Answer:
1508527.582 cm³/min
Step-by-step explanation:
The net rate of flow dV/dt = flow rate in - flow rate out
Let flow rate in = k. Since flow rate out = 6800 cm³/min,
dV/dt = k - 6800
Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone
dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)
So, dV/dt = (πr²dh/dt)/3
Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min
Now, by similar triangles, h/r = h'/r'
r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm
Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.
The net rate of increase of water is dV/dt = (πr'²dh/dt)/3
dV/dt = (π(262.5 cm)² × 21 cm/min)/3
dV/dt = (π(68906.25 cm²) × 21 cm/min)/3
dV/dt = 1447031.25π/3 cm³
dV/dt = 4545982.745/3 cm³
dV/dt = 1515327.582 cm³/min
Since dV/dt = k - 6800 cm³/min
k = dV/dt - 6800 cm³/min
k = 1515327.582 cm³/min - 6800 cm³/min
k = 1508527.582 cm³/min
So, the rate at which water is pumped in is 1508527.582 cm³/min
if triangle 3 shows a 100 degree rotation of triangle 1 about point p what is the degree of intersection of lines m and n?
The given transformations are rigid transformations, such that
the image and the preimage have the same dimensions.
Correct responses:
The degree of the intersection of lines m and n is; 50°This image also shows two A. reflection about lines m and then line n. How can the angle between the lines be determined, and what is a reflection?Given;
The images of triangle 1 are; Triangle 2, and triangle 3
Taking the image of line m as line m, we have;
Required:
The degree of the intersection of lines m and n
Solution:
Triangle 2 is the reflection of triangle 1 across line m, and
triangle 3 is the reflection of triangle 2 across line n
The distance of triangles 1 and 2 from line m are equal
The distance of triangle 2 and 3 from line n are equal.
Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is
equal to the degree of rotation of triangle 2 to triangle 3, θ₂,
we have;
θ₁ = θ₂
100° = θ₁ + θ₂ = 2·θ₁
θ₁ = θ₂ = 100° ÷ 2 = 50°
The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°
The degree of the intersection of lines m and n = 50°The transformation to give triangle 2 from triangle 1 is a reflection about line m.
Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.
Therefore;
The image also shows two A. Reflections about line m and then line n.Learn more about rigid transformations here:
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https://brainly.com/question/12040896
Which proportion would you use to find what number 15 is 30% of?
A: n/100 = 15/30
B: n/100 = 30/15
C: 30/100 = n/15
D: 30/100 = 15/n
Answer:
A: n/100 = 15/30 is the correct option
Betty rolled a fair number cube and a fair game die with eight sides numbered 1 through 8. What is the probability of getting an odd number on both?
Answer:
4/8 or 1/2
Step-by-step explanation:
Find the surface area and the volume of the prism.
10
26
18
Needing a little help
Simplify as far as possible
Please help
x²+3x²-4x²+5x
Answer:
I think 5x is the answer
stay safe
What is the function of this
Answer:
f(x) = x⁴ + 2x³ - 3x² - 4x + 4
Step-by-step explanation:
we have 3 turnarounds and no negative y values (so, it should be a function based on x⁴), 2 of these turnarounds are also directly on the x-axis (y=0).
f(0) = 4
f(1) = 0
f(-2) = 0
an equation based on x⁴ would have 4 interceptions with the x-axis. since we have only 2 here, then there must be 2 pairs of equal interceptions.
based on the known x-interceptions (x=1, x=-2) we can start with the approach
(x-1)(x+2)
this world give us a quadratic equation (based on x²).
the trick is now to get this to x⁴ without adding additional x-interceptions. that is done by simply "reusing" the ones we already used.
(x-1)(x+2)(x-1)(x+2) = (x-1)²(x+2)²
(x-1)²(x+2)² = (x² - 2x + 1)(x² + 4x + 4) =
x⁴ - 2x³ + x² + 4x³ - 8x² + 4x + 4x² - 8x + 4 =
x⁴ + 2x³ - 3x² - 4x + 4
What is the measure of an interior angle in a regular octagon
Answer:
I think the sum of the measures of the interior angles of an octagon =(8−2)180° . The sum of the measures of the interior angles of an octagon is 1080° .
I hope this help!:)
Answer:
[tex]135^{\circ}[/tex]
Step-by-step explanation:
The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, the sum of its interior angles is equal to:
[tex](8-2)180=6\cdot 180=1,080^{\circ}[/tex]
By definition, a regular polygon is a polygon with equal sides and angles. An octagon has 8 sides and 8 angles. Therefore, a each interior angle of a regular octagon must be equal to:
[tex]\frac{1,080}{8}=\boxed{135^{\circ}}[/tex]
PLS HELP!!! The problem is in the photo attached
Answer:
The answer is C!
Step-by-step explanation:
Answer:
D
NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"
Step-by-step explanation:
Help me solve this problem please
Answer:
A is ur answer
Step-by-step explanation:
Which expression is equivalent to 2(a+2b)-a-2b
o 3a+2b
o 3a-2b
o a-2b
Answer:
a -2b
Step-by-step explanation:
2(a+2b)-a-2b
Distribute
2a+4b -a-2b
Combine like terms
a -2b
Thank you so much thank y’all
Answer:
x > 20
Step-by-step explanation:
5x + 20 > 120
Divide 5 on both sides,
x + 4 > 24
x + 4 - 4 > 24 - 4
x > 20
Match each cone's measures to its corresponding volume.
Answer:
base area=16π in² height=6 in ⇒ base area= πr²
16π²=π(r)²
r=4 in
v=1/3 ×π (4)²×(6)
v=32π in²
-------------
v=1/3 π(12/2)²×5
v=1/3π(31)×5=
v=60π in³
-------------
v=1/3 π×(25×4)=
v=100π/3 in³
OAmalOHopeO
Find the equation of the line formed made by joining the pints (-2,-4),(-8,10)
Answer:
y = (-7/3)x - 26/3
Step-by-step explanation:
To find the equation of a line given two points, we can first define an equation of a line to be y= mx +b, with m being the slope and b being the y intercept.
To calculate the slope, we can use the formula (change in y)/(change in x), or
(y₂-y₁)/(x₂-x₁). If we define (-2, -4) as point 1 (meaning -2 is x₁ and -4 is y₁) and (-8, 10) as point 2 (it doesn't matter which point is point 1/2), we can say that the slope is equal to
(10-(-4)) / (-8-(-2)
= 14/(-6)
= -7/3
Therefore, our formula so far is
y = (-7/3)x + b
To figure out b, we can plug in a point, e.g. (-8, 10) and solve for b. Plugging this in, we get
10 = (-7/3)(-8) + b
10 = 56/3 + b
subtract 56/3 from both sides
10 - 56/3 = b
= 30/3 - 56/3
= -26/3
Therefore, our equation is
y = (-7/3)x - 26/3
Kasey has three pieces of wood that measure 9 inches, 12 inches, and 21 inches. Can she make a right triangle
with the three pieces of wood (without cutting or overlapping)?
Answer: No
Step-by-step explanation:
Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:
9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.
What type of graph can show positive correlation, negative correlation, or no correlation?
Answer:
A scatter plot can show a positive relationship, a negative relationship, or no relationship. If the points on the scatter plot seem to form a line that slants up from left to right, there is a positive relationship or positive correlation between the variables.
What is the product of `4` and `-2x + 3`?
9514 1404 393
Answer:
-8x +12
Step-by-step explanation:
The distributive property can help you simplify the product.
(4)(-2x +3) = (4)(-2x) +(4)(3) = -8x +12
The speed of a toy car is 20 m/s. The time taken for a trip is 200seconds. Find the
distance covered in meter
Distance = time/ speed
Distance = 200 seconds / 20 m/s
Distance = 10 meters
Answer:
Distance:
[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 20 \times 200}} \\ { \tt{ = 4000 \: metres}}[/tex]
On a unit circle, the terminal point of 0 is (1/2, square root of 3/2) what is 0
Answer: pi/6
explanation: took test
The value of θ on a unit circle where the terminal point of θ is (1/2,square root 3/2), is 60°.
Terminal PointThe measure of the angle in degrees or radians over the circle, at the endpoint on the coordinate plane is known as terminal point
How to solve this problem?Given On a unit circle, the terminal point of θ is [tex](\frac{1}{2},\frac{\sqrt{3} }{2} )[/tex]According to image below the value of θ at terminal point (1/2,square root 3/2) is 60 degrees.Thus the value of θ at terminal point on a unit circle (1/2,square root 3/2) is 60 degrees.
Learn more about Terminal Point here:
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#SPJ2
53. A right triangle has a hypotenuse measuring 15 inches and one leg measuring 9 inches What is the length, in inches, of the other leg of the triangle?
A. 3
B.6
C. 10
D. 12
Answer:
D
Step-by-step explanation:
Pythagorean
[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)
=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]
Now measure the lengths of the sides of polygon ABCD and tbe lengths of the sides of the translated images. Record the measurements in the table.
Answer:
3.16, 3.16, 3.16
3.16, 3.16, 3.16
1.41, 1.41, 1.41
3.16, 3.16, 3.16
Step-by-step explanation:
Answer:
Length Length Length
3.16 3.16 3.16
3.16 3.16 3.16
1.41 1.41 1.41
3.16 3.16 3.16
Step-by-step explanation:
An automobile manufacturing plant produced vehicles today: were sedans, were trucks, and were motorcycles. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. What is the probability that two motorcycles will be selected
Answer:
120 / 561
Step-by-step explanation:
An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected
16/34 X 15 X 33
Can someone help me with this math homework please!
Answer:
X1 = 2 Y1 = -5
Step-by-step explanation:
math simple slope
Please help me find this box guys I’m struggling
Answer:
(0,-9)
Step-by-step explanation:
To find the y-intercept, substitute x=0
y=(0)^2+4(0)-9
=-9
Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation
Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
The equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 4x - 9 ← is in standard form
with a = 1, b = 4 , then
x = - [tex]\frac{4}{2}[/tex] = - 2
x = - 2 is the equation of the axis of symmetry
Substitute x = - 2 into the equation for corresponding y- coordinate of vertex
y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13
vertex = (- 2, - 13 )
To find the y- intercept let x = 0 and solve for y
y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9
y- intercept = (0, - 9)
From the standard form of the parabola
• If a > 0 then vertex is a minimum
• If a < 0 then vertex is a maximum
Here a = 1 , that is > 0
vertex (- 2, - 13 ) is a minimum
The cars of a circular Ferris wheel at an amusement park are equally spaced about the wheel's circumference. They are numbered consecutively beginning with 1. The cars numbered 14 and 30 lie on opposite ends of a diameter. How many cars are on the Ferris wheel?
Answer:
32 cars
Step-by-step explanation:
we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32
Math step-by-step:
30-14=16
16×2=32
for 10 points Valerie set out to bicycle from TBLS to the beach, a distance of 10 miles. After going a short
while at 15 miles per hour, the bike developed a flat tire, and the trip had to be given up. The
walk back to TBLS was made at a dejected 3 miles per hour. The whole episode took 48
minutes. How many miles from TBLS did the flat occur?
Answer:
2 miles
Step-by-step explanation:
Given that :
Total distance = 10 miles
Distance = speed * time
Let distance from TBLS to flat Tyre spot = d
Time = distance / speed
Since the distance to and distance fro took a total of 48 minutes;
Hence ;
d/15 + d/3 = 48 minutes
48 minutes = 48/60 = 0.8 hours
d/15 + d/3 = 0.8
(d + 5d) / 15 = 0.8
d + 5d = 15 * 0.8
6d = 12
d = 12 / 6
d = 2 miles
Distance from TBLS to point bicycle had flat tyre is 2 miles
When each edge of a cube is increased by 50%, by what percent is the surface area of the cube increased?
Answer:
125 % increase
Step-by-step explanation:
assume a cube of side 10
then each side surface area = 100 * 6 = 600 units
now consider sides 15 (+50%)
each side = 225 .... 225 * 6 = 1350
(1350 - 600)/600 = 1.25 = 125 % increase
| 2. You are given an isosceles trapezoid ABCD with median XY. Complete the following.
m
Answer:
m∠CDA=65°
Step-by-step explanation:
This is because an isosceles trapezoid has both pairs of base angles that are equivalent to one another.
Find the distance between the two points rounding to the nearest tenth (if necessary). ( − 8 , 6 ) and ( − 6 , 0 )
Answer:
[tex]\sqrt{40\\}[/tex], [tex]2\sqrt{10}[/tex], or 6.3 (rounded).
Step-by-step explanation:
Use the distance formula, [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \\x_1 is -8, y_1 is 6, x_2 is -6, y_2 is 0.[/tex]
A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this spinner 1000 times, how many times do you expect it to land on Red?
Answer:
83 spins
Step-by-step explanation:
Number of red spins = n
Number of orange spins = 8n
Number of yellow spins = 3n
Total number of trials = 240
Total number of spins :
(n + 8n + 3n) = 240
12n = 240
n = 240 / 12
n = 20
Number of red spins = 20
(1000/240) * n
4.1666666 * 20
= 83.333
= 83 spins
