The rate of change of volume is 418.6 inch³/s .
Rate of increase of radius with time is ( dr/dt ) = 5
rate of decrease of height with time is (dh/dt ) = -3
volume of a cone is given by (V) = [tex]\frac{1}{3} \pi r^{2}h[/tex]
Now the rate of change of volume with respect to time is given by dV/dt
∴ dV/dt = d( [tex]\frac{1}{3} \pi r^{2}h[/tex]) / dt
dV/dt = [tex]\frac{1}{3} \pi (2rh\frac{dr}{dt} + r^{2}\frac{dh}{dt} )[/tex]
value of radius and height when volume is changing are :
r = 20 inches
h = 40 inches
dV/dt = [tex]\frac{1}{3} \pi ([/tex] 2×20×40 ×5 - [tex]20^{2}[/tex]×3 )
dV/dt = [tex]\frac{1}{3} \pi[/tex](1600 - 1200)
dV/dt = (400/3) 3.14
dV/dt = 418.66 inch³/s
So the rate of change of the volume is 418.66 inch³/s.
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A line with a slope of –
5 passes through the points (7,–
2) and (8,q). What is the value of q?
The line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.
How to find the value of q with the slope?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (7, –2) and (8, q) with a slope of - 5.
Hence, let's find q.
y = - 5x + b
Let's find y-intercept
-2 = -5(7) + b
b = -2 + 35
b = 33
Therefore,
y = -5x + 33
Hence, let's find q.
y = -5(8) + 33
q = -40 + 33
q = -7
Therefore, q = - 7
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-8-(b-3)=13-4b i need an answer but not a fraction or decimal
Answer:b=2/3 if u don't need an answer that is not a fraction or decimal u can write 17. as a whole number.
Step-by-step explanation:
what's the distance between points A and B
Answer:
AB = 10 units============
GivenEndpoints A(-8, -4) and B(2, - 4)Find the length of ABSince both points have same y-coordinate, the distance between the points is the difference of x-coordinates:
AB = 2 - (-8) = 2 + 8 = 10 unitsFind the x- and y-intercepts of the graph of 8x - 10y = 32. State each
answer as an integer or an improper fraction in simplest form.
A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
They should produce 1091 units each day to yield a minimum cost.
What is the vertex formula?
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
We have,
C = 70,000 - 120x + 0.055x²
C = 0.055x² - 120x + 70,000
Hence, for this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, find and put the values of x.
minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )
= 120 ÷ 0.11
= 120 ÷ 0.11
= 1090.90 ≈ 1091 units
The minimum cost will be yield for 1091 units.
Therefore, They should produce 1091 units each day to yield a minimum cost.
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A tree that is 10 feet tall casts a shadow that is 8 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.
9.4 feet
12.8 feet
3.2 feet
2.8 feet
The distance from the top of the tree to the tip of the shadow is 12.8 ft
Pythagorean theorem:
According to the Pythagorean theorem, In a right-angled triangle, the sum of the squares of the side will equal the square of the hypotenuse.
Here hypotenuse is the longest side.
=> Hoptenuse² = side² + side²
Here we have
The length of the tree = 10 feet
Length of shadow = 8 feet
Here we need to find the distance from the top of the tree to the tip of the shadow
If we join the top of the tree to the tip of the shadow we will observe a right-angled triangle as shown below
From the figure,
AC² = AB² + BC² [ ∵ ABC is right angle triangle ]
=> AC² = 10² + 8²
=> AC² = 100 + 64
=> AC² = 164
=> AC = 2√41
=> AC = 12.8 ft
Therefore,
The distance from the top of the tree to the tip of the shadow is 12.8 ft
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Answer:
b) 12.8 feet
Step-by-step explanation:
Now we have to,
→ find the required distance.
Forming the equation,
→ x² = 10² + 8²
Then the distance will be,
→ x² = 10² + 8²
→ x² = 100 + 64
→ x² = 164
→ x = √164
→ [ x = 12.8 feet ]
Hence, distance is 12.8 ft.
Point O is the center of this circle. What is mzBCA?
A. 56
B. 62
C. 72
D.76
Answer:
B
Step-by-step explanation:
∠ ADB and ∠ AOB sum to 180° , that is
56° + ∠ AOB = 180° ( subtract 56° from both sides )
∠ AOB = 124°
An angle on the circle is half the central angle subtended on the same arc , so
∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°
Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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Use Heron's Formula to find the area of AHKP if h' = 24 ft, k = 21 ft, and p = 13 ft. *
(1 Point)
192. 67 sq units
435. 90 sq units
113. 38 sq units
136. 23 sq units
The area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
Define the term Heron's Formula?This formula is well-known for its straightforward computation that supports the length for three triangle sides. If the lengths of the 3 sides are a, b, and c, the semi-perimeter is; s = (a+b+c)/2.Area ; A = √s(s−a)(s−b)(s−c)The three sides of the triangle are-
h = 24 ft, k = 21 ft, and p = 13 ft.
s = ( 24 + 21 + 13 ) / 2
s = 29
s - a = 29 - 24 = 5
s - b = 29 - 21 = 8
s - c = 29 - 13 = 16
Put in the formula,
Area = √s(s−a)(s−b)(s−c)
A = √ 29 x 5 x 8 x 16
A = 136.23
Thus, the area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
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Consider the infinite geometric sequence 4480, -3360, 2520, -1890…
a. Find the common ratio, r.
b. Find the 20th term.
c. Find the exact sum of the infinite sequence.
The common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
a.
common ratio r = a2/a1
= -3360/4480
= -0.75.
r = a3/a2
= 2520/-3360
= -0.75
b.
[tex]a_{n}[/tex] = a*r^(n-1)
here a = 4480 and r = -0.75.
= 4480(-0.75)^(20-1)
= 4480(-0.75)^19
= 4480*(-0.00422)
[tex]a_{20}[/tex] = -18.9056.
c.
[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))
= 4480*((1--0.75^4)/(1--0.75))
= 4480*((1-0.31640625)/(1--0.75))
= 4480*(0.68359375/1.75)
= 4480*0.390625
= 1750
Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
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can someone do these for me pls i’m lazy
Walt Disney Co paid a $1.42 annual dividend on a day it closed at a price of $96 per share.
What was the annual dividend for 500 shares?
The annual dividend for 500 shares was $710.
How is the annual dividend computed?The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.
Dividends are always declared per share with a stated dollar amount or percentage.
Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.
Dividends are a kind of financial reward to stockholders for their investment in the entity.
The dividend per share = $1.42
Market price per share = $96
The number of shares held = 500
The dividend received for the year = $710 ($1.42 x 500)
Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.
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Which equations are true? Select all that apply.
Answer:
The equation that is true is equation two
Find the variables in the figure (x and y) please and thank you!!
Read the left colum top to bottom then the right column top to bottom, hope this helps
solve the system by substitution
Answer:
Step-by-step explanation:
since x=y, you can either substitute for x or for y,
lets do x
-3x - x = 4
-4x=4
x=-1
Now we can just plug in
-3(-1) - y = 4
3-y = 4
y=-1
A movie theater showed an old, classic movie on Saturday and Sunday. Tickets cost c dollars for children under the age of 13 and d dollars for others.
On Saturday they sold 84 children's tickets and 157 tickets for others and collected $2,640 from ticket sales. On Sunday they sold 67 children's tickets and 134 other tickets and collected $2,211 from ticket sales. This can be represented by this system of equations
84c + 157d = 2,640
67c + 134d = 2,211
A. What could the equation 17c + 23d = 429 mean in this situation?
B. The solution to the original system is the pair c = 9 and d = 12. Explain why it makes sense that this
pair of values is also a solution to the equation 17c + 23d = 429.
The equation in the given question is answered in main body.
What is equation?
In arithmetic , an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =
Main body:
according to question :
A) equation for Saturday sale = 84c +157d = 2640
equation for Sunday sale = 67c +134d = 2211
when subtracted we will get, 17c +23d = 429
This equation shows the difference in sales of these 2 days in terms of ticket sold and collection.
B) According to second part solution are c= 9 , d= 12.
equation given : 17c+23d = 429
now substituting value of c and d.
⇒17(9) + 23(12)
⇒153+276
⇒429 = R.H.S
Hence equation satisfies.
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Hi I'm honestly really confused on this problem and have no idea what I'm meant to do. It'd be helpful if someone could explain this
As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.
What does converse of corresponding angles theorem states?
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
How can we show two lines are parallel to each other?
We can show lines are parallel by finding a pair of corresponding angles that are congruent.
Proving if two lines are parallel then third line is parallel too.
According to the given data:
It is given in the question that line x is parallel to line yTherefore, ∠5 ≅ ∠7 (i.e. corresponding angles)
∠5 = ∠7
Similarly as given line y is parallel to line z∠6 ≅ ∠8 (Corresponding angles are equal)
∴ Measure of angles is also equal ⇒ ∠6 = ∠8
∠5 = ∠8 (transitive property of equality of angles which says if
∠a = ∠b and ∠b = ∠c then ∠a = ∠c)
∠5 ≅ ∠8 (If measure of angles is same then they are congruent)
Therefore, line x || line z
(Converse of the Corresponding Angles Theorem).
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A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the yield 3 years later? Round to the nearest tenth of a percent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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a fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. what is the length of the shortest lad-der that will reach from the ground over the fence to the wallof the building? g
The length of the shortest ladder is 16.64 ft.
In triangle ABC, using Pythagoras theorem
[tex]AC^{2} = AB^{2} + BC^{2}[/tex] OR
[tex]L^{2} = h^{2} + (x+4)^{2}[/tex] .....(1)
We also have similar triangles if we consider:
△ABC and △DEC
Which gives us the proportional relationship:
AB:DE = BC:EC
or h/8 = (4+x) / x
h = 8( 4+x) /x
Substituting this last expression for h into Eq [1] we get:
[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]
Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:
[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]
At a critical point the derivative is zero and so we have the equation:
= [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]
From here we can find the value x :
x + 4 = 0 1 - [tex]\frac{256}{x^{3} }[/tex] = 0
x = -4 x = [tex]\sqrt[3]{256}[/tex]
We require x > 0 so we neglect the -ve solution and only take +ve solution
therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.
[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]
L² = 277.14
L = 16.64 ft
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HELPPP MEEeeeeeeeeee
Find the measure of the exterior angle.
The measure of the exterior angle as shown in the triangle is 140°.
What is exterior angle?
Exterior angle is the angle between a side of a polygon and an extended adjacent side.
Exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
From the diagram below, applying the theorem above,
k = 64+76k = 140°Hence, the exterior angle is 140°.
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When Lily left her house in the morning, her cell phone battery was partially charged. The charge remaining in Lily's battery, as a percentage, can be modeled by the equation B=-4t+52,B=−4t+52, where t is the number of hours since Lily left her house. What is the x-intercept of the equation and what is its interpretation in the context of the problem?
The x-intercept of the equation is 13 and its interpretation in the context of the problem is the number of time in hours for which Lily left her house.
What is x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
Next, we would determine the number of time for which Lily has left her house since in the morning by substituting the value of B with zero (0) as follows:
B = -4t + 52
0 = -4t + 52
4t = 52
Time, t = 52/4
Time, t = 13 hours.
Therefore, the x-intercept of the given equation is (0, 13).
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the little twelve basketball conference has two divisions, with six teams in each division. each team plays each of the other teams in its division twice and every team in the other division once. how many conference games are scheduled?
There are 96 basketball conference games are scheduled.
What is termed as the division?Multiplication is the reciprocal of division. If 3 groups of 4 add up to 12, then 12 classified into three groups of equal size results in 4 in each group. Developing equal groups or defining how many people are within each group after a fair distribution is the basic function of division.For the given question;
Every squad competes in ten games within its own division and six games against opponents from the opposing division. The 12 teams thus play a total of 16 conference games.There are N games on the schedule because there are two teams in each game.
N = 12×16/2
N = 96
Thus, there are 96 basketball conference games are scheduled.
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Select all correct answers. which values are part of the solution set based on the result of the inequality? -4x + 24 < -2x + 2 9.5 -10 11.5 15 10 -3
11.5 and 15 are the values that are part of the solution set of the inequality.
Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-4x + 24 < -2x + 2
-4x + 2x < -24 + 2
-2x < -22
22 < 2x
11 < x
Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.
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My science class is pretty small. There are just 18 students in the class. My
teacher, Ms. Microbe, has an unusual system for pairing us up for labs. She
has given each of us a number from 1 through 18, and on lab days, she pulls
our numbers out of a bag to determine who is paired with whom. When we
did our last lab, I happened to notice that the sum of each person's number
with his/her lab, partner's number was a perfect square!
How were the partners assigned?
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9).
Square numbers:A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.
For example:
Square of 2 = 4
Square of 3 = 9
Square of 4 = 16
Here we have
A science class is pretty small
There are just 18 students in the class.
The teacher gave each of them numbers from 1 through 18 on lab days
Start from 1 and find by adding which number we will get a square number
Here 1 + 15 = 16
2 + 14 = 16
3 + 13 = 16
4 + 12 = 16
5 + 11 = 16
6 + 10 =16
After the above combinations, the remaining numbers are
7, 8, 9, 16, 17, 18
which can be added as given below to get square number 25
=> 18+7=25
=> 17+8=25
=> 16+9=25
Therefore,
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9)
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125 in the ratio 2:3
Answer:
50:75
Step-by-step explanation:
let the ratio of 2:3 be x
now,
125=2+3x
or,5x=125
therefore,x=125/5
x=25
now,
2x=25*2
=50
3x=25*3
=75
help meeeeeeeeeeeeeeeeee please
Answer:
I believe it's 4.5 seconds
an airplane is preparing to land at an airport. it is 48,000 feet above the ground and is descending at the rate of 3,200 feet per minute. at the same airport, another airplane is taking off and will ascend at the rate of 2,800 feet per minute. when will the two airplanes be at the same altitude and what will that altitude be?
Answer:
After 8 minutes ; altitude = 22,400 feet
Step-by-step explanation:
s1 = 2800t
s2 = -3200t + 48 000
2800t = -3200t + 48 000
28t = -32t + 480
7t = -8t + 120
7t + 8t = 120
15t = 120
15/15 t = 120/15
t = 8 minutes
s = 8 * (2800) = 22400 feet
In peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses
Step-by-step explanation:
In Peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses?
with glasses: x
without glasses: 3x
x + 3x = 28
4x = 28
x = 7 with glasses
7 * 3 = 21 without glasses
Feng invests money in an account paying simple interest. He invests $70 and no money is added or removed from the investment. After one year, he has $70.70. What is the simple percent interest per year?
The simple interest is given as PRT/100, thus the simple percent interest per year is 1%.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.
As per the given,
Investment = $70
Investment after one year is $70.70
Interset = 70.70 - 70 = $0.70
The interest is given as = PRT/100
0.70 = PR(1)/100
R = (0.70×100)/70
R = 1%
Hence, "The simple interest is given as PRT/100, thus the simple percent interest per year is 1%".
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