Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{8}{25 \pi} \ ft/min[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]
r is radiush is heightDiameter: d = 2r
Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{dV}{dt} = 2 \ ft^3/min\\b = h\\h = 5 \ ft[/tex]
Step 2: Rewrite Volume Formula
We need to rewrite the cone volume formula in terms of height h only.
Base b = diameter d of the circular base
Define: b = dSubstitute: b = 2rWe are given that the base of the cone is the same as the height.
Define: b = 2rSubstitute: h = 2rNow solve for height.
Divide 2 on both sides: h/2 = rRewrite expression: r = h/2Now find new volume formula.
Define [VC]: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Substitute: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{h}{2})^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{h^2}{4})h[/tex]Multiply: [tex]\displaystyle V = \frac{1}{12} \pi h^3[/tex]We now have the same volume formula in terms of height h only.
Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{1}{12} \pi \cdot 3 \cdot h^{3-1} \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{1}{4} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Solve for height rate
Substitute: [tex]\displaystyle 2 \ ft^3/min = \frac{1}{4} \pi (5 \ ft)^{2} \frac{dh}{dt}[/tex]Isolate h rate: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{1}{4} \pi (5 \ ft)^{2}} = \frac{dh}{dt}[/tex]Exponents: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{1}{4} \pi (25 \ ft^2)} = \frac{dh}{dt}[/tex]Multiply: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{25}{4} \pi \ ft^2} = \frac{dh}{dt}[/tex]Divide: [tex]\displaystyle \frac{8}{25 \pi} \ ft/min = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{8}{25 \pi} \ ft/min[/tex]Here this tells us that the rate at which the height is moving at a rate of 0.101859 feet per minute.
Write the expression in standard form. -2(8m + 3)
Answer:
-16m-6
Step-by-step explanation:
use distributive property, you get -16m-6
I hope this helped, and if my answer was right, please mark this as brainliest! Thank you!
Hey there!
Hey there!
–2(8m + 3)
Distribute
–2(8m) + –2(3)
–2(8m) = –16m
–2(3) = —6
Answer: –16m – 6 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Express each of the following fractions as a mixed number (the sum of a whole number and the remaining fractional units).
8 over 5=
13 over 12= pleas awnser this im 10 and this is giveing me a hard time to figer out
8/5 = 1 3/5
(5 x 1 = 5 + 3 = 8, to get 8/5)
13/12 = 1 1/12 (12 x 1 = 12 + 1 = 13, to get 13/12)
Hope this helped! :D
Make the biggest possible number using the digits below only once2,3,1
Write the fractions from parts (a) and (b) as a proportion, and solve to find out how many miles Alex's friend's house is from school. Round your answer to the tenths place. *
Question:
Alex skateboards at a constant speed from his house to school 3.8 miles away. It takes him 18 minutes.
a. What fraction represents his constant speed, c?
b. After school, Alex skateboards at the same constant speed to his friend’s house. It takes him 10 minutes. Write the fraction that represents constant speed, c, if he travels a distance of y.
c. Write the fractions from parts(a) and (b) as a proportion, and solve to find out how many miles Alex’s friend’s house is from school. Round your answer to the tenths place.
Answer:
(a) [tex]c = \frac{3.8}{18}[/tex]
(b) [tex]c = \frac{y}{10}[/tex]
(c) 2.1 miles
Step-by-step explanation:
Solving (a):
Given
[tex]Distance = 3.8\ miles[/tex]
[tex]Time = 18\ minutes[/tex]
Required
Determine the constant speed, c.
Speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
So, we have:
[tex]c = \frac{3.8}{18}[/tex]
Solving (b):
Given
[tex]Distance = y[/tex]
[tex]Time = 10\ minutes[/tex]
Required
Determine the constant speed, c.
Speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
So, we have:
[tex]c = \frac{y}{10}[/tex]
Solving (c): Write (a) and (b) as proportions and solve for y.
As a proportion, we have
[tex]\frac{y}{10} = \frac{3.8}{18}[/tex]
Multiply both sides by 10
[tex]10 * \frac{y}{10} = 10 * \frac{3.8}{18}[/tex]
[tex]y = 10 * \frac{3.8}{18}[/tex]
[tex]y = \frac{38}{18}[/tex]
[tex]y = 2.11111[/tex]
[tex]y = 2.1\ miles[/tex] ---- approximated
A solid silver spoon has a mass of 65.1g.
The volume of the spoon is 6.2cmº.
Calculate the density of silver.
Answer:
D=M/V
D=65.1/6.2
Density is 10.5 grams per centimetre cube
Step-by-step explanation:
How do you solve this trigonometry problem? Thank you
Answer:
3348 ft
Step-by-step explanation:
sin 21° = BC/AB = 1200/AB
AB = 1200 / sin 21° = 1200 / 0.358 = 3352 ≈ 3348
While sightseeing in Rome, Lance stopped to see the Colosseum. He learned that the height of the outer wall of the Colosseum measures 48 meters tall. If 1 meter is approximately 3.28 feet, about how high is the outer wall in feet?
Answer:
157.44 feet
Step-by-step explanation:
Given that:
Lance is out for sightseeing in Rome.
Lance went to see the Colosseum.
Height of the outer wall of the Colosseum = 48 meters
Unit Conversion formula:
1 meter = 3.28 feet
To find:
Height of the outer wall of the Colosseum in feet.
Solution:
It is simple problem for the conversion of unit where we already know the value in one unit and the conversion formula as well.
We have to simply find how much 48 meters will be when converted in feet.
1 meter = 3.28 feet
48 meter = 48 [tex]\times[/tex] 3.28 = 157.44 feet
PLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
The 7th graders at Wilson Middle School are taking a field trip to the science museum. So far, 12 students have turned in a total of $81 to pay for their ticket.
1. Write an equation to represent the cost.c, for t ticket
2. If all 72 students turn in their ticket money, how much money will be collected?
Answer: c = t * 6.75
Step-by-step explanation: each ticket costs $6.75
In the diagram, which pair of angles are vertical angles? 12 56 4 3 87 21 and 22 O 24 and 26 O Z6 and 28 O 25 and 23
Answer:
6 and 8
Step-by-step explanation:
vertical lines yes, theyre across from each other making it vertical line
Vertical angles are the angles at the opposite sides of a transversal
The vertical angles are <6 and <8
How to determine the vertical anglesFor a pair of angles to be vertical angles, there must be a transversal line, and the two angles must be at the either sides of the transversal
This means that the following angles are vertical angles
Angles 1 and 3Angles 2 and 4Angles 5 and 7Angles 6 and 8Hence, the vertical angles are <6 and <8
Read more about vertical angles at:
https://brainly.com/question/14362353
m∠2 = 4x + 4 and m∠1 = 5x − 2. Find x.
SHOW WORK
I ONLY NEED THE WORK!!!!!
Answer:
x = 6
Step-by-step explanation:
angles 1 and 2 are equal because the entire angle is bisected
so, 5x - 2 = 4x + 4
x - 2 = 4
x = 6
If you substitute 6 into each expression, they should be equal:
4(6) + 4 = 5(6) - 2
24 + 4 = 30 - 2
28 = 28
7th grade help me please:)
Answer:
4^9
262144
Step-by-step explanation:
Candice is taking a group nature hike in a park. There is a
$11.00 fee just to enter the park. In addition, the tour
group charges $0.14 per mile they hike. She brought
$81.00 with her. Find the maximum amount of miles
Candice can hike.
Answer:
500 miles
Step-by-step explanation:
81-11 is 70. 70 divided by .14 is 500 so that's 500 miles she can bike.
Answer:
500 miles
Step-by-step explanation:
To find out how many miles Candice can hike at max, use the equation 11 + 0.14x = 81.
11 + 0.14x = 81
Subtract 11 from both sides. This undoes the +11.
0.14x = 81 - 11
Subtract 11 from 81 to get 70.
0.14x = 70
Divide both sides by 0.14. This undoes the multiplication by 0.14.
x = 70/0.14
I recommend converting 0.14 into a fraction. That would be 7/50.
x = 70/(7/50)
Find the reciprocal of 7/50 (50/7). Switch the sign from division to multiplication.
x = (70 * 50)/7
Multiply 70 by 50 to get 3500.
x = 3500/7
Divide 3500 by 7 to get 500.
x = 500
At max, Candice can hike 500 miles.
What is the value of (1/7) 3?
Answer: 3/7
Step-by-step explanation:
1/7 x 3/1
MULTIPLY ACROSS
so 1 x 3 = 3 AND 1 x 7 = 7
so the answer is 3/7
Pls help me meememememmmememe
Step-by-step explanation:
A= 4(pi)r^2
A=4(3.14159265359)13^2
A=2123.72
**I dont know if it's right or wrong.**
For this, find the value of X for this parallelogram!! Thank you :)
Answer:
[tex]\huge\boxed{\sf x = 12 }[/tex]
Step-by-step explanation:
Opposite sides and angles of a parallelogram are equal.
So,
3x - 1 = 35
Add 1 to both sides
3x = 35 + 1
3x = 36
Divide 3 to both sides
x = 36 / 3
x = 12
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807how much is 45T in ounces
Answer:
Assuming T = ton:
1440000 ounces
Step-by-step explanation:
1 ton = 2000 pounds
1 pound = 16 ounces.
So 45 tons = 2000 * 16 * 45 ounces.
If PTS ~ PQR, find the value of x.
Step-by-step explanation:
[tex] \frac{6x - 2}{30} = \frac{5x + 13}{36} \\ 36(6x - 2) = 30(5x + 13) \\ 6(6x - 2) = 5(5x + 13) \\ 36x - 12 = 25x + 65 \\ (36 - 25)x = (65 + 12) \\ 11x = 77 \\ x = \frac{77}{11} \\ x = 7[/tex]
You can use the properties that similar triangles have sides scaled.
The value of x is 7.
Since it is given that PTS ~ PQR, thus, let the scaling is done by factor f. Then we have:
[tex]|PT| = f \times |PQ|\\ |TS| = f \times |QR|\\ |SP| = f \times |RP|[/tex]
Thus, we get the ratio of length of PT and length of TS as:
[tex]\dfrac{|PT|}{|TS|} = \dfrac{f \times |PQ|}{f \times |QR|} = \dfrac{|PQ|}{|QR|}[/tex]
How to find the value x?Using the values specified in the given figure for above obtained equation, we get:
[tex]\dfrac{|PT|}{|TS|} = \dfrac{|PQ|}{|QR|}\\
\\
\dfrac{36}{30} = \dfrac{5x + 13}{6x-2}\\
\\
\text{Cross multiplying, the denominators},\\\\
36(6x-2) = 30(5x+13)\\
216x - 72 = 150x + 390\\
216x - 150x = 390 + 72\\
66x = 462\\\\
x = \dfrac{462}{66}\\\\
x = 7[/tex]
Thus, the obtained value of x is 7.
Learn more about similar triangles here:
https://brainly.com/question/19387334
What is the first step in simplifying the expression
-5x2(4x3 - x2)2 ?
O Distribute -5x?
Square 4x - x2
Subtract 4x3 - 2
Answer:
Square 4x³ - x²
Step-by-step explanation:
Given the expression -5x²(4x³ - x²)²
The first step in simplifying the expression is to open the parenthesis by taking the square of 4x³ - x² as shown;
-5x²(4x³ - x²)²
= -5x²[(4x³)²- 2x²(4x³) + (x²)²]
= -5x²[16x^6- 8x^5 + x^4]
Hence the correct answer is Square 4x³ - x²
Ok I need help solving this...
A. 105
B. 120
C. 50
D. 125
Answer:
A - 105
Step-by-step explanation:
since the two measurements are supplements, you do x+82+x+112=180. then you get x=-7. then you do 112-7=105
Answer:
105°
Step-by-step explanation:
A line equals 180, so take the two expressions and set them equal to 180:
x+82+x+112=180
simplify:
2x+194=180
2x=-14
x=-7
now plug the x value into the bolded expression
x+112
-7+112 = 105°
Decimal and fraction form round it all the way
Answer:
The answer to the question provided is
[tex] \frac{22}{7} [/tex]
Answer:
x=-1
Step-by-step explanation:
A school conducts a survey about favorite sports.
The coach asks members of the basketball team to
name their favorite sport. Give a reason why the
sampling method may be biased.
Answer:
This survey may be unfair because they are asking the question to a group of kids who are already biased because they all play a specific sport and are most likely going to chooses that sport. Therefore the answers will most likely be basketball because it is the basketball team taking the survey
Step-by-step explanation:
Teri incorrectly solved the system of equations below. Correctly identify the error Teri made. 2x - 10 y = -30 x - 5y = 20 Step 1: x - 5y = 20 x = 5y + 20 Step 2: 2(5y + 20) - 10 y = -30 10y + 40 - 10y = -30 40 = -30
Answer:
See explanations below
Step-by-step explanation:
Given the system of equation
2x - 10 y = -30 ... 1
x - 5y = 20 ... 2
Step: From 2;
x = 20 + 5y ...3
Step 2: Substitute equation 3 into 1
2x - 10y = -30
2(5y+20) - 10y = -30
Open the bracket
10y + 40 - 10y = -30
10y - 10y + 40 = -30
0+40 = -30
40 = -30
The steps taken by Teri are correct all through. He didn't make any error whatsoever
2. What is the y-intercept of this graph?
O A. 1
O B.-2
O C. 2
O D.-4
Answer:
1
Step-by-step explanation:
Because it is where the like crosses with the y axis
Sketch a graph of the polynomial function f(x) =x3− 2x2. Use it to complete the following:
f is------ on the intervals (−∞, 0) and (0, 2).
f is------ on the interval (2,∞).f is on the interval (0, 4__3).
f is------ on the intervals (−∞, 0) and(4__3, ∞).
Answer:
We have the function:
f(x) = x^3 - 2*x^2
To sketch this, we need to graph some points, and then just draw a line that passes through the points.
The graph of this equation is shown below.
Now we can complete the question.
If the graph is below the x-axis in some interval, the function is negative in that interval
If the graph is above the x-axis in some interval, the function is positive in that interval.
If the graph goes up in a interval, then the function is increasing in that interval
If the graph goes down on an interval, then the function is decreasing in that interval.
Then:
1) f is------ on the intervals (−∞, 0) and (0, 2).
Here we can see that the graph is below the x-axis in those intervals, then here we have:
f is negative on the intervals (−∞, 0) and (0, 2).
2) f is------ on the interval (2,∞)
Here the answer is positive:
f is positive on the interval (2,∞)
3) fi is ------ on the interval (0, 4/3)
In the graph, you can see that the graph goes down in that interval, then the correct answer here is:
f is decreasing on the interval (0, 4/3)
4) f is------ on the intervals (−∞, 0) and (4/3, ∞).
In this case, we can see that the graph goes up in these intervals, then the correct answer here is:
f is increasing on the intervals (−∞, 0) and (4/3, ∞).
what is 1 3/4 divided by 4
Answer:
The correct answer is,
[tex] \frac{7}{16} [/tex]
hope it helps.
have a great day.
Answer:
1 3/4 ÷ 4 = 7/16.
Step-by-step explanation:
Is your answer.
If A is 13 cm B is 12 cm and c is 5cm then what is the area if that triangle
is the expression 3 (x + 1 1/2) - 3 equivalent to 3x + 1 1/2?
Answer:
Yes
Step-by-step explanation:
If you multiply the 3 into the equation it will give you 3x+3 3/2 -3 and if you simplify it the answer is 3x+4 1/2 -3=3x +1 1/2.
3x+1 1/2 = 3x + 1 1/2
Larry spent 75% of his weekly allowance a ticket for a concert. The ticket cost $15. How much is Larry's weekly allowance?
Answer:
20
Step-by-step explanation:
75% of 20 = 15
I believe this is correct and hope it helps :)
Find the area of a trapezoid Q Is 4 cm S is 7 cm are is 3 cm
Answer:67
Step-by-step explanation:
Please Help Me!!!!!!!
Answer:
D
Step-by-step explanation:
(6, 24) this ordered pair has an x-value of 6 and a y-value of 24
The only equation, if you substitute those values into it, which works is D.
24 = 4(6)
24 = 24