Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker
Two workers finished a job in 7.5 days.
How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
let t = time required by one worker to complete the job alone
then
(t+8) = time required by the other worker (shirker)
let the completed job = 1
A typical shared work equation
7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1
multiply by t(t+8), cancel the denominators, and you have
7.5(t+8) + 7.5t = t(t+8)
7.5t + 60 + 7.5t = t^2 + 8t
15t + 60 = t^2 + 8t
form a quadratic equation on the right
0 = t^2 + 8t - 15t - 60
t^2 - 7t - 60 = 0
Factor easily to
(t-12) (t+5) = 0
the positive solution is all we want here
t = 12 days, the first guy working alone
then
the shirker would struggle thru the job in 20 days.
Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15
Step-by-step explanation:
Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x,
y'' - 6y' + 9y = 0
If y = C₁ exp(3x) + C₂ x exp(3x), then
y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))
y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))
Substituting these into the DE gives
(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))
… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))
… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))
= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))
… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))
… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)
= 0
so the provided solution does satisfy the DE.
Please help!!! Find the domain of the function y = 2 cot(5∕8x).
A) All real numbers except odd integer multiples of 8π∕5
B) All real numbers except 0 and integer multiples of 8π∕5
C) All real numbers except 0 and integer multiples of 4π∕5
D) All real numbers except odd integer multiples of 4π∕5
Answer:
B) All real numbers except 0 and integer multiples of 8π∕5
Step-by-step explanation:
Cotangent function:
The cotangent function is given by:
[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]
Domain:
All real values except those at which:
[tex]\sin{ax} = 0[/tex]
The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]
In this question:
[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.
How many tens are in 6 hundreds
Answer:
60
Step-by-step explanation:
10 x 6 = 60
Hope this helped! :)
What is the endpoint of a line segment if the midpoint M( – 3, 4) and the other endpoint is E(7, – 2)?
Answers
(– 13, 10)
(10, – 13)
(– 1, 2)
(2, – 1)
9514 1404 393
Answer:
(-13, 10)
Step-by-step explanation:
If M is the midpoint of segment DE, then ...
D = 2M -E
D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)
The other end point is (-13, 10).
please help, it’s urgent !!!
D
A
B
C
for more explanation please don't hesitate to just respond
Hi, help with question 18 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle y^2 = 1 + \sin x[/tex]
And we want to prove that:
[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]
Find the first derivative by taking the derivative of both sides with respect to x:
[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]
Divide both sides by 2y:
[tex]\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}[/tex]Find the second derivative using the quotient rule:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]
Combine fractions:
[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]
Cancel:
[tex]\displaystyle -\sin x + y^2 = 1[/tex]
Substitute:
[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]
Simplify. Hence:
[tex]1\stackrel{\checkmark}{=}1[/tex]
Q.E.D.
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew $60 from his bank account 3 times.
what is the change in mikes account balance after all 3 withdrawals?
a+b=60000
[tex]\frac{a}{b}=\frac{4}{1}[/tex]
a=?
b=?
Answer: a = 25.67
Step-by-step explanation:
use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.
minus sign ironically makes it go to the right
because the function crosses the y axis at -13
It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of transformation, we have to compare the two equations and look for changes.
In the equation y = x - 13, we subtract 13 from the value of x.
This means that the graph of y = x is shifted 13 units downwards,
since every point on the graph has 13 subtracted from its y-coordinate.
Hence, It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
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The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
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The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
The restricted domain for ƒ is ?
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
he ride a bike for 15 miles oer hour how many miles did he ride
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
What is the answer to this? Is it d?
Answer:
Step-by-step explanation:
yeah of course..your answer is true.. it's part d and there is no solution for that system...w and v both of them remove in solution of system and we don't have any unknown variable for solving.
9514 1404 393
Answer:
D. no solutions
Step-by-step explanation:
The first equation can be simplified to standard form:
0.5(8w +2v) = 3
4w +v = 3 . . . . . . . eliminate parentheses
__
The second equation can also be simplified to a comparable standard form:
8w = 2 -v +4w
4w +v = 2 . . . . . . add v -4w
__
Comparing these two equations, we find the variable expressions to be the same, but the constants to be different. If any set of variable values were to satisfy one of these equations, it could not satisfy the other equation. There are no solutions to the system.
The length of a rectangle is 4 meters and the width is 4 meters. What is the perimeter of the rectangle? Do not include units in your answer.
The area of rectangle is 105cm².If it length is 21 cm,what is its length and perimeter.
Answer:
length of other side is 5cm and the perimeter is 52
Step-by-step explanation:
The area is side x times side y.
Knowing that the area A is 105cm2 and side x is 21cm
A= x*y
105cm2= 21 y /21
Arranging for y we get
y= 105/21
y= 5 cm
The perimeter is all sides added up
P= 21+21+5+5=52cm
Answer:
length 5cm and perimeter 52 cm
Step-by-step explanation:
length=area/breadth
=105/21
=5 cm
perimeter=2(length+breadth)
=2(5+21)
=52 cm
what is the average speed for the interval t=1 hour to t=3 hours
Step-by-step explanation:
2 hours
3+1 / 2 = 4/2 = 2 hours speed average
Taree fourts of the 64 books were math books. determine the percent of the books that were math books.
Answer: 75% - these are books on mathematics.
Step-by-step explanation:
[tex]\dfrac{3}{4} \cdot 64 = 48\\[/tex]
64 - 100%
48 - x%
[tex]\dfrac{64}{100} =\dfrac{48}{x}\\\\x=\dfrac{48 \cdot 100}{64} \\\\x=75 \%[/tex]
Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express a simplified ratio
Answer:
5:12
Step-by-step explanation:
125:300 simplified = 5:12
I hope this helps
Counting numbers are to be formed using only the digits 1, 3, 7,5,4,8, and 2. Determine the number of different possibilities for two-digit numbers.
Answer:
11699 numbers and 42 two-digit numbers
Martinez' General Store is having a 45% off sale on men's clothing. John paid $70.95 for a jacket that was on sale. What was the original price of the jacket?
Answer:
$129
Step-by-step explanation:
We can use this equation:
x - 0.45x = 70.95
0.55x = 70.95
x = $129
So for this problem, I almost got it however my rounding is off causing my answers to be wrong. Can someone please help me with the two that are wrong. Thank you for your help!
Answer:
it 94x26.2 i think it right if not sorry :/
Step-by-step explanation:
PLEASE HELP ME PLEASE AND BE CORRECT
Answer:
12 cm²
Step-by-step explanation:
area = L *B
a = 6 * 2
a = 12cm²
A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy a rectangular pool that is 20' x 15' in 54 inches deep or a cylindrical pool that has a 3.3 m radios and is 1.8 m deep
Answer:
20'×15 in 54 inches
Step-by-step explanation:
The Best as a pool should be rectangular in shape and 54inches deep for safety of life's
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2}[/tex]h
The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;
= [tex]\pi r^{2}[/tex]h
[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]
The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;
V = 20 x 15 x 54
V = 16,200 cubic meter.
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
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Find the value of x in each case and give an explanation plzzz, thank youu :)
Answer:
Step-by-step explanation:
the arrows from the picture tells us that TV is parallel to RS
since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x
(alternate interior angles)
sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°
2x = 45*2 = 90°
Answer ASAP
Will give brainliest!
More information pleaseeeeeeee
which transformation of the red triangle on the graph maps it into the missing peice of the square?
A. a translation 16 units right
B. a reflection across the y-axis
C. a 90° counterclockwise rotation about the origin
D. a 90° clockwise rotation about the origin
E. a 180° rotation about the origin
Answer:
D
The missing piece (triangle) is facing right side up but the red triangle has its point facing left
TO get it facing up, turn it by 90 degrees clockwise
3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(X) is shown on the provided graph.
Graph the result of the following transformation on fx).
f(x)+6
