Answer:
900,000
I think is the answer
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.
What is the degree of 9x^4 + 3x
Answer:
4
Step-by-step explanation:
I really need help. And its setted up-
Answer:
4: 300
5: 95
have a good day :]
HELP ME PLEASE I NEED THESE
Answer:
13.5
Step-by-step explanation:
equilateral triangle (all sides are equal) thus, if one side is 4.5 u will need to take 4.5x3=13.5
Well let me help.
For the first Question, the question is asking for the perimeter of the plot so assuming the plot is a rectangle, the perimeter will be (2*3)+(2*4.3)
=6+8.6
=14.6km.
Question 2
The problem involves finding the perimeter of the triangular garden. since the garden is an equilateral triangle, the perimeter will be thrice the side given ("equilateral" means "equal sided triangle"). So the answer will be 3*4.5
= 13.5 km.
Question 3
Same type of question as Q2 but this type is isosceles triangle (only two equal sides with one being different)
So the perimeter will be (2*15)+20
=30+20
=50km.
I hope this'll help
A 24-f0ot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder
and the house both stt on level ground.
To the nearest whole nurmber, find the following values:
A The measure of the angle formed by the base of the ladder and level ground is
B. The measure of the angle formed by the top of the ladder and the second story window is
C. The distance, on level ground, between the base of the ladder and the house is
feet
degrees.
feet.
Answer:
c
Step-by-step explanation:
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.
https://brainly.com/question/8011401
#SPJ2
pls help
Quadrilateral ABCD is an isosceles trapezoid. What is the m∠B?
Answer:
<B=105°
Step-by-step explanation:
as it's an isosceles trapezoid. AD parallel to BC
ACCORDING TO THE QUESTION
75°+<B=180°
<B=180°-75°
<B=105°
1234567791234556677889
Step-by-step explanation:
The rate of pictures per minute.
8 pictures per minute
8 pictures/ minute
You are opening a savings account with $500 that you have saved. The bank offers 3.2% interest, compounded yearly. How much money will you have in you account after 7 years?
Answer:
You will have $623.3441462 in your account after 7 years
Step-by-step explanation:
The formula of the compounded interest is A = P [tex](1+\frac{r}{n})^{nt}[/tex] , where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periodst is the time in years∵ You are opening a savings account with $500
∴ P = 500
∵ The bank offers 3.2% interest, compounded yearly
∴ r = 3.2% ⇒ divide it by 100 to change it to decimal
∴ r = 3.2 ÷ 100 = 0.032
∵ The interest is compounded yearly
∴ n = 1
∵ The time is 7 years
∴ t = 7
→ Substitute these values in the rule above to find A
∵ A = 500 [tex](1+\frac{0.032}{1})^{1(7)}[/tex]
∴ A = 500 [tex](1.032)^{7}[/tex]
∴ A = 623.3441462
∴ You will have $623.3441462 in your account after 7 years
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.
The diagram shows a square based cuboid. Work out the volume of the cuboid. State the units of your answer.
Answer:
160cm³
Step-by-step explanation:
square based means equal sides
therefore 4cm×4cm=16cm²
16cm²×10cm=160cm³
easy question in photo
Answer:
14
Step-by-step explanation:
always subtract the highest number from the lowest and I believe that is your range
Answer:
14
Step-by-step explanation:
the first 3 terms of the arithmetic sequence are given. find an expression t_ n in the terms of n and write the tenth term of each sequence
Answer:
We get tₙ: [tex]\mathbf{t_n=an}[/tex]
10th term is [tex]t_{10}=10a[/tex]
Step-by-step explanation:
The given arithmetic sequence is: a,2a,3a
We need to find tₙ and tenth term
Finding tₙ
The formula used is: [tex]t_n=t1+(n-1)d[/tex]
We need to find d, the common difference
a₁ = a
a₂ = 2a
We can find common difference using the formula:
[tex]t_n=t_1+(n-1)d\\Put\:n=2\\t_2=t_1+(2-1)d\\2a=a+d\\d=2a-a\\d=a[/tex]
So, we get common difference d = a
Now, finding tₙ
[tex]t_n=t_1+(n-1)d\\t_n=a+(n-1)a\\t_n=a+an-a\\t_n=an[/tex]
So, we get tₙ: [tex]\mathbf{t_n=an}[/tex]
Now, finding 10th term
By putting n=10 in the equation [tex]t_n=an[/tex]
[tex]t_n=an\\Put\:n=10\\t_{10}=a(10)\\t_{10}=10a[/tex]
So, 10th term is 10a
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:
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 :)❤
ASAP! Please do 1-5 and show work if possible!
Answer :
(1) The radius of a circle is 1.5 m.
(2) The diameter of a circle is 28 ft.
(3) The radius of a circle is 10 in.
(4) The circumference of circle is 47.14 m.
(5) The circumference of circle is 44 yd.
Step-by-step explanation :
Part 1:
Given: d = 3 m
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{3m}{2}=1.5m[/tex]
The radius of a circle is 1.5 m.
Part 2:
Given: r = 14 ft
Now we have to determine the diameter of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Diameter of a circle = [tex]Radius\times 2[/tex]
Diameter of a circle = [tex]14ft\times 2=28ft[/tex]
The diameter of a circle is 28 ft.
Part 3:
Given: d = 20 in
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{20in}{2}=10in[/tex]
The radius of a circle is 10 in.
Part 4:
Given: d = 15 m
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
where,
C = circumference
d = diameter
So,
[tex]C=\frac{22}{7}\times 15m[/tex]
[tex]C=47.14m[/tex]
The circumference of circle is 47.14 m.
Part 5:
Given: r = 7 yd
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
or we can write,
[tex]C=\pi (2\times r)[/tex]
where,
C = circumference
d = diameter
r = radius
So,
[tex]C=\frac{22}{7}\times (2\times 7yd)[/tex]
[tex]C=44yd[/tex]
The circumference of circle is 44 yd.
Is RS perpendicular to DF? Select Yes or No for each statement ...
Answer:
depends
Step-by-step explanation:
Determine 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
Help would be great thank you!
Answer:
I think 3x doesn't belong because it is the only positive number.
I think -5x doesn't belong because it is the only one without a 3.
I think -3 doesn't belong because it is the only one without an x.
I think -3x² doesn't belong because it is the only one with an exponent.
Step-by-step explanation:
Just use one of the ones above!
(hope this helps!)
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.
Joe bought some CD's and DVD's at the store.
• He bought a total of 12 items.
• The CD's were $14.
• The DVD's were $22.
• He spent $200.
How many of each did he buy?
Answer: x=8 and y=4
Step-by-step explanation:
x+y=12 x=12-y x=12-4
14x+22y=200 x=8
14(12-y)+22y=200
168-14y+22y=200
-168 -168
-14y+22y=32
8y=32
8y/8=32/8
y=4
Determine the value of x in the diagram.
Answer:
65
it's 65 because it is.. cool
Herman is decorating his bedroom ceiling with lights. If the rectangular ceiling is 15 meters by 8 meters, how long will the string of lights need to be to reach from one corner of the ceiling to the opposite corner?
Answer:
x = 17 m
Step-by-step explanation:
The dimensions of the rectangular ceiling are 15 m by 8 m
We need to find the length of the string of lights need to be to reach from one corner of the ceiling to the opposite corner. Let it is x.
We need to find the diagonal of the rectangular ceiling. It can be calculated using Pythagoras theorem.
[tex]x^2=15^2+8^2\\\\x^2=225+64\\\\x^2=289\\\\x=\sqrt{289}\\\\x=17\ m[/tex]
So, the length of the string of lights is 17 m.
Write the equation in slope-intercept form.
(2,-3) and (1,3)
Lenny has a model train layout on a large, rectangular board. The length, l, of the board is 3 times the width, w. Which equation can be used to find P, the perimeter of the board?
Answer:
8w
Step-by-step explanation:
Given that:
Length = l
Width = w
l = 3w
Perimeter of rectangular board :
Perimeter of a rectangle = 2(l + w)
Perimeter = 2(3w + w)
Perimeter = 2(4w)
Perimeter of rectangular board = 8w
Solve the system: (MAFS.912-A-REI.3.6)
4+7=41
4
x
+
7
y
=
41
4+7=41
4
x
+
7
y
=
41
−7=−16
Step-by-step explanation:
[tex]4x + 7y = 41 \\ 4 \times ( - 7) + 7 \times ( - 16) = 41[/tex]
Find the missing side. Round your
answer to the nearest tenth.
9514 1404 393
Answer:
missing side: 29.7 feetmissing angle: 53.5°Step-by-step explanation:
The missing side is found using the Pythagorean theorem:
X = √(37^2 -22^2) = √885 ≈ 29.7 . . . feet
The missing angle is found using the cosine relation:
Cos = Adjacent/Hypotenuse
cos(x) = 22/37
x = arccos(22/37) ≈ 53.5°
_____
The posted question asks for side length; the picture asks for angle.
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
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
On a standardized test, Rasi answered the fast: 22 questions in 5 minutes. There are 7]
questions on the test. If he continues to answer questions at the same rate how long will
it take him to complete the test?
Answer:
they are directly proportional
so
5/22*7=1.59
he would finish in 1.59 min