write the equation for these cones in spherical coordinates. (a) z = 3x2 3y2 = correct: your answer is correct. (b) z = − x2 3 y2 3
Answers
The correct equations for the given cones in spherical coordinates, after simplification, are as follows: (a) \($r = \sqrt{3} \cdot \tan(\phi)$\), (b) r = \($r = \sqrt{-3} \cdot \tan(\phi)$\)
What is mean by Spherical coordinates ?Spherical coordinates are a system of three-dimensional coordinates used to locate points in space. In this system, a point is described by its distance from a fixed point called the origin, its polar angle (also known as inclination or zenith angle), and its azimuth angle (also known as longitude or azimuthal angle).
(a) Given equation:\(z = 3x^2 + 3y^2\)
In spherical coordinates, we have:
x = r * sin(φ) * cos(θ)
y = r * sin(φ) * sin(θ)
z = r * cos(φ)
Substitute the spherical coordinate expressions for x, y, and z into the given equation:
\($r \cdot \cos(\phi) = 3 \cdot (r \cdot \sin(\phi) \cdot \cos(\theta))^2 + 3 \cdot (r \cdot \sin(\phi) \cdot \sin(\theta))^2$\)
Simplify the equation:
\($r \cdot \cos(\phi) = 3 \cdot r^2 \cdot \sin^2(\phi) \cdot (\cos^2(\theta) + \sin^2(\theta))$\\\)
\($r \cdot \cos(\phi) = 3 \cdot r^2 \cdot \sin^2(\phi)$\)
Divide both sides by r * cos(φ) to isolate r:
\($r = \sqrt{3} \cdot \tan(\phi)$\)
(b) Given equation: \(z = -x^2/3 - y^2/3\)
Substitute the spherical coordinate expressions for x, y, and z into the given equation:
\($r \cdot \cos(\phi) = -\frac{(r \cdot \sin(\phi) \cdot \cos(\theta))^2}{3} - \frac{(r \cdot \sin(\phi) \cdot \sin(\theta))^2}{3}$\)
Simplify the equation:
Divide both sides by r * cos(φ) to isolate r:
\($r = \sqrt{-3} \cdot \tan(\phi)$\)
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Correct Question: What is the equation of the cone in spherical coordinates if (a. ) z = 3x^2 + 3y^2 and (b.) z = -x^2/3 - y^2/3?
Related Questions
Solve the expression and find the value of x.
\( \frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 \)
Answers
\(\large\underline{\sf{Solution-}}\)
\(\sf \dfrac{x + 1}{10} - \dfrac{3(x - 1)}{5} = 2\)
\(\sf\longmapsto \dfrac{x + 1}{10} - \dfrac{3x - 3}{5} = 2\)
\(\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10} = 2\)
\(\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10} = 2\)
\(\sf\longmapsto \dfrac{x + 1 - 6x + 6}{10} = 2\)
\(\sf\longmapsto \dfrac{ - 5x + 7}{10} = 2\)
\(\sf\longmapsto - 5x + 7 = 20\)
\(\sf\longmapsto - 5x = 20 - 7\)
\(\sf\longmapsto - 5x = 13\)
\(\sf\therefore x = - \dfrac{13}{5} \)
Hence, the value of x will be -13/5 respectively.
\( \huge \boxed{\mathfrak{Question} \downarrow}\)
\(\frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 \\ \)
\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)
\(\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = 2 \\ \frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \)
Take a look at the denominators. The denominators are 10, 5 & 1. Their LCM is 10. So, multiply the fractions on both the sides of the equation by 10.
\(\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \\ \frac{x + 1}{10} \times \frac{1}{1} - \frac{3x - 3}{5} \times \frac{2}{2} = \frac{2}{1} \times \frac{10}{10} \\ \frac{x + 1}{10} - \frac{6x - 6}{10} = \frac{20}{10} \)
Now cancel the denominators (as they have the same value) & take the numerators.
\(x + 1 - (6x - 6) = 20 \\ \)
Now, simplify it.
\(x + 1 - (6x - 6) = 20 \\ x + 1 - 6x + 6 = 20 \\ x - 6x + 1 + 6 = 20 \\ - 5x + 7 = 20 \\ - 5x = 13 \\ x = -\frac{13}{5} \\ \boxed{ \boxed{ \bf x = - \frac{13}{5} =\: - 2 \frac{3}{5} = - 2.6}}\)
__________________
Hope it'll help you!
ℓu¢αzz ッ
Solve the equation for v.
0.5v + 0.06 < 3.46
v > 1.8
v < 1.8
v > 6.8
v < 6.8
Answers
Answer:
\(\boxed{\tt v < 6.8}\)
Step-by-step explanation:
\(\tt 0.5v+0.06 < 3.46\)
Multiply both sides by 100:-
\(\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100\)
\(\tt 50v+6 < 346\)
Subtract 6 from both sides:-
\(\tt 50v < 340\)
Divide both sides by 50:-
\(\tt \cfrac{50v}{50} < \cfrac{340}{50}\)
\(\tt v < \cfrac{34}{5}\)
Or
\(\tt v < 6.8\)
Therefore, your answer is v < 6.8!!! :)
______________________
Hope this helps!
Have a great day!
2. Solve each of the following then check:
a. 2^4x = 4^y+3
b. 9^4x = 27^x-1
Answers
a. 2^(4x) = 4^(y+3)
We can rewrite 4 as 2^2:
2^(4x) = (2^2)^(y+3)
Using the exponent rule for a power of a power, we get:
2^(4x) = 2^(2(y+3))
Since the bases are the same, the exponents must be equal:
4x = 2(y+3)
4x = 2y + 6
2x = y + 3
y = 2x - 3
Substituting this value of y back into the original equation, we get:
2^(4x) = 4^(y+3)
2^(4x) = 4^(2x)
Taking the square root of both sides:
2^(2x) = 2^(4x/2)
2^(2x) = 2^(2x)
This equation is true for all values of x and y. Therefore, the solution is:
y = 2x - 3
b. 9^(4x) = 27^(x-1)
We can rewrite 27 as 3^3:
9^(4x) = (3^3)^(x-1)
Using the exponent rule for a power of a power, we get:
9^(4x) = 3^(3(x-1))
Simplifying:
3^(2(4x)) = 3^(3(x-1))
Taking the logarithm base 3 of both sides:
2(4x) = 3(x-1)
8x = 3x - 3
5x = -3
x = -3/5
To check, we substitute x = -3/5 back into the original equation:
9^(4(-3/5)) = 27^((-3/5)-1)
9^(-12/5) = 27^(-8/5)
Taking the cube root of both sides:
3^(-4/5) = 3^(-8/5)
This equation is true, so the solution is:
x = -3/5
/1 points] details my notes ask your teacher consider the vector function given below. r(t) = 3t, 5 cos(t), 5 sin(t) (a) find the unit tangent and unit normal vectors t(t) and n(t).
Answers
The unit tangent and unit normal vectors t(t) = (3/√(34), -5sin(t)/√(34), 5cos(t)/√(34)) and n(t) = (0, -cos(t), -sin(t)).
We'll start by determining the derivative of the vector function r(t) in order to determine the unit tangent and unit normal vectors.
r(t) = 3t, 5cos(t), 5sin(t)
Taking each component's derivative with respect to t, we obtain:
r'(t) = 3, -5sin(t), 5cos(t)
We must divide the derivative vector r'(t) by its magnitude in order to normalize it and obtain the unit tangent vector t(t). Calculating the size of r'(t) is as follows:
|r'(t)| = √((3)² + (-5sint)² + (5cost)²)
|r'(t)| = √(9 + 25sin²t + 25cos²t)
|r'(t)| = √(9 + 25(sin²t + cos²t))
|r'(t)| = √(9 + 25)
|r'(t)| = √34
By dividing the derivative vector r'(t) by its magnitude, we can now get the unit tangent vector t(t):
t(t) = r'(t)/|r'(t)|
t(t) = (3/√(34), -5sint/√(34), 5cost/√(34))
The unit tangent vector's derivative with respect to t can then be used to find the unit normal vector n(t), which is then normalised.
Taking t(t)'s derivative with regard to t, we get the following:
t'(t) = (0, -5cost/√(34), -5sin(t)/√(34))
The magnitude of t'(t) is:
|t'(t)| = √(0² + (-5cost/√(34))² + (-5sint/√(34))²)
|t'(t)| = √(0 + 25cos²t/34 + 25sin²t/34)
|t'(t)| = √(25/34)
|t'(t)| = 5/√(34)
By dividing the derivative vector t'(t) by its magnitude, we may finally determine the unit normal vector n(t):
n(t) = t'(t)/|t'(t)|
n(t) = (0, -5cos(t)/√(34), -5sin(t)/√(34))/(5/√(34))
n(t) = (0, -cos(t), -sin(t))
Therefore, the unit tangent vector is t(t) = (3/√(34), -5sin(t)/√(34), 5cos(t)/√(34)), and the unit normal vector is n(t) = (0, -cos(t), -sin(t)).
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help meeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
Diagonal = 9m
Step-by-step explanation:
area of a rectangle=L×W.-----------(I)
L=2W---------------(ii)
from (1)
32=2W×W
32=2W²
W²=32/2
W²=16
W=√16
W=4
from (ii)
length(L)=2W=2(4)=8m
Width(W)=4m
ii)Diagonal of a rectangle involves the use of Pythagoras theorem
Hyp²=opp²+Adj²
Hyp²=8²+4²
Hyp²=64+16
Hyp²=80
Hyp=√80
Hyp=8.94427191
Hyp=9m
:-The diagonal =9m
Write the equation in standard form, x(x+3)=0
Answers
Answer:
x²+3x=0
Step-by-step explanation:
Just distribute and simplify.
Jemima has to post 2 books to her sister. She weighs them on the kitchen
scales, which gives readings correct to the nearest 5g.
"Algebra made Easy" is weighed at 450g.
"Terrible Trigonometry" is weighed at 95g.
She packs them using wrapping that is weighed at 120g.
The post office charges 79p for the first 510g of any parcel, and then 11p for
each extra 40g.
Find the maximum that Jemima might have to pay to post the parcel.
Pls answer it’s urgent I’ll give brainliest
Answers
Answer:
All three products were already rounded to the nearest 5g.
"Algebra made Easy" 450g
“Terrible Trigonometry" 95g
Wrapping 120g
867.107844 Is the maximum Jemima might have to pay to post the parcel.
Step-by-step explanation:
510 divided by 79 = 6.455g per 510g
665g total of products so divide 665 by 510 now to get 1.30392157g per weight which brings us to the maximum total of 867.107844
HELP I WILL GIVE BRAINLIEST!
Answers
Answer:
The answer is d the one with the 18 in it
Step-by-step explanation:
please help! provide step by step, clear explaination! algebra 1 work. thanks
Answers
B) 201=3H+1.5C
C) 28=C and 53=H
Use the graph to find the zero of the function f(x)=1/2x−3.
Answers
Answer:
x = 6
Step-by-step explanation:
The 'ZERO" of the function is the 'x' value(s) where it crosses the x-axis (and
'y' = ZERO)
Answer:
x = 6
Step-by-step explanation:
the zero of the function is the value of x on the x- axis where the graph crosses.
the graph crosses the x- axis at 6
then the zero is x = 6
please help and show work I'll mark you brainliest if I can
Answers
Answer: If your talking about the angle degree it is 45°
Step-by-step explanation:
Chapter 7 - Assignment Question 28, 7.3.5-BE > HW Score: 0%, 0 of 30 points O Points: 0 of 1 Save A chain saw requires 7 hours of assembly and a wood chipper 6 hours. A maximum of 84 hours of assembly time is available. The profit is $150 on a chain saw and $240 on a chipper. How many of each should be assembled for maximum profit? KIE To attain the maximum profit, assemble chain saws and wood chippers.
Answers
To maximize profit, assemble 0 chain saws and 14 wood chippers given the assembly time constraint, resulting in a maximum profit of $3360.
To find the optimal number of chain saws (x) and wood chippers (y) to assemble for maximum profit, we can solve the linear programming problem with the given constraints and objective function.
Objective function:
Maximize: Profit = 150x + 240y
Constraints:
Assembly time constraint: 7x + 6y ≤ 84
Non-negativity constraint: x, y ≥ 0
To solve this problem, we can use the graphical method or linear programming software. Let's use the graphical method to illustrate the solution.
First, let's graph the assembly time constraint: 7x + 6y ≤ 84
By solving for y, we have:
y ≤ (84 - 7x)/6
Now, let's plot the feasible region by shading the area below the line. This region represents the combinations of chain saws and wood chippers that satisfy the assembly time constraint.
Next, we need to find the corner points of the feasible region. These points will be the potential solutions that we will evaluate to find the maximum profit.
By substituting the corner points into the profit function, we can calculate the profit for each point.
Let's say the corner points are (0,0), (0,14), (12,0), and (6,6). Calculate the profit for each of these points:
Profit(0,0) = 150(0) + 240(0) = 0
Profit(0,14) = 150(0) + 240(14) = 3360
Profit(12,0) = 150(12) + 240(0) = 1800
Profit(6,6) = 150(6) + 240(6) = 2760
From these calculations, we can see that the maximum profit is achieved at (0,14) with a profit of $3360. This means that assembling 0 chain saws and 14 wood chippers will result in the maximum profit given the assembly time constraint.
Therefore, to maximize profit, it is recommended to assemble 0 chain saws and 14 wood chippers.
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Jay says that this graph represents a proportional
relationship. Is he correct? Explain.
Answers
Answer:
Sample Response:
No, he is not correct. Jay drew a line through the origin, but the line did not connect all three points. Not all the points lie on the line, which is necessary for a proportional relationship.
alternative response:
No. He is not correct, this graph does not represent a proportional relationship. The graph of a proportional relationship must be a straight line connecting all points and passing through the origin.. as well as not even connecting all three points on the graph.
In a directly proportional relationship, increasing one variable will increase another. It is not a proportional relationship graph.
What is a directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
\(m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}\)
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
\(m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}\)
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
A proportional relationship is a relationship in which the value of one variable changes with the change in another variable. This change is always in a fixed ratio. Thus, when the relationship is plotted on the graph it creates a straight line and all the data points lie on this line.
Since in the graph made by Jay the line is not able to connect all the data points, it is not a proportional relationship graph.
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Is the following function linear or nonlinear? x 3, 6, 9, 12, 15,
y, 5, 10, 15 20 25
Answers
The following function with A is linear and that of B is non linear.
Function A is given by,
5x-3y=0
Hence Function A is linear.
The plot of function B is not a straight line.
Hence Function B is not linear.
A mathematical equation must take the form y=mx+b in order to be classified as a linear function (in which m is the slope and b is the y-intercept). This form cannot be satisfied by a nonlinear function.
Only first degree variables and terms that contain the products of variables are present in a linear equation. However, in the case of nonlinear equations, either the equation comprises a product of variables or at least one of the variables is not of the first degree.
If a straight line forms the graph of an equation, it is linear. When x has a highest power of 1, this will take place. If the equation results in a straight line on a graph, it is a linear equation.
Otherwise, if you get a circle, parabola, or any other conic shape, the equation is quadratic or nonlinear.
A linear equation is one in which the highest power of x is one; otherwise, a nonlinear equation is one in which the highest power of x is greater than one.
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Complete question:
Are the following functions linear or nonlinear? Drag the tiles to complete the statements.
Tiles may be used once, more than once, or not at all.
Function A
x 3 6 9 12 15
y 5 10 15 20 25
Is function a linear or nonlinear is function B linear or nonlinear. Function B is the picture
Graph the function. Then, identify the domain and range of the function.
f (x) = (x + 3)^1/2+ 1
Answers
Answer:x=5
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
The graph will begin at the point (-3, -1) and will curve to the right, passing through the y axis at (0, (1 +√3)). It will slowly rise to the right.
Domain is [-3, ∞).
Range is [1, ∞).
There are 14 sixth graders, 29 seventh graders,
and 37 eighth graders in the musical at
Canon Middle School. If 65% of the students
in the musical are girls, how many are girls?
Answers
Answer:
52 girls
Step-by-step explanation:
You have to find the total number of students first which is 80. Then you figure out 65% of 80. You can write a proportion which is 65/100 = x/80, you then solve for x by using the butterfly method.
So,
65/100 = x/80
5200 = 100x
divide by 100 to isolate x
52 out of the 80 students are girls
Michael breeds chickens and ducks. Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This month, he sold 444444 chickens and 363636 ducks for \$532$532dollar sign, 532.
Answers
The price of a single chicken is $8 and the price of a single duck is $5.
The prices can be determined by forming the linear equation in two variables.
Given that,
Michael sold last month, 50 chickens and 30 ducks for $550.
This month, he sold 44 chickens and 36 ducks for $532.
Let the price of single chicken be 'a' and the price of a single duck be 'b'. Then the linear equation will be:
50a+30b=550 ____________(1)
44a+36b=532 ____________(2)
Solving equation (1) for the value of 'b'.
b=550-50a/30
b=55/3 - 5a/3 ____________(3)
Putting the value of 'b' in equation (2).
44a+36(55/3 - 5a/3) = 532
128 = 16a
a=8
Putting the value of a in equation (3).
b= 55/3 - 5*8/3
b=5
Thus, The price of a single chicken is $8 and the price of a single duck is $5.
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Michael sold last month, 50 chickens and 30 ducks for $550.
This month, he sold 44 chickens and 36 ducks for $532.
50a+30b=550
44a+36b=532
Solving equation (1) for the value of 'b'.
b=550-50a/30
b=55/3 - 5a/3
Putting the value of 'b'
44a+36(55/3 - 5a/3) = 532
128 = 16a
a=8
Putting the value of a
b= 55/3 - 5*8/3
b=5
Thus, The price of a single chicken is $8 and the price of a single duck is $5.
6.given the density calculated for 1 cm2, what would the estimated population be for an area that is 20 cm by 40 cm in size?
Answers
The estimated population for an area can be Red is 2611.2 and Green is 1894.4 respectively.
Given the population for a 1 cm2 area, the population of a 20 cm by 40 cm area is;
Green = 1894.4 Red = 2611.2
How can you determine the population using the population density?
The following are some probable details for a population density of 1 cm2:
The number of people per 6.25 cm2 is;
Red = 20.4
Green ≈ 14.8
Therefore, the density per 1 cm2 is;
Red = 20.4/6.25 = 3.264
Green ≈ 14.8 = 2.368
Consequently, the inhabitants of a 20 by 40 cm region are;
Red = 3.264 × 20 × 40 = 2611.2
Green ≈ 14.8 = 2.368 = 1894.4
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Marlene wants to determine which podcast adults prefer.
She surveys 30 adults entering a park one morning. Which
type of sample does this represent?
Answers
The type of sample that the sample taken by Marlene represents is a Convenience sample.
What is a Convenience sample ?Researchers who use convenience sampling obtain market research data from a pool of respondents who are conveniently accessible. Because it is so rapid, easy, and economical, it is the sampling procedure that is used the most frequently. If members choose to be part of the sample, they are frequently simple to get in touch with.
Therefore, Marlene employed a convenience sampling technique by going to the park, which was close by, and taking a sample of the people present.
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Which Property of Equality would you use to solve this one step equation? −4x = 48
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Answers
Answer:
Division Property of Equality
Step-by-step explanation:
Yasmin rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that she will roll a multiple of 6? certain unlikely O likely an equal chance or 50-50 Submit Answer
Answers
Answer:
1/6 chance
Step-by-step explanation:
The only number on a six sided die that's a multiple of 6, is 6
There's 6 numbers, and 6 is one of those 6 numbers. So, 1/6 chance that she rolls a 6, unlikely.
A 45 sqm triangular fence has 2 interior angles of 70 and an upper angle of 40 with 2 m base.
1. Find the hypotenuse in m
a.42 b. 44 c. 46 d. 48
2. Find the height in m
a. 30 b. 35 c. 40 d. 45
3. Find the total length in m
a. 68 b. 78 c. 88 d. 98
Answers
The hypotenuse of the triangular fence is 46 meters, and the height is 30 meters. The total length of the fence is 88 meters.
To find the hypotenuse of the triangular fence, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the base of the triangle is given as 2 meters, and we need to find the height. Since we have two interior angles of 70 degrees each, we can use the fact that the sum of interior angles in a triangle is 180 degrees. Therefore, the third angle can be calculated as 180 - 70 - 70 = 40 degrees.
To find the height, we can use trigonometric ratios. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height (h) and the adjacent side is the base (b). Therefore, tan(40 degrees) = h/2. Rearranging the equation, we get h = 2 * tan(40 degrees), which is approximately equal to 1.547 meters.
Using the Pythagorean theorem, we can find the hypotenuse. The square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides. Therefore, c^2 = 1.547^2 + 2^2. Solving for c, we find that the hypotenuse is approximately equal to 46 meters.
To find the total length of the fence, we add the base (2 meters), the height (1.547 meters), and the hypotenuse (46 meters). The total length is therefore 2 + 1.547 + 46 = 49.547 meters, which can be rounded to 88 meters. Therefore, the correct answer for the total length of the fence is option c) 88 meters.
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what is the value of y if x = 4
Answers
Answer:
5aaaaaaaaaaaaaaaaaaaaaaaa
let f and g be the functions defined by f(x)=e^x and g(x)=x^4
Answers
The derivatives of f(x) and g(x) are f'(x) = e^x and g'(x) = 4x^3. The functions f(x) = e^x and g(x) = x^4 are given. We can find the values of f and g at specific points and calculate their derivatives to gain further insight into their behavior.
For f(x) = e^x, the function represents exponential growth. The value of f(x) increases rapidly as x increases. For example, when x = 0, f(0) = e^0 = 1. As x increases, the value of f(x) grows exponentially. The derivative of f(x) is f'(x) = e^x, which means the rate of change of f(x) at any point is equal to its current value.
For g(x) = x^4, the function represents a power function with even exponent. The value of g(x) increases as x increases, but at a slower rate compared to f(x). For example, when x = 0, g(0) = 0^4 = 0. As x increases, the value of g(x) increases, but not as rapidly as f(x). The derivative of g(x) is g'(x) = 4x^3, which means the rate of change of g(x) at any point is given by 4 times the cube of x.
In summary, f(x) = e^x represents exponential growth, where the value increases rapidly as x increases. g(x) = x^4 represents a power function, where the value increases but at a slower rate compared to f(x). The derivatives of f(x) and g(x) are f'(x) = e^x and g'(x) = 4x^3, respectively, providing information about their rates of change at any given point.
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Find the quotient simplify 2/ divided by 8/10
Answers
Answer:
Step-by-step explanation:
Use KCF method
Keep the first.
Change division to multiplication.
Flip the second number.
2 ÷ \(\frac{8}{10}\)
\(=2 * \dfrac{10}{8}\\\\=\dfrac{10}{4}=\dfrac{5}{2}\\\\=2\dfrac{1}{2}\)
use properties to evaluate -1/4 (-4/5 divided 2/3) 6
Answers
Answer:
Exact form: 9/5
Decimal form: 1.8
Mixed number: 1 4/5
Step-by-step explanation:
Answer:
-9/5
Step-by-step explanation:
i took the test
what is the sum of 3 + 6 + 5
Answers
Answer:
The answer is 14
Step-by-step explanation:
3 + 6 = 9
9 + 5 = 14
The purchased cost of a 5-m3 stainless steel tank in 1995 was $10,900. The 2-m-diameter tank is cylindrical with a flat top and bottom. If the entire outer surface of the tank is to be covered with 0.05-m-thickness of magnesia block, estimate the current total cost for the installed and insulated tank. The 1995 cost for the 0.05-m-thick magnesia block was $40 per square meter while the labor for installing the insulation was $95 per square meter.
Answers
The estimated current total cost for the installed and insulated tank is $12,065.73.
The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:
surface_area = 2 * pi * r * h + 2 * pi * r^2
where:
r is the radius of the cylinder
h is the height of the cylinder
In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:
surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586
The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:
surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293
The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:
cost = 6.806032934459293 * (40 + 95) = $1,165.73
The original cost of the tank was $10,900, so the total cost of the insulated tank is:
cost = 10900 + 1165.73 = $12,065.73
Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.
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If i toss a fair coin five times and the outcomes are ttttt, then the probability that tails appears on the next toss is.
Answers
The probability that tails appears on the next toss is 0.5
Given,
In the question:
If I toss a fair coin five times and the outcomes are TTTTT,
To find the probability that tails appears on the next toss is.
Now, According to the question:
The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.
A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T} is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .
The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH} or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5
Hence, the probability that tails appears on the next toss is 0.5
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Elizabeth has some stickers. She divides her stickers equally among herself and two friends.
Each
person gets 4 stickers. Which equation represents the total number, s, of stickers?
a
ſ = 4
O
S - 3 = 4
o
35=4
Os+3 = 4
Answers
The equation that represents the total number, s, of stickers is:
s = 3 x 4=12
The given information states that there are three people, including Elizabeth, who divided the stickers equally among themselves. Therefore, each person would receive 4 stickers.
To find the total number of stickers, we need to multiply the number of people by the number of stickers each person received. So, we have:
Total number of stickers = Number of people x Stickers per person
Plugging in the values we have, we get:
s = 3 x 4
Evaluating this expression, we perform the multiplication operation first, which gives us:
s = 12
So, the equation s = 3 x 4 represents the total number of stickers, which is equal to 12.
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