Answer:
She spent 17/30 of her money and still has 13/30 of her money
Step-by-step explanation:
The first step to solve is to find a common denominator. The common denominator of this problem is 30. So 1/6 turns into 5/30, and 2/5 becomes 12/30. Then you add them together to get 17/30. If you subtract 17 from 30 you will get your answers.
rationalize the denominator of the fraction (6)/(4+\sqrt(5))
The rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
The given expression is
[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]
By rationalizing the denominator of the fraction
[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]
Thus, the rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
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The formula for calculating percentage marckup is :
A. sticker price - invoice price/invoice price • 100 = percent markup
B. sticker price - invoice price/invoice price • 100 = markup
C. Invoice price - sticker price/sticker price • 100 = percent markup
D. Invoice price - sticker price/invoice price • 100 = percent markup
The formula for calculating the mark up percentage is as follows:
sticker price - invoice price/invoice price • 100 = percent mark up
How to find the percentage mark up?Percentage mark up can be described as follows:
percentage mark up = selling price per unit - cost price per unit / cost price per unit × 100
Therefore,
Mark up is the difference between a product's selling price and cost as a percentage of the cost.
Therefore, the formula for calculating the mark up percentage is as follows:
sticker price - invoice price/invoice price • 100 = percent mark up
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PLEASE HELP!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!! A triangle has a base length of 3ac2 and a height 5 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 5.
Answer:
the Area = 100in^2
Step-by-step explanation:
pls mark brainiest
Area of triangle is 10 square cm.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
Given
Base = 4
Height = 5
Area of triangle = [tex]\frac{1}{2}[/tex] × b × h
= [tex]\frac{1}{2}[/tex] × 4 × 5
= 2 × 5
= 10
Hence, area of triangle is 10 square cm.
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PLS PLS PLS HELP!!!
The perimeter of a square is given as 6c - 4(c-5) Which expression give the length of one side of the square?
A 2c + 20
B 1/2c + 20
C 1/2c+5
D 8c+20
Are the two expressions, 6c-4(c-5) and the answer you chose to the
question above equivalent?
Explain why or why not in 1 to 2 sentences.
Answer:
( we know that square of perimeter is 4L now,4L=6c-4(c-5),4L=6c-4c+20,4L=2c+20,then L=(c+10)/2
The side of a given square is c/2+5. Therefore, option C is the correct answer.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Given that, the perimeter of a square is 6c-4(c-5).
We know that, the perimeter of a square is 4a, where a is the side.
Now, 4a=6c-4(c-5)
4a=6c-4c+20
4a=2c+20
a=c/2+5
Therefore, option C is the correct answer.
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Which expression is equivalent to -1/2 (1/4 x - 3/8). SHOW WORK
A. -1/8x + 3/16
B. -1/8 x + 3/8
C. 1/8x - 3/16
D. 1/8x - 3/8
Answer:
A. -1/8 x + 3/16
Step-by-step explanation:
Distribute -1/2 over the parentheses
-1/2 ( 1/4 x - 3/8 )
-1/2 (1/4 x) - 1/2 (-3/8 )
multiply fractions to simplify
-1/8 x + 3/16
A is correct
Write 83.07718 correct to two decimal places
Answer:
83.08
Step-by-step explanation:
this means that they want only two numbers after the decimal point
if the number is up to five round it up and call it one the add it to the number before it
hope it helps
83.08 is the correct notation of 83.07718 to two decimal places.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To write a number correctly to two decimal places, you need to look at the third decimal place digit.
If this digit is 5 or greater than 5, you will need to round up the second decimal place digit by adding 1 to it.
If this digit is less than 5, you simply leave the second decimal place digit as it is.
In the case of 83.07718, the third decimal place digit is 7, which is greater than 5. Therefore, we need to round up the second decimal place digit (7) by adding 1 to it, resulting in 83.08. This is the number written correctly in two decimal places.
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Find the area of the shapes below. Make sure to label your answers with units.
Answer:
Step-by-step explanation:
Area of shapes a) Trianglebase = b = 7 km
altitude or height = h = 3.8 km
[tex]\sf \boxed{\text{\bf Area of triangle =$\dfrac{1}{2}b*h$ }}[/tex]
[tex]= \dfrac{1}{2}*7*3.8\\\\= 7 * 1.9\\\\= 13.3 \ km^2[/tex]
b) Rectangle:length = l = 8.2 cm
width = w = 7 cm
[tex]\sf \boxed{\text{\bf Area of rectangle = l*w}}[/tex]
= 8.2 * 7
= 57.4 cm²
c) Parallelogrambase = b = 9.1 km
height = h = 5 km
[tex]\sf \boxed{\text{\bf Area of parallellogram =b*h}}[/tex]
= 9.1 * 5
= 45.5 km²
d) TrapeziumParallel sides a = 8.9 m & b = 2.7 m
height = h = 4.2 m
[tex]\sf \boxed{\text{\bf Area of trapezium =$\dfrac{(a +b)*h}{2}$}}[/tex]
[tex]\sf =\dfrac{(8.9+2.7)*4.2}{2}\\\\=\dfrac{11.6*4.2}{2}\\\\= 5.8 * 4.2\\\\= 24.36 \ m^2[/tex]
Answer:
1# 13.3 Km
2# 57.4 Km
3# 45.5 Km
4# 24.36 Km
Question 1: 5 pts
Bill wants to plant roses in his triangular plot. There will be 1 plant at a corner. Each row will have 6
additional plants. He wants the plot to have as many lows as possible with 150 rose plants. How many
rows will Bill's plot have?
O 7 rows
O 8 rows
O 6 rows
O 5 rows
The arrangement of the rose plants on the triangular plot is such that they
form a series or progression that is defined.
The number of rows on Bill's plot is; 8 rows
The given parameters for the triangular plot are;
Number of plants at the corner = 1 plant
Number of additional plants per row = 6 plants
Number of rose plants = 150 rose plants
The number of rows in the plot.
The difference between successive rows, d = 6
The number rose at the top vertex, a = 1
Therefore, the rose in the garden forms an arithmetic progression
The first term, a = 1
The common difference, d = 6
The number of rows Bill's plot will have, n is given by the sum of n in terms of
an arithmetic progression, Sn, is given as follows;
[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]
When Sn = 150, we get;
[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
Taking only the positive solution for n, we have;
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]
[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]
The number of rows Bill's plot has, n ≈ 7.3965
Given that the 7th row is completed, an 8th row will be present on Bill's plot
The number of rows Bill's plot will have = 8 rows
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E Homework: 3.1 Homework
Evaluate the following function at the values 2, -3, and x-2.
f(x) = x² +5
f(2)= (Type an integer or a simplified fraction.)
Answer:
Question 13 of 16 Evaluate the following function at the values 2, -4, and x-1. f(x)=x2-5 = ..... f(2)= (Type an integer or a simplified fraction.) f(-4)=L(Type an integer or a simplified fraction.) f(x-1)= (Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)
State your conclusion in the form of a theorem, and then prove the theorem using a two-column proof. When you write the proof, refer to the diagram you created in part A. It will be helpful to use point labels to state what is given and what you have to prove and to use those labels throughout the proof.
As part of the proof, you’ll have to construct a line segment connecting the top intersection point on one of the transversals with the lowest intersection point of the other transversal, thus forming two triangles. Take a screenshot of the construction, save it, and insert the image in the space below before you begin your written proof.
The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.
How to illustrate the theorem?Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.
To find the midpoint, one can measure the distance between the two end points and divide the results by 2.
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What is the product of 4/15 and 3/8?
Hi there.
[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]
What we should do here is multiply the fractions. We know this information because it says in our problem - "the product".
.
If ever we come across the word "the product of" in any mathematics problems, we should know that the operation we should use is "multiplication".
.
.
This is how we multiply fractions:
.
First, we check: Is there any way we can reduce the fractions?
.
.
We cannot divide the top and bottom of these two fractions by the same number, but there is some reducing that can be done:
.
.
Notice that 4 and 8 have a common factor - 2.
.
Since 4 and 8 have a 2 in common, we divide 8 and 4 by 2:
.
[tex]\bf{\displaystyle\frac{4}{15} *\frac{3}{8}}[/tex]
.
[tex]\bf{\displaystyle\frac{1}{15} *\frac{3}{2}}[/tex]
.
.
Now, 15 and 3 also have a common factor - 3:
.
[tex]\bf{\displaystyle\frac{1}{5} *\frac{1}{2}}[/tex]
.
.
What we should do now is multiply 1 by 1 and 5 times 2:
.
[tex]\bf{\displaystyle\frac{1}{10}}[/tex]
.
I hope that this helps clear your doubts; if any are left, please ask.
.
I wish you a nice rest of your day.
.
[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\bf{n}\sf{g}\:\bf{A\:\sf{L}\bf{e}\sf{t}\bf{t}\sf{e}\bf{r}.[/tex]
--
[tex]\huge\textbf{What does \boxed{product} mean?}[/tex]
[tex]\bullet\large\text{ Product simply means multiplication/multiply}[/tex]
[tex]\huge\textbf{So, what are we doing in the equation?}[/tex]
[tex]\bullet\large\text{ We are multiplying! :)}[/tex]
[tex]\huge\textbf{What should our equation look like?}[/tex]
[tex]\rm{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]
[tex]\huge\textbf{What are the steps?}[/tex]
[tex]\mathsf{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]
[tex]\mathsf{= \dfrac{4\times 3}{15\times 8}}[/tex]
[tex]\mathsf{= \dfrac{12}{120}}[/tex]
[tex]\mathsf{= \dfrac{12\div2}{120\div2}}[/tex]
[tex]\mathsf{= \dfrac{6}{60}}[/tex]
[tex]\mathsf{= \dfrac{6\div3}{60\div3}}[/tex]
[tex]\mathsf{= \dfrac{2}{20}}[/tex]
[tex]\mathsf{= \dfrac{2\div2}{20\div2}}[/tex]
[tex]\mathsf{= \dfrac{1}{10}}[/tex]
[tex]\huge\textbf{What is your answer to the question?}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{1}{10}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The graph shown below expresses a radical function that can be written in the form f(x) = a(x + k)^1/n + c. What does the graph tell you about the value of a in this function?
Answer:
Graphs can be used to represent functions
The value of a is less than 0.
The function is given as:
The parent function of f(x) is:
So, by comparison:
The function becomes:
Next, we identify the vertex (in this case, the vertex is the minimum point on the graph)
So, we have:
Substitute these values in
So, the function becomes
From the graph, we have the following point;
So, the function becomes
Subtract 2 from both sides
Square both sides
Divide both sides by -9
So, we have:
-1 is less than 0.
Hence, the value of a is less than 0.
Step-by-step explanation:
Answer:
The value of a in this function is 0
Step-by-step explanation:
The given function is
[tex]f(x) = a(x + k)^\frac{1}{n} + c.[/tex]
Here , f(x) is y = [tex]x^{\frac{1}{2} }[/tex] So , n = 2.
By substituting the value we get the function :
[tex]f(x) = a(x + k)^\frac{1}{2} + c.[/tex]
The vertex of the graphs are : (k, c) = (-5 ,2)
The function becomes:
[tex]f(x) = a(x + 5)^\frac{1}{2} + 2[/tex]
The following point on the graph shows : (x, y) = (-4 , 5)
The function becomes:
[tex]5 = a(-4+ 5)^\frac{1}{2} + 2\\5 = a(-9)^\frac{1}{2} + 2\\\\\3 = a(-9)^{\frac{1}{2} }(Subtract 2 from both side )\\\\9 = a (-9) ( Square both sides) \\\\-1 =a ( Divide both side by -9)\\[/tex]
a = -1
Here , -1 is less than zero
Hence , the value of a is less than o.
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The sum of a number and 64 is no more than 36.
[tex]\text{Let the number be x,}\\\\~~~~~~~~x+64\leq 36\\\\\implies x \leq 36 - 64\\\\\implies x \leq -28[/tex]
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.
please help
The height and the base area of both the design must be equal. Then the correct option is A.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.
Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.
The figure shows both designs.
The volume of the cylinder will be given as
V = πr² h
If the volume of the oblique cylinder and right cylinder is the same.
Then the height of both the designs must be equal and the base area of both the design must be equal.
Then the correct option is A.
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Answer:
D
Step-by-step explanation:
did the test on edmentum
It takes 9 builders 54 days to complete a house.
How long would it take 6 builders to complete the same house?
Answer:
81 days
Step-by-step explanation:
Formula to solve this type of equation [tex]t=\frac{k}{p}[/tex]
t is time
k is a constant
p is people
We must substitute the values into the equation
[tex]54=\frac{k}{9}[/tex]
[tex]k=486[/tex]
Now we must substitute it to find the time
[tex]t=\frac{486}{6}[/tex]
you get 81
It would take [tex]6[/tex] builders [tex]36[/tex] days to complete the same house.
Who are builders?Builders are those person whose job is to build or repair houses and other buildings.
We have,
[tex]9[/tex] builders take [tex]54[/tex] days to complete a house.
So,
[tex]1[/tex] builder will take [tex](\frac{54}{9})[/tex] days to complete a house,
In the same way,
[tex]6[/tex] builder will take [tex](\frac{54}{9}*6)[/tex] days to complete a house,
i.e.
[tex]6[/tex] builder [tex]=(\frac{54}{9}*6)= 36[/tex] days.
Hence, we can say that it would take [tex]6[/tex] builders [tex]36[/tex] days to complete the same house.
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Two complementary angles are in the ratio 5 to 7 find the angles
Answer:
37.5°, 52.5°
Step-by-step explanation:
Let the two angles be 5x and 7x
Total ratio= 5+7 =12
5x = (5/12) ×90° ( sum of complementary angles = 90°)
= (5/2)×15°
75/2= 37.5°
Similarly
7x = (7/2)×15°
=105/2= 52.5°
Verification37.5°+52.5°=90° (sum of complementary angles= 90°)
Subtract (-2x4-4y3+4z3+6) - (-9x4-3y3+4z3+9)
Answer:
Step-by-step explanation:
-2x^4 - 4y^3 + 4z^3 + 6 + 9x^4 + 3y^3 - 4z^3 - 9
7x^4 - y^3 - 3
Answer:
28x-3y-3
Step-by-step explanation:
(-2x × 4 - 4v × 3 + 4z× 3 + 6) - (-9× × 4 - 3v× 3 + 4
Multiply the monomials
（-8×-4y×3+ 42×3+6)-（-9××4-3y×3+42×3+9
Multiply the monomials
(-8x-12y + 4z × 3 + 6) - (-9x× 4 - 3y × 3 + 4z × 3 + 9)
Multiply the monomials
(-8x - 12y + 12z +6) - (-9× × 4 - 3y × 3 + 4z × 3 + 9)
Multiply the monomials
(-8x-12y +12z +6) - (-36x -3y × 3+ 4z × 3 + 9)
Multiply the monomials
(-8x-12y + 12z + 6) - (-36x - 9y + 4z × 3 + 9)
8×-12y+122+6-（-36×-9y+122+9
Remove the parentheses for addition or
subtraction
-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9
-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9
Reorder and gather like terms
(-8x + 36x) + (-12y + 9y) + (12z - 12z) + (6 - 9) 3 steps
Collect coefficients of like terms
(-8+36) ××+ (-12 + 9) × y+ (12 - 12) × z+ (6 - 9)
which graph represents the linear function y=-5x+2?
Answer:
The second picture is the correct answer the graph must be decreasing..
Step-by-step explanation:
The second picture is the correct answer the graph must be decreasing..
pls help me out with this question
Height be h
[tex]\\ \rm\Rrightarrow tan\Theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\\ \rm\Rrightarrow tan54=\dfrac{h}{60}[/tex]
[tex]\\ \rm\Rrightarrow h=60tan54[/tex]
[tex]\\ \rm\Rrightarrow h=82.6\approx 83m[/tex]
Answer:
83 m (nearest metre)
Step-by-step explanation:
This can be modeled as a right triangle, where the base is 60 m and the height is the height of the building.
Alternate Interior Angles Theorem (Z-angles)
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Using the Alternate Interior Angles theorem, the angle between the ground and the dashed line (angle of elevation) is 54°.
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = 54°O = height of building (h)A = 60Substituting the given values into the formula and solving for h:
[tex]\implies \sf \tan(54^{\circ})=\dfrac{h}{60}[/tex]
[tex]\implies \sf h=60 \tan(54^{\circ})[/tex]
[tex]\implies \sf h=82.58291523...[/tex]
[tex]\implies \sf h=83\:\:m\:(nearest\:metre)[/tex]
how do you get 14 divided by 9 as a decimal
Answer:
14 divided by 9 = 1.5
The result of 14/9 is a non-terminating, repeating decimal.
Answer:
1.56 [?]
this question's wording was slightly confusing but I think this is what you meant
Step-by-step explanation:
by dividing the two numbers, (you can use long division or a calculator) while they are not in a fraction state (don't rewrite it as [tex]\frac{14}{9}[/tex], actually divide
14 by 9) you will end up with a number:
1.55555556
(repeating decimal)
So, you can either write this as 1.5 with a little dash over the 5
Or, you can round the decimal to 1.56 .
(method: by actual division)
A circle has four sections. Only three sections are labeled. The labels are 29.78% 24.73% and 19.49%. What is the missing section should be?
Answer:
26
Step-by-step explanation:
You would add the 3 numbers and then minus that from 100
5x+3
Write the fraction below as a sum or difference.
=?
4
(Simplify your answer. Use integers or fractions for any numbers in the
expression.)
To write this sum as a fraction, you can use the following formula: 5x/4 + 3/4.
How to transform a fraction into a sum?To transform a fraction into a sum we must perform the following procedure:
[tex]\frac{5x + 3}{4}[/tex] = [tex]\frac{5x}{4} + \frac{3}{4}[/tex]According to the above, all we have to do is divide the fraction using each digit of the numerator and put the same denominator.
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I need help with this is 8th grade math
Answer:
5 hours
Step-by-step explanation:
Mark recieves 3mg per hour. This can be rewritten as y=3x. Cassie recieves 2x+5. To solve, use substitiution. 3x=2x+5. To solve, subtract "2x" from "3x." You then get x=5.
solve
16x+8>=12x+20
A. x<=3
B. x<=7
C. x>=3
D. x>=7
Answer: C
Step-by-step explanation:
[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]
Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 14 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
Find answers to the questions in the attached file.
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A problem in a test given to small children asks them to match each of three pictures
of animals to the word identifying that animal. If a child assigns the three words at
random to the three pictures, find the probability distribution for Y , the number of
correct matches.
Answer:
3
Step-by-step explanation:
because there are only three pictures
how to graph
f(x) = x² + 5x + 2
Which of the following is equal to 5 1/3?
Is the integer below prime or composite?
26
Agnes who loves adventure tries to jump towards Gru who is sitting motionless on a raft with negligible mass. He tries to catch the 30 kg Agnes who is running 1.2 m/s towards him. As he caught Agnes, the motionless raft started to move. How heavy is Gru if the raft started to move with a speed of 0.5 m/s? (Note: Include correct units and sign. Ex. "20 kg*m/s" , "20 N*s" , "20 kg")
By conservation of momentum, we will see that the mass of Gru is 32 kilograms.
How heavy is Gru?
Here we need to use the conservation of momentum.
Initially, Gru is stop, and Agnes with a mass of 30kg has a velocity of 1.2 m/s, so the total initial momentum is:
P = 30kg*1.2m/s = 36 kg*m/s.
At the end, the total mass is M, the mass of Gru, plus the mass of Agnes:
(M + 30kg).
And the final speed is 0.5 m/s, then the final momentum is:
P' = (M + 30kg)*0.5m/s
And the final momentum must be equal to the initial momentum:
36 kg*m/s = (M + 30kg)*0.5m/s
Now we can solve that for M:
( 36 kg*m/s)/(0.5 m/s) = M + 30kg
72kg = M + 30kg
72kg - 30kg = 32 kg = M
The mass of Gru is 32 kilograms.
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