Answer: 4+2n³
Explanation:
5+5n³ - 1-3n³
Step 1. Collect like terms
(5−1)+(5n³-3n³)
Step 2. Simplify
4+2n³
Answer:
4+2n³ o 2(2+n³)
Step-by-step explanation:
5. Sand is dumped off a conveyor belt into a pile at the rate of 2 cubic feet per minute. The sand pile is shaped like a cone whose height and base diameter are always equal. At what rate is the height of the pile growing when the pile is 5 feet high? (The volume of a cone is fr2h where r is the radius of the base and h is the height:)
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.
A cabinet holds 16 plates and
12 bowls. What is the ratio of plates
to bowls written in simplest form?
Answer:
4:3
Step-by-step explanation:
choose the definition for the function y={x+1 x≤2 x+2 x>2 y={x+1 x>2 x+2 x≤2 y={x+1 x
Answer:
D
Step-by-step explanation:
1234567791234556677889
Step-by-step explanation:
The rate of pictures per minute.
8 pictures per minute
8 pictures/ minute
Using trigonometry Solve the triangle please help me
Answer:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
Step-by-step explanation:
Given
The right-angled triangle ΔWXZ
m ∠ X = 90°m ∠ Z = 57°Hypotenuse WZ = 18We know that the sum of the measure of angles in any triangle is 180°.
Therefore,
m ∠ W + m ∠ X + m ∠ Z = 180°
substiute m ∠ X = 90° and m ∠ Z = 57° in the formula
m ∠ W + 90° + 57° = 180°
m ∠ W + 147 = 180°
m ∠ W = 180° - 147
m ∠ W = 33°
Therefore, the angle m ∠ W = 33°
NOW,
Determining the lengths of WX and XZ
Length XZ
Using the trigonometric ratio
The adjacent to 57° is XZ.
so
cos 57° = adjacent / hypotenuse
substituting adjacent = XZ, and hypotenuse = 18
cos 57° = XZ / 18
XZ = 18 × cos 57°
XZ = 9.80 units
Therefore, the length of XZ = 9.8 units
Length WX
As
m ∠ W = 33°
The adjacent to m ∠ W = 33° is WX.
so
cos 33° = adjacent / hypotenuse
substituting adjacent = WX, and hypotenuse = 18
cos 33° = WX/ 18
WX = 18 × cos 33°
WX = 15.1 units
Therefore, the length of WX = 15.1 units
Summary:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
Maya left her house and drove to the store. She stopped and went inside. From there,
she drove in the same direction until she got to the bank. She stopped and went
inside the bank. Then she drove home. The graph below shows the number of blocks
away from home Maya is 3 minutes after she left her house, until she got back home. How far away from her house was maya after 6 minutes?
It take her 20 minutes, but I don't know how the graph looks like yet, so I can only tell you that xx=20
-Millie
Maya is 6 blocks away from her home after 6 minutes of driving.
What is reflection of a geometrical image? What is a mathematical function, equation and expression? graph : A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is a graph in the question as shown in the image attached.
It can be seen that after 6 minutes of the home, Maya is 6 blocks away from the graph. The [y] coordinate corresponding to 6 minutes is 6 blocks away from the house.
Therefore, Maya is 6 blocks away from her home after 6 minutes of driving.
To solve more questions on graphical distances, visit the link below -
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One way to rename 5 3/10 is 4 8/10. True or False
Answer:
4 13/10
Step-by-step explanation:
im pretty sure this is right bc essentialy a group of one is because bc you took 1 away from 5 but it has to be 10 bc the denominator is 10 and then you addd the 10 to 3
Answer:
The statement above is false
Step-by-step explanation:
5 3/10= 5*10+3=53/10
now to simplify 53/10=1 43/10=2 33/10=3 23/10=4 13/10=5 3/10
So it's false.
Travis scored 18 point in the first basketball game of the season. he scored 3 fewer points in the second game than in the first game. find the total number of points Travis scored in the first and second games.
Answer:
isn't it 33?
Step-by-step explanation:
because at first they said he scored 18 and the second time he scored 3 fewer points than the first one so its 18+(18-3)=33
You are hiring a limousine. One company charges a $60 reservation fee plus another $15 per hour. A second company charges a $25 reservation fee plus another $20 per hour. Write and solve a linear equation to find the number of hours at which the total cost is the same for both companies.
Answer:
7 hours
Step-by-step explanation:
Step one:
given data
let the total charges be y and the number of hours be x
Company A charges
$60 reservation fee plus another $15 per hour.
so
y=60+15x----------1
Company B charges
$25 reservation fee plus another $20 per hour
y=25+20x------------2
Step two:
equate the 2 expressions above we have
60+15x=25+20x
collect like terms
60-25=20x-15x
35=5x
divide both sides by 5
x= 35/5
x= 7 hours
I need help pls so I can get a good grade
Answer:
Step-by-step explanation:
C is the answer.
Please help ASAP
Please I’ll mark you as brainlister
Answer: 15.
Step-by-step explanation:
You divide the degrees by the side length. You get 15. So 15 is the answer.
which translation moves the point back to its original position?
ii) Find the value of if the pair of parallel lines are cutting by a transversal and give reason for your answer
Please help me :(
Answer:
50
Step-by-step explanation:
When two parallel lines are cut by a transversal, we see that same side exterior angles sum to 180 degrees.
It's like the blue angle and the green angle add together to sum 180. So you can construct an equation knowing this to find what x is:
[tex]2x+30+x=180\\3x+30=180\\3x=180-30\\3x=150\\x=\frac{150}{3}\\x=50[/tex]
(The reason for the answer is the first line I wrote)
Andrew can type 1.5 pages in 10 minutes. At this rate, how many pages can Andrew type in 1 hour? pls help me hurry have do be done today
Answer:
Andrew will be able to type 9 pages in 1 hour
Step-by-step explanation:
1.5 x 6 = 9
Hope this helped !
Answer:
9 pages
Step-by-step explanation:
because if he typed 1.5 in 10 min, then 1.5 times 6 equals 9Determine the constant of proportionality in each of the representations below.
Answer:
Pretty sure is 15
Step-by-step explanation:
90 divided by 6 is 15.
Answer:
The constant of proportionality, k is 15
Step-by-step explanation:
The constant of proportionality is the ratio between two directly proportional quantities.
Proportional quantities can be described by the equation y = kx, where k is a constant ratio.
Here, "x" is the number of tickets and "y" is the number of dollars.
k = 30/2 = 15/1 or 15
k = 15
k = 60/ 4 = 30/2 = 15/1 or 15
k = 15
k = 90/6 = 30/2 = 15/1 0r 15
k = 15
When we take the ratio of x and y for all the given values, we get an equal value for all the ratios.
Therefore, the constant of proportionality, k is 15
Write the equation in slope-intercept form.
(2,-3) and (1,3)
Rauol measured the height of 12 different plants in his garden in April. He measured them again in June. What is the difference between the mean height in April and the mean height in June?
The question is incomplete. Here is the complete question.
Raoul measured the ehight of 12 different plants in his garden in April. He measured them again in June.
April Heights (in inches) 12 15 23 11 42 45 44 39 12 19 20 12
June Heights (in inches) 45 45 40 43 11 14 12 13 41 40 45 41
What is the difference between the mean height in April and the mean height in June?
Answer: The difference between means is 8.0
Step-by-step explanation: Mean is the average of a set of numbers.
It is calculated as:
[tex]\mu=\frac{\Sigma x}{n}[/tex]
where
x is the numbers in the set
n is how many numbers are there in the set
For heights in April, the mean is:
[tex]\mu_{1}=\frac{12+15+23+11+42+45+44+39+12+19+20+12}{12}[/tex]
μ₁ = 24.5
For heights in June, the mean os:
[tex]\mu_{2}=\frac{45+45+40+43+11+14+12+13+41+40+45+41}{12}[/tex]
μ₂ = 32.5
The difference between means:
μ₂ - μ₁ = 32.5 - 24.5 = 8.0
The difference between the mean height in April and in June is 8.0 inches.
plss help me find this hcf
3a-6,a²-4
Step-by-step explanation:
1st expression = 3a - 6 = 3 ( a - 2 )
2nd expression = a² - 4 = a² - 2² = ( a + 2) (a - 2)
The HCF is (a -2).
Hope it helps :)❤
Can someone please please answer this and explain it? my math teacher didn’t :( will give brainliest points for explanation!!! (Ignore work above that was for a different question)
Answer:
QR = 1
Step-by-step explanation:
PR = PQ + QR
PR = x + 19
PQ = 9
So now put what you know in the equation above.
PR = 9 + 2x + 19
PR also equals x + 19
so
x + 19 = 9 + 2x + 19
x + 19 = 2x + 28
19 - 28 + x = 2x
-9 + x = 2x
-9 = 2x - x
-9 = x
===================
QR = 2x + 19
QR = 2*-9 + 19
QR = -18 + 19
QR = 1
This really is kind of a nasty question. You don't expect to get a minus number of x.
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FU=-v+
Of(x) = - 3x + 4
o f(x) = -x +
Of = -3y + 4
Answer:
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
f(x) = -3x + 4
Step-by-step explanation:
I hope it's help
how to calculate directly propotonal
Answer: Direct Proportion
In mathematical statements, it can be expressed as y = kx. This reads as “y varies directly as x” or “y is directly proportional as x” where k is constant in the equation. Example: y is directly proportional to x, when x = 15, y = 30.
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5%
Complete Question
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5% for 3 years
Answer:
$ 12,934.61
Step-by-step explanation:
The formula for Compound Interest Compounded continuously is given as:
A = Pe^rt
A = Amount after t years
r = Interest rate = 2.5%
t = Time after t years = 3
P = Principal = Initial amount invested = $12,000
First, convert R percent to r a decimal
r = R/100
r = 2.5%/100
r = 0.025 per year,
Then, solve our equation for A
A = Pe^rt
A = 12,000 × e^(0.025 × 3)
A = $ 12,934.61
The total amount from compound interest on an original principal of $12,000.00 at a rate of 2.5% per year compounded continuously over 3 years is $ 12,934.61.
what percentage of a dollar is a half cent
Answer:50
Step-by-step explanation:
Answer: 0.005
Step-by-step explanation:
Half a dollar is 0.50.
1 cent of a dollar is 0.01.
half of 0.01 is 0.005
all parts please, i need this by the end of today and pls write answer in comments
Answer:
A
[tex] = \frac{78}{360} \\ = \frac{13}{60} [/tex]
B
[tex]let \: total \: number \: be \: x \\ \frac{13}{60} x = 1164 \\ x = \frac{1164 \times 60}{13} \\ x = 5372 \: movies[/tex]
C
A year has (4 × 12) weeks
= 48 weeks.
In 1 week = 9,568,000 movies
48 weeks = (48 × 9,568,000) movies
Average movies = 459.264 movies
D
Since 9.568 million movies are rented.
How about in one year ( 48 weeks )
Convert 1 year to weeks and compare with 1 week
There are 25 students in Mrs. Murphy's math class. Of these students, 10 have brown hair, 8 have black hair, 5 have blonde hair, and 2 have red hair. What percentage of students in Mrs. Murphy's class have blonde hair?
The percentage of students in Mrs. Murphy's class who have blonde hair will be 20%.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
There are 25 students in Mrs. Murphy's math class. Of these students, 10 have brown hair, 8 have black hair, 5 have blonde hair, and 2 have red hair.
Then the percentage of students in Mrs. Murphy's class who have blonde hair will be
Total students = 25
Then we have
[tex]\rm P = \dfrac{5}{25} \times 100\\\\P = 0.20 \times 100\\\\P = 20 \%[/tex]
More about the percentage link is given below.
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The line graph below shows the number of chocolate bars and ice lollies sold at a small shop over a year.
Pick the month below in which more ice lollies were sold than chocolate bars.
January
July
April
May
Answer:
July
Step-by-step explanation:
Month in which more ice lollies were sold than chocolate bars are: Jun, Jul, Aug
This means that from the answer options only July is valid.
Please helppp 21 points pleaseeeeeeee. If you don’t know the answer don’t answer please.
Answer:
f(x)=50x+20
0<x x<2
Step-by-step explanation:
hope it helps!
Paul's basketball coach decides that he will play only the first three quarters of every game this season. If he starts
the first 20 games, what expression can you write to model how much playing time he actually gets?
o 3.20
O = 20
o * + 20
03 - 20
Answer:
im thinking the answer is 3/4 x 20
Answer:
3.20
Step-by-step explanation:
i used math
Which of the following expression is equivalent to
Answer:
C
Step-by-step explanation:
No, the answer is C because when you raise a number to a negative exponent it is equivalent to one over the number to the same exponent, but positive. So, [tex]6^{-7} = \frac{1}{6^{7}}[/tex] and not [tex]\frac{1}{6^{-7}}[/tex].
Determine the value of x in the diagram.
Answer:
65
it's 65 because it is.. cool