The rate of change of the height is approximately -1.67 meters per minute.
The volume of a cone can be written as V = (1/3)πr²h.
Differentiating with respect to time t, we get
dV/dt = (1/3)π (2rh dr/dt + r² dh/dt)
Given that the radius is decreasing at a constant rate of 1 meter per minute and the volume is decreasing at a rate of 61 cubic meters per minute, we can substitute these values into the equation to find dh/dt:
61 = (1/3)π (2rh + r² dh/dt)
dh/dt = (61 - (2rh)) / (r² * (1/3)π)
Substituting in the given values of r = 2 meters and h = 41 cubic meters, we get:
dh/dt = (61 - (2 * 2 * 41)) / (2² * (1/3)π)
dh/dt = (61 - 164) / (4 * (1/3)π)
dh/dt = -103 / (4 * (1/3)π)
Approximating π to 3.14, we get
dh/dt = -103 / (4 * (1/3) * 3.14)
dh/dt ≈ -1.67
So the rate of change of the height is approximately -1.67 meters per minute.
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Find the measure of the three missing angles in the rhombus below.
Answer:
see below
Step-by-step explanation:
Remember this definition:
A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.
so if you know only 1 angle, you'll know all of them
because z is opposite to the given angle 69 so z=69
the other 2 angles are the same = 180 -69 =111
Please help been stuck on this for hours
The size of angle ACB to the nearest degree is 88 degree.
How is a triangle ABC put together?
Construction Steps:
Create a line segment BC with the property AC = 4 cm.
Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.
Join AB and AC now. Consequently, the necessary triangle is ABC.
With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.
Cut an arc of 3 cm from point B.
Embrace BC and AC
Triangle with angle ABC is necessary.
< ACB = 88 degree
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Use the number line below to determine which of the following answer choices had statements that are all true
The choice that had statements that are all true is (a) Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2
How to determine the choices that had statements that are all trueThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The number line
On the number line, we have the following
A = -4
B = -2 1/2
C = 1
D = 1 3/4
When the above values are compared with the list of options, we have
Option (A) = true
This is so because in (a)
Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2
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Three large cones hang from the ceiling in an office building in front of a bank of windows. The height of each cone is 12 feet and the circumference of the base of each cone is 8π feet. The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black. What is the total surface area painted black? Use π≈3.14. Enter your answer, rounded to the nearest tenth, in the box.
The total surface area painted black = 90.5 square feet to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Given:
Three large cones hang from the ceiling in an office building in front of a bank of windows.
The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.
The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.
Circumference of the base of the cone = 8π feet.
2πr = 8π
πr = 4π
The surface area of the cone = πr x height
The surface area of the cone = 12 x 4π
The surface area of the cone = 48π.
The total surface area painted black = 60% of 48π.
The total surface area painted black = 90.5 square feet to the nearest tenth.
Therefore, the result is 90.5 square feet to the nearest tenth.
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Determine all numbers at which the function is continuous.
Answer:
(-infinity,-1)U(-1,infinity)
Step-by-step explanation:
plug in the number where the piecewise function changes which is -1 and 1
(-1)^2-(-1)-2 =0
(-1)=-1
These aren't equal so the function is discontinuous at x = -1 because of a jump
(1) = 1
-2(1) + 3 = 1
These are equal so the function is continuous at x = 1
So from negative infinity to -1 the function is continuous and from -1 to infinity
(-infinity,-1)U(-1,infinity)
Find the range, interquartile range, quartile deviation, mean absolute
deviation, population variance, and population standard deviation of
the given ungrouped data.
There are 12 sections of Statistics 1 in a state university. Listed below
are the number of students enrolled in each section.
23 43 56 43 23 56 43 23 15 14 38 44
The required range of the given data set is 42 and defined for the interval (14, 56).
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Range: The range is the difference between the largest and smallest values in a set of data.
Here,
The largest value is 56 and the smallest is 14, so the range is given as,
= 56 - 14 = 42.
Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
Quartile deviation (QD): The QD is also known as the semi-interquartile range, and is half the interquartile range (IQR).
Mean Absolute Deviation (MAD): The MAD is a measure of variability that is calculated by finding the average of the absolute deviations of each data point from the mean.
Population Variance: The population variance is a measure of how much the data points in a population deviate from the mean.
Population Standard Deviation: The population standard deviation is the square root of the population variance, and is a measure of how spread out the data points in a population are.
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Note: The calculation of IQR, QD, MAD, population variance, and population standard deviation would require more steps, but these calculations are beyond the scope of this answer.
What percent of 12 is 7 written out
18. Casey wants to start a garden.
A) If Casey buys 9 plants
how much was spent on
gardening supplies?
100
Total
cost of 80
garden 60
supplies
(S)
40
20
B) How many plants can
Casey get if her total budget
is $60 for gardening supplies?
C) What is the rate of change?
H
3 6 9 12
9 12 15
Number of plants bought
20
B) What c
3 Bed
C) Is the
20. Bria
and serv
beef is p
table.
BARB
Numb
a) The amount of the supplies is $70
b) The number of the plants is 3
c) The rate of change is 1/20.
What is a proportional relationship?
A proportional relationship is a mathematical relationship between two variables where their ratio is constant. In other words, as one variable increases or decreases, the other variable also increases or decreases in the same ratio.
We have to note that we can read up the relationship from the graph. The amount of the supplies for 9 plants is $70. If the total budget is $60 then we can only have three plants. The rate of change is therefore 1/20.
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HELP
______________________________
The graph of the function is given by the image presented at the end of the answer.
The minimum value on the interval [-2,0] is given as follows:
y = -1 at x = -2.
The maximum value on the interval [-2,0] is given as follows:
y = 1 at x = 1.
How to obtain the minimum and the maximum values of a function?The minimum value of a function in an interval is the lowest value of y assumed by the function.
The maximum value of a function in an interval is the lowest value of y assumed by the function.
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Fred wants to buy a new car. If he puts $7,000 in a savings account that earns 8% interest each year,
how long will it take for Fred to have $30,100 for a new car.
a. Write the exponential equation.
b. Solve the problem. Round up to the nearest whole number.
The exponential equation is P = 7000 * (1 + 0.08)ᵗ and the nearest whole number.
What is the exponential equation?
In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.
a. To write the exponential equation, let t be the number of years and let P be the amount of money in the account after t years. The exponential equation can be written as:
P = 7000 * (1 + 0.08)ᵗ
b. To solve for t, we need to find the number of years it takes for P to reach $30,100. We can set up an equation and solve for t:
30,100 = 7000 * (1 + 0.08)ᵗ
Dividing both sides by 7000:
30,100 / 7000 = (1 + 0.08)ᵗ
Taking the natural logarithm of both sides:
ln (30,100 / 7000) = t * ln (1 + 0.08)
Solving for t:
t = ln (30,100 / 7000) / ln (1 + 0.08)
Using a calculator, we get:
t = 21.1397
Rounding up to the nearest whole number, it will take Fred 22 years to have $30,100 for a new car.
Hence, the exponential equation is P = 7000 * (1 + 0.08)ᵗ and the nearest whole number.
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Before refrigerators existed some people have blocks of ice delivered to their homes that delivery wagon had a storage box in the shape of a rectangular prism that was 7 1/2‘ x 6‘ x 6‘ the cubic ice blocks stored in the box head slight side lengths, one and a half feet how many ice blocks fit in the storage box
The required number of ice blocks that fit in the storage box is 80 ice blocks.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
The volume of the storage box is,
= 7.5 feet × 6 feet × 6 feet
= 270 cubic feet.
Each ice block has a volume,
= 1.5 feet × 1.5 feet × 1.5 feet
= 3.375 cubic feet.
Therefore, the number of ice blocks that fit in the storage box is,
= 270 / 3.375
= 80 ice blocks.
Thus, the required number of ice blocks that fit in the storage box is 80 ice blocks.
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How much money needs to be set aside today to purchase a new piece of equipment in 3 yrs? The money is expected to 9% interest compounded annually and the piece of equipemt is expected to increase by 3% per year. The present cost of the equipment is $75,000.00.
To calculate the amount of money that needs to be set aside today to purchase a new piece of equipment in 3 years, we need to find the future value of the equipment and calculate the present value of that future amount.
First, let's find the future value of the equipment:
The cost of the equipment is expected to increase by 3% per year, so after 3 years the cost will be:
$75,000 * (1 + 0.03)^3 = $78,225
Next, let's find the present value of that future amount:
The money is expected to earn 9% interest compounded annually, so to find the present value, we need to discount the future amount by the interest rate. We can use the formula:
PV = FV / (1 + r)^t
where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years.
Plugging in the values, we get:
PV = $78,225 / (1 + 0.09)^3 = $73,232.57
So, to purchase the equipment in 3 years, we need to set aside $73,232.57 today.
David has two part time jobs. He earns $14/h at one and $11/h at the other. David wants to know how many hours it will take him to earn $1000. Find the combinations of the numbers of hours David could work at each job to earn $1000
Answer:
Step-by-step explanation:
To find the number of hours David has to work at each job, we can set up an equation. Let's say David works x hours at the first job and y hours at the second job. Then, we have:
14x + 11y = 1000
Next, we need to find the possible combinations of x and y that satisfy this equation. To do this, we can use trial and error, or use the substitution method. Let's use the latter method. Solve for x in terms of y:
14x = 1000 - 11y
x = (1000 - 11y) / 14
Now, we can substitute this expression for x into the original equation to get a new equation in terms of y:
11y = 1000 - 14x
y = (1000 - 14x) / 11
We can use this equation to find possible values of y. For example, if x = 40 hours, then y = (1000 - 14 * 40) / 11 = (1000 - 560) / 11 = (440) / 11 = 40. So, David could work 40 hours at the first job and 40 hours at the second job to earn $1000.
We can repeat this process for other values of x to find more combinations. Some possible combinations of the numbers of hours David could work at each job to earn $1000 are:
40 hours at the first job and 40 hours at the second job
45 hours at the first job and 35 hours at the second job
50 hours at the first job and 30 hours at the second job
55 hours at the first job and 25 hours at the second job
60 hours at the first job and 20 hours at the second job, etc.
I got the answer,( thx to the person who helped me) but I need help with the ratio table and the ordered pairs.
The required cost of the construction of a 4.5-inch tower is $114.75.
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, and thereafter solving those equations. and a single variable.
The parameters given are;
The cost of construction = $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 * 4.5
= $114.75.
We conclude that, the figure above is the amount to fund 4.6 inhces
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Complete question is;
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?
given measure in standard position
2.280°
X
In standard position, 2.280° refers to an angle in the Cartesian plane with its beginning side on the positive x-axis and its terminal side establishing an angle of 2.280° with the positive x-axis counterclockwise.
What is angle?An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle is formed by joining two rays (half-lines) that have a shared terminal. The latter is referred to as the angle's vertex, while the rays are referred to as the angle's sides, legs, and arms.
Here,
The measure of 2.280° in standard position refers to an angle in the Cartesian plane, with its initial side on the positive x-axis and its terminal side making an angle of 2.280° with the positive x-axis in a counterclockwise direction.
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PLS ANSWER QUICK CORRECTLY!!!! help ya girl ouu!
what is the period of the sinusoidal function? enter your answer in the box.
The period of the sinusoidal function in this problem is given as follows:
10 units.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating in intervals over the domain.
Then the period of the function is defined as the difference between two points in which the function has the same behavior.
For this problem, the function has the same behavior at x = 8 and at x = -2, hence the period of the sinusoidal function is calculated as follows:
Period = 8 - (-2)
Period = 8 + 2
Period = 10 units.
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How many ways can you scramble the word “Oaxaca”
Answer:
oaxaca
oacaxa
xaoaca
xacaoa
caoaxa
caxaoa
aoaxac
axaoac
aoacax
acaoax
axacao
acaxao
aoxaca
aocaxa
acoaxa
acxaoa
axoaca
axcaoa
aoaxca
axaoca
aoacxa
axacoa
acaoxa
acaxoa
Looks like 24 to me.
6 arrangements of “oa” “xa” and “ca”
those same 6 reversed
those same 6 with the first pair reversed
those same 6 with the first two pairs reversed.
reversing the last pair or the last two pairs only is illegal, so this is comprehensive.
Step-by-step explanation:
12
Erin
Enn (EDUID: 517931638) 10-2525-19
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....
An average ant can lift a maximum of 50 times its own body weight.
An average ant weighs 4 milligrams.
An average human being weighs 80 kilograms.
Enter the maximum amount of weight, in kilograms, a human being could lift if it could lift as much as an average
ant.
The maximum amount of weight, a human being could lift is 0.0002 kilograms.
How to determine the maximum amount of weightSince an average ant can lift a maximum of 50 times its own body weight, and it weighs 4 milligrams,
The maximum weight it can lift is
50 * 4 milligrams = 200 milligrams.
To convert milligrams to kilograms, we divide by 10^6:
200 milligrams / 10^6 = 0.0002 kilograms
So, the maximum amount of weight a human being could lift if it could lift as much as an average ant is 0.0002 kilograms.
Therefore, the answer is 0.0002 kilograms or 0.2 grams
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The ten numbers from 1 to 10 are split into two groups. The sum of the numbers in one group is n, and the product of the numbers in the other group is n. What is the largest possible value of n?
Y varies directly as X and Y=39 when X = 52 find Y when X = 22
35?
I just subtracted 39 from 52 and i got 14 so i added 13 to 22 and i got 35 so i assume thats it
DIG DEEPER In each level of a video
game, you can earn up to 10 points
and lose up to 3 points. Your friend
earns 9 points in the first level. If he
earns and loses the maximum number
of points each level, how many total
points will he have after level 6?
Answer:51
Step-by-step explanation:
9+7+7+7+7+7+7
(or 9+7^6)
100 POINTS! Please help
Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
The axis of symmetry for each function is given as follows:
f(x): x = -4.g(x): x = 4.h(x): x = 1.Hence the rank from smallest to largest axis of symmetry is given as follows:
f(x), h(x), g(x).
How to obtain the axis of symmetry?The axis of symmetry of a quadratic function is given by the x-coordinate of the vertex of the quadratic function.
For function f(x), considering the vertex-form definition, the x-coordinate of the vertex is given as follows:
x = -4.
For function g(x), considering the standard definition, the x-coordinate of the vertex is given as follows:
x = -(-16)/2(4).
x = 16/4.
x = 4.
For function h(x), considering the graph of the function, the x-coordinate of the vertex is given as follows:
x = 1.
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When an integer is subtracted from 2 times the next consecutive integer, the difference is -7. Find the value of the lesser integer.
The value of the lesser integer is -9. The solution has been obtained by using algebra.
What is algebra?
In the area of mathematics known as algebra, abstract symbols rather than actual numbers are used to perform operations or manipulations.
Let the integer be 'x'.
We are given that when an integer is subtracted from 2 times the next consecutive integer, the difference is -7.
So, from this we can form the equation as
⇒2(x+1) - x = -7
⇒2x + 2 - x = -7
⇒x = -7 - 2
⇒x = -9
Hence, the value of the lesser integer is -9.
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As dry air moves upward, it expands and cools. Suppose that the ground temperature is 20°C and
the temperature at a height of 1 km is 10°C.
Input Variable: Height (h), Output Variable: Temperature (T)
Axes: h (km) | 0 | 1 , T (°C) | 10 | 10
Slope: 0 (The temperature does not change with increasing height)
What is ideal gas law?The theory used in this question is the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are directly proportional.
As the dry air moves upward, it expands and the temperature decreases. This is why the temperature at a height of 1 km is 10°C.
Determine the input and output variables:
The input variable is the height (h) and the output variable is the temperature (T).
Draw and label two axes: On the x-axis, label it "h (km)" and on the y-axis, label it "T (°C)".
Plot and label the two points you were given:
Plot a point at (0, 10) and another point at (1, 10).
Determine the slope of the line between your two points:
The slope of the line between the two points is 0, indicating that the temperature does not change with increasing height.
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Cannot figure out how to answer this question
The correct statement regarding the continuity of the function is given as follows:
All three conditions for continuity are true, so f(x) is continuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For this problem, we must look at the turning point at x = 3, hence:
The lateral limits are equal, as the graph approaches x = 3 by the left and by the right of x = 3 at the same point.f(a) = f(3), due to the closed interval on the graph.Hence all conditions are satisfied and the correct option is given by the fourth option.
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NEED ANSWER ASAP!!
How much water should be added to 18 mL of 15% alcohol solution to reduce the concentration to 9%?
What is the value of x (x+30) 2x
Answer: 30
Step-by-step explanation:
Vertical angles are congruent.
[tex]x+30=2x \implies x=30[/tex]
4. The density and strength of concrete are determined by the ratio of cement and aggregate. Suppose that a contractor has 450 cubic feet of a dry concrete mixture that is 60 % sand by volume. How much pure sand must be added to form a new mixture that is 80% sand by volume?
The amount of sand that must be added to form a new mixture that is 80% sand by volume will be 90 cubic feet.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The thickness and strength of not entirely set in stone by the proportion of concrete and total. Assume that a project worker has 450 cubic feet of a dry substantial blend that is 60 % sand by volume.
The amount of sand that must be added to form a new mixture that is 80% sand by volume is given as,
⇒ 0.80 x 450 - 0.60 x 450
⇒ 360 - 270
⇒ 90 cubic feet
The amount of sand that must be added to form a new mixture that is 80% sand by volume will be 90 cubic feet.
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Please show all work n tyy :))
The Angle C is 83.2°
Describe Law of Cosines?The Law of Cosines, also known as the Cosine Formula, is a mathematical relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles. The law states that in a triangle ABC with sides a, b, and c opposite to angles A, B, and C, respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab cos(C)
where "cos" represents the cosine function. The Law of Cosines can be used to find missing sides or angles in a triangle when given sufficient information. It is widely used in geometry, trigonometry, and engineering. The Law of Cosines is an extension of the Pythagorean theorem and can be used when the triangle is not a right triangle. It is a powerful tool for solving a variety of problems in a wide range of fields.
To find the angle C in triangle ABC, you can use the Law of Cosines. The Law of Cosines states that in a triangle ABC with sides a, b, and c and opposite angles A, B, and C, the following equation holds:
c² = a² + b² - 2abcos(C)
In this case, a = 20 cm, b = 29 cm, and c = 24 cm, and we are given that angle BAC = 82 degrees. Using this information, we can calculate cos(C) as follows:
cos(C) = (a² + b² - c²)/(2ab) = (20² + 29² - 24²)/(2×20×29) = 0.2618
Finally, we can use the inverse cosine function (arccos) to find angle C:
C = arccos(cos(C)) = arccos(0.2618) = 83.2 degrees (rounded to one decimal place).
So, angle C in triangle ABC is approximately 83.2 degrees.
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Write a formula for the function obtained when the graph is shifted as described.
When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!
f(x)=x^3 is shifted up 3 unit and to the left 7 units.
The new equations f(x)=Answer
The formula for the function obtained when the graph is shifted is f(x)=(x+7)^3+3.
How do we make graph of a function?Suppose the considered function whose graph is to be made is function f(x). The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
Given;
f(x)=x^3 is shifted up 3 unit and to the left 7 units.
Now,
To shift upwards, we will add outside of the argument
To shift to the left, we will add inside of the argument
Therefore, the function will be f(x)=(x+7)^3+3
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