what is the radius of the sphere with volume of 10000
The radius of the sphere with a volume of 10000 m³ is approximately 13.4 meters.
What is the radius sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).
Given that the volume of the sphere is 10000 m³, we can set up the equation:
Volume = (4/3)πr³
r³ = Volume / (4/3)π
r = ∛( Volume / (4/3)π )
r = ∛( 10000/ ( (4/3) × 3.14) )
r = 13.4 m
Therefore, the radius is 13.4 m.
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Find the slope of a line perpendicular to the line whose equation is 6x + 5y = -30.
Fully simplify your answer.
Answer:
[tex]6x + 5y = - 30[/tex]
[tex]5y = - 6x - 30[/tex]
[tex]y = - \frac{6}{5} x - 6[/tex]
Since the slope of this line is -6/5, the slope of a perpendicular line is 5/6. The slopes of perpendicular lines are negative reciprocals.
An oil company has a cylindrical drum with a capacity of 806 cubic yards. To construct this drum, the
cost of material for the top of the drum is $2 per square yard, $2 per square yard for the bottom of
the drum, and $17 per square yard for the side wall of the drum. What dimensions must this
cylindrical drum have to be constructed at minimum cost?
The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.
How to Solve the Problem?Let's expect that the round and hollow drum includes a stature of h and a span of r.
The volume of a barrel is given by: V = πr^2h.
We know that the drum includes a capacity of 806 cubic yards, so able to compose:
πr^2h = 806
We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.
The zone of the beat and foot of the drum is given by: A = πr^2.
The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:
C_topbottom = 2A = 2πr^2
The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:
A_side = 2πrh
The whole fetched of building the drum is in this manner:
C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh
Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:
h = 806/(πr^2)
Substituting this expression for h into the taken a toll condition, we get:
C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r
To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:
dC/dr = 4πr - 27404/r^2 =
Fathoming for r, we get:
r = (27404/(4π))^(1/3) ≈ 10.19 yards
Substituting this esteem of r back into the expression for h, we get:
h = 806/(π(10.19)^2) ≈ 2.46 yards
Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:
Span: 10.19 yards
Stature: 2.46 yards
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Let z = 3( cos pi/2 + i sin pi/2). Find the exact value of z^7 where 0 (less than equal to) theta (less than equal to) 2pi.
From the given value of z = 3(cos pi/2 + isin pi/2), the exact value of z⁷ is -2187i.
Given z = 3(cos pi/2 + isin pi/2)
which can be represented as 3sin(pi/2) in polar form.
Now, by applying De-Moivre's theorem,
z⁷ = (3cis(pi/2))⁷
= 3⁷cis(7pi/2)
= 3⁷cis(3pi/2) [7pi/2 --- 3pi/2 ]
To write it in complex form,
z⁷ = 3⁷(cos(3pi/2) + isin(3pi/2))
z⁷ = 3⁷(0-i) [cos(3pi/2) = 0 and sin(3pi/2) = -1]
z⁷ = 3⁷(-i)
z⁷ = -2187i
From the above explanation, we can conclude that the value of z⁷ is -2187i.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The correct statements about the circle equation are:
The radius of the circle is 3 units. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Which statements are true?Remember that the general circle equation is:
(x - a)² + (y - b)² = R²
Where (a, b) is the center and R is the radius.
Here the given equation is.
x² + y² - 2x - 8 = 0
We can complete squares in x to get:
(x - 1)² - 1 + y² - 8 = 0
(x - 1)² + y² = 9
(x - 1)² + y² = 3
So, the center is (1, 0) and the radius is 3.
The correct statements are:
The radius of the circle is 3 units.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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solve for x ( needed quickly)
For each equation, decide whether the line it represents is parallel to p, perpendicular to p, or neither.
y=-3x+10
type your answer.....
y-5=-(2+2) type your answer...
type your answer...
-3x+y=1 type your answer.....
The lines are neither parallel nor perpendicular to line p
Deciding whether the line are parallel or notFrom the question, we have the following parameters that can be used in our computation:
y = -3x + 10
As a general rule
Parallel lines have equal slopesPerpendicular lines have their slopes to be opposite reciprocalsUsing the above as a guide, we have the following:
y - 5 = -(2+2) is neither parallel nor perpendicular to y = -3x + 10-3x + y = 1 is neither parallel nor perpendicular to y = -3x + 10Read more about linear relations at
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inverse of f(x)=(x+3)^3
Answer:
( x - 3 ) 3 .
Step-by-step explanation:
Since f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) ) = x , then f−1(x)=3√x+3 f - 1 ( x ) = x 3 + 3 is the inverse of f(x)=(x−3)3 f ( x ) = ( x - 3 ) 3 .
is abc ~ Def explain
The two triangles are congruent since they have equal angles and equal sides.
What is congruent triangles?Congruent triangles are two triangles that have exactly the same size and shape.
In other words we can say that they have the same angles and the same side lengths.
So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.
For the given triangles
The missing value of angle C = 180 - (18 + 110) = 52⁰
The missing value of angle F = 180 - (18 + 52) = 110⁰
So it is obvious that the two triangles are congruent since they have equal angles and equal sides.
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HELP ASAP ASAP PLS PLS ALSO BRAINLIEST
A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
4 8 one half
6
At this rate, how much sauce and oregano will be needed to make 6 servings?
The recipe will need 12 cups of sauce and three fourths teaspoons of oregano for 8 servings.
The recipe will need 12 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and three fourths teaspoons of oregano for 8 servings.
For 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.
To find how much sauce and oregano will be needed to make 6 servings, we can use the ratio of sauce to oregano in the recipe.
For 4 servings, the recipe calls for 8 cups of sauce and 1/2 teaspoon of oregano. To find how much sauce and oregano are needed for 6 servings, we can set up a proportion:
sauce : oregano = 8 cups : 1/2 teaspoon = 16 cups : 1 teaspoon
So, for 6 servings, we need:
sauce : oregano = 16 cups : 1 teaspoon
To convert this to cups and tablespoons, we can multiply both sides of the proportion by 3/4:
sauce : oregano = (16 x 3/4) cups : (1 x 3/4) teaspoons
sauce : oregano = 12 cups : 3/4 teaspoon
sauce : oregano = 48 cups : 3 teaspoons
Therefore, for 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.
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Ryan earns 52 dollars per week working part-time at a book store. He makes one dollar more for each book that he sells. The amount, A (in dollars), that Ryan earns in a week if he sells b books is given by the following function.
Answer:
a=52+b
Step-by-step explanation:
he earns $52 without selling books.
since he only earns 1$ per book, there is no need to put it as the coefficient of b since it won't change
therefore,
$52+b=a or a=$52+b
What is the product of the rational expressions below?
6-X 6+** 2-X Zt
The value of the product of the rational expressions is,
⇒ (4x - 32) (x² - 36)
We have to given that;
The rational expressions is,
⇒ 4x/(x+6) times (x-8) / (x-6)
Now, We can multiply as;
⇒ 4x/(x+6) times (x-8) / (x-6)
⇒ 4x/(x+6) × (x-8) / (x-6)
⇒ 4 (x - 8) / (x + 6) (x - 6)
⇒ (4x -32) / (x² - 6²)
⇒ (4x - 32) (x² - 36)
Thus, The value of the product of the rational expressions is,
⇒ (4x - 32) (x² - 36)
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A(t)=600e^-0.05t
Find the half life of the material to the nearest 10th of a day
The half life of the decaying material is found to be 13.9 days to the nearest 10th of a day.
Using the radioactivity formula given to find out the concertation and the half life of the material. In this case, we are given the function A(t) = 600e^(-0.05t), which represents the quantity of the material at time t.
Let A(0) be the initial amount of the material, then we have,
[tex]A(0) = 600e^{-0.05(0)} = 600[/tex]
To find the half-life, we need to solve for t when A(t) = A(0)/2:
A(t) = A(0)/2
[tex]600(e^{-0.05t}) =\frac{600}{2}[/tex]
Taking natural logarithm,
[tex]ln(e^{-0.05t}) = ln(\frac{1}{2})[/tex]
-0.05t = ln(1/2)
t = -ln(1/2)/0.05
t ≈ 13.9
Hence, the half life is found to be about 13.9 to the nearest tenth of the day.
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The function d = 45t gives the distance d in miles a car travels in t hours. Graph this function
A graph of this function d = 45t is shown in the image below.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
d = kt
Where:
d represents the distance in miles.t represents the time in hours.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 45/1 = 90/45
Constant of proportionality, k = 45.
Therefore, the required linear equation or function is given by;
d = kt
d = 45t
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-5|x-8|+2=2 pls help me pls
Answer:
x = 8
Step-by-step explanation:
[tex]5|x-8|+2=2 \\ −5∣x−8∣=0 \\ ∣x−8∣=0 \\ x = 8[/tex]
First, you need to cancel out the 2 by subtracting 2 from both sides. Then, we divide both sides by -5. And finally, we remove the absolute value.
Ronnie records the number of chirps per minute (x) that crickets make at
different temperatures (y) in degrees Fahrenheit.
He determines that the association is linear and that the line of best fit is
y = x + 60.
What is the interpretation of the slope and y-intercept of this equation?
Temperature (°F)
8888888888
100
90
80
70
60
50
40
30
20
10
•
1
=x+
y=
X+60
5 10 15 20 25 30 35 40 45 50
Chirps per minute
The interpretation of the slope and y-intercept of this equation is that: C. The slope predicts a temperature increases of about 1/6 for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 60 degrees.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Since Ronnie determined that the association between the number of chirps per minute (x) that crickets make at different temperatures (y) in degrees Fahrenheit is linear and that the line of best fit is given by;
y = 1/6(x) + 60
By comparison, we have the following:
Slope, m = 1/6.
y-intercept = 60.
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Stephan is 46 inches tall. His sister is 6 inches taller than he is how tall is may
Answer:
May is 52 inches tall
Step-by-step explanation:
stephan=46in
sister=6+stephan(in inches)=6+46=52
Rosanna sells m small bags of marbles and p large bags of marbles.
Each small bag contains 15 marbles.
Each large bag contains 40 marbles.
The total number of marbles that Rosanna sells is T
Write down a formula for T in terms of m and p
The formula for T in terms of m and p is: [tex]T = 15m + 40p[/tex]
How do we determine the T in terms of m & p?We are given that number of marbles in each small bag is 15, and Rosanna sells m small bags, so the total number of marbles in the small bags is: [tex]15m[/tex]
Also given that number of marbles in each large bag is 40, and Rosanna sells p large bags, so the total number of marbles in the large bags is:[tex]40p[/tex]
So, total number of marbles that Rosanna sells is the sum of the marbles in the small bags and in the large bags will be addition of both values which will give us: [tex]T = 15m + 40p[/tex].
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Bao walked 15 miles in 6 hours. What was her walking rate in miles per hour?
Group of answer choices
2.5 miles per hour
2 miles per hour
1 mile per hour
1.5 miles per hour
The solution is, 2.5 miles per hour was her walking rate in miles per hour.
We know that,
Speed is measured as distance moved over time.
The formula for speed is speed = distance ÷ time.
To work out what the units are for speed, you need to know the units for distance and time.
In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
Here, given that,
Bao walked 15 miles in 6 hours.
so, we get,
in 6 hours = 15 miles
so, in 1 hour = 15 / 6 miles
=2.5 miles
Hence, The solution is, 2.5 miles per hour was her walking rate in miles per hour.
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Two more then a product of 11 and a number
Step-by-step explanation:
( 11 * x ) + 2 where 'x' is a number
matet please
-6+28÷(-4)
Answer:
-13
Step-by-step explanation:
-6 + 28 ÷ (-4)
= -6 - 7
= -13
So, the answer is -13
given a function,how can the range be determined
To determine the range you need to evaluate and find a maximum/minimum if you can.
How to determine the range?For a function f(x) = y, we define the range as the set of the possible outputs of the function.
So, to find the range of any function, we need to evaluate it and try to find the minimum and maximum values of the function. To do so it is useful to understand the behavior of different types of functions.
For example linear ones have a range of all the real numbers.
Quadratic ones have a range that depends on its vertex, and so on.
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Joshua and Amahle are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small
boxes of fruit and large boxes of fruit. Joshua sold 15 small boxes of fruit and 15 large boxes of fruit for a
total of $390.00. Amahle sold 20 small boxes of fruit and 25 large boxes of fruit for a total of $592.50. Find the cost of one small box of fruit and the cost of one large box of fruit.
Cost of small box: $
Cost of large box: $
The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.
What is the cost of small and large box?Let
cost of one small box of fruit = x
cost of one large box of fruit = y
15x + 15y = 390
20x + 25y = 592.50
From (1)
x + y = 26
x = 26 - y
Substitute x = 26 - y into (2)
20x + 25y = 592.50
20(26 - y) + 25y = 592.50
520 - 20y + 25y = 592.50
- 20y + 25y = 592.50 - 520
5y = 72.50
divide both sides by 5
y = 72.50/5
y = 14.5
Substitute y = 14.5 into
15x + 15y = 390
15x + 15(14.5) = 390
15x + 217.5 = 390
15x = 390 - 217.5
15x = 172.5
divide both sides by 15
x = 172.5/15
x = 11.5
Therefore, small box cost $11.5 and large box cost $14.5
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f(1)=0
f(n)=f(n−1)+2
Answer: f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
Step-by-step explanation: Using the given recursive formula:
f(1) = 0
f(n) = f(n-1) + 2
We can find the values of f(n) for different values of n:
f(1) = 0
f(2) = f(1) + 2 = 0 + 2 = 2
f(3) = f(2) + 2 = 2 + 2 = 4
f(4) = f(3) + 2 = 4 + 2 = 6
f(5) = f(4) + 2 = 6 + 2 = 8
And so on.
We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:
f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
if it takes 7 plumbers 15 days to install a gas risers how many plumbers would be needed to install the same riser in 10 days, please such work!!
To install the gas riser in 10 days, a total number of 11 plumbers would be needed.
We can use the formula:
(number of workers) × (time) = (constant amount of work)
Let's let x be the number of plumbers needed to install the gas riser in 10 days. We can set up the equation:
(7 workers) × (15 days) = (x workers) × (10 days)
Simplifying the left side, we get:
105 worker-days = (x workers) × (10 days)
Dividing both sides by 10 days, we get:
10.5 workers = x
Since we can't have a fraction of a worker, we need to round up to the nearest whole number.
Therefore, we would need 11 plumbers to install the gas riser in 10 days.
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The radius of Mercury is approximately 2 × 103 kilometers, and the radius of Uranus is approximately 2 × 104 kilometers. To determine approximately how many times bigger the radius of Uranus is than the radius of Mercury, Ken performs the following operation. Approximately how many kilometers bigger is the radius of Uranus than the radius of Mercury?
The diameter of Earth is about 2.7 times greater than the diameter of Mercury.
We have,
to determine the scale factor
Given the following values
Diameter of Mercury = 4.9×10^3km
Diameter of Earth = 1.3×10^4km
Taking the ratio of the diameters:
Ratio = 1.3×10^3/4.9×10^4
Ratio = 2.7
This shows that the diameter of Earth is about 2.7 times greater than the diameter of Mercury.
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complete question:
The diameter of Mercury is approximately 4.9×103 kilometers. The diameter of Earth is approximately 1.3×104 kilometers. About how many times greater is the diameter of Earth than the diameter of Mercury? 2.7 27 270 2700
What is the length of the unknown leg of the triangle?5 ft 8 ft
1/2x+1/3y=7
1/4x+2/3y=6
4
What is the solution of the system shown?
6,12
1/6,14
10 2/3, 5
The solution to the system of linear equation is:
x = 10 2/3, y = 5
The correct option is the last option 10 2/3, 5
Solving system of linear equationsFrom the question, we are to solve the given system of linear equation.
The given system of linear equations is
1/2x + 1/3y = 7
1/4x + 2/3y = 6
Multiply the first equation by 2
1/2x + 1/3y = 7 × 2
x + 2/3y = 14
Subtract the second equation from the resulting equation
x + 2/3y = 14
- 1/4x + 2/3y = 6
--------------------------
3/4x = 8
Multiply both sides of the equation by 4/3
4/3 × 3/4x = 8 × 4/3
x = 32/3
x = 10 2/3
Substitute the value of x into
x + 2/3y = 14
To determine y
(10 2/3) + 2/3y = 14
32/3 + 2/3y = 14
Multiply through by 3
32 + 2y = 42
Subtract 32 from both sides
32 - 32 + 2y = 42 - 32
2y = 10
Divide both sides by 2
2y / 2 = 10 / 2
y = 5
Hence, the solution is:
x = 10 2/3, y = 5
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when will 65x +20= y and 730+35x=y meet on the graph?
To find when the two equations 65x + 20 = y and 730 + 35x = y will meet on the graph, we need to solve for the value of x that satisfies both equations.
We can begin by setting the right-hand sides of the two equations equal to each other:
65x + 20 = 730 + 35x
Subtracting 35x from both sides, we get:
30x + 20 = 730
Subtracting 20 from both sides, we get:
30x = 710
Dividing both sides by 30, we get:
x = 23.67
Now that we have found the value of x that satisfies both equations, we can substitute it into either equation to find the corresponding value of y. Let's use the first equation:
y = 65x + 20
y = 65(23.67) + 20
y = 1539.55
Therefore, the two equations will meet on the graph at the point (23.67, 1539.55).
please HELPP! Graphing Linear Equations
Answer: 2 2/3+ 8
Step-by-step explanation: it goes 2 under the ten
Answer:
See provided explanation
Step-by-step explanation:
Slope=change in y/change in x
General equation for a line: y=mx+b
You know that the slope(m) is 8/3, and the y-intercept is 8. So your graph will intersect the y axis at the point (0,8). from there, use slope=rise/run to graph the remaining points. Starting at (0,8), move 8 up and 3 right, this is your next point. Do the same in the other direction, starting at (0,8) move down 8 and left 3 points. Doing this will get you the points (-3,0) and (3,16). repeat this process until you have enough points to form a line. I attatched a picture of what the graph should look like.