The radius of the Sphere that submerged in the water is 178.9 mm.
Volume of the Cuboid:
Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space.
The general form of the Volume of the Cuboid is,
Volume of a cuboid = l × b × h [cubic units]
Where,
l = length
b = breadth
h = height
Given,
A water tank is a cuboid 45cm long, 30cm wide and 26cm high.
It contains water to a depth of 21cm.
A sphere is placed in the tank and is fully submerged. the water level rises by 1.8cm.
Here we need to find the radius of the Sphere and we have to use the Volume of the sphere as 4/3πr³.
First, we need to find the volume of the water,
For that, we have to take the measurement of it.
l = 45 cm
b = 30 cm
h = 21 cm
( here we have to find the volume of water, so we have take the water depth as its height)
Now, the volume of the water is,
V₁ = 45 x 30 x 21
V₁ = 28350 cm³
After placed the sphere on the tank the water level is increased as 1.8 cm,
So, the new height = 21 + 1.8 = 22.8
Now the new volume is,
V₂ = 45 x 30 x 22.8
V₂ = 30780 cm³
So, the Volume of the increased water level is,
=> 30780 - 28350
=> 2430 cm³
Now we have to consider this as the Volume of the Sphere and calculate the radius through it,
=> 4/3πr³ = 2430
=> r³ = 2430 x 3/4 x π
we know that the value of π = 22/7
So,
=> r³ = 2430 x 3/4 x 22/7
=> r³ = 5727.86
=> r = ∛5727.86
=> r = 17.89
Therefore, the radius of the sphere is 17.89 cm
Now we have to convert it into mm,
=> 1 cm = 10 mm
So,
=> 17.89 cm = 178.9 mm
Therefore, the radius of the sphere is 178.9 mm.
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two primary services of operating system
Answer:
Step-by-step explanation:
it provides services to both the user and the programs.
it provides program an environment to execute.
Answer:
manage the computer's resources, such as the central processing unit, memory, disk drives, and printersestablish a user interfaceexecute and provide services for applications software.Step-by-step explanation:1. √256
O 12
14.
016h
O 18
Answer:
16
Step-by-step explanation:
[tex]16^{2} =256[/tex]
Find the centroid of the region in the first quadrant bounded by the given curves. y = x4, x = y4
The given bounded region is the set
[tex]R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}[/tex]
assuming the curves are [tex]y=x^4[/tex] and [tex]x=y^4\implies y=x^{1/4}[/tex] (since [tex]x>0[/tex] in the first quadrant).
The coordinates of the centroid are [tex](\bar x, \bar y)[/tex] where [tex]\bar x[/tex] and [tex]\bar y[/tex] are the average values of [tex]x[/tex] and [tex]y[/tex], respectively, over the region [tex]R[/tex]. These are given by the ratios
[tex]\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}[/tex]
Compute the area of [tex]R[/tex].
[tex]\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35[/tex]
Integrate [tex]x[/tex] and [tex]y[/tex] over [tex]R[/tex].
[tex]\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}[/tex]
[tex]\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}[/tex]
Then the centroid's coordinates are
[tex]\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463[/tex]
[tex]\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}[/tex]
what is the approximate value of this square root? 162‾‾‾‾√ enter your answer, rounded to the nearest tenth, in the box.
Answer:
If what youre asking is √162, then the answer is 9√2
Step-by-step explanation:
Answer: 12.73
type it in your calculator if you can
Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure
of one of the angles formed is 72°, what are the measures of the other three angles? Explain
The other angle opposite the given 72° angle is also 72°. This is because vertical angles are congruent.
The other two opposite angles are 180-72 = 108° each
See the diagram below. Notice how all four angles add to 360 degrees. Any adjacent pair of angles add to a straight line of 180 degrees.
BELL RINGER # 6
If the function f is defined by f(x) = 3x + 4,
then 2 f(x) + 4 =
(A) 5x + 4
(B) 5x + 8
(C) 6x +4
(D) 6x+8
(E) 6x + 12
Answer:
(E) 6x+12
relations: A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of X × Y. The set of all primary elements of the ordered pairs is called a domain of R and the set of all second elements of the ordered pairs is called a range of R.
functions: A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.
f(x) = 3x + 4
2 * f(x) + 4 = (2 × f(x)) + 4
From above equation
= (2 × (3x + 4)) + 4
= (2 × 3x) + (2 × 4) + 4
= 6x + 8 + 4
= 6x + 12
Therefore, the value of 2f(x) + 4 is ′6x + 12′.
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what is 3(+4)=42 in algebra
Of all of the common assumptions that we discussed in class, I think one of the most common is the idea that a children’s text should in some way teach the reader something. We of course talked about the term didactic, and how a didactic book strongly pushes a lesson onto the reader, telling them that they should believe this or that. Many times a reason for that lesson isn’t even given, as though the young person reading the book should just accept that lesson because they are told to, because the other knows better. As I was reading Cat in the Hat by Dr. Seuss, the book I selected for the assignment, I was hoping that it wouldn’t be as didactic as most other children’s books, and that it would be as playful and exciting as I remember as a child. On the last two pages of the book, however, the absent mother returns home, the cat has disappeared, the children are behaving nicely, sitting in chairs, and it is pretty obvious that even though they got into mischief they are still good children after all. Nothing really has changed at the end of the book. Although all sorts of things got played with, and the children broke the rules I am sure they know about (like, “Don’t fly kites in the house”), major boundaries were never crossed.
We talked about how the opposite of a didactic book might be an ambiguous book, or a book that encourages the reader to think about issues, to make decisions for themselves. In that kind of book, the author usually wants to the reader to think for her or himself, to understand that some things are difficult, even for adults. The author may present a problem and ask you what you think, or might just never come around to saying exactly what you are supposed to believe. The last page of Cat in the Hat ends with the narrator saying, referring to the mother, “Should we tell her about it? / Now what SHOULD we do? / Well . . . / What would YOU do / If your mother asked you?” (61). In some ways, this is probably a pretty ambiguous ending. The author asks the reader that if your mother left, if someone wanted you to do what you weren’t supposed to, if you did it anyway, and if you didn’t get caught, then would you tell your mother or father what happened? Most adults wouldn’t tell what happened themselves, but the question is there anyway, and it seems to be really asking children what they believe.
But it doesn’t seem really that ambiguous. If the book were really ambiguous it would be breaking the Typical Case Prototype of children’s books, and in almost every other way the book keeps to those prototypes. As Nodelman describes it, children’s books are typically bright, colorful, funny, entertaining, and maybe sometimes rhyming. Children’s books portray children as the way adults typically think of them, as crazy kids who aren’t serious like adults, or innocent angels who would never really do any harm when they play. Dr. Suess portrays typical kids, bored by the rain, wanting to do something wild. Although Seuss’s style is strange, the children even look like the sort of standard white children that appear in most books, the girl in a dress and ribbon in her hair. We saw in class how these children are a lot like the standard one’s in Cassie’s history textbook And although strange things happen in the book – a talking cat, a couple of strange Things, a lot of things getting thrown around – it is the kind of play we come to expect in children’s lives, especially in the sorts of standard things shown on television and in movies.
In fact, the children never quite seem to trust the Cat, and they always just sort of watch him play. The children never really do anything that crazy themselves. The Fish, who sounds a lot like an adult, is always there to warn them, and in the end everything gets cleaned up. Of course the book is fun and playful, and is obviously one of the most famous and liked picture books ever made, but it is still pretty straightforward. Cat in the Hat reinforces and demonstrates almost all of the typical assumptions about childhood, and it fulfills all of the typical case prototypes of children’s books. Examining it made me think about how the book might have changed in recent years, especially since children are rarely bored when they are at home any more (with all of the stuff they own to play with). But more than that, it made me think about why we expect all children’s books to be like this, why it is always considered one of the best books for children. Although I like typical children’s books, it makes me also interested in books that don’t do what we expect. The book was written 1957, and in so many ways children’s books have become so incredibly different since then. But in a lot of other ways, some good, some bad, they haven’t changed at all.
-5/9 - (-7/27)
Can someone help
Answer:
[tex]\frac{-8}{27}[/tex]
Step-by-step explanation:
[tex]\frac{-5}{9}[/tex] - [tex]\frac{-7}{27}[/tex] Subtracting a negative is the same as adding a positive. So I would change the form to addition.
[tex]\frac{-5}{9}[/tex] + [tex]\frac{7}{27}[/tex] Now to add, we need a common denominator. Let's us 27
[tex]\frac{-5}{9}[/tex] = [tex]\frac{-15}{27}[/tex] We multiple the numerator and denominator (top and bottom) by 3 to make an equivalent fraction.
[tex]\frac{-15}{27}[/tex] + [tex]\frac{7}{27}[/tex] the bottom number stays the same and we add the top numbers
-15 + 7 = -8
[tex]\frac{-8}{27}[/tex]
Answer: -8/27
Step-by-step explanation:
[tex]\displaystyle\\-\frac{5}{9} -(-\frac{7}{27} )=\\\\-\frac{5*3}{9*3} +\frac{7}{27} =\\\\\frac{-15}{27}+\frac{7}{27}=\\\\ \frac{-15+7}{27}=\\\\ \frac{-8}{27} =\\\\-\frac{8}{27}[/tex]
Add. (x^2+1−4x^3+3x^4)+(−x^2−2x^4+x^3+4) Express the answer in standard form.
Answer:
x^4−3x^3+5
Step-by-step explanation:
Simplify the answer and convert it to standard form.
Answer: ANSWER
The simplified polynomial in standard form is
EXPLANATION
The given expression is
We group the terms with the same exponents,
We simplify to obtain,
Since the expression is a polynomial, writing it in standard form means writing the simplified form in descending powers of x.
Step-by-step explanation: gl
what value of x makes the equation 2(3 - 7x) = 4 - 6x true?
Linear equations are equations that has a leading degree of 1. The value of x that makes the equation true is 1/4
Solving linear equationsLinear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b
Given the expression below
2(3 - 7x) = 4 - 6x
Expand
6 - 14x = 4 - 6x
Collect the like terms
6 - 14x = 4 - 6x
-14x + 6x = 4 -6
-8x = -2
Divide both sides by -8
-8x/-8 = -2/-8
x = 1/4
Hence the value of x that makes the equation true is 1/4
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Let (-4,-4) be a point on the terminal side of theta in standard position. find exact values of the six trigonometric functions of theta
The six trigonometric functions of theta for the point (-4, -4) is
sin Θ = -1/√2
cos Θ = -1/√2
tan Θ = 1
cosec Θ = -√2
sec Θ = -√2
cot Θ = 1
Trigonometric Functions:
Trigonometric functions are defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle.
The six trigonometric functions are,
Sin Θ =Opposite/Hypotenuse
Cos Θ = Adjacent/Hypotenuse
Tan Θ = Opposite/Adjacent
Sec Θ = Hypotenuse/Adjacent
Cosec Θ = Hypotenuse/Opposite
cot Θ = Adjacent/Opposite
Given,
Let (-4,-4) be a point on the terminal side of theta in standard position.
Here we need to find the exact values of six trigonometric functions.
Here the give point (-4,-4) represents the values of (opposite, adjacent).
So, the opposite = -4
and adjacent = -4
Now we have to find the hypotenuse of the point,
For that, we have to use the Pythagoras theorem,
hypotenuse = √oppostie² + adjacent²
Therefore,
=> hypotenuse = √(-4)² + (-4)²
=> hypotenuse = √16 + 16
=> hypotenuse = √32
it can be written as,
=> hypotenuse = √2 x 16
=> hypotenuse = 4√2
Now the six trigonometric functions are based on the formula,
sin Θ = -4/4√2 => sin Θ = -1/√2
cos Θ = -4/4√2 => cos Θ = -1/√2
tan Θ = -4/-4 => tan Θ = 1
cosec Θ = 4√2/-4 => cosec Θ = -√2
sec Θ = 4√2/-4 => sec Θ = -√2
cot Θ = -4/-4 => cot Θ = 1
So, all the six trigonometric values are identified.
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25*371-371*16+371
can someone help me please?
Answer:
It would be 3710.
Step-by-step explanation:
Find the sum of 2.53 x 1019 and 3.197 x 1017. 2.56197 x 1019 3.2223 x 1019 2.56197 x 1036 3.2223 x 1036
17716.09385 is sum of multiplication .
What does multiply mean?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.= 2.53 x 1019 + 3.197 x 1017 + 2.56197 x 1019 + 3.2223 x 1019 + 2.56197 x 1036 + 3.2223 x 1036
= 2578.07 + 3251.349 + 2610.64743 + 3283.5237 + 2654.20092 + 3338.3028
= 17716.09385
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Answer:
180
Step-by-step explanation:
Because its true
answer this question
Answer: 166
We’ll give it your best mate keep it up
1
Which is equivalent to 64^1/4
There are a total of 463,100 books in a library. What is the value of the exponet when this number is written in scientific notation?
Answer: 4.631*10^5
Step-by-step explanation:
463,100=
400,000+63,100=
4*100,000+(63,100/100,000)*100,000=
4*10^5+(631/1000)*10^5=
4*10^5+0.631*10^5=
(4+0.631)*10^5=4.631*10^5
what is the net force on the object with a mass of 32kg and accelerating at 4.5m/s²
pls help me
Answer: 144N
Step-by-step explanation:
A=acceleration. N=net force. M=mass
A=N/M
4.5=N/32
4.5*32=N
N=144N
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Net Force acting on a body can be determined by formula :
[tex]\qquad \sf \dashrightarrow \: f = m \times a[/tex]
where,
f = force acting on the bodym = massa = Acceleration of the body due to net force exerted on it[tex]\qquad \sf \dashrightarrow \: f = 32 \times 4.5[/tex]
[tex]\qquad \sf \dashrightarrow \: f = 144 \: \: N[/tex]
So, the net force acting on the body is 144 Newtons.
Complete the proof.
If 7 + 5x + 9 = −3x, then x = −2.
Drag and drop the reasons to correctly complete each box.
Answer:
distributive property
subtraction
division property of equality
Write a function to describe the following scenario.
A taxi driver charges a flat rate of $7.25 plus
$0.65 per mile.
y = [?] + [?]x
Answer: Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.
Step-by-step explanation:
A Taxi driver charges a flat rate = 7.25 dollars
taxi fare for 1 mile = 0.65 dollars
Suppose we consider Total money taxi driver can spend = 10 dollars
Let taxi driver travel x miles
Total charges = flat rate charge + taxi fare for each mile(distance) travelled
Find the value y = [?] + [?]x
suppose these two question marks indicate z1,z2
replace with y=10 and z1=1.75 and z2=0.65 values
Then y = [z1] + [z2]x
10 = 1.75 + 0.65(x)
0.65(x) = 10 - 1.75
0.65(x)= 8.25
x = 8.25/0.65
x = 12.7 miles
If Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.
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3x - 5y = 13
y=x-3 please helo
find the difference 78,003-32,136
Answer:
=45867
Step-by-step explanation:
[tex]\frac{\begin{matrix}\:\:&\textbf{\:\:}&7&9&9&13\\ \:\:&\textbf{7}&\linethrough{8}&\linethrough{10}&\linethrough{10}&\linethrough{3}\\ -&\textbf{3}&2&1&3&6\end{matrix}}{\begin{matrix}\:\:&\textbf{4}&5&8&6&7\end{matrix}}[/tex]
Write 0.5 as a fraction. Do not try to simplify your answer.
Answer:
1/2
Step-by-step explanation:
0.5 is half of 1 so 1/2 is 0.5 as a fraction
Find the largest possible area for a rectangle with base on the x-axis and both upper vertices are on the curve y=11-x^2
The largest area of rectangle can be A= (11√11)/√2
What is area of rectangle?To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Area = l × w. l = length. w = width.
Given:
y=11-x²
Consider,
x is the length of the base
y is the vertices on the curve (width)
As, the area of a rectangle with its base on the x-axis.
So, base =2x
Then Area of rectangle
A = 2x(11-x²)
Foe maximum area, dA/dx=0
dA/dx = 22-4x²
22-4x² =0
22=4x²
11/2 = x²
x=√(11/2)
Now, Put x=√(11/2) in area
A= 2*√(11/2) ( 11-11/2)
A= √22(11/2)
A= (11√11)/√2
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A local hamburger shop sold a combined total of 380 hamburgers and cheeseburgers on Saturday. There were 70 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Saturday?
Answer:
310 hamburgers were sold on Saturday
Step-by-step explanation:
1x + 70 =380
-70 -70 Reverse
1x = 310
/1 /1 Divide
x =310
What is 4/7-(-3/8) ?
_____________________
Solution:
Exact Form:
[tex]\frac{4}{7}-(-\frac{3}{8}) = \frac{53}{56}[/tex]
______________________
(^Note^)
To subtract fractions, find the LCD (Least Common Denominator), then combine.
Hope this helps! If so, please lmk! Thanks and good luck!
Answer: 53/56
Step-by-step explanation:
sorry if im wrong but since there is 2 negative signs it is going to become positive. so..
4/7+3/8
then make the denominators the same (56)
then multiply the numerators by the number you multiplied for the denominator for the question.
answer: 32/56+21/56 = 53/56
help pls! example is not needed
Answer: 401
Step-by-step explanation:
-177 + 578 = 401
You are given two wind instruments of identical length. one is open at both ends, whereas the other is closed at one end. which is able to produce the lowest frequency?
The wind instrument with the closed end.
Why is it known as a node?
Node is the actual name in use. It was initially intended to be used as a web application, but the author changed the name to node after realizing it could be applied to a variety of situations.
Pipe standing wave resonances exhibit a number of intriguing characteristics. When sounding a resonance, the closed end of the pile must have a "node." An "anti-node" is required if a pipe's end is open.The lowest frequency resonance occurs in the case of a pipe that is closed at one end when there is just one node at the closed end and an anti-node at the other end. This sound has a wavelength that is four times as long as the pipe. This is referred to as a quarter-wave resonator.When a pipe is opened on both ends, the lowest frequency resonance has an anti-node at either end and a node in the center. A half-wave resonance is present here; The pipe is able to contain half of the wavelength. The frequency of this resonance will be twice that of the closed pipe if this pipe is the same length as the closed pipe.Learn more about node
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If you have the x and y components of a vector, which trigonometry function can you use to determine its angle relative to the x-axis?.
If we have the x and y components of a vector, the trigonometry function that can be used to determine its angle relative to the x-axis is cosine function.
For given question,
Let α be an angle between vector a and vector b.
The angles between two vectors is given by,
cos(α) = [tex]\frac{\vec a . \vec b}{|\vec a | | \vec b|}[/tex]
The x component of vector is usually denoted by [tex]\vec i[/tex]
Let vector be [tex]x\vec i + y\vec j[/tex]
Let [tex]\vec a=\vec i, ~ \vec b=x\vec i + y\vec j[/tex]
[tex]\vec a . \vec b=x[/tex]
[tex]|\vec a|=1[/tex]
[tex]|\vec b|=\sqrt{x^2+y^2}[/tex]
So, the angle between the vector and x-axis is [tex]cos^{-1}(\frac{x}{\sqrt{x^2+y^2} } )[/tex]
Therefore, if we have the x and y components of a vector, the trigonometry function that can be used to determine its angle relative to the x-axis is cosine function.
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What is the quotient -3 divided by 9 fractions
Answer:
well it would be [tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
Simply put [tex]-\frac{3}{9}[/tex]. The top and bottom are divisible by 3 so you simplify and you end up with negative one third.
Help me Help me Help me Help me Help me
ANSWER THE FOLLOWING QUESTIONS:
1. What are the missing numbers?
2. Does it show a pattern?
3. Describe the pattern.
Answer:
Week 1 =11
Week 2 = 9
Week 3 = 7
Week 4 = 5
Week = 3
11 + 9 + 7 + 5 + 3 = 35
Pattern: She is losing 2 less pounds each week. There is a pattern.
