $3000, A = $3499.20
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Step-by-step explanation:
The amount A in an account after 2 years when a principal of P dollars is invested at annual interest rate r (in decimal form) compounded annually is given by A = P(1 + r). Find r.
P= $3000, A = $3499.20. Explain
r = (3499.20 - 3000) / 3000 = 0.1664
Therefore, the annual interest rate r (in decimal form) is 0.1664.
Solve the following equation for b. Be sure to
take into account whether a letter is
capitalized or not.
n³b - tb = 5g
Answer: The correct answer is b=5g/(n^3−t)
Step-by-step explanation:
Solve for b in the following equation
n³b - tb = 5g
First factor out variable b
b(n^3−t)=5g
Divide both sides by n^3-t
b(n^3−t)/n3−t=5g/n^3−t
b=5g/(n^3−t)
Fast Please
Jack studies 3 and a half hours each night. If Jack wants to calculate how many total hours he studies, what equation should he use for the proportional relationship?
The equation of the total number of hours that Jack could use is t = 3.5n
How to determine the equation of the total number of hours?From the question, we have the following parameters that can be used in our computation:
Number of hours of study each night = 3 and a half hours
To start with, we need to represent the given parameter using numbers (fractions or decimal)
Using decimals, we have the following representation
Number of hours of study each night = 3.5 hours
Represent the number of nights as follows
Number of nights = n
Represent the total number of hours as follows
Total number of hours = t
So, we have the following equation
Total number of hours = Number of nights * Number of hours of study each night
Substitute the known values in the above equation, so, we have the following representation
t = 3.5 * n
Evaluate
t = 3.5n
Hence, the equation is t = 3.5n
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Answer: y=3.5x
Step-by-step explanation:
A formula for 6 gallons of light green paint uses 3/8 gallon of white paint. Liam has 9/16 gallon of white paint. Does Liam have enough white paint to make 8 gallons of light green paint? If not, how much more does he need?
If Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint
What is word problem?A word problem in mathematics is a maths question written as one sentence or more that requires the application of mathematics knowledge to a 'real-life' scenario.
Given that 6 gallons of light green paint use 3/8 gallon of white paint, this can be expressed as:
3/8 gallons of white paint = 6 gallons of light green
We are to determine if 9/16 gallons will be enough to make 8 gallons of light green paint. This can be expressed as
9/16 gallons of white paint = x
Divide both expressions
3/8 x 16/9 = 6/x
2/3 = 6/x
By cross multiplying
2x = 3 x 6
2x = 18
x = 18/2
x = 9
This shows that if Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint
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5. At a restaurant, the total bill and the percentage of the bill left as a tip is
represented in the scatter plot. (Lesson 3-4)
Percentage
32
28
24
20
16
12
8
4
4 8 12 16 20 24 28 32
Total
The best fit line is represented by the equation y = -0.632x + 27.1, where x
represents the total bill in dollars, and y represents the percentage of the
bill left as a tip.
a. What does the best fit line estimate for the percentage of the bill left as
a tip when the bill is $15? Is this reasonable?
b. What does the best fit line predict for the percentage of the bill left as a
tip when the bill is $50? Is this reasonable?
a) The estimate for the percentage of the bill left as a tip with a bill of $15 is of 17.62%, which is reasonable.
b) The estimate for the percentage of the bill left as a tip with a bill of $50 is a non-reasonable -4.5%.
What is the line of best fit?The line of best fit in this problem is defined as follows:
y = -0.632x + 27.1.
In which the variables are defined as follows:
x is the total bill, in dollars.y is the percentage of the total bill left as a tip.Hence, for a bill of $15, the estimate is found replacing x by 15, as follows:
y = -0.632(15) + 27.1 = 17.62%.
Which is reasonable, as it is a positive number.
For a bill of $50, the estimate is obtained as follows:
y = -0.632(50) + 27.1 = -4.5%.
Which is not reasonable, as it is a negative number.
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15 points Find the unknown side length. Round to the nearest tenth. Enter your answer in the box
Answer: 24.5
Step-by-step explanation:
Find the x-intercept of the line 7x+7y= – 1.
Answer:
(-1/7 ; 0)
Step-by-step explanation:
the line intercepts the x axis when y = 0
7x + 0 = -1
7x = - 1
7/7 x = -1/7
x = -1/7
Answer:
The x intercept is -1/7
( -1/7 , 0)
Step-by-step explanation:
To find the x intercept, set y =0 and solve for x
7x+7y = -1
y =0
7x+7(0) = -1
7x +0 = -1
7x = -1
Divide by 7
7x/7 = -1/7
x = -1/7
The x intercept is -1/7
( -1/7 , 0)
A shop makes a profit of £2 750 in March
It has an Easter sale and the profit for April is £3 162.50
Work out the profit percentage increase
The percent increase of the profit is 15%
How to determine the percent increase of the profit?In this question, the figures are given as
Profit in March = £2750
Profit in April = £3162.50
The percentage of the increase of the profit is then calculated using the following equation
Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%
Substitute the known values in the above equation, so, we have the following representation
Increase percentage = (3162.50 - 2750)/2750 * 100%
Evaluate
Increase percentage = 15%
Hence, the increase in percentage is 15%
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HELP PLEASE NEED IT THANKS
Answer:
<
Step-by-step explanation:
1) Substitute 5 into the question
[tex]\frac{4(5)}{4}[/tex][tex]2(5)-3[/tex]2) Work out the sides
[tex]\frac{4(5)}{4} =5[/tex][tex]2(5)-3=7[/tex]3) Put it into an inequality
5 < 7
Hope this helps, have a great day!
Question 2 (1 poing
This table shows the total shipping costs for objects of
different weights.
Shipping Costs
$6.00
$3.00
$1.50
O $1.25
Weight of Object
(in pounds)
4
8
12
16
Total Shipping Cost
(in dollars)
5
11
17
23
Based on the information in the table, by how many dollars
does the total shipping cost increase if the weight of an
object increases by 1 pound?
The total shipping cost increase by $1.50 if the weight of an
object increases by 1 pound
By how many dollars does the total shipping cost increase if the weight increases by 1 pound?
A rate of change describes how one quantity changes in relation to another quantity. Mathematically, it is defined as the change in one divided by the change in the other quantity.
rate of change = change in total shipping cost / change in weight
Using the information in the table:
rate of change = 11-5 / 8-4 = 6/4 = 1.5
Therefore, the total shipping cost increase by $1.50 if the weight of an
object increases by 1 pound. Option c. is the answer
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If cos of Ф = 2/5, find sin Ф/2 and cos Ф/2. Assume the angles are in the 1st quartile
The exact values of the sine and the cosine of the half angle are √(3 / 10) and √(7 / 10), respectively.
What are the exact values of two trigonometric functions?
Herein we know the exact value of the cosine of an angle set in the first quadrant. Then, the half angle is also in the first quadrant, whose sine and cosine are, respectively:
cos 0.5Ф > 0, sin 0.5Ф > 0
sin 0.5Ф = √[(1 - cos 0.5Ф) / 2]
cos 0.5Ф = √[(1 + cos 0.5Ф) / 2]
First, replace the values of the cosine of the half angle:
sin 0.5Ф = √[(1 - 2 / 5) / 2]
cos 0.5Ф = √[(1 + 2 / 5) / 2]
Second, simplify the resulting expression:
sin 0.5Ф = √[(1 - 2 / 5) / 2]
sin 0.5Ф = √[(3 / 5) / 2]
sin 0.5Ф = √(3 / 10)
cos 0.5Ф = √[(1 + 2 / 5) / 2]
cos 0.5Ф = √[(7 / 5) / 2]
cos 0.5Ф = √(7 / 10)
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is 31.43 a integer ?
Algebra (Comparing Two Linear Functions)
The equation that represent each situation, in terms of x, is
A = 19 + 0.50xB = 13 + 1.50xThe number of monthly movies watched, x, that would make the two plans have an equal monthly cost is 6 movies.
How to write and solve equation?Let
Monthly cost of plan A = AMonthly cost of plan B = BNumber of monthly movies watched = xPlan A:
A = 19 + 0.50x
Plan B:
B = 13 + 1.50x
Equate A and B
19 + 0.50x = 13 + 1.50x
collect like terms
19 - 13 = 1.50x - 0.50x
6 = x
Hence,
x = 6 movies
In conclusion, the number of monthly movies watched to have an equal amount is 6 movies.
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f(x) = 2x² + 6x - 4
g(x) = 5x³6x² – 3
-
Find (f + g)(x).
A. (f+g)(x) = 5x³ + 2x² − 7
B. (f+g)(x) = 5x³ − 4x² + 6x - 7
-
O c. (f+g)(x) = −5x³ + 8x² + 6x – 1
OD. (f+g)(x) = 7x³ - 7
Answer:
Step-by-step explanation:
The expression which represents the function evaluation (f -g)(x) according to the task content is; (f -g)(x) = 2x³ +5x² -8x -4.
Which expression represents (f-g)(x) according to the functions given?
It follows from the task content that the required function evaluation required is; (f -g)(x).
Given;
f(x) = 2x³ +5x² - 6x - 7
g(x)=2x-3
To find;
(f-g)(x).
Since; (f -g)(x) = f(x) - g(x), the resulting expression for (f -g)(x) is;
(f -g)(x) = 2x³ +5x² -6x -7 -2x +3
Collect like terms;
(f -g)(x) = 2x³ +5x² -6x -2x -7 +3
Hence, (f -g)(x) = 2x³ +5x² -8x -4
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18 Tony wants to give his server a tip of 20%. He calculates that the tip is $8.50. What is the cost of Tony's meal excluding the tip?
Answer:
42
Step-by-step explanation:
8.50 x 20 and then divide by 100
I hope this helps good luck!
what is the value of 8.4n-3.2p when n=2 and p=4
Answer:
your answer is 4
Step-by-step explanation:
8.4(2)-3.2(4)=4
Answer: 4
Step-by-step explanation:
Equation: 8.4n - 3.2p
1. Substitute the variables with the given numbers
8.4(2) - 3.2(4)
2. Solve 8.4 × 2
16.8 - 3.2(4)
3. Solve 3.2 × 4
16.8 - 12.8
4. Solve
16.8 - 12.8 = 4
Which of these is the most reasonable estimate for how many more hours Mina spent playing the piano last week than Ling? O between 1 and 2 hours O between 2 and 2 hours O between 2 and 3 hours O between 3 and 3 hours
Answer: between 2 and 3 hours
Step-by-step explanation:
Easiest method is to convert mixed fractions to decimals:
1-2/3 = 1.67
4-3/10 = 4.3
Ming hrs - Ling hrs = 4.3 - 1.67 = 2.63 hrs
2 < 2.63 < 3
pla hrlp with this question
Answer: A
Step-by-step explanation:
4 1/2 is the same thing as 4.5
2 3/4 is the same thing as 2.75
4.5 - 2.75 = 1.75 = 1 3/4
Answer:
1 3/4
Step-by-step explanation:
Given the table below, write a linear equation that defines the
dependent variable, c, in terms of the independent variable, a.
a
0
4
8
12
с
15
8
1
-6
Someone help me please
The linear equation can be written as 4c + 7a -60 = 0.
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
As per the given problem a function can be defined as,
c = f(a)
Now, in order to write a linear equation from the given table take any two values of the variables as,
a = 0 and c = 15, a = 4 and c = 8.
Then, the linear equation can be written as follows,
(c - 15)/(a - 0) = (15 - 8)/(0 - 4)
=> c - 15 = -7/4a
=> 4c + 7a -60 = 0
Hence, the linear equation that defines the given table is 4c + 7a -60 = 0.
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Quick easy story and answer one easy question! help wanted 20 points! please i beg of u to help it would mean alot
QUESTION 3
Only TWO descriptions are used, one for theme 1. and one for theme 2. Match ONE description to each theme to show how the theme is developed in the story.
THEMES:
1. Friends know just what we need.
2. Sometimes life changes whether we want it to or not.
A. ::through the shared interests of the boys
B. ::through the father's promotion
C. ::through the father's advice to his son
D. ::through the gifts that the boys give each other
During her most recent check-up, Estefania’s doctor told her that she is 150.2 centimeters tall. Her doctor also told her that has grown 8.7 centimeters taller since her previous visit. How tall, in centimeters, was Estefania during her previous visit?
the answer is 21
according to my calculations 9+10= 21
[tex]27x^{3} - 125[/tex]
I've been having trouble with this question. It's sum or differences of cubes. if you can, please send a picture or explain the steps.
Answer:im not sure
Step-by-step explanation:
a?
Answer:
Well, in order to dissect this obstreperous equation, you would require this expertly-crafted formula: Goo gle + IQ of over 70 = success.
Step-by-step explanation:
PLEEEEEASE HEEEEEELPPPP
Answer:
x≤20
Step-by-step explanation:
x+5≤25
-5. -5
x≤20
Hopes this helps please mark brainliest
Answer:
The answer is B
Step-by-step explanation:
20+5=25 and x can be greater than or equal to 25
A house on the market was valued at $402,000. After several years, the value increased by 17%. By how much did the house’s value increase in dollars? What is the current value of the house?
The market value of house increased by $68,340 and the current value of the house is $470,340.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
The market value of house before several years =$402,000
Also, the value of house increased by 17%.
The rise in value of house = 402,000 x 17/100
= 68340
The value of house increased by $68,340.
The current value of house = 402,000 + 68340 = 470340
The current value of house is $470,340.
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Identify the inverse g(x) of the given relation f(x) f(x)=(8,1),(4,3),(0,-1),(-4,-3)
Answer:
Step-by-step explanation:
g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}
Each cement block is 4 centimeters thick and each clay block is 6 centimeters thick. Mike
made a stack of 17 blocks that was 82 centimeters thick. How many of each type of block did
Mike use?
Answer:
Step-by-step explanation:
heheh
When dad pulled out
the lights to hang on
the tree, he tested
them. Out of the 284
lights on the string, 6
of them were out.
What percentage of
the lights were out?
Oleaching with a Mountain View
Answer:
2.113%
Step-by-step explanation:
%out=out/total×100
6/284×100
=~2.113%
Maleka charges $8 per hour for babysitting. The amount of money she makes varies directly with the number of hours she babysits. Write a direct variation equation for the amount Maleka earns for babysitting hours. Then graph.
Answer:
[tex]y = 8x[/tex], where y = the total cost and x = amount of hours.
(-4, 2) and (12, 6)?
16. Which TWO equations represent the line that passes through the points
Answer:
Step-by-step explanation:
Hey! I am super stuck on this math work sheet I would love if someone would help THANK YOU 10c + 8 + c -3