The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]
Step-by-step explanation:
Given information:
[tex]\text{\bold{The diameter of cone}}=10\;\rm{ ft.}[/tex]
[tex]\rm{The\; height\; of\; the\; cone}= 15\;\rm{ ft.}[/tex]
[tex]\text{The rate at which the water is leaking }= 12 \; \rm ft^3/hr.[/tex]
[tex]\text{Volume of water tank}=27 . \pi \; \rm ft^3[/tex]
Now,
If ,we take a right circular cone with radius r and height h , its volume
[tex]\text{volume (V)} = (1/3) \times \pi \times \rm{r^3 \times h[/tex]
Now, the radius of cone when the volume of water tank is given
[tex]\frac{1}{3}\times \pi \rm\times{r^2 \times h = 27 \times \pi[/tex]
The ratio of height to radius of the cone :
[tex]\text {h/r} =3[/tex]
[tex]\text r = \text h/3[/tex]
Now calculate :
[tex]dV/dt= dV/dh \times dh/dt[/tex]
Which gives:
[tex]12 = \frac{d(\text h^3/27 \pi)}{dh} \times \frac{d\text h}{dt} \\\\\frac{d\text h}{dt} = \frac{12}{\pi \text h^2/9}[/tex]
As ,
[tex]27=\frac{1}{27 \times h}[/tex]
[tex]\text h^3=27^2\\\text h= 9\\[/tex]
Now,
[tex]dh/dt=12/(\pi.\text h^2/9)\\dh/dt=4/3\pi\\dh/dt=0.4244\\[/tex]
Hence, The rate at which the height of water tank changing is [tex]0.4244 \; \text {ft./hr}[/tex]
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Simplify 7 +(-3). (1 point)
Answer:
4
Step-by-step explanation:
7-3=4
Answer:
7-3=4
Step-by-step explanation:
Im not quite sure if this is what you were asking for but here
what is -12x-17=-125
Answer:
X = 9
Step-by-step explanation:
A circle has a circumference of 452.16 units. what is the radius
Answer:
Circumference = 2*r*pi
452.16 = 2*r*pi
226.08 = r*pi
226.08 = r*(3.14)
72 = r
The radius is 72
Step-by-step explanation:
The rule R x-axis ∘ T⟨–5, 3⟩ is applied to the point (–3, –2). Where is the image in the coordinate system?
Given:
Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩.
The point is (-3,-2).
To find:
The image of given point after the transformation.
Solution:
Consider the given point be P(-3,-2).
Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩. If means first we have apply translation T⟨–5, 3⟩ after that we have to apply reflection R x-axis.
If a figure translated by T⟨–5, 3⟩, then
[tex](x,y)\to (x-5,y+3)[/tex]
[tex]P(-3,-2)\to P'(-3-5,-2+3)[/tex]
[tex]P(-3,-2)\to P'(-8,1)[/tex]
If a figure reflected by R x-axis, then
[tex](x,y)\to (x,-y)[/tex]
[tex]P'(-8,1)\to P''(-8,-1)[/tex]
Therefore, the image of given point after transformation is (-8,-1).
3. Let f(x) = 4x + 3 and g(x) = x - 2, find:
a) f(g(5))
if two thirds of a number is 56, what is three-quarters of that number?
Answer:
84
Step-by-step explanation:
56/2 = 28
28 x 3 = 84
To check work: 84/3 =28
What is an equation of the line that passes through the point (-2,-3) and is parallel to the line 5x+2y=14
Answer: y=-5/2x-8
Step-by-step explanation:
The equation of the line that passes through the point (-2,-3) and is parallel to the line 5x+2y=1 is
y = (-5/2)x - 8
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
We have,
An equation of the line that passes through the point (-2,-3) and is parallel to the line 5x+2y=14.
The equation of a line can be written as:
y = mx + c _____(1)
The line 5x + 2y = 14 can be written in the form y = mx + c.
5x + 2y = 14
2y = -5x + 14
y = -5/2x + 7
m = -5/2 ____(2)
The equation of the line passes through the point (-2, -3) so,
From (1) and (2) we get,
y = mx + c
-3 = -5/2 x -2 + c
-3 = 5 + c
c = -3 - 5
c = -8 ____(3)
Now,
From (1) , (2), and (3) we get,
The equation of the line is
y = (-5/2)x - 8
Thus,
The equation of the line that passes through the point (-2,-3) and is parallel to the line 5x+2y=1 is
y = (-5/2)x - 8
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Solve the following equation (image attached).
Answer:
Step-by-step explanation:
Tickets for the school play cost $7 each. Each member of the cast gets 1 free ticket for a family member. For the run of the play, 210 tickets are collected, including all the free tickets, and the box office makes $1,358 from ticket sales. The equation that models this situation is7(210 – c) = 1,358 where c is the number of cast members. How many cast members are in the play?
Answer:
there are 16 cast members.
Step-by-step explanation:
7(210-c)=1358 multiply everything in the parentheses by 7
1470-cx=1358
-7c=-112 subtract 1470 from both sides
c=16 divide -112 by -7
c=16
13) If a+b+c+d+e=0 and a+c+e=b+d then which of the following is factor of ax^4+bx^3+cx^2+dx+e
x+1
x-1
x^2-1
All the above
Answer:
I think its opinion 3 or all the above am not sure
!PLEASE ANSWER FAST! !30 POINTS!
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In the 1960s, the average price for an ear of corn was 4.17 cents. In the 1980s, the average price went up to 9.83 cents. How much did the average price go up?
4.97 cents
5.66 cents
7 cents
14 cents
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I'm pretty dumb so I don't know the answer to this :b
so please answer this :(
Answer:
5.66
Step-by-step explanation:
Answer:
im pretty sure you just subtract 4.17 from 9.63 LOL so 5.66 HAHA
Step-by-step explanation:
8x + 7(2-3x) = -6(2x + 5)
Answer:
x = 44
Step-by-step explanation:
8x + 7(2-3x) = -6(2x + 5)
8x + 14 -21x = -12x - 30
-13x + 14 = -12x - 30
-x + 14 = -30
-x = -44
x = 44
5.
Solve
3/5x + 1/3 <4/5x+-1/3
Answer:
Inequality form: x>10/3
Interval Notation: (10/3, infinity)
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x > 10/3
Step-by-step explanation:
Your cell phone plan costs $34.99 per month plus $0.15 for each text message you send or receive. You have at most $40 to spend on your cell phone bill. what is the maximum number of text messages that you can send or receive next month?
Answer:
33 texts
Step-by-step explanation:
34.99+0.15(t)=40
lets say t is number of texts
subtract 34.99 from both sides
0.15(t)=$5.01
divide 5.01 by .15
33.4
but you cant send .4 of a text
so 33 texts
complete the missing value in the solution to the equation.
i need help by 5 divided by 7/10
Hope this helps!
Also can I please have Brainliest?
Only if I'm right of course...
Point P′(–6, –4) is the image of point P(–2, 3) under a translation. What is the image of (5, –1) under the same translation?
A. (9, 6)
B. (–1, –5)
C. (1, –8)
D. (3, 2)
Answer:c
Step-by-step explanation:
A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16 t 2 + 128 t + 144 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown. What is the maximum height of the ball?
Answer:
400mStep-by-step explanation:
Given the quadratic equation that models the height of the ball above the ground as;
h ( t ) = − 16 t^2 + 128 t + 144
t is in seconds
To get the maximum height of the ball, first we must know the time taken by the ball to reach the maximum height.
Note that the ball has a velocity of zero at its maximum height.
v(t) = dh/dt
v(t) = -32t+ 128
at max height, v(t) = 0
0 = -32t + 128
32t = 128
t = 128/32
t = 4secs
To get the maximum height of the ball, you will substitute t = 4 into the modeled function as shown;
h ( t ) = − 16 t^2 + 128 t + 144
h ( 4 ) = − 16 (4)^2 + 128 (4) + 144
h ( 4 ) = − 256 + 512 + 144
h(4) = 400m
Hence the maximum height of the ball is 400m
Plz hurry!!
Click the answer that shows the numbers in order from least to greatest.
A. 1.6, 0.9, 0.2, -0.8, -2.4
B. -0.8, -2.4, 0.2, 0.9, 1.6
C. -2.4, -0.8, 0.2, 0.9, 1.6
D. -0.8, 1.6, 0.9, -2.4, 0.2
Answer:
C is the correct answer
Find the slope of the line through
3) (-1, 17). (6, 12)
Dave wrote the equation
, and Bonnie graphed the function shown below.
Answer:
dolor sit amet, coisse. Enim neque volutpat ac tincidunt vitae. Leo a diam sollicitudin tempor id eu nisl nunc. A diam maecenas se ut sem viverra.dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut ln tempor id eu nisl nunc. A diam maecenas sed enim ut sem viverra.dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Habitant morbi tristique senectus et netus et
Step-by-step explanation:
dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Habitant morbi tristique senectus et netus et malesuada fames. Pharetra massa massa ultricies mi. Tortor at risus viv et egestas quis ipsum suspendisse. Enim neque volutpat ac tincidunt vitae. Leo a diam sollicitudin tempor id eu nisl nunc. A diam maecenas sed enim ut sem viverra.dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Habitant morbi tristique senectus et netus et malesuada fames. Pharetra massa massa ultricies mi. Tortor at risus viv et egestas quis ipsum suspendisse. Enim neque volutpat ac tincidunt vitae. Leo a diam sollicitudin tempor id eu nisl nunc. A diam maecenas sed enim ut sem viverra.
What is the slope of the line that passes through the points (-8, 3) and (-8, 5)?
Answer:
The slope is undefined
Step-by-step explanation:
Slope (m) = infinity (undefined)
θ = π = 90°
2
distance (d) = 2
ΔX = 0
ΔY = 2
Evaluate the following expression:
3.65+(-8.2)=
MUST SHOW WORK!
Answer:
-4.55
Step-by-step explanation:
8.20
- 3.65
4.55
then just add a negative sign to it !
-4.55
hope this helps : )
have a good day
What is 6/7 of 2/3?
Answer:
4/7
Step-by-step explanation:
6 times 2 = 12 and 7 times 3= 21
12/21
put the answer on simpliest form 4/7
13) Find the value for x and y.
Someone help me please thanks
Answer:
x=14 y=37
Step-by-step explanation:
-2(m + 2) - 12 = -8 help
Answer:
m = -4
Step-by-step explanation:
-2m-4-12 = -8
-2m = -8+4+12
-2m = 8
m = -8/2
m = -4
Answer:
m=12
Step-by-step explanation:
Substitute 12 for m.
Sara measures and finds that she can do a vertical jump that is 27% of her height. If she is 63 inches tall, how high (in inches), can she jump
Answer:
sara can jump 17.01 inches high
Step-by-step explanation:
0.27×63=17.01
For those who are good with equations....(unlike me when it comes to this)
Answer:
a = 5
Step-by-step explanation:
When the coefficients of the variables are equal with different constants, then you will get an equation which is never true.
For this particular equation, when a on the right side has a coefficient of 5, you will get the equation: 4(a - 2) + a = 5a - 4.
When you distribute the factors in the parenthesis and add the like terms of a together, 4(a - 2) + a will become 5a - 8. This is because 4(a - 2) + a = 4(a) + 4(-2) + a = 4a - 8 + a = 5a - 8.
Now when you simplify 5a - 8 = 5a - 4 by subtracting 5a from both sides, you will get an equation with unlike constants. For instance 1 = 0.
Now:
5a - 8 = 5a - 4
-5a -5a
-8 = -4
This is never true, so therefore, there is no solution.
Answer:
It is 5
Step-by-step explanation:
PLEASE HELP, WILL GIVE BRAINLIEST
Explain the process you would use to determine what form a solution to a system of inequalities should take. What are some tips and tricks?
Answer:
Solving a system of inequalities is almost like solving a system of equations. Pretend that the inequality signs are equal signs for a moment. Then, solve the system for the two unknown variables just like how you would solve for in a system of equations.
But, there's a catch. If you divide both sides of the inequality by a negative number, you have to flip the inequality sign. For example, if you are trying to solve the inequality -x > 4 you would have to divide both sides of the equation by -1. We would get x < -4 (see how I switched the inequality sign from > to <).
Once you find the values of x and y (they will be an inequality), graph the solutions.
find the measuremeant of the angle indicated??
Answer:
140°
Step-by-step explanation:
The opposite angles in a parallelogram are congruent, thus
∠ K = ∠ M = 140°
