The rate of change of the depth of water in the tank when the tank is half
filled can be found using chain rule of differentiation.
When the tank is half filled, the depth of the water is changing at 1.213 ×
10⁻² ft.³/hour.
Reasons:
The given parameter are;
Height of the conical tank, h = 8 feet
Diameter of the conical tank, d = 10 feet
Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.
Required:
The rate at which the depth of the water in the tank is changing when the
tank is half full.
Solution:
The radius of the tank, r = d ÷ 2
∴ r = 10 ft. ÷ 2 = 5 ft.
Using similar triangles, we have;
[tex]\dfrac{r}{h} = \dfrac{5}{8}[/tex]
The volume of the tank is therefore;
[tex]V = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}[/tex]
[tex]r = \dfrac{5}{8} \times h[/tex]
Therefore;
[tex]V = \dfrac{1}{3} \cdot \pi \cdot \left( \dfrac{5}{8} \times h\right)^2 \cdot h = \dfrac{25 \cdot h^3 \cdot \pi}{192}[/tex]
By chain rule of differentiation, we have;
[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \cdot \dfrac{dh}{dt}}[/tex]
[tex]\dfrac{dV}{dh}=\dfrac{d}{h} \left( \dfrac{25 \cdot h^3 \cdot \pi}{192} \right) = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64}}[/tex]
[tex]\dfrac{dV}{dt} = \dfrac{3}{5} \ ft.^3/hour[/tex]
Which gives;
[tex]\dfrac{3}{5} = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64} \times \dfrac{dh}{dt}}[/tex]
When the tank is half filled, we have;
[tex]V_{1/2} = \dfrac{1}{2} \times \dfrac{1}{3} \times \pi \times 5^2 \times 8 =\mathbf{ \dfrac{25 \cdot h^3 \cdot \pi}{ 192}}[/tex]
Solving gives;
h³ = 256
h = ∛256
[tex]\dfrac{3}{5} \times \dfrac{64}{25 \cdot h^2 \cdot \pi} = \dfrac{dh}{dt}[/tex]
Which gives;
[tex]\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}[/tex]
When the tank is half filled, the depth of the water is changing at 1.213 × 10⁻² ft.³/hour.
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If a function g is defined as
g(x) = 6 - 4x,
and y=g(x), what can we say about the relationship between x and y?
Select the correct answer below:
Answer:
(d) y is dependent on x
Step-by-step explanation:
The relation ...
y = g(x)
tells you that y is dependent on x; x is the independent variable.
What is the value of 5³ ? 15 25 125 625
Answer:125
Step-by-step explanation:
5*5*5=125
Answer:
125Step-by-step explanation:
5*5=25
25*5=125
700+500+100-300 Giving Brainliest
Step-by-step explanation:
= 700 + 500 + 100 - 300
= 1200 + 100 - 300
= 1300 - 300
= 1000
What is the slope of the line parallel to the line below?
Answer:
-3/4
Step-by-step explanation:
Katie gets an order for 325 cupcakes which of these correctly shows the number
Answer:
A and C
Step-by-step explanation:
325 and 300 + 20 +5= 325
There is a sale on a gallon of milk at the grocery store. The original price was $2.99 and the new price is $2.49. What is the percentage of decrease on the gallon of milk? Round your answer to the nearest whole percent
A) 17%
B) 50%
C) 23%
D) 20%
Answer:
c
Step-by-step explanation:
Answer: a
Step-by-step explanation:
2.99 - 17% = 2.49
William and Ronald share 160 g strawberries.
They divide the fruit in the ratio 2:8
How many strawberries does Ronald get?
Answer:
128 g
Step-by-step explanation:
Ronald's share of the strawberries can be found from the proportion ...
ronald's/total = 8/(2+8)
ronald's = (160 g)(8/10) = 128 g
Ronald got 128 g of strawberries.
_____
William got 32 g.
Step-by-step explanation:
total ratio=10
William's ratio=2
Roland's ratio=8
Roland's share=8/10×160g
=4/5×160g
Roland's share =128g.
Two angles are supplementary if their sum is 180°. The larger angle measures six degrees more than five times the measure of a smaller angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.
Step-by-step explanation:
smaller is X
larger is 6X
Their sum is 180
X + 6x = 180
7x = 180
x = 25.7142
The smaller angle is 25.7142
The larger angle is 154.2857142857
Help me plsssssssssssssssss
Answer:
5/2
Step-by-step explanation:
(5/3+4/3)/4-2=3/4-2=-5/4
(-5/4)*(-2)=5/2
can someone help me please
Answer:
21
Step-by-step explanation:
which of the following statement is correct
A,. 0.72 is greater than 8/11
B, 0.72 is equal to 8/11
C. 8/11 is less than 0.72
D. 8/11 is greater than 0.72
What is the area of this figure
Enter your answer in the box
8m
5m
9m
Answer:
9 m
Step-by-step explanation:
Area of parallelogram: Base x height
Area of triangle: 1/2 x base x altitude
=> (9 x 5) + (1/2 x 9 x 8) m² = Area of the figure.
=> 45 + (9 x 4) m² = Area of the figure.
=> 45 + 36 m² = Area of the figure.
=> 81m² = Area of the figure.
=> 9m = Area of the figure.
Therefore, 9 m is your answer.
Hoped this helped.
Answer:
81
Step-by-step explanation:
how can you use act it out to show the related addition facts? use the math word addend and sum in your answer . 6+2=8 2+6=8
Answer:
6+3=9 3+6=9 are sum other sum are
4+3=7 3+4=7
5+4=9 4+5=9
Acting out scenarios with objects like apples can visually demonstrate the commutative property of addition for related facts like 6+2=8 and 2+6=8.
⇒ For 6+2=8; Imagine you have 6 apples, and a friend gives you 2 more apples. Physically place 6 apples in one pile, then add 2 more apples to the pile. Count all the apples together to reach 8.
⇒ For 2+6=8; Similarly, start with 2 apples and then have your friend give you 6 apples. Place the 2 apples in one pile and then add 6 more apples. Count all the apples together to again reach 8.
By acting out these scenarios with physical objects like apples, we are visually representing the addition facts. This helps to understand concept that addition is commutative, meaning the order of the numbers doesn't affect the sum.
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Complete the equation so that it has one solution.
-2z+3-z=□-4z+2
Select all the possible answers.
A. 7
B. -z
C. z
D. z-4
E. z+2
F. 2z+3
PLEASE HELP
2(3x - 1) = 6x - 2
What the answer
Answer:
2(3x-1)=6x-2
6x-2=6x-2
6x-6x=2-2
x=0
Step-by-step explanation:
l
Find the area:
giving 100 points
In order to determine the area of a composite shape, the shape must divide into smaller shapes, the areas of which must then add back together.
[tex]6*12+8*10=152[/tex]
The area is 152 squared inches.
Answer:
152 in²
Step-by-step explanation:
Separate the composite figure into two rectangles (see attachment).
Area of a rectangle
[tex]\large\boxed{A = wl}[/tex]
where:
w is the width.l is the length.Area of rectangle 1
[tex]\begin{aligned}\implies A&=6 \times 20\\&=120\; \sf in^2\end{aligned}[/tex]
Area of rectangle 2
[tex]\begin{aligned}\implies A&=(10-6) \times 8\\&=4 \times 8\\&=32\; \sf in^2\end{aligned}[/tex]
Total Area
[tex]\begin{aligned}\implies \textsf{Total Area}&=120+32\\&=152\; \sf in^2\end{aligned}[/tex]
Does the point (3,1) satisfy the equation y=9x? Explain how you know
Answer:
No
Step-by-step explanation:
Swap the points into the equation:
y=9x
1=9*3
1=27
The equation is false, hence it doesn't satisfy the
equation
A gumball machine contains 3 red gumballs and 3 white gumballs.
Two gumballs are purchased, one after the other, without replacement.
Find the probability that at least one gumball is white.
State your answer as a decimal rounded to the nearest hundredth.
Answer:
i dont answer this question only explain
Step-by-step explanation:
A gumball machine contains 7 red, 8 orange, 9 purple, 7 white, and 5 yellow gumballs. Tyson buys 3 gumballs. Find each probability, assuming that the machine dispenses the gumballs at random.
What is 147+34,526x268-140
Answer:
9252975
Step-by-step explanation:
34,526x268=9252968
9252968+147=9253115
9253115-140=9252975
Use the order of operations to order the steps to evaluate the expression
(60 + 15) + 3 - 2(4) + 23
Divide 75 by 3
Multiply 2 by 4
Cube 2
Add 17 and 8
Subtract 8 from 25.
Add 60 and 15.
Answer:
93Step-by-step explanation:
I answer for what I understand,
the question is really confused.
(60 + 15) + 3 - 2(4) + 23 =
75 + 3 - 8 + 23 =
78 - 8 + 23 =
70 + 23 =
93
Answer:
Step-by-step explanation:
Add 60 and 15
Cube 2
Divide 75 by 3
Multiply 2 by 4
Subtract 8 and 25
Add 17 and 8
Sorry for the scribbling on the book it wasn’t me but I need real answers don’t give me no blank answer bs
Hi there!
-----------------------------------------------------------------------------------------------------------------
y=2-3x
2=2-3(0)
2=2-0
2=2
So we get a true statement. So Option 1 is correct.
-5=2-3(1)
-5=2-3
-5=-1
We get a false statement. Therefore, this isn't the right ordered pair.
Now, let's try the next ordered pair:
-7=2-3(3)
-7=2-9
-7=-7
So this ordered pair is a solution of this equation as well.
Now, try the next one:
5=2-3(-1)
5=2+3
5=5
So this is a solution as well.
8=2-3(-2)
8=2+6
8=8
So this pair is a solution as well.
-3=2-3(-3)
-3=2+9
-3=11
So here, we get a false statement. Therefore, this isn't the solution.
y=-x/3-2
-4=-3/3-2
-4=-1-2
-4=-3
We get a false statement. Therefore, this isn't the solution.
(2, -6) isn't a solution as well.
Hope it helps!
~SparklingFlower (:
--------------------------------------------------------------------------------------------------------------
-1/3 + 1
Please answer quickly
Answer:
2/3
Step-by-step explanation:
-1/3 + 1
2/3
This problem is the same as writing 1 - 1/3.
1 can become 1/1, which can become 3/3.
3/3 - 1/3 = 2/3
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
0.6 (its repeating meaning there are an infinite amount of 6's) or the fraction form, 2/3
Step-by-step explanation:
which point lies on the function y=3x+9
A. (-4,3)
B. (3,18)
C. (-2,5)
D. (2,14)
Answer:
B is the answer.
Step-by-step explanation:
Im just smart.
Need help pre college
Answer:
y = -2x + 12
Step-by-step explanation:
Use the slope intercept equation y=mx+c
Now, c is unknown so substitute all known information to calculate it
That is, 2=-2(5)+c
Solving that we get, c=12
We already know m=-2
Substituting m and c into the slope intercept equation we find that the answer is, y= -2x+12
Write y-4x=7 in standard form
Answer:
y-4x-7.
HOPE ITS HELPSS
a house has increased in value by 33% since it was purchased. if the current value is 532,000, what was the value when it was purchased?
Answer:
$400,000
Step-by-step explanation:
532000 = x(1 + 0.33)
x = 532000 / 1.33
x = 400000
Consider the line y = -6x + 9
Find the equation of the line that is perpendicular to this line and passes through the point (3, 6)
Find the equation of the line that is parallel to this line and passes through the point (3,6)
Answer:
6x - y -12=0
Step-by-step explanation:
Given line ,
=> y = -6x + 9
On comparing to the slope intercept form ,
m = -6The slope of the perpendicular line will be negative reciprocal of its slope , say m'
m' = 1/6The given point is (3,6) . On using point Slope form of the line we have ,
=> x - 3 = 1/6 ( y - 6)
=> x - 3 = y/6 - 1
=> x -2 = y/6
=> 6x - 12 = y
=> 6x - y -12 = 0
The amount of pollution entering the atmosphere varies directly as the number of people living in an area. If 40,000 people create 29,600 tons of pollutants,
how many tons enter the atmosphere in a city with a population of 500,000?
Help please
Answer:
370 000
As it varies directly we know the values are directly proportional.
This means we can calculate the ratio of people to tons of pollutants and apply it to 500 000
So, 29600/40000= 0.74
Now, 500 000 × 0.74 = 370000
Answer: 370000 t
Step-by-step explanation:
[tex]40000 ~p - 29600 ~ t \\\\ 500000 ~ p- x ~ t \\\\ x=\dfrac{500000\cdot 29600}{40000}=\dfrac{50\cdot 29600}{4} =7400\cdot 50 =\bf 370000 \ t[/tex]
the next model of sports car will cost 4.5% less than the current model. the current model costs 53,000. how much will the price decrease in dollars? what will be the price of the next model
Answer: $50,615
Step-by-step explanation:
53,000×4.5%=2,385
53,000 - 2,385 = $50,615
A line passes through point (-10, 1) and has a slope of -
2
Write an equation in Ax+By=C form for this line.
Use integers for A, B, and C.
Step-by-step explanation:
(X1, Y1) = (-10 , 1)
slope/m = -2
y - y1 = m(x - x1)
y - 1 = -2(x + 10)
y = -2x - 20 + 1
y = -2x - 19
2x + y = -19 → equation
