Mrs Rani is 36 years old and her daughter is 4 years old. In how many years’ time
will she be three times her daughter’s age?
Answers
Answer:
MRS RANI 39 AND DAGHTER 7
Related Questions
Let us also recall that it took the bus 36 s to cover 400 m, that the student was 200 m ahead of the bus, and it took the student 1.70 s to accelerate.
(a) What is the distance covered by the bus, from the moment the student starts chasing it and till the moment when the bus passes by the stop? You can use either equations or the v(t) graph. Give your answer in meters.
(b) What is the distance covered by the students in these 36 s (from the beginning of her race and till the bus passes by the stop)? You can use either equations or the v(t) graph. Give your answer in meters.
(c) Hence, by how much does the student miss the bus? Give the answer in meters. Use your answers from parts (a) and (b)
Answers
(c) The student misses the bus by the difference between the total distances covered by the bus and the student.
(a) To determine the distance covered by the bus from the moment the student starts chasing it until the moment the bus passes by the stop, we need to consider the relative motion between the bus and the student. Let's break down the problem into two parts:
1. Acceleration phase of the student:
During this phase, the student accelerates until reaching the bus's velocity. The initial velocity of the student is zero, and the final velocity is the velocity of the bus. The time taken by the student to accelerate is given as 1.70 s.
Using the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the acceleration of the student:
a = (v - u) / t
= (0 -\(v_{bus}\)) / 1.70
Since the student starts 200 m ahead of the bus, we can use the following kinematic equation to find the distance covered during the acceleration phase:
s = ut + (1/2)at^2
Substituting the values:
\(s_{acceleration}\) = (0)(1.70) + (1/2)(-\(v_{bu}\)s/1.70)(1.70)^2
= (-\(v_{bus}\)/1.70)(1.70^2)/2
= -\(v_{bus}\)(1.70)/2
2. Constant velocity phase of the student:
Once the student reaches the velocity of the bus, both the bus and the student will cover the remaining distance together. The time taken by the bus to cover the remaining distance of 200 m is given as 36 s - 1.70 s = 34.30 s.
The distance covered by the bus during this time is simply:
\(s_{constant}_{velocity} = v_{bus}\) * (34.30)
Therefore, the total distance covered by the bus is:
Total distance = s_acceleration + s_constant_velocity
= -v_bus(1.70)/2 + v_bus(34.30)
Since the distance covered cannot be negative, we take the magnitude of the total distance covered by the bus.
(b) To determine the distance covered by the student during the 36 s, we consider the acceleration phase and the constant velocity phase.
1. Acceleration phase of the student:
Using the equation of motion:
s = ut + (1/2)at^2
Substituting the values:
\(s_{acceleration}\) = (0)(1.70) + (1/2\(){(a_student)}(1.70)^2\)
2. Constant velocity phase of the student:
During this phase, the student maintains a constant velocity equal to that of the bus. The time taken for this phase is 34.30 s.
The distance covered by the student during this time is:
\(s_{constant}_{velocity} = v_{bus}\) * (34.30)
Therefore, the total distance covered by the student is:
Total distance =\(s_{acceleration} + s_{constant}_{velocity}\)
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the high school swimming team can have at most 45 members. the sign-up list contains 28 athletes. how many athletes can still join the team?
Answers
Answer:
17
Step-by-step explanation:
45 - 28
Hope this helps!!!!!!!
Answer:
17
Step-by-step explanation:
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. 9. y= x
,y=0,x=4
Answers
The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.
To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:
First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.
Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.
The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.
The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.
The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.
Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:
V = ∫[a, b] 2πrh dy
Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).
Substituting t
he values of r and h into the integral, we have:
V = ∫[0, 9] 2πy(y) dy
Simplifying, we get:
V = 2π ∫[0, 9] y^2 dy
Evaluating the integral, we have:
V = 2π [y^3/3] from 0 to 9
V = 2π [(9^3/3) - (0^3/3)]
V = 2π [(729/3) - 0]
V = 2π (243)
V = 486π
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christa started her math homework at school after school she spent 4 more minutes on it altogether she spent 12 minutes on her homework how long did she work on the homework during class
Answers
60PTSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HELP IMA FAIL
1.Which recursive formula fits the following pattern?
50, 25, 12.5, 6.25, 3.125...
A(n+1) = A(n) ÷ 2, A(1) = 50
A(n+1) = A(n) − 2, A(1) = 50
A(n+1) = A(n) ÷ 50, A(1) = 50
A(n+1) = A(n) − 50,A(1) = 50
2.
What does a7 mean?
3.
Write a Recursive and Explicit Sequence for the following pattern.
1, 5, 9, 13, 17...
4.What are the first 5 terms in the following recursive sequence?
A(n+1) = A(n) × 3 A(1) = 2
5.
Which Explicit formula would fit this pattern?
3,7,11,15,19...
*Remember, you can check by plugging in the term numbers to see if you get the correct output*
Answers
1. Answer:
i dont know
Step-by-step explanation:
they didnt teach me this
2. Answer:
a7 means what ever a is you have to multiply it by 7
Step-by-step explanation:
When ever you see a letter infornt or followed by a number you always multiply it by the number.
3. Answer:
1, 5, 9, 13, 17, 21, 25, 29, 33, ect.
Step-by-step explanation:
Just keep adding four
5. Answer:
3, 7, 11, 15, 19, 23, 27, 31, ect.
Step-by-step explanation:
Just keep adding four
Answer:
1) A(n+1) = A(n) ÷ 2, A(1) = 50
2) 7 multiplied by a.
3) 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, .... (add 4 each time)
4) A(n+1)=A(n) x 3A(1)=2
2, 5, 8, 11, 14
5) 3, 7, 11, 15, 19,... A(n+1)=A(n)+4, A(1)=3
Step-by-step explanation:
Order these numbers from least to greatest.
5.77, 5 5/6, 4.717, 23/4
Answers
The given numbers 5.77, 5 5/6, 4.717, 23/4 can be ordered from least to greatest as 4.717 , 23/4, 5.77, 5 5/6.
How can the number be arranged?The order of arrangement refers to the way in which objects or elements are organized or placed in a sequence. It takes into account the position or order of each element in the sequence, and the number of possible arrangements depends on the total number of elements and the number of elements that are selected or arranged at a time.
Given that 5.77, 5 5/6, 4.717, 23/4
Let us check the number one after the other by converting them into decimals;
5.77 = 5.77
5 5/6 = 35/6 = 5.83
4.717=4.717
23/4 = 5.75
Then we can now arranged as instructed as ; 4.717 , 5.75 , 5.77 , 5.83
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plsss help mehhh...
Answers
Step-by-step explanation:
(2, m) => (n, 5) => (10, 2)
We have 2n = 2 + 10 and 2(5) = m + 2
Hence n = 6 and m = 8.
Find the slope of the line.
(picture)
Answers
Answer:
2/3
Step-by-step explanation:
Help me pls pls pls
Answers
Answer:
Here x=20 so
15+20=35
18+80=98
47
35+98+47=180
Sabrina wanted to wrap a giftbox of length 8 inches, height 6 inches, and width 4 inches. How much wrapping paper does Sabrina need to buy?
Answers
Answer:
208inches
Step-by-step explanation:
Surface Area=2x(8x6+8x4+6x4)=208 feet^2
Which one is the correct answer, a b c d
Answers
\(g(f(x))=\sqrt{\frac{2301+100x^2}{23+x^2} }\)
Step-by-step explanation:\(Substitute\ and\ calculate:\\ \downarrow\\ g(f(x))=\sqrt{\frac{2301+100x^2}{23+x^2} }\)
I hope this helps you
:)
Please help I don't understand this and I don't want to fail!!!
Answers
Answer:
8 is the hypotenuse.
sen(angle) = x/8
sen60 = x/8
0.87 = x/8
0.87·8 = x
x = 6.96
Help!!!!!!!!!!!!!!!!!!!!!!
Answers
The two circle pictured above represent two congruent circles.
True
or
False
Answers
Answer:
False
Step-by-step explanation:
If two circle are congruent, the two circles will have same radius.
As inner circle radius is smaller than outer circle radius.
These two circle have same center. They are called concentric circles
4a-b=10 . 2a + 3b=12
Answers
Answer:
a = 3
b = 2
Step-by-step explanation:
Solve 4a - b = 10 for b:
\(4a - b = 10\) \(4a - b - 4a = 10 - 4a\) (Subtract 4a from both sides)\(-b = -4a +10\) \(\frac{-b}{-1} = \frac{-4a+10}{-1}\) (Divide both sides by -1)\(b = 4a - 10\)Substitute 4a - 10 for b in 2a + 3b = 12
\(2a + 3b = 12\) \(2a + 3(4a-10)=12\) \(2a + 12a -30 = 12\) (Simplifying)\(14a - 30 = 12\) (Simplifying\(14a - 30 + 30 = 12 + 30\) (Add 30 to both sides)\(14a = 42\) \(\frac{14a}{14} = \frac{42}{14}\) (Divide both sides by 14)\(a = 3\)Substitute 3 for a in b = 4a - 10
\(b = 4a - 10\) \(b = 4(3) - 10\) \(b = 12 - 10\) \(b = 2\)Therefore, a = 3 and b = 2.
jamie is buying 5 concert tickets , but he wants his total cost to be no more than 4$ above or below 80$. which inequality models the cost x, in dollars , of a ticket?
Answers
jamie paid $14.00 per ticket.
Write an equation for the line that passes through (3,-14) and (2,5). Give the answer in standard form
Answers
The equation of a line in standard form looks like this...
\(aX+bY=c\)Points
(x1,y1) = (3 , -14)
(x2,y2) = (2 , 5)
\(\text{if y=mx+b; then m is the slope m=(y2-y1)/(x2-x1)}\)\(m=\frac{5-(-14)}{2-3}=-\frac{19}{1}=-19\)\(y=-19x+b\)if we substitute for the first point:
\(\begin{gathered} -14=-19\cdot(3)+b \\ -14=-57+b \\ b=57-14=43 \end{gathered}\)Therefore,
\(y=-19\cdot x+43\)Now, we want to write this equation in standard form:
\(\begin{gathered} y=-19x+43 \\ +19x+y=+19x-19x+43 \\ 19x+y=43 \end{gathered}\)Therefore a=19 ; b=1 and c=43
the sum of 3 and twice a number is 33
Answers
hello
to solve this question, we should let the unknown number be represented by x
\(\begin{gathered} x+2x=33 \\ 3x=33 \\ \text{divide both sides by the coefficient of x} \\ \frac{3x}{3}=\frac{33}{3} \\ x=11 \end{gathered}\)the first number (x) is equal to 11, we can find the other number.
\(2x=2\times11=22\)from the calculations above, the numbers are 11 and 22
DeAndre downloaded 8 apps onto his tablet in 12 seconds. At this rate, how many apps could he download in one minute? (12 seconds = 15 minute)
HELP
Answers
Explanation:
60 divided by 12 is 5. That’s how many downloading sessions could fit in a minute. Multiply 5 by the number of apps, which is 8. Your answer is 40 apps.
You are provided with the following system equation:
6 dy/dt – 7y = 4 du/dt - 3u
with u denoting an input, and y an output variable. Which one of the following conclusions can be drawn about this system? a. It is stable Ob. It is unstable It is critically damped d. It is marginally stable
Answers
Based on the provided equation, no definitive conclusion can be drawn about the stability of the system without additional information or analysis.
To determine the stability of a system, further analysis is required. The given equation is a linear ordinary differential equation relating the derivatives of the output variable y and the input variable u. The coefficients in the equation, 6 and -7 for dy/dt and y, respectively, as well as 4 and -3 for du/dt and u, do not provide sufficient information to determine stability.
Stability analysis typically involves assessing the behavior of the system's response over time. Stability can be classified into several categories, including stable, unstable, critically damped, or marginally stable. However, in this case, the given equation does not provide the necessary information to make any definitive conclusion about the stability of the system.
To assess stability, one would typically examine the characteristic equation, eigenvalues, or transfer function associated with the system. Without such additional information or analysis, it is not possible to determine the stability of the system solely based on the given equation.
The provided equation does not provide enough information to draw a conclusion about the stability of the system. Further analysis using techniques like eigenvalue analysis or transfer function analysis would be necessary to determine the stability characteristics of the system.
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Between 2004 and 2015, did the percentage of homes with landlines decrease at the same rate at which the percentage of cell-phones-only homes increased? Explain or show your reasoning
Answers
No, the percentage of homes with landlines did not decrease at the same rate at which the percentage of cell-phones-only homes increased between 2004 and 2015.
According to data from the National Center for Health Statistics, the percentage of homes with landlines decreased from 89.7% in 2004 to 50.8% in 2015. Meanwhile, the percentage of cell-phones-only homes increased from 3.2% in 2004 to 47.4% in 2015. While both trends show a decrease in landlines and an increase in cell-phones-only homes, the rate of change is not the same.
The step-by-step explanation of the reasoning is:
1. Find the difference in the percentage of homes with landlines between 2004 and 2015: 89.7% - 50.8% = 38.9%
2. Find the difference in the percentage of cell-phones-only homes between 2004 and 2015: 47.4% - 3.2% = 44.2%
3. Compare the two differences: 38.9% ≠ 44.2%
4. Conclusion: The percentage of homes with landlines did not decrease at the same rate at which the percentage of cell-phones-only homes increased.
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What single factor made the Hindu arabic number system superior
Invention of 0
What are the two purposes of numerals or digits
Show the cardinal value (how many)
And show the place value (10s, 100s, 1000s)
Natural numbers in a counting process
Does not include 0
1-2-3-4-5-6-7-8-9-10-11- infinity
Principle of closure
Addition- if you add any two natural numbers, the result will always be a natural number. Called closed under addition
Multiplication- if you multiply any two naturals, you get naturals. Called closed under addition
Subtraction- you cannot achieve closure when subtracting larger number from smaller number (i.e. 6-7)
Division - when you divide two natural numbers, it is possible to get a fraction. Not closed by division.
Integers
Positive and negative numbers, start at 0 and expand infinitely at both ends.
Closed under addition, multiplication, subtraction. NOT DIVISION
Rational numbers
Numbers that can be expressed as fractions, that is the quotient of two integers
Irrational numbers
Non terminating, repeating decimals
Three axioms of equality
Reflexive- law of identity. Any number reflects itself or is equal to itself (i.e. A=A)
Symmetric- any equality is reversible (i.e. A=B, then B=A)
Transitive property - possible to identity two numbers as being equal to a third quantity (a=b and b=c then a=c)
Commutative property
When adding, it doesn't matter the order
a+b=b+a
Order in which things are multiplied does not affect product (a*b=b*a)
Associative property
Law states that the order in which Addends are grouped, the sum will be unaffected. (a+b)+c = a + (b+c)
(A*b)*c = a(b*c)
Distributive property
Multiplication can be distributed over addition.
a(b+c)= (a*b) + (a*c)
Unity element
Number 1 is the identity element of multiplication. Any number multiplied by one equals itself
Zero element
Identity element for addition
Will destroy number, anything multiplied by 0 =0
Dividing by 0 is error.
0 /# = 0
Answers
The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.
The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.
The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.
Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.
Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.
The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).
The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.
The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.
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find the measure of one interior angle in each polygon. Round your answer to the nearest tenth if Necessary.
Answers
An interior angle of a polygon is an angle formed inside the two adjacent sides. In our case, an interior angle is the angle in red color:
In our case, there are 8 sides so our polygon is an octagon. So, the size of each interio angle is given by
\(\frac{(8-2)\times180}{8}=\frac{6\times180}{8}=135\)Therefore, the answer is 135 degrees:
True or False? suppose bx and dx both contain positive integers. if adding them produces a negative result, the overflow flag will be set.
Answers
True.
If adding two positive integers results in a negative number, it means that an overflow has occurred. The overflow flag is set when the result of an operation is too large to be represented with the given number of bits.
If bx and dx both contain positive integers and adding them produces a negative result, the overflow flag will be set. This is because when two positive integers are added, the result should also be a positive integer. If the result is negative, it means there was an overflow during the addition process, and the overflow flag will be set to indicate this issue.
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Elena is feeding her neighbor's dogs. Each dog gets 2/3
cup of dog food, and she uses 3 1/3 cups of food. How many dogs does her neighbor have?
5 5/8 cups of water fill 4 1/2 identical water bottles. How many cups fill each bottle?
Answers
Answer:
5 dogs
1 1/4 cups per bottle
Step-by-step explanation:
10/3 ÷ 2/3 get solved by 10/3 x 3/2, which gives you 30/6 or 5
45/8 ÷ 9/2 is 45/8 x 2/9 which is 5/4 or 1 1/4
find an expression which represents the difference when (-5x 7) is subtracted from (9x 5)in simplest terms.
Answers
-14x + 2 is the expression which represents the difference when (-5x + 7) is subtracted from (9x + 5) in simplest terms, as obtained by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now,
Given: Two expressions: (-5x + 7) and (9x + 5).
To find: Expression obtained when (-5x + 7) is subtracted from (9x + 5).
Finding:
By basic algebra, we can write:
=> ( -5x + 7) - (9x + 5) = ( -5x + 7) - 9x - 5
=> -5x - 9x + 7 - 5 = -14x + 2
Hence, -14x + 2 is the expression which represents the difference when (-5x + 7) is subtracted from (9x + 5) in simplest terms, as obtained by basic algebra.
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Evaluate x2 when x =5
Answers
Answer:
10
Step-by-step explanation:
If x=5 then
Plug in the x
(5)2 then multiply
(5)2=10
how do I solve
-3(1+6r)=14-r
Answers
Step by step: -3(1 + 6r) = 14 - r
Start by distributing the -3 into the parenthesis
-3 -18r = 14 -r
Now add 3 to each side to eliminate it from the left
-18r = 17 -r
Now add 1r on each side to eliminate it from the left
-17r = 17
Now divide -17 by both sides
R = -1
Answer: -1
Step-by-step explanation:
Multiply -3 to (1+6r)
-3 - 18r = 14 - r
Then, group like terms and change the signs
-18r + r = 14 + 3
Add
-17r = 17
Divide 17 by 17 to solve for r
r = 17/-17
r = -1
Guadalupe drove 45 miles in 1 1/3 hours. on average how fast did she drive per hour
Answers
Guadalupe drove at an average speed of 33.75 miles per hour.
To find the average speed, we need to divide the total distance by the total time:
Average speed = t d/t t
Guadalupe drove 45 miles in 1 1/3 hours, which is the same as 4/3 hours.
So, average speed = 45 miles / (4/3) hours
= 45 x 3/4
= 33.75 miles per hour (rounded to two decimal places)
Therefore, Guadalupe drove at an average speed of 33.75 miles per hour.
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Calculate the slope given the two points on a line: (7,8) and (10,17)
Answers
Answer:
gvvvvvbb
Step-by-step explanation:
gghhhhbbhhjhhhhh