Answers
Answer:
a) 1.50 m/s²
b) 675m
c) 11.25 m/s
Step-by-step explanation:
1. a) Acceleration can be found from the gradient of a speed-time graph, which is the graph we have here.
Notice that the graph from t=0 to t=10 has the same gradient thoughout (since it is a straight line). Hence, the acceleration when t=4 is the same as the acceleration from t=0 to t=10.
To find the gradient of the graph from t=0 to t=10, use the gradient formula below:
gradient=[tex] \frac{y1 - y2}{x1 - x2} [/tex]
The coordinates of the point at t=0 is (0,0) and the point at t=10 is (10,15).
Thus, gradient
[tex] = \frac{15 - 0}{10 - 0} \\ = \frac{15}{10} \\ = 1.5[/tex]
Therefore the acceleration when t=4 is 1.50 m/s².
*Acceleration is the rate of change of velocity (or speed).
b) Distance travelled can be found by calculating the area under a speed-time graph.
The area under the graph is the orange trapezium that the question has shaded for you already.
Formula for area of trapezium= ½(a+b)(height)
a+b is the total length of the two parallel horizontal lines of the trapezium.
Let the top line be a and the bottom line be b.
length of a= distance between (10,15) and (40,15)
Length of a
= 40 -10
= 30 units
Length of b
= 60 -0
= 60 units
height of trapezium= 15 units
Area of trapezium
= ½(30 +60)(15)
= 675 units²
Thus, the distance travelled is 675m.
c) Avg speed= total distance ÷ total time
From part b, we know that the total distance travelled is 675m. The total time is 60s since the graph is from t=0 to t=60.
Hence, average speed
= 675 ÷60
= 11.25 m/s
Related Questions
13. If 3 times a number minus 2 equals 13, what is the number?
A. 4
old
B. -6
OOOO
C.5
D.2
Answers
Answer:
5
Step-by-step explanation:
Answer:
The number is 5
Step-by-step explanation:
3x -2 = 13
Add 2 to each side
3x-2+2 = 13+2
3x = 15
Divide each side by 3
3x/3 = 15/3
x = 5
Please hurry
Which quadratic function has a vertex of (1, 4) and passes through
the point (0, 3)?
Answers
Answer:
f(x)=−(x−1)^2+4
Step-by-step explanation:
Find the value of n.
Answers
Answer:
n = -1.5
Step-by-step explanation:
[tex]\frac{1}{(\sqrt2)^{3} } } = 0.353553[/tex]
log ( [tex]2^{n}[/tex] ) = log (.353553)
n = [tex]\frac{log (0.353553) }{log (2)} = -1.5[/tex]
Which table shows the function y = -2x + 4?
es
Answers
Answer:
To figure this out you have to plug in values
c
4-5/8(-4)=6.5
4-5/8(2)=2.75
4-5/8(4)=1.5
4-5/8(8)=-1
Step-by-step explanation:
Put the steps in the correct order to show how a budget is made.
First Step
T1 Total up spending
11 Reduce expenses in flexible categories to save or increase savings
Ti Calculate income
Ti Determine if spending is below income
11 Categorize expenses
Final Step
Answers
Answer:
The correct answer is: Calculate income, Total up spending, Categorize expenses, Determine if spending is below income, and Reduce expenses in flexible categories to save or increase savings. When making a budget, it's first necessary to figure out how much money comes in and goes out, and then to compare expenses to income to make cuts if necessary.
Step-by-step explanation:
Nelson decides to invest $1,000,000 in a period annuity that earns 4.8% APR
compounded monthly for a period of 15 years. How many years will it take
Nelson to earn back his initial investment?
Answers
Answer:
21yearsStep-by-step explanation:
Amount invested by Nelson = $1,000,000
Interest rate per month = 4.8%
Simple Interest = Principal * Rate * Time/100
simple Interest = $1,000,000 * 4.8 *(1/12)/100
simple Interest = $1,000,000 * 4.8/1200
simple interest = $4,000/ month
Simple interest for one year = $4,000*12 = $48,000
In order to determine the number of years it will take Nelson to earn back his initial investment, we will divide its initial investment by the interest earned on the investment yearly as shown;
amount of years = $1,000,000/ $48,000
Amount of years = 20.8years ≈ 21years
10.7 years
Step-by-step explanation:
hope this helps
PLS SHOW ALL WORK AND ANSWER CORRECTLY
Answers
Answer:the solution was long so there are 3 pictures hope it helps u
Step-by-step explanation:
Which equation correctly represents the distance between - 15.1 and -3.9 on a number line?
- 3.9 - (-15.1)] = 11.2
-3.9 - 15.1 = -11.2
|- 15.2 + (-3.9) |= 19
-15.1 - 3.9 = -19
Answers
Answer:
Step-by-step explanation:
Keep in mind that distance is positive, not negative. Eliminate the negative results.
- 3.9 - (-15.1)] = 11.2 is correct. -(-15.1) - 3.9 is approximately 15 - 4, or 11, which agrees with the 11.2 correct result.
The volume of a cylinder is given by V = ar?h
where ris the radius of the cylinder and his the
height. Which expression represents the volume of
this can?
Answers
Answer:
D
Step-by-step explanation:
[tex]V=\pi r^{2}h\\ =\pi*(x+2)*(x+2)*3x+8\\ =\pi *x(x+2)+2(x+2)*3x+8\\ =\pi *x^{2}+4x+4*3x+8\\ =3x(x^{2}\pi+4x\pi+4\pi)+8(x^{2}\pi+4x\pi+4\pi0 \\ =3x^{3}\pi+20x^{2}\pi+44x\pi+32[/tex]
At 50, Brian sets up an IRA, where he plans to deposit $12,000 at the end of each year until age 75. Find the amount of the annuity if he invests in a stock fund that yields 4% compounded annually.
Answers
Answer: the amount of the annuity is $501000
Step-by-step explanation:
We would apply the future value which is expressed as
FV = C × [{(1 + r)^n - 1}/r]
Where
C represents the yearly payments.
FV represents the amount of money
in your account at the end of 25 years.
r represents the annual rate.
n represents number of years or period.
From the information given,
r = 4% = 4/100 = 0.04
C = $12000
n = 75 - 50 = 25
Therefore,
FV = 12000 × [{(1 + 0.04)^25 - 1}/0.04]
FV = 12000 × [{2.67 - 1}/0.04]
FV = 12000 × 41.75
FV = $501000
Which is the equation in slope-intercept form for the line that passes through (3, 3) and is parallel to x + 3y=4?
Answers
Answer:
hope this is correct
Which graph represents the function f(x) = (1∕4)x – 1?
Answers
Answer:
Where's the graph?
Step-by-step explanation:
Answer:
Step-by-step explanation:
math way
Which of the following is most likely the next step in the series?
Answers
Answer:
it's D
Step-by-step explanation:
Explanation:
1. What is the median of the data below? 2. What is the value at Q1 (or the lower quartile)?
Answers
Answer:
the median is the middle line
Step-by-step explanation:
Answer:
fkjshfkjdhfjksdhfjkshdfkjshd
Step-by-step explanation:
How many 3-digit multiples of 13 are there?
Answers
Answer:
There are 69
Step-by-step explanation:
1+(104-998)/13=69
AB is included between
A. BC and AC
B.
C. < A and
D. AB and BC
Answers
Answer:
Option C.
Step-by-step explanation:
By the property of unique triangles (ASA), one side is included between the two angles.
By this property, if included side of the triangle ABC is AB then this side will be included between the two angles A and B.
Therefore, [tex]\bar{AB}[/tex] is included between ∠A and ∠B.
Option C. will be the answer.
10. Rhonda Harmon's credit card statement showed an $839.78 balance. Since then, she has made a $110.50 payment
and purchases totaling $143.75. What is Rhonda's new balance?
NEED HELP PLSS
Answers
Answer:
585.53 new balance
$839.78 - 110.50 - 143.75
Answer: 585.53
Step-by-step explanation:
839.78 - 110.50 = 729.28
729.28 - 143.75 = 585.53
Find h, assuming the triangles formed are similar.
Answers
Answer:
h=18
Step-by-step explanation:
Answer:
Step-by-step explanation:
Similar triangles, the sides are in proportion
[tex]\frac{20}{8}=\frac{h}{6}\\\\\frac{20}{8}*6=h\\\\5*3=h\\[/tex]
h = 15
The volume of the cone is 540π , work out the height of the cone.
radious = 6cm
Answers
Answer:
14.32
Step-by-step explanation:
The volume of the cone is 540π , work out the height of the cone.
radious = 6cm
Answer:
14.32
Step-by-step explanation:
a²=m. Find a⁶
pls help
Answers
Answer:
M^3
Step-by-step explanation:
Dose anyone know what is coefficient too -7yz2?
Answers
Answer:
-7
Step-by-step explanation:
Coefficients are the numbers that multiply the following variables, so in the case of -7yz^2, the coefficient would have to be -7.
Please help me answer all parts of this in the next two hours!
Answers
Answer:
1) Yes, table shows a probability distribution
2) Mean = 1.5
3) Standard Deviation = 1.1
Step-by-step explanation:
PART 1:
For the table to show a probability distribution, the sum of all probabilities should be equal to 1
Sum of probabilities = 0.358 + 0.443 + 0.174 + 0.025
Sum of probabilities = 1
Hence, the table shows the probability distribution.
PART 2:
The formula for mean is given by:
Mean = Sum of terms/ Total no. of terms
Mean = (0+1+2+3) / 4
Mean = 1.5
PART 3:
The formula for standard deviation is given by:
[tex]\sigma=\sqrt{\frac{\sum(x_i-\mu)^2}{N}}[/tex]
Solve using a calculator, we get
σ = 1.118
Round off to one decimal place
σ = 1.1
Write in simplest form:
4 1/3 : 7
Answers
Answer:
13 : 21
Step-by-step explanation:
4 1/3 : 7
13/3 : 7
3*13/3 : 3*7
13 : 21
It is less important to account for factors like warranties and durability when purchasing a A: durable goods B: long-term product C:nondurable D: very expensive item PLz answer
Answers
Answer:
the answer is C Non durable
Step-by-step explanation:
what is th rate equivalent to an annual rate of 20% with monthly capitalization
Answers
Answer:
about 21.9%
Step-by-step explanation:
The effective annual multiplier is ...
(1 +r/n)^n = (1 +0.20/12)^12 ≈ 1.21939
The rate equivalent is 1 less than this:
1.21939 -1 = 0.21939 = 21.939%
-6 + 4 i need help plz
Answers
The answer is -2
If f(x) = 3x - 2, find f(4).
Answers
Answer:
10
Step-by-step explanation:
f(x) = 3x - 2
Let x=4
f(4) = 3*4 - 2
=12-2
=10
Answer:
10
Step-by-step explanation:
Replace 4 for all the x values and solve
f(4)=3(4)-2
f(4)=12-2
f(4)=10
Given the figure as marked, identify the most specific type of quadrilateral.
Select the best answer from the choices provided.
A.
parallelogram
B.
rhombus
C.
rectangle
D.
square
Answers
Answer:
the answer is c. rectangle
Renee can see a 25 square foot quilt in 16 hours. Genera can sew the same size quilt in 12 hours. How long would it take them to see the quilt together?
Answers
28 hours because they are too long from each other
Answer:
Approximately 6.86 hours.
Step-by-step explanation:
Renee sews at a rate of 1.5625 sq ft an hour. Found using square feet divided by hours.
Genera sews at a rate of 2.084 sq ft an hour. Found using square feet divided by hours.
To find how fast they can sew the quilt together, we must add their sewing speeds together: 1.5626 + 2.084 = 3.64583333.
Using this equation we can divide a 25 sq ft quilt by their speed of 3.64583333 to get approximately 6.86 hours.
The answer is approximate because we used rounded decimals.
In approximately two to three sentences, explain how you would convert
14/ 25
to a percent
