The velocity-time graph for a cycle is shown.
104
8
8
Velocity (m/s)
2
0
0 2 4 6 8 10 12 14 16 18 20
Time (seconds)
a) Work out the distance travelled on the cycle in the first 14 seconds.
b) Work out the acceleration in the first 4 seconds.
Answers
Answer:
a) 98m
b) 2m/s
Step-by-step explanation:
a) 2+4+6+8+10(8) = 98m
b) a = change/time = 8m/4s = 2m/s
not completely sure about a) so pls double check that <//3
good luck and hope this helped a bit!
The correct answers for the given problem are: (a) The distance travelled on the cycle in the first 14 seconds is 96 m and (b)The acceleration in the first 4 seconds is 2 m/s².
How to find the area under a graph?The area under a graph can be found by dividing the graph into equal intervals of very small width and then find the area of the rectangle for each intervals. After summing all the areas of rectangles the area under the graph can be approximated.
The velocity time graph given in the problem can be used to find the distance travelled.
The distance travelled in first 14 seconds is equal to the area of the graph from t = 0 to t = 14.
This area consists of a triangle of height h = 8 and base b = 4 and a rectangle of length l = 8 and width b = (14 - 4) = 10.
Now, the total area is given as,
1/2 × b × h + l × b
= 1/2 × 4 × 8 + 8 × 10
= 16 + 80
= 96
(b) The acceleration is given as the rate change of velocity with respect to time.
The acceleration in first 4 seconds is given as,
a = (8 - 0)/4
= 2
Hence, the distance travelled in first 14 seconds and acceleration in first 4 seconds is given as 96 m and 2 m/s² respectively.
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Related Questions
What is the value of x?
Answers
Answer:
X
Step-by-step explanation:
X+y=X so the answers x
The value of x using the two rectangles is 8.
We have,
Rectangle A:
Area
= length x width
= 6 x 4
=24 cm²
Rectangle B:
Area
= length x width
= 3x cm²
Now,
The area of both triangles is the same.
This means,
Area of first rectangle = Area of the second rectangle
24 = 3x
x = 24/3
x = 8
Thus,
The value of x using the two rectangles is 8.
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Toby is packaging 21 baseball cards and 12 football cards to sell at a swap meet. He had determined that it would be best to package them in packets of 3 cards each with 7 packs of baseball cards and 4 packs of football cards. However, Toby then decided to keep one baseball card for himself and sell the rest. How does this change how many packets of each card type there are and how many cards are in each packet? There would be [?] packets of baseball cards and [?] packets of football cards. Each packet would contain [?] cards.
Answers
Answer:
Before, he had 21 baseball cards and 12 football cards.
we know that:
21 = 7*3
12 = 4*3.
He decided to pack the cards in groups of 3, because 3 is the only common factor between 21 and 12.
Now, if he decides to keep one baseball card, now he has:
20 baseball cards and 12 football cards.
Now he has two possibilities for how many cards are in each pack, this is because:
12 = 4*3 = 2*2*3
20 = 4*5 = 2*2*5
12 and 20 have two common factors, 4 and 2.
a) Then he can sell them in packets of 2 cards each with:
12/2 = 6 packs of football.
20/2 = 10 packs of baseball.
b) Or he can sell them in packets of 4 cards each with:
12/4 = 3 packs of football.
20/4 = 5 packs of baseball.
Write 65% as a fraction and a decimal
Answers
Answer:
Fraction: 13/20
Decimal: 0.65
Step-by-step explanation:
Fraction: 65/100
You can divide both numbers by 5
13/20
Decimal: move the decimal point 2 left
65.0 --> 6.5 --> 0.65
hopefully this is right if not i am sorry
Amaya is standing 30 ft from a volleyball net. The net is 8 ft high. Amaya serves the ball. The path of the ball is modeled by the equation y=-0.02(x-18)^2+12, where x is the ball's horizontal distance in feet from Amaya's position and y is the distance in feet from the ground to the ball. a. How far away is the ball from Amaya when it is at its maximum height? Explain. b. Describe how you would find the ball's height when it crosses the net at x=30. a. How far away is the ball from Amaya when it is at its maximum height? Explain. The ball is nothing ft away from Amaya when it is at its maximum height. Use the ▼ y-coordinate x-coordinate of the vertex.
Answers
Answer:
a) 30feet
b) 9.12feet
Step-by-step explanation:
a) Given the path of the ball is modeled by the equation y=-0.02(x-18)²+12, where;
x is the ball's horizontal distance in feet from Amaya's position
y is the distance in feet from the ground to the ball.
The ball will be at the maximum height when dy/dx = 0
Differentiate the function:
dy/dx = 2(-0.02)(x-18)^(2-1)+0
dy/dx = -0.04(x-18)
Equate the resulting expression to zero and find x as shown;
-0.04(x-18) = 0
Open the parentheses
-0.04x+0.04(18) = 0
-0.04x+0.72 =0
-0.04x = -0.72
x = -0.72/-0.04
x = 18ft
Hence the ball is 18ft away from Amaya when it is at its maximum height
b) To get the balls height y when x = 30, we will substitute x = 30 into the equation given and calculate the value of y as shown:
y=-0.02(x-18)²+12
y = -0.02(30-18)²+12
y= -0.02(12)²+12
y = -0.02(144)+12
y = -2.88+12
y = 9.12 feet
Hence the Ball's height is 9.12feet when it crosses the net at x = 30.
Ben and Jerry together own 75 comic books. If Ben owns 31 comic books, how many does Jerry own?
Answers
Answer:
44
Step-by-step explanation:
75-31=44
Answer:
44 books
Step-by-step explanation:
75-31=44
simple math
plzzzz
Select the equation of the line that passes through the point (3,-1) and is parallel to the line on the
graph. (2 points)
O y = -1
O y = 3
O y = x-1
O y = 3x - 1
Answers
Answer:
y = -1
Step-by-step explanation:
there is no graph
but only this answer passes the (3,1)
Please add picture next time
<3
Red
The harbormaster wants to place buoys where the river bottom is 20 feet below the surface of the water. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed. blank = 1/5|s blank|blank
Answers
Answer:
The answer is below
Step-by-step explanation:
The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed
Answer:
To solve the problem, the depth of the water would be equated to the position of the river bottom.
[tex]d(h)=river \ bottom\\\\The \ river \ bottom=-20\ feet(below)\\\\d(h) = -20\\\\\frac{1}{5}|h-240|-48=-20\\ \\\frac{1}{5}|h-240|=-20+48\\\\\frac{1}{5}|h-240|=28\\\\|h-240|=28*5\\\\|h-240|=140\\\\h-240=140\ or\ h-240=-140\\\\h=140+240\ or\ h=-140+240\\\\h=380\ or\ h=100\\\\The\ buoys\ should\ be\ placed\ at\ 100\ feet\ and\ 380\ feet\ from\ left-hand\ shore[/tex]
Leeza is 6 years older than two times her brother Sammy’s age. Let s represent Sammy’s age.
Which expression represents Leeza’s age?
a.6s + 2
b.2s
c.s + 6
d.2s + 6
Answers
✧･ﾟ: *✧･ﾟ:*hello there!*:･ﾟ✧*:･ﾟ✧
✧here is your answer:
.・゜゜・d. 2s + 6・゜゜・．
♥⛧i hope this helps!!
✧༺♥༻∞lmk if you need help on anything else!!∞༺♥༻✧
❀-kay♬
Hope you have a nice dayyyyyyyyyy
Antonio is going to make a new summer drink. He needs 1/3 of a glass of orange juice and 2/4 of a glass of lime juice. The rest is water. To make one drink, what fraction of the glass will be water?
Answers
Answer:
1/6!!!! C
Step-by-step explanation:
Find common denominater. 12.
1/3 goes to 4/12.
2/4 goes to 6/12.
6/12+4/12 is 10/12
Remaining is 2/12!
That is 1/6 simplified!
a. 3/4 b.4/7 c.1/6 d. 5/
A line PR, 3 cm long, is divided into equal segments. Point Q lies on the line such that the ratio of the length of PQ to that of PR is 4:9. What is the length of QR? Give the answer as a fractional value.
Answers
Answer:
8/3
Step-by-step explanation:
4:9
pq:pr
x:3
Cross multiply and make x subject of the formula
X=4/3
3-4/3=8/3
Katherine invests $7770 in a six-month money market account giving 5.8% simple annual interest and $12,500 in a
three-year CD giving 7 25% simple annual interest. Assuming that Katherine does not reinvest or renew these
investments, how much money will she have when both investments reach maturity, to the nearest dollar?
$2,944
b. $15,219
$23,214
d. $30,886
a
С.
Answers
Answer:
Katherine will receive $23214 to the nearest dollar from both investments.
Step-by-step explanation:
Simple interest = Principal × Time × rate
Le's work out the interest Katherine earns from the two investments.
Money Market Account
Simple interest = 7770 × 5.8/100 × 6/12
= 7770 × 0.058 × 0.5 = $225.33
So, the amount she gets at maturity is:
$7770 + $225.33= $7995.33
CD account
Simple interest = 12500 × 0.0725 × 3 = $2718.75
The amount she receives at the end of period is:
$12500 + $2718.75 = $15218.75
The total amount she receives from both investments at maturity is:
$15218.75 + $7995.33 = $23214.08
This to the nearest dollar is:
= $23214
Answer:
It's C on Edge
Step-by-step explanation:
An ant with a mass of 4 x 10-6 kg is carrying a bread crumb back to its anthill . The bread crumb has a mass of 8 x 10-5 kg. The mass of the bread crumb is how many times the mass of the ant?
Answers
Answer:
Mass of bread crumb is 20 times the mass of the ant..
Step-by-step explanation:
Mass of an ant = [tex]4\times 10^{-6}[/tex] kg
Ant carries a weight of bread crumb to its anthill.
Mass of the bread crumb = [tex]8\times 10^{-5}[/tex] kg
Ratio of their masses,
[tex]\frac{\text{Mass of the ant}}{\text{Mass of bread crumb}}=\frac{4\times 10^{-6}}{8\times 10^{-5}}[/tex]
[tex]\frac{\text{Mass of the ant}}{\text{Mass of bread crumb}}=\frac{1}{2\times 10^{(-5+6)}}[/tex]
[tex]\frac{\text{Mass of the ant}}{\text{Mass of bread crumb}}=\frac{1}{20}[/tex]
Mass of the bread crumb = 20×(Mass of the ant)
Therefore, mass of the bread crumb is 20 times the mass of the ant.
Which expression means “12 less than the product of 2 and a number b”?
Answers
Less than sign
Please help!!! Will mark brainliest if you show your work and the answer!
Answers
Answer: Mario
Step-by-step explanation: 8 squared is 64 and 12 squared is 144, 18 squared is 324. According to the Pythagorean theorem, A squared + B squared = C squared but in this case, A squared and B squared doesn't add up to C squared so it is wrong
Jada makes sparkling juice by mixing 2 cups of sparkling water with every 3 cups of apple juice.
How much sparkling water does Jada need if she uses 15 cups of apple juice?
Answers
Answer:
she will need 5 more 3 cups of apple juice
Step-by-step explanation:
15÷3=5
3×3×3×3×3=15
Write 3.19×10−2 in standard form.
Answers
Answer:
It is already in standard form
My teacher asked me to round 71,500 to the nearest thousand. I think that the answer is 72,000. Did I round correctly?
Answers
Answer:
yeah, that's right!!!!
Which of the following is the correct value for x
Answers
The youth center needs to buy 50 tennis balls. They come in cans that hold 6 balls each. How many complete cans of tennis balls will they need to buy? Explain your thinking.
Answers
Answer:
9 complete cans
Step-by-step explanation:
50/6=8 remainder of 2
8 is not enough, they need 9 o
97 divided by 17 round it
Answers
Answer:
6
Step-by-step explanation:
Write an equation, in slope-intercept form, that passes through point (-4,- 3) with slope 3.
Answers
Answer:
y=3x+9
Step-by-step explanation:
Slope intercept form: y=mx + b
m= slope
b= y-intercept
-Plugin the point
-3=3(-4)+b
-3(+12) = -12 + b(+ 12)
9=b
y = 3x + 9
help me please!!!!!
Answers
Answer:
5/6 and 6/7
Step-by-step explanation:
Answer:
5/6 then 6/7
Step-by-step explanation:
Both the numerator and denominator are being increased by 1.
The top (numerator) is one less than the denominator in each term.
So the answers are 5/6 and then 6/7.
Hans is using frequent flier miles to fly to a location 750 miles away, but the airline he is using still charges $20.19 for fees and taxes and $0.15 to redeem each mile. In the equation below, x represents the distance Hans is flying, and y represents the cost of the trip. Y = $0.15x + $20.19 How much did Hans pay for his trip?
Answers
Answer:
Cost of the trip = $132.69
Step-by-step explanation:
Given:
Total distance = 750 mile
Fixed charge = $20.19
Variable charges = $0.15 per mile
Find:
Cost of the trip
Computation:
Y = $0.15x + $20.19
Y = $0.15(750) + $20.19
Y = $132.69
Cost of the trip = $132.69
write four integers between -10 and 3
Answers
Answer:
-4, -3, -2, -1
Step-by-step explanation:
all the integers between -10 and 3
-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2
Answer:
-9, -8, 2, 1
Step-by-step explanation:
Integers are whole number that can either be positive or negative.
Help in this one please
Answers
What is the answer to 0.75 (6+d)=12 step by step
Answers
Answer:
step 1: 0.75 x 6 = 4.5
step 2: 0.75 x d = 0.75d
step 3: 4.5 + 0.75 = 5.25
It's correct answer
Step-by-step explanation:
1. 30 inches to 24 inches
Find the percent of change and round to the nearest whole percent
Answers
Answer:
6
Step-by-step explanation:
subtract if that makes sense
Tim has been saving for a down payment on a car. He invested $4,000 in an account earning 2.5% interest compounded semi-annually. After 7 years, he is ready to buy his new car. How much does he have in his account for a down payment? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.
Answers
Answer:
$4754.4Step-by-step explanation:
The expression for compound interest is given as
A=P(1+r)^t
given data
P=$4,000
r=2.5%= 0.025
t=7years
The final amount can be solved as
A=4000(1+0.025)^7
A=4000(1.025)^7
A=4000*1.1886
A=4754.4
The amount on the account is $4754.4
Which of the following are ways to find the rate of change or slope
1 . Rise over run
2 . Subtract Y coordinates over subtract X coordinates
3 . Change in Y over change in X
4 . All of the above
Answers
The rate of change or slope can is the ratio of the change in horizontal axis to the change in the vertical axis, Hence, all the equations stated above can be used to obtain the slope.
The slope or rate of change can be obtained using the following expression :
Slope = Rise / Run Slope = (y2 - y1) ÷ (x2 - x1) Slope = (△Y ÷ △X)Therefore, all the given equations in the option can be used to obtain the slope value of a line.
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Explain the difference between (-5)2 and -52. Your answer:
Answers
Answer:
-5(2) is different from -52 because -5(2) equals -10.
Step-by-step explanation:
-5(x) implies that -5 is being multiplied by x. Any time 2 numbers (one in parenthesis) are next to each other without a symbol inbetween it implies multiplication