Which angle is coterminal to StartFraction 3 pi Over 4 EndFraction radians? Negative StartFraction 5 pi Over 4 EndFraction radians Negative StartFraction 3 pi Over 4 EndFraction radians StartFraction 5 pi Over 4 EndFraction radians StartFraction 7 pi over 4 EndFraction radians
Answers
Answer:
The co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] is [tex]-\frac{5\pi}{4}\ \text{radians}[/tex].
Step-by-step explanation:
The angle provided is, [tex]\frac{3\pi}{4}\ \text{radians}[/tex].
Convert the angle into degrees as follows:
[tex]\frac{3\pi}{4}\ \text{radians}=\frac{3\times180^{o}}{4}=135^{o}[/tex]
Co-terminal angles are those angles that share the same terminal and initial sides.
To find the co-terminal angle of a provided angle, we just need to add or subtract 360° or 2π to it.
Determine the co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] as follows:
[tex]\text{Co-terminal Angle}=\frac{3\pi}{4}+2\pi[/tex]
[tex]=\frac{3\pi+8\pi}{4}\\\\=\frac{11\pi}{4}[/tex]
[tex]\text{Co-terminal Angle}=\frac{3\pi}{4}-2\pi[/tex]
[tex]=\frac{3\pi-8\pi}{4}\\\\=-\frac{5\pi}{4}[/tex]
Thus, the co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] is [tex]-\frac{5\pi}{4}\ \text{radians}[/tex].
Answer:
Its A
Step-by-step explanation:
edge
Related Questions
What is the equation for the line of symmetry in this figure?
Answers
Answer:
y=3
Step-by-step explanation:
The size of a television screen is given as 95 cm, correct to the nearest 5 cm.
Write down the upper bound of the size of the television screen.
Answers
Answer:
The upper bound is 97.5 cm
Step-by-step explanation:
The upper bound is given as the value that is larger than or equal to all values in a data set, for example, in the data set, {3, 6, 16, 23, 25}, an upper bound is 25, however, where the accuracy of the data is given, the upper bound can be found by the following relation
Where the number is given to the nearest 100, add and subtract half of hundred to obtain the upper bound and lower bound respectively
For the question, given that the size of the television is given as 95 cm, correct to the nearest 5 cm, we add add half of 5 cm to get the upper bound as follows;
Upper bound = 95 cm + 5/2 cm = 97.5 cm
The upper bound = 97.5 cm.
Find all complex numbers $z$ such that $z^4 = -4.$
Note: All solutions should be expressed in the form $a+bi$, where $a$ and $b$ are real numbers.
Answers
Converting -4 to polar form gives [tex]-4=4\exp(i\pi)[/tex].
Then the 4th roots of -4 would be the numbers
[tex]4^{1/4}\exp\left(i\dfrac{\pi+2k\pi}4\right)[/tex]
where k is taken from {0, 1, 2, 3}.
So we have
[tex]z_1=4^{1/4}\exp\left(\dfrac{i\pi}4\right)=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)=1+i[/tex]
[tex]z_2=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4\right)=-1+i[/tex]
[tex]z_3=\sqrt2\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=-1-i[/tex]
[tex]z_4=\sqrt2\left(\cos\dfrac{7\pi}4+i\sin\dfrac{7\pi}4\right)=1-i[/tex]
How do I solve this question 5x - [7 - (2x - 1)] = 3(x - 5) + 4(x + 3)
Answers
Answer:
x = 6/4, or x = 3/2, OR x = 1 1/2
Step-by-step explanation:
5x - [7 - (2x-1)] = 3(x-5) + 4(x+3)
Pick one side to work on first, I will chose the right side,
Distribute on the right side.
5x - [7 - (2x-1)] = 3x - 15 + 4x + 3
Now, add like terms on the right side.
5x - [7 - (2x-1)] = 7x - 12
Now, to isolate 7 - (2x -1), subtract 5x from both sides.
so now,
-7 - (2x-1) = 2x - 12
Now, we can add 7 to both sides of the equation to isolate -(2x-1)
we add instead of subtract because the seven is a negative.
-(2x-1) = 2x - 5
Now, there is still a negative sign in front of the (2x-1), so we distribute the - to the equation.
-2x + 1 = 2x - 5
Now, we can isolate the variable and numbers bu adding five to both sides, and adding 2 to both sides. This is to make the equation easier by removing any negative terms.
6 = 4x
Divide both sides by 4
x = 6/4, or x = 3/2, OR x = 1 1/2
Simplify the following: a) [ -6 +22 – 6 + 8 ] ÷ ( -9 ) b) 400 ÷ { 40 – (-2) -3 – ( -1)} c) 40 x -23 + 40 x -17 d) 1673 x 99 – (-1673) e) 490 x 98
Answers
Step-by-step explanation:
a) [ -6 +22 – 6 + 8 ] ÷ ( -9 )[ -6 +22 – 6 + 8 ] = 18
18 ÷ (-9) = -2
b) 400 ÷ { 40 – (-2) -3 – ( -1)}{40 – (-2) -3 – ( -1)} = { 40 + 2 -3 + 1} = 40
400 ÷ 40 = 10
c) 40 x -23 + 40 x -17(40 x 23) + (40 x -17)
920 + (-680)
= 240
d) 1673 x 99 – (-1673)(1673 x 99) + 1673
1673 x 100
= 167300
e) 490 x 98 = 48020Hope this helps ^-^
Select the equivalent expression.
(x^-3*y^3)^-7=?
Choose 1 answer:
Answers
Answer:
The equivalent expression for this equation is x²¹ × y⁻²¹
Step-by-step explanation:
When you are multiplying exponents that are in parentheses, you multiply the exponential numbers together. So, for this problem, we will multiply the exponents together so we can get our final equivalent expression.
(x⁻³ × y³)⁻⁷
So, we will multiply -3 by -7 and we will also multiply 3 by -7 because those are our exponential numbers.
x²¹ × y⁻²¹
So, this is the final expression that is equivalent to our equation.
The expression (x⁻³.y³)⁻⁷ is equivalent to x ²¹ . y ⁻²¹.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given expression is,
(x⁻³.y³)⁻⁷
To find the solution for the expression,
Simplify the power terms,
x⁽⁻³ˣ⁻⁷⁾ . y ³ˣ⁻⁷
x ²¹ . y ⁻²¹
The simplified form of the expression (x⁻³.y³)⁻⁷ is x ²¹ . y ⁻²¹.
Hence, option (A) is correct.
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Consider an election with 681 votes a) If there are 5 candidates, what is the smallest number of first-place votes a candidate could win with under the Plurality method?
Answers
Answer:
137 votes
Step-by-step explanation:
considering an election with 681 votes and 5 candidates up for the election
dividing the votes among'st 5 candidates
= 681 / 5 = 136.2 hence the least number of first-place votes needed by a candidate using the plurality method would be = 137 votes
136.2 + 136.2 + 136.2 + 136.2 + 136.2 = 681 ( dividing the votes equally )
136 + 136 + 136 + 136+136 = 680
hence the remaining vote = 681 - 680 = 1
least first-place vote = 136 + 1 = 137 votes
how to do this question plz answer me step by step plzz plz
Answers
Answer:
2 Pi
Step-by-step explanation:
Notice that the shape is made of:
● 1 square with a side of 1 meter length
● 4 half-circles wich means 2 cicles with a diameter lf 1 meter.
■■■■■■■■■■■■■■■■■■■■■■■■■■
The square is inside so it isn't necessary to calculate the perimeter.
The perimeter of a circle is:
P' = d × Pi
We have 4 half-squares wich means two circles
So the total perimeter is:
● P = 2×P'
● P = 2 × d × Pi
● P = 2 × 1 × Pi
● P = 2Pi
A triangle has one side that lies along the line y=1/4x and another that lies along the line y=-1/4x. Which of the following points could be a vertex of the triangle?
Answers
Answer:
We know that our triangle has one side along the line:
y = (1/4)*x
And other side along the line:
y = -(1/4)*x.
Now, we want to find the vertex.
And we know that the vertex is the point where the two sides conect, so the vertex must be a common point of both lines.
Then we have:
y = (1/4)*x = -(1/4)*x
x = -x
The only solution to that equation is x = 0.
now we evaluate our lines in x = 0 and get:
y = (1/4)*0 = 0
y = -(1/4)*0 = 0
Then the lines intersect in the point (0, 0)
Then the vertex must be in the point (0, 0)
the cylindrical part of an architectural column has a height of 305 cm and a diameter of 30 cm find the volume of the cylindrical part of the column.use 3.14 for pi and round youre answer to the nearest cubic centimete if needed.
Answers
Answer:
215483 cm³
Step-by-step explanation:
Formula for volume of a cylinder = πr² · h
radius = 1/2diameter
1. Set up the equation
(3.14)(15²)(305)
2. Solve
215482.5
rounded to the nearest cubic centimeter = 215483 cm³
Answer:
215483 cm³
Step-by-step explanation:
credit goes to person up top
Look at the figure below: Triangles ABC and BDC have a common base BC. E is the point of intersection of BD and AC. AE = EC and ED = BE Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? HELPPPPP MEEEEEE WILL GIVE BRAIN POINTS
Answers
Answer:
AEB and CED
Step-by-step explanation:
Given the two pairs of congruent sides, you now use the vertical angles as the pair of congruent included angles, <AEB and <DEC.
The congruent triangles are:
AEB and CED
Answer:
B- Triangle AEB and triangle CED
Step-by-step explanation:
I took the test and it was correct
55.5% repeating as a decimal
Answers
Answer:
0.555
Step-by-step explanation:
When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.
First, we will tell you why it is useful to know 55.5 as a decimal.
Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.
Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.
55.5 percent means 55.5 per hundred. Therefore, to get 55.5 as a decimal, all you have to do is divide 55.5 by 100 like so:
55.5 ÷ 100 = 0.555
The solution is, as a decimal of 55.5% is, 0.555
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.
First, we will tell you why it is useful to know 55.5 as a decimal.
Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.
Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.
55.5 percent means 55.5 per hundred. Therefore, to get 55.5 as a decimal, all you have to do is divide 55.5 by 100 like so:
55.5 ÷ 100 = 0.555
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What is the perimeter (in centimeters) of a rectangle with length 4.5 cm and width 8.2 cm
Answers
Answer:
25.4 cm
Step-by-step explanation:
will make it simple and short
2*b + 2*h
2*4.5 + 2*8.2 = 25.4 cm
Hey there! I'm happy to help!
The perimeter is the distance around the rectangle.
In a rectangle, there are two pairs of opposite sides, and those opposite sides are equal. They are known as the length and the width.
In a rectangle, you have two sides that have the same length and two that have the same width. If you add these all up, you get the perimeter.
If our length is L and our width is W, we can write this equation.
P=2L+2W
So, we can plug in our lengths and widths to find the perimeter!
P=2(4.5)+2(8.2)
P=9+16.4
P=25.4
Therefore, our perimeter is 25.4 cm.
Have a wonderful day! Feel free to message me if you have any questions! :D
Find the approximate volume of this prism (Image down below)
Answers
Answer:
about 62m^3
Step-by-step explanation:
Musah stands at the center of a rectangular field.He takes 50 steps north,then 25 steps West and finally 50 on a bearing of 315°. Sketch Musah's movement How far west is Musah's final point from the center? How far north is Musah's final point from the center?
Answers
Answer:
The distance of Musah's final point from the center in the west direction is 60.355 steps
The distance of Musah's final point from the center in the north direction is 85.355 steps
Step-by-step explanation:
Given that :
Musah stands at the center of a rectangular field.
He takes 50 steps north, then 25 steps West and finally 50 on a bearing of 315°.
The sketch for Musah's movement is seen in the attached file below.
How far west is Musah's final point from the centre?
In order to determine how far west is Musah's,
Let d be the distance of how far west;
Then d = BC + CD cos θ
In the North West direction,
cos θ = cos 45°
d = 25 + 50( cos 45°)
d = 25 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex] )
d = 25 + 50( 0.7071)
d =25 + 35.355
d = 60.355 steps
How far north is Musah's final point from the center?
Let d₁ be the distance of how far North;
Then d₁ = AB + CD sin θ
d₁ = 50 + 50 sin 45°
d₁ = 50 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex] )
d₁ = 50 + 50( 0.7071)
d₁ = 50 + 35.355
d₁ = 85.355 steps
select all options that represents the side lengths of a 30 60 90 triangle.
Answers
Answer:
Options (B) and (D)
Step-by-step explanation:
If a triangle is a 30° - 60° - 90° triangle, measure of the angle between the leg and hypotenuse will be either 60° or 90°.
Therefore, by applying Cosine rule in the given options.
c² = a² + b² - 2abCosC
All the given options are the right triangles.
[Since they follow the Pythagoras theorem]
Option (A),
Angle between the sides having measures 3 and 5 units,
4² = 3² + 5² - 2(3)(5)CosC
16 = 9 + 25 - 30.CosC
30.CosC = 18
[tex]C=\text{Cos}^{-1}(\frac{5}{6} )[/tex]
C = 33.56°
Therefore, this triangle is not a 30-60-90 triangle.
Option (B),
Angle between the sides measuring 5 and 10 units,
[tex](5\sqrt{3})^2=5^2+10^2-2(5)(10)\text{CosC}[/tex]
75 = 125 - 100(CosC)
Cos(C) = 0.5
C = 60°
Therefore, other angles of the triangle will be 30° and 90°.
And it's a 30°-60°-90° triangle.
Option (C),
10, 10, 10√2
It's a right triangle and the measure of legs are equal.
Since legs of this sides are equal, angles opposite to these equal sides will be equal.
Sum of all interior angles = 180°
m∠A + m∠B + m∠C = 180°
If m∠B = 90°
m∠A + 90° + m∠C = 180°
2(m∠A) = 90°
m∠A = 45°
Therefore, the given sides make a 45°- 45°- 90° triangle.
Option (D).
Angle between the sides 3 and 6,
(3√3)² = 3² + 6² -2(3)(6)CosC
27 = 9 + 36 - 36.(CosC)
CosC = [tex]\frac{18}{36}[/tex]
C = [tex]\text{Cos}^{-1}(\frac{1}{2})[/tex]
C = 60°
Therefore,
These sides make a 30°- 60°- 90° triangle.
Options (B) and (D) are the 30°- 60°- 90° triangle.
3. A ship sails 35 km on a bearing of 042º.
a) How far north has it travelled?
b) How far east has it travelled?
4 A ship sails 200 km on a bearing of 243.7°
a) How far south has it travelled?
b) How far west has it travelled?
3 and 4 please
Answers
Answer:
3(a). The ship travelled in north is 26.0 km.
(b). The ship travelled in east is 23.4 km.
4(a). The ship travelled in south is -88.61 km.
(b). The ship travelled in west is -179.29 km.
Step-by-step explanation:
Given that,
(3). Distance = 35 km
Angle = 42°
Let distance in north is y km.
We need to calculate the distance
Using vertical component
[tex]y = d\cos\theta[/tex]
Put the value into the formula
[tex]y = 35\cos42[/tex]
[tex]y=26.0\ km[/tex]
Let distance in east is x km
We need to calculate the distance
Using horizontal component
[tex]x =d\sin\theta[/tex]
Put the value into the formula
[tex]x = 35\sin42[/tex]
[tex]x=23.4\ km[/tex]
(4). A ship sails 200 km on a bearing of 243.7°
Let distance in south is y km.
We need to calculate the distance
Using vertical component
[tex]y = d\cos\theta[/tex]
Put the value into the formula
[tex]y = 200\cos243.7[/tex]
[tex]y=-88.61\ km[/tex]
Let distance in west is x km
We need to calculate the distance
Using horizontal component
[tex]x =d\sin\theta[/tex]
Put the value into the formula
[tex]x = 200\sin243.7[/tex]
[tex]x=-179.29\ km[/tex]
Hence, 3(a). The ship travelled in north is 26.0 km.
(b). The ship travelled in east is 23.4 km.
4(a). The ship travelled in south is -88.61 km.
(b). The ship travelled in west is -179.29 km.
An isosceles triangle has a side that measures 12 inches. What is the length of the hypotenuse
Answers
Answer:
[tex] \boxed{12 \sqrt{2} }[/tex]
Step-by-step explanation:
Isosceles triangle are those triangle which have two equal sides.
Perpendicular ( p ) = 12 inches
Base ( b ) = 12 inches
Hypotenuse ( h ) = ?
Now,Using Pythagoras theorem,
[tex] \mathsf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Plug the values
[tex] \mathsf{ {h}^{2} = {12}^{2} + {12}^{2} }[/tex]
Evaluate the power
[tex] \mathsf{ {h}^{2} = 144 + 144}[/tex]
Calculate the sum
[tex] \mathsf{ {h}^{2} = 288}[/tex]
Squaring on both sides
[tex] \mathsf{h = 12 \sqrt{2} }[/tex]
Hope I helped!
Best regards!
A candy store sells only one type of candy, which comes in different colors. Each color is a different flavor, and some flavors cost more than others. Specifically, 1 red piece costs the same as 3 blue pieces, 2 orange pieces cost the same as 5 green pieces, and 2 blue pieces cost the same as 10 green pieces. If 1 orange piece costs 13 cents, how much will 8 red pieces cost?
Answers
Answer:
$6.24
Step-by-step explanation:
1 orange=%0.13
2 orange=5 green=$0.26
10 green=2 blue= $0.52
.52+.26=.78
1 red=3 blue=$0.78
0.78*8=6.24
Which graph has a slope of 4/5?
Answers
Answer:
[tex]\boxed{ Graph. B}[/tex]
Step-by-step explanation:
Hey there!
Well slope is aka rise/run,
so starting at the red dot and rising 4 units an ruing to the right 5 units,
graph b is the correct answer.
Hope this helps :)
Graph B has a slope of 4/5.
How is a slope calculated?Slope is calculated with the aid of finding the ratio of the "vertical change" to the "horizontal alternate" among (any) distinct factors on a line.
What is a slope in a straight line?Typically, the slope of a line offers the measure of its steepness and path. The slope of an instant line among two factors says (x1,y1) and (x2,y2) may be without problems decided by finding the difference between the coordinates of the points. The slope is commonly represented by using the letter 'm'.
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What is the y-intercept of the line that passes through the points (2, 5) and (3, 6)?
Answers
Answer:
(0, 3)
Step-by-step explanation:
First, find the slope using rise/run (y2 - y1) / (x2 - x1)
Plug in the points:
(6 - 5) / (3 - 2)
1/1 = 1
Now, we can plug in the slope and a point into the equation y = mx + b to find b (y-intercept)
y = 1x + b
5 = (1)(2) + b
5 = 2 + b
3 = b
= (0, 3)
A random number generator chooses 2 numbers between 1 and 5. This table demonstrates all possible outcomes. 1 2 3 4 5 1, 1 1, 2 1, 3 1, 4 1, 5 2 2, 1 2, 2 2, 3 2, 4 2, 5 3 3, 1 3, 2 3, 3 3, 4 3, 5 4 4, 1 4, 2 4, 3 4, 4 4, 5 5 5, 1 5, 2 5, 3 5, 4 5, 5 What is the probability that the computer will pick two 5s?
Answers
Answer as a fraction = 1/25
Answer in decimal form = 0.04
Answer in percent form = 4%
Explanation:
There are 5*5 = 25 different outcomes, of which only one outcome has 5,5. The probability of picking two 5s is 1/25 = 0.04 = 4%
Answer:
4%
Step-by-step explanation:
Compare the functions shown below: f(x) cosine graph with points at 0, negative 1 and pi over 2, 1 and pi, 3 and 3 pi over 2, 1 and 2 pi, negative 1 g(x) x y −6 −11 −5 −6 −4 −3 −3 −2 −2 −3 −1 −6 0 −11 h(x) = 2 cos x + 1 Which function has the greatest maximum y-value?
Answers
Answer:
f(x) and h(x) have the same maximum value: 3
Step-by-step explanation:
The maximum value of f(x) is 3 at (π, 3).
The maximum value of g(x) is -2 at (-3, -2).
The maximum value of h(x) is 3 at (0, 3).
Both f(x) and h(x) have the same (greatest) maximum value.
___H2 + ___Br2 → ___HBr
Answers
Answer:
H2+Br2 HBrH2+Br2. 2HBrwhat is the equation, in factored form, of the quadratic functions shown in the graph?
Answers
Answer:
(x+3)(x-2)
Step-by-step explanation:
We can immediately see that there are roots at x = -3, and x = 2.
Because the website gives us that this in the form of (x + _) (x - _), our anwser is (x+3)(x-2)
oops I just saw your comment. Too late i guess...
Answer:
f(x)=1(x+3)(x-2)
Step-by-step explanation:
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answers
Answer:
3x^2
Step-by-step explanation:
Given:
(3x) * {(1/x)^-4 }* (x^-3)
=(3x) * {1 ÷ (1/x)^4} * {1/x^3}
=(3x) * {1(x/1)^4} * (1/x^3)
=(3x) * (x^4) * (1/x^3)
=(3x) (x^4) (1) / x^3
Multiply the denominators
=3x^5 / x^3
Can also be written as
=3*x*x*x*x*x / x*x*x
Divide the x
= 3*x*x / 1
=3x^2
what is an equivalent expression for 3a + 5 ?
Answers
Answer:
Equivalent expression:
6a + 10
or
9a + 15
21 22 23 24 25 Won has a container with the shape below. A rectangular prism with length of 18 centimeters, width of 10 centimeters, and height of 12 centimeters. A rectangular pyramid has a base of 18 centimeters by 10 centimeters and height of 10 centimeters. Which statements are true about the container? Select three options. The shape can be broken into a rectangular prism and a triangular prism. The shape can be broken into a rectangular prism and a rectangular pyramid. The formula for the volume of this figure is V = B h + one-third B h. The volume of the container is 2,760 centimeters cubed. The volume of the container is 3,060 centimeters cubed.
Answers
Answer:
2nd statement
3rd statement
4th statement
Step-by-step explanation:
The 2nd statement we know is true since the container was already described with a rectangular pyramid and a rectangular prism.
The 3rd statement is true since the volume for a rectangular prism is,
V=wlh or V=bh (b=wl)
The volume of a rectangular pyramid is
V=1/3*wlh or V= 1/3*bh (b=wl)
The 4th statement is true since the formula for the volume of this container is V=wlh+wlh/3. So substitute the values of the rectangular prism and rectangular pyramid and,
V=10*18*12+(18*10*10)/3
V=2160+1800/3
V=2160+600
V=2760
how many are 4 raised to 5 ???
Answers
Answer:
Step-by-step explanation:
4^5 is equivalent to 4^2*4*3, which, in turn, is equivalent to:
16*64 = 1024.
Also:
8*128 = 1024, and
4*256 = 1024, and so on.
Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself?
Answers
Answer:
Clarissa will take 10 hours by herself
Step-by-step explanation:
Let s = time for shawna
s-5 = time for clarissa
The formula for determining the time is
1/a + 1/b = 1/c where a and b are the times alone and c is the time together
1/s + 1/(s-5) = 1/6
Multiply each side by 6s(s-5) to clear the fractions
6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)
Distribute
6(s-5) + 6s = s(s-5)
Distribute
6s -30 +6s = s^2 -5s
Combine like terms
12s -30 = s^2 -5s
Move everything to the right
0 = s^2 -5s -12s +30
0 = s^2 -17s +30
Factor
0 = ( s-15) (s-2)
Using the zero product property
s-15 =0 s-2 =0
s =15 s=2 ( This is not a reasonable answer since it is less than the time together)
s=15
s-5 = 10
Clarissa will take 10 hours by herself
