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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A student wrote four statements during math class. Which statement contains an error?
Answer:
C
Step-by-step explanation:
The answer is C if you multiply (a)38×18=684
(b)46×16=736 (c)54×14=756 the question is 766 miles meaning that c is the wrong answer .i hope this was helpful.
HURRRRY!!!! Thank you
Answer:
C
Step-by-step explanation:
Uhm I tried my best im so sorry if it's wrong
it is B yep he was right have a nice day
Using the divisibility rules, explain why 678 is divisible by 2, 3, and 6.
Answer:
678
678 is even, so it's divisible by 2
6+7+8 = 21, which is divisible by 3, so 678 is divisible by 3
Since 678 is divisible by both 2 and 3, it has to be divisible by 6
Step-by-step explanation:
Find x (Type the number answer)
Answer:
18.41
Step-by-step explanation:
[tex]x^{2} = 12^{2} + 8^{2} - 2(12)(8)(cos 133)\\\\x= \sqrt{338.94} = 18.41[/tex]
what is -2(15 ÷ 5) + 7(-2)
Answer:
-20
Step-by-step explanation:
Challenger Elementary School has 800 students. Every Wednesday, 12% of the students stay after school for Chess Club. How many students attend on Wednesday’s?
Answer:
96 students attend chess club after school on Wednesday's.
Step-by-step explanation:
To solve this problem, simply multiply 800 x 0.12.
800 x 0.12 = 96
I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer Brainliest. It would help a lot. Have a great day!
Answer:
[tex]\huge\boxed{\text{96 students}}[/tex]
Step-by-step explanation:
In order to find how many students stay back for Chess Club, we want to find 12% of 800.
To do this, we can set up a percentage proportion.
[tex]\frac{12}{100} = \frac{x}{800}[/tex]
We can now solve for x by cross multiplying.
[tex]800 \cdot 12 = 9600\\9600 \div 100 = 96[/tex]
So, 96 students attend Chess Club on Wednesdays.
Hope this helped!
Stan, Greg, and Seth were cleaning the school gym in shifts. Stan
cleaned first, then Greg, then Seth. If they each cleaned the same
amount of time for a total of 11 hours, how many minutes did each one
clean?
Find 0.038 as a fraction in its lowest terms
Answer:
19 / 500
Pls mark as brainliest!!!
Answer:
19/5
Step-by-step explanation:
If you're using a scientific calculator you will be able to find this answer by just simply pressing 0.038 x 100 divided by 1
9. a - 2a +5
pls help i’m kinda dumb
the diagram shows a circle inside a square ABCDB AB = 20 cm. the radius of the circle is 9 cm. work out the area of the shaded region
Step-by-step explanation:
Area of the square = a²
= 20²
= 400cm²
Area of the circle = πr²
= 22/7 × 9²
= 22/7 × 81
= 254.57cm²
Area of the shaded region = Area of the square - Area of the circle
= 400cm² - 254.57cm²
= 145.43cm²
Make & the subject of the
Formula
6x ta=5(x+t)
What is the answer please
Answer:
x = 5t - a
Step-by-step explanation:
The problem deals with making a variable the subject of the formula in the expression.
Given expression:
6x + a = 5(x + t)
We are to make x the subject of the formula in the expression
Solution:
6x + a = 5(x+t)
On the right hand side, expand the parentheses and distribute the term outside;
6x + a = 5x + 5t
Bring the term desired to be the subject to one side by adding (-5x) to both sides;
6x + (-5x) + a = 5x + (-5x) + 5t
x + a = 5t
Now add (-a) to both sides
x + a + (-a) = 5t + (-a)
x = 5t - a
Solve the right triangle
Answer:
JK = 50; IJ = 25√3
Step-by-step explanation:
HAVE: sin ∠J = sin 30° = [tex]\frac{IK}{JK}[/tex]
=> [tex]\frac{IK}{JK}=\frac{25}{JK}=\frac{1}{2}=> JK = 25.2 = 50[/tex]
cos ∠J = cos 30° = [tex]\frac{IJ}{JK}[/tex]
=> [tex]\frac{IJ}{JK}=\frac{IJ}{50}=\frac{\sqrt{3} }{2} => IJ = \frac{\sqrt{3} }{2}.50=25\sqrt{3}[/tex]
Suzy ordered some games online for $19 each. She paid a total of $8 for shipping. The total cost of the purchase was $122. How many games did she buy? 7) Using the word problem above, write an equation to find the number of games Suzy bought. (Hint: Don't do any of the steps to solve it, just write the equation) Your answer
Answer:
6
Step-by-step explanation:
122-8 shipping =114 /19=6
PLEASE HELP ME AND EXPLAIN.
Answer:
9*8=72 which would be more than enough to cover the wall
HELP:( I know I’m slow and all asking all these question today but...
Second answer
Step-by-step explanation:
HELP ME PLEASE!
Complete the work to find the equation of a line that passes through point (–5, –3) and is parallel to line y – 3x = –7. Step 1: Write the equation of the given line in slope intercept form: y = 3x – 7. Step 2: Determine the slope of the parallel line: m = 3. Step 3: Substitute the slope and given point into y = mx + b to find the y-intercept of the new line. –3 = 3 (–5 ) + b 3 = –15 + b b = 12 Step 4: Write the equation of the line parallel to 3x – y = 7 that passes through point (–5, –3).
Answer:
Y=3x+12 (its the first option)
Step-by-step explanation:
I did the assignment.
The equation of the line parallel to (3x - y = 7) passes through the point (-5, -3) is y = 3x + 2 and this can be determined by using the one-point slope form.
Given :
The line passes through the point (-5, -3) and is parallel to the line (y - 3x = -7).
The following steps can be used in order to determine the equation of a line that passes through the point (-5, -3) and is parallel to the line (y - 3x = -7):
Step 1 - The one-point form of a line is used in order to determine the equation of a line that passes through the point (-5, -3) and is parallel to the line (y - 3x = -7).
Step 2 - The one-point form is given below:
[tex](y-y_1) = m (x-x_1)[/tex]
Step 3 - According to the given data, the line is parallel to the line (y = 3x - 7). So, the slope of the line is 3.
Step 4 - Now, substitute the values of slope and the point in the above expression.
[tex](y+3) = 3 (x+5)[/tex]
y = 3x + 2
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Im so confused pls help
Step-by-step explanation:
[tex] f(x) \: = \: \frac{4}{5} - \frac{5}{x + 1} [/tex]
[tex]f(x) \: \: = \: \: \frac{(4)(x + 1) - 5(5)}{5x + 5} [/tex]
[tex]f(x) \: \: = \: \: \frac{4x + 4 - 25}{5x + 5} [/tex]
[tex]f(x) \: \: = \: \: \frac{4x - 21}{5x + 5} [/tex]
f(x) = g(x)
[tex] \frac{4x - 21}{5x + 5} = \frac{2}{5x + 5} [/tex]
4x - 21 = 2
x = (21 + 2)/4
x = 5.75
How many modes, if any, does the group of data have?
Kate, Tim, John, John, Angela, Tim, Sue 1 mode 2 modes no mode 3 modes
The number of modes in the dataset is 1. The dataset is unimodal. The correct option is therefore;
1 mode
What is a unimodal data?A unimodal data is a set of data that has only one mode. The mode is a measure of central tendency.
The data in the question can be presented as follows;
Kate, Tim, John, John, Angelam, Tim, Sue
The frequency of each of the data is therefore;
Kate; 1, Tim; 1, John; 2, Angela; 1, Tim; 1, Sue; 1
The mode of a dataset, is the value that has the highest frequency, or that appears the most in the dataset.
The data that has the highest frequency is John, the mode of the dataset is therefore, John, which has a frequency of 1
The dataset, therefore, has only 1 mode.Learn more on the measures of central tendency, mode median, and mean, of a dataset here: https://brainly.com/question/24994390
#SPJ1
I need help on this one
Answer:
A
Step-by-step explanation:
Select all that apply.
40 is what percent of 25. Hint: There are 2 correct answers.
А160%
B 62.5%
C 1600%
D625/1000
E 160/100
F1600/100
Answer:
B and D
Step-by-step explanation:
Hope this helps :3
if it did pls mark brainliest
Answer:
A & E
Step-by-step explanation:
First, multiply 40 by 100, giving you 4000. You then divide 4000 by 25, where you will get a quotient of 160. Now, this can be represented as 160% or 160/100 because a percentage is always out of 100.
2+10= 12
True or False??
Just for points:)
Answer:
True thank you for the points
Answer:
true
Step-by-step explanation:
2+10=12
true. do i get the points?
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
Find the zero of the function.
f(x) = 4x2 – 12x + 9
The zero of the function is x=
Answer:
x= 3/2
Step-by-step explanation:
I apologize if it is wrong!
find the x and y intercept
y=5x-13
Answer:
X int = 13/5 Y int= -13
Step-by-step explanation:
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
Let x = the number of packages of pasta and y = the number of jars of pasta sauce.
One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry?
How many packages of pasta?
How many jars of pasta sauce?
Explain your reasoning.
Answer:
8 packages of pasta and 8 jar of sauce which is $32 dollars and 20lbs in total
Step-by-step explanation:
8 pack of pasta is 8$ and 8lbs
8 jars of sauce is 24$ and 12lbs
8 plus 12 is 20 which is the max of lbs Tyler can carry.
PLEASE help find measure of angle - TEst review today
Answer:
both measured would be 25 and 19
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
if x equals 4 then 21x+4 equals 88 and 23x-4 equals 88 too.
A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00for 20 hours of work. Find the amount of pay for 31 hours of work. ONLY NUMERICAL VALUE
Answer:
$190.65 for 31 hours
Step-by-step explanation:
P= ha
123=20a
123/20=a
6.15=a
P=6.15h
P= 6.15(31)
p=190.65
Which rational number equals 0.7 ? 1 10 Flo 11
Answer:
0.7 is a rational number... but 7/10
Step-by-step explanation:
Hope I helped!
Answer: This absolutely makes no sense
Step-by-step explanation:
Find the third side in simplest radical form:
1&3
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
[tex]1^{2} + 3^{2} =x^{2} \\1+9=x^{2} \\10=x^{2} \\\sqrt{10} =x\\[/tex]
Find the measures of the exterior angles of the polygon.
Step-by-step explanation:
180 - 34 = 146
one angle is a right angle, angle across it is 146, 360 - 90 - 146 = 124
divide that by two to get the measures of the remaining two angles (62 degrees)
180 - 62 = x
118 = x
:
/ = .
-- :
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