The rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min. Computed using differentiation.
The sand is falling onto a conical pile, thus we get the pile in the shape of a cone, whose volume is given as:
V = (1/3)πr²h,
where V represents the volume of the cone, r represents its radius, and h represents its height.
In the question, we are given that the rate of piling is 16 ft.³/min, which implies that:
dV/dt = 16 ... (i)
We are also given that the diameter is three times the altitude (height), which can be shown as:
2r = 3h,
or, r = (3/2)h.
Thus, the volume can now be shown as:
V = (1/3)π{(3/2)h}²h,
or, V = (3πh³)/4.
Differentiating this with respect to time, we get:
dV/dt = (3π/4)(3h²)dh/dt.
Now, we need to calculate the rate of change of height, when the height is 2 feet, thus we take h = 2
Using dV/dt = 16 from (i), we can write:
16 = (3π/4)(3(2)²)dh/dt.,
or, 16 = 9π(dh/dt),
or, dh/dt = 16/9π = 0.5659 ft./min.
Thus, the rate at which the height of the pile is changing when the height is 2 ft. is 0.5659 ft./min.
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Please help ASAP
Please help ASAP
Please help ASAP
Answer:
Step-by-step explanation:
Answer:
9% only a guess.May not be correct..
Part of the graph of the function f(x) = (x + 4) (x - 6) is shown below. A 2 Which statements about the function are truc? Select two options.
The true options include the following:
The vertex of the function is at (1,–25).The graph is negative on the entire interval –4 < x < 6.What is a Graph?This is defined as a pictorial representation of data or variables in an organized manner.
Function f(x) = (x + 4)(x – 6)
Graph intersects the x-axis at points (-4,0) and (6,0).
x-coordinate of vertex = -4+6/2 = 1
y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25
The vertex is at the point (1,-25).
The graph is positive for all x< -4 or x>6.
The graph is negative for –4 < x < 6.
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PLEASE HELP!!!
Angle CAE is congruent to angle___
Angle CBF is congruent to angle___
Answer:
Angle CAE is congruent to angle CBE
Angle CBF is congruent to angle CAF
===================================================
Explanation:
Angle CAE is an inscribed angle that subtends the minor arc CE
Minor arc CE is the distance around the circle from C to E following the shorter path. All minor arcs are smaller than 180 degrees.
What other inscribed angle also subtends minor arc CE? That would be inscribed angle CBE
Notice that CAE and CBE both have "C" and "E" as the first and last items. The only change is the middle letter. This is a quick nonvisual way to determine inscribed angles.
Recall that if two inscribed angles subtend the same arc, then they are congruent. Therefore, angle CAE is congruent to angle CBE
-------------------
For similar reasoning, angles CBF and CAF are congruent inscribed angles that subtend minor arc CF.
For more information, check out the inscribed angle theorem. Also I recommend using GeoGebra as a handy tool.
more math i need help in
Answer:
It is B
Step-by-step explanation:
Alice is able to produce 3 dozen cupcakes in 90 minutes. How many cupcakes can she produce in 8 hours
Answer:
[tex]\boxed{192~cupcakes}[/tex]
Step-by-step explanation:
dozen = 12
3 × 12 = 36 cupcakes
I.
36 cupcakes ---------------- 90 minutes
x ---------------- 60 minutes
[tex]x=\dfrac{36\cdot 60}{90 } ~ cupcakes\\\\x=24~cupcakes[/tex]
II.
24 cupcakes ---------------------- 60 minutes = 1 hour
y ---------------------- 8 hours
[tex]y=\dfrac{8\cdot 24 }{1} ~cupcakes\\\\\boxed{y=192~cupcakes}[/tex]
They will produce 192 cupcakes in 8 hours.
HELP HELP HELP
Just 5 quick algebra 1 questions for 50 points!
1. x = a
2. y = b
3. It has an undefined slope.
4. You can either use, rise/run or change in y / change in x.
5. Rewrite the given equation in slope-intercept form, then determine the y-intercept, b, of the line.
What is the Equation of a Line?Equation of a line with m as slope and b as y-intercept is given as: y = mx + b.
1. Vertical lines have undefined slope. This implies that, for a given point, (a, b), the equation that models the line would be expressed as x = a, where a is the x-intercept.
Vertical line equation is: x = a.
2. Horizontal lines have 0 as a slope value, therefore, given (a, b), the equation that models the line is: y = b.
3. Equation for a vertical line cannot be written in slope-intercept form because the slope for a vertical line is undefined.
4. Using the following, rise/run or change in y / change in x, the slope (m), can be calculated given the coordinates of two points on a line.
5. To find an equation in point-slope form, e.g. y - 3 = 6(x - 4), rewrite the equation in slope-intercept form:
y - 3 = 6x - 24
y = 6x - 24 + 3
y = 6x - 21
The y-intercept, b, is: -21.
Therefore, the coordinate of the y-intercept would be: (0, -21).
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You have 4/6 cup of cornmeal in your cupboard. A recipe for 2/5 muffins calls for
cup of cornmeal. How much cornmeal would you have left if you made the
muffins?
Suppose cotangent (theta) = startfraction 5 over 12 endfraction, where pi less-than theta less-than startfraction 3 pi over 2 endfraction. what is sin(θ)?
sin(Q) = -(12/13)
What are trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively. It is a branch of mathematics that deals with the relation between the angles and sides of a right-angled triangle.
cot(Q) = 5/12
sin(Q) = 1/cosec(Q)
[tex]sin(Q) = \frac{1}{\sqrt{1+{cot}^2(Q)}}\\sin(Q) = \frac{1}{\sqrt{1+\frac{25}{144}}}\\sin(Q) = \frac{1}{\sqrt{\frac{169}{144}}}\\[/tex]
sin(Q) = ±12/13
Because, π < Q < (3/2)π
Therefore, sin(Q) = -12/13
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Answer:
A- -12/13
Step-by-step explanation:
A running track in the shape of an oval is shown. The ends of the track form semicircles.
A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 46 m and length of one straight edge 150 m.
What is the perimeter of the inside of the track?
The perimeter of the inside of the track is 444.44m
How to calculate the perimeter?Based on the information given, the length will be 150m and the width is 46m.
The circumference will be:
=2πr
= (2 × 3.14 × 46/2)
= 144.44
The length will be:
= 2 × 150
= 300
The perimeter of the oval will be:
= 300 + 144.44
= 444.44m
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
The Three options are
1. m∠5 + m∠6 = 180° ...........Linear Pair
2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle
3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property
Step-by-step explanation:
Consider Δ ABC with Exterior angles as
∠ 1 , ∠ 4 ,and ∠ 6
Exterior angle Property of Triangle:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠ 1 we have
∠ 1 = ∠ 5 + ∠ 3 .................Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 4 we have
∠ 4 = ∠ 5 + ∠ 2.................Exterior angle Property of Triangle
Similarly,
For Exterior ∠ 6 we have
∠ 6 = ∠ 2 + ∠ 3.................Exterior angle Property of Triangle
Triangle Sum Property:
Ina triangle sum of the measures of angles is equal to 180°
∴ m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property
Linear Pair:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
∴ m∠5 + m∠6 = 180° ...........Linear Pair
Answer:
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
got it correct on my test
PLEASE show me a fifth-degree polynomial with three terms in standard form
Answer:
a. 6x^5- 3x^3+ 21
b. (6x^5+ 4x^4+21) - (4x^5+ 3x^4+11)= 2x^5+ x^4+10
Step-by-step explanation:
The degree of the polynomial is the highest power of the terms of the polynomial .e.g
x³+ 2ax+ b² is a polynomial of 3rd degree because the highest power of the terms given is 3.
As we need a polynomial of 5th degree the highest power will be
5.6x^5+ 4x^4+ 3x^3+ 5x^2+ x+21
But this polynomial has 5 terms. We need a 5th degree polynomial with three terms so it can be any one of the following
6x^5- 3x^3+ 21
6x^5+ 4x^4+21
6x^5+ 5x^2+21
6x^5 + x+21
All of the above polynomials are in the standard form because the powers of the terms are given in decreasing order. The first term has the highest power and so on.
Part B:
Suppose we have 2 polynomials
6x^5+ 4x^4+21 and 4x^5+ 3x^4+11
When the closure property of subtraction is applied
(6x^5+ 4x^4+21) - (4x^5+ 3x^4+11)
= 6x^5+ 4x^4+21 - 4x^5- 3x^4-11 → coefficients are changed b/e of subtraction
= 2x^5+ x^4+10
the coefficients are changed because of subtraction.
In Polynomials the sign is changed due to subtraction and same degree terms ( like terms) are subtracted to get the answer.
Help!
What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values.
The graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x
How to determine the regression equation?From the table of values, we can see that:
As the time increases, the distance increases
However, the increment in the distance is not a linear increment.
This means that:
The graph cannot be (a) and (d); these graphs show scattered pointsThe graph cannot be (c); it shows that distance decreases, as time increasesThe graph (b) represents an exponential model.
When the points on the table are entered in a graphing calculator, we have the regression equation to be
y = 1.030 * 3.709^x
Hence, the graph of the model is (c) and the equation of the model is (d) y = 1.030 * 3.709^x
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Jackson conducted a survey at his school about its students' favorite
sport. He chose a name at random from a list of all the students in the
school, and chose every 10th student after that for the sample.. Was this
a random sample, and if so, which sampling method did Jackson use?
OA) Yes, simple random sample.
O B) Yes, systematic random sample.
OC) Yes, stratified random sample.
OD) No, it was not a random sample.
Answer:
OB
Step-by-step explanation:
it's not a beacuasenhes not doing everyone
and we have no info on whether anyone serveylayed a sport so the only possible option is 2
I need answer quickly
Answer:
b = 4.5
Step-by-step explanation:
a = 4
c = 6
c² = a² + b²
6² = 4² + b²
36 = 16 + b²
b² = 36 - 16
b² = 20
[tex]b = \sqrt{20} [/tex]
b = 4.5
i need help with this question guys i’ll give you brainly
Answer:
C
Step-by-step explanation:
C is most relevant to the question
144 = -12(x+5)
I need help with solving this problem it’s very difficult too solve
[<Answer>] (3):
Hello! I'm Avery. And I would love to help you :)
---------------------------------------------------------------------------------------------------------
[<The Explanation>}:
Step one: Distribute
[tex]144 = -12(x + 5)[/tex]
[tex]144 = -12x - 60[/tex]
Step two: Add 60 to both sides
[tex]144 = -12x - 60\\144 + 60 = -12 - 60 + 60[/tex]
Step three: Simplify
Adding..Adding..(Done!): [tex]204 = -12x[/tex]
Step four: Divide both sides by the same factor
[tex]204 = -12x\\\frac{204}{-12} = \frac{-12x}{-12}[/tex]
Last and not least..Step five:
Divide then, Cancel the terms, Move the Variable to the left...
And.. x = -17 is the answer :D
----------------------------------------------------------------------------------------------------------
[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! >:D
Bye! Hope this works for you :)
Have a nice day! - Avery <3
The figure shows a circle circumscribed around a triangle.
Triangle U T V is inscribed within a circle. A point is at the center of the triangle. Lines are drawn from the points of the triangle to the point in the middle. Lines are drawn from the point in the middle to the sides of the triangle to form right angles.
What is constructed first when creating the circle?
perpendicular segments to the vertices of the triangle
perpendicular bisectors of the sides of the triangle
angle bisectors of each angle of the triangle
the incenter of the triangle
Option B is right perpendicular bisectors of the sides of the triangle
What circumcircle?If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.
One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.
When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.
When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C
In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC
Therefore Option B is right perpendicular bisectors of the sides of the triangle.
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Simplify the expression by combining like
terms:
4x² + 6x + 5x²-x
Enter the number that belongs in the green box.
[?]x² + [ ]x
Answer:
9x² + 5x
Step-by-step explanation:
4x² + 6x + 5x²-x
Combine like terms:-
4x² + 5x² = 9x²
6x - x = 5x
9x² + 5x
-----------------------------
IJ=
Measure of IJ
Help me thanks
Answer: 11
Step-by-step explanation:
By the secant-secant theorem,
[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]
Select the correct answer.
Serena's financial goal is to reduce debt. Which statement could make Serena's financial goal specific and timely?
Serena should focus on a certain credit card and give herself a deadline.
Serena should focus on a certain amount and track her spending.
Serena should track the amount of debt reduced over a period of six months.
Serena should track her purchases at gas stations for one year.
O A.
O B.
O C.
O D.
Serena should focus on a certain amount and track her spending. Option B
What Serena should doFrom the information given, Serena wants to reduce debt and to do this she needs to pay attention on how she borrows and the possible way to pay her debts.
Some possible ways to reduce debts include;
Develop a budgetTrack your expensesDo not take more debtPay bills in timeCheck bills carefullyThus, Serena should focus on a certain amount and track her spending. Option B
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Write a paragraph proof to determine whether quadrilateral PQRS is a parallelogram.
Based on the vertices of quadrilateral PQRS, we can infer that quadrilateral PQRS is NOT a parallelogram.
Why is quadrilateral PQRS not a parallelogram?Quadrilateral PQRS would be a parallelogram if the sides have the same slope as this would prove that they are parallel.
The slope of PQ is:
= (6 - 5) / (6 - 4)
= 1/2
The slope of RS is:
= (2 - 4) / (7 - 9)
= -2 / -2
= 1
The slopes are not the same so quadrilateral PQRS is NOT a parallelogram.
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Answer: The quadrilateral is not a parallelogram.
Step-by-step explanation:
I am given that the vertices of quadrilateral PQRS are P(4,5), Q(6,6), R(9,4) and S(7,2). The slope formula applied to each pair of adjacent vertices gives the slopes of the sides:
slope of PQ= 1/2
slope of QR= -2/3
slope of RS= 1
slope of SP= -1
Since each side has a different slope, none of the sides are parallel. So quadrilateral PQRS is not a parallelogram.
Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.
Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof?
Given: AngleB ≅ AngleN; BC ≅ NM; AngleC is right; AngleM is right
Prove: TriangleABC ≅ TriangleQNM
AngleA ≅ AngleQ because of the third angle theorem.
AB ≅ QN because they are both opposite a right angle.
BC ≅ NM because it is given.
AngleC ≅ AngleM because right angles are congruent.
What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.
In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.
Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.
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Answer:
AngleA ≅ AngleQ because of the third angle theorem
Step-by-step explanation:
right on edge
Everyday Math
425. Cooking Natalia's pasta recipe calls for 2 pounds of pasta for 1 quart of sauce. How many pounds of pasta should Natalia cook if she has 2.5 quarts of sauce?
Answer:
5
Step-by-step explanation:
........................
Answer:
If Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.
Then she needs to cook 5 pounds of pasta if she has 2.5 quarts of sauce.
Step-by-step explanation:
Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.We need to find pounds of pasta to be cooked if she has 2.5 quarts of sauce.Use the unitary method to find the pounds of pasta to be cooked.Step 1 of 2
Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.
If one quart of sauce calls for two pounds of pasta,
Then to find how much pasta is needed for 2.5 quarts of sauce we need to form a proportion.
Let the pounds of pasta needed be x .
[tex]$$\begin{aligned}\frac{\text { pasta }(\text { inPounds })}{\text { Sauce }(\text { inQuarts })} &=\frac{\text { pasta }(\text { inPounds })}{\text { Sauce(inQuarts })} \\\frac{2}{1} &=\frac{x}{2.5}\end{aligned}$$[/tex]
Multiplying both sides by 2.5 we get,
[tex]$$\begin{aligned}\frac{2}{1} \times 2.5 &=\frac{x}{2.5} \times 2.5 \\x &=2 \times 2.5 \\x &=5\end{aligned}$$[/tex]
Step 2 of 2
To check if the answer is reasonable, we substitute it back in the formed proportion
[tex]$\frac{2}{1}=\frac{x}{2.5}$$[/tex]
We found x=5 hence,
[tex]$$\begin{aligned}\frac{2}{1} &=\frac{5}{2.5} \\2 &=2\end{aligned}$$[/tex]
Here, LHS =RHS
Hence, our answer is correct.
Raul is building a house. On day 1, he uses 3 bags of cement. On each of the following 3 days, he uses 3 times the number of bags used the previous day. How many bags of cement does he use in the last 3 days?
Answer:
117 bags
Step-by-step explanation:
Day 1: 3 bags
Day 2: 3 × 3 = 9 bags
Day 3: 9 × 3 = 27 bags
Day 4: 27 × 3 = 81 bags
Total: 9 + 27 + 81 = 117 bags
Answer:
81 bags of cement in the last 3 days.
Step-by-step explanation:
On the first day he used 3 bags.
The second day he used twice that amount so that would be 3²=9
The third day he used twice the amount he used the second day. So that would be 9²=81.
He used 81 bags of cement in the last 3 days.
Hope this helps!
If not, I am sorry.
What is 16% of 750?
Answer:
120
Step-by-step explanation:
For this, all we have to do is multiply 750 by 16%. We know, from percent to decimal conversion, that 16% is 0.16 (divide the percent by 100 to convert to a decimal). From there, if we multiply 750 by 0.16, we get our answer to be 120
Please helpppppppppp
Answer:
1 4/5
Step-by-step explanation:
On the number line, for every whole integer, the line is divided into fifths. The dot is one fifth away from the number two. Therefore, it is 4/5 in from 1 and the answer is 1 [tex]\frac{4}{5}[/tex].
There are five different points on a line. how many segments are there on the line?
There are 10 line segments on a line with five different points on it.
What are a line and a line segment?Line:
A line is formed with infinite points and it is extended infinitely along a straight path in both directions.
Line segment:
The part of the line that lies between two distinct points on the line. This is also called the shortest distance between two points on the line.
How many segments are there on the line with five different points?Consider a line with five points on it as A, B, C, D, and E.
So, the possible line segments are
AB, AC, AD, AE, BC, BD, BE, CD, CE, DE
So, there are 10 line segments are formed on line with five different points.
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35/6 divided by 5/4 in ait simplest form
The simplest form of 35/6 ÷ 5/4 is 14/3
Given,
35/6 ÷ 5/4
hence it is written as= 35/6 ×4/5
= 7×2/3×1
= 14/3
The simplest form of fractions are determined by following the given steps:
List the denominator's and numerator's factors.Find the common factors between the denominator and numerator.The fraction obtained is in the reduced form when the numerator and denominator are divided by the common factors until they have no common factor but 1.This number can't be further subdivided. Hence we get the the simplest form of 35/6 ÷ 5/4 as 14/3.
If we get numbers which share common highest common factor then divide the number by both numerator and denominator to bring the simplest form of number.
Therefore we get the simplest form of number as 14/3.
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A
B
Value: 10
AB=
12√2
BC=
45°
Find the missing side lengths. (Enter your answer
without units.)
C
Answer:
12
Step-by-step explanation:
This is a special triangle with angle measure 45-45-90
The side lengths for this special right triangle is as follows:
The side length that sees angle measure 90 is represented by a[tex]\sqrt{2}[/tex]
The side lengths that see angle measures 45 is represented by a
We can see from the image hypotenuse (the side that sees angle 90)
is given as 12[tex]\sqrt{2}[/tex] that means a = 12
So the missing side lengths (both see angle measure 45) = 12
Four students are trying to find the rule that translates point N(–2, –4) to N prime (2, 4). Each student’s reasoning is shown below. Raheem: The rule is (x times (negative 1), y times (negative 1)) because Negative 2 times (negative 1) = 2 and Negative 4 times (negative 1) = 4. Casey: The rule is (x + 2, y + 4) because the image is (2, 4). Andrew: The rule is (x + 4, y + 0) because the coordinates are opposites. Lo: The rule is (x + 4, y + 8) because Negative 2 + 4 = 2 and Negative 4 + 8 = 4. Which student is correct?
Answer:
Raheem
Step-by-step explanation: