Answer:
The rate at which the water level is falling when the water is 4 meters deep to the nearest hundredth is 0.02 meters per minute.
Step-by-step explanation:
The volume of a cylinder ([tex]V[/tex]), measured in cubic meters, is represented by the following formula:
[tex]V = \pi\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Radius, measured in meters.
[tex]h[/tex] - Height, measured in meters.
Then, we differentiate (1) in time:
[tex]\dot V = 2\pi \cdot r\cdot h \cdot \dot r +\pi \cdot r^{2}\cdot \dot h[/tex] (2)
Where:
[tex]\dot V[/tex] - Rate of change of the volume, measured in cubic meters per minute.
[tex]\dot r[/tex] - Rate of change of the radius, measured in meters per minute.
[tex]\dot h[/tex] - Rate of change of the height, measured in meters per minute.
Then, we clear the rate of change of the height:
[tex]\pi \cdot r^{2}\cdot \dot h = \dot V-2\pi \cdot r\cdot h \cdot \dot r[/tex]
[tex]\dot h = \frac{\dot V - 2\pi \cdot r\cdot h\cdot \dot r}{\pi \cdot r^{2}}[/tex]
[tex]\dot h = \frac{\dot V}{\pi \cdot r^{2}}-\frac{2\cdot h\cdot \dot r}{r}[/tex]
[tex]\dot h = \frac{1}{r}\cdot \left(\frac{\dot V}{\pi \cdot r}-2\cdot h\cdot \dot r \right)[/tex] (3)
If we know that [tex]\dot V = -3\,\frac{m^{3}}{min}[/tex], [tex]r = 7\,m[/tex], [tex]h = 4\,m[/tex] and [tex]\dot r = 0\,\frac{m}{min}[/tex], then the rate of change of the height is:
[tex]\dot h = \left(\frac{1}{7\,m} \right)\cdot \left[\frac{-3\,\frac{m^{3}}{min} }{\pi\cdot (7\,m)-2\cdot (4\,m)\cdot \left(0\,\frac{m}{min} \right)} \right][/tex]
[tex]h = -0.019\,\frac{m}{min}[/tex]
The rate at which the water level is falling when the water is 4 meters deep to the nearest hundredth is 0.02 meters per minute.
Find the value of X in the triangle shown
Help ASAP help quick
Answer:
Step-by-step explanation:
Original price 95$ sale price 61.75 what is percent discount
Answer:
If i'm not mistaken the answer should be a 35% discount.
Step-by-step explanation:
Answer:
35%
Step-by-step explanation:
$95 × 0.35 = $33.25
$95 - 33.25 = $61.75
A TV has an original price of $399. Enter the new price after the given percent of change.
20% decrease
The new price is $ ?.
Answer:
Step-by-step explanation:
399 x .20 = 79.8
399 - 79.8 = 319.2
The new price of the TV after a 20% decrease is $319.20
When taking the sine and cosine of different angles in your calculator, why are they sometimes the same? Why do they sometimes produce the same answer? ex: sin 55* = 0.819152044 and cos35* = 0.819152044 or sine 30* and cos 60*
Answer:
sin(theta) = 90 - cos(theta)
cos(theta) = 90 - sin(theta)
Need help with this question it’s my first time on here !
Answer:
We conclude that the statement 'To host a wedding with 104 people, 13 tables will be needed'.
Hence, option C is correct.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
where 'k' is termed as the 'constant of variation'.
Given that a wedding reception seats 8 people at each table.
Given that the relationship between the number of people 'p' and the number of tables 't'.
p = 8t
CHECKING OPTION A
substitute t = 22 in the given equation
p = 8 × 22 = 176 people
It means to host 176 people, 22 tables will be needed.
Hence, OPTION A is INCORRECT!
CHECKING OPTION B
substitute t = 8 in the given equation
p = 8 × 8 = 64 people
It means to host 64 people, 8 tables will be needed.
Hence, OPTION B is INCORRECT!
CHECKING OPTION C
substitute t = 13 in the given equation
p = 8 × 13 = 104 people
It means to host 104 people, 13 tables will be needed.
Hence, OPTION C is CORRECT!
CHECKING OPTION D
substitute t = 6 in the given equation
p = 8 × 6 = 48 people
It means to host 48 people, 6 tables will be needed.
Hence, OPTION C is INCORRECT!
Thus, we conclude that the statement 'To host a wedding with 104 people, 13 tables will be needed'.
Hence, option C is correct.
Pls help me plsss I’m failing bad
Answer:
$82.22
Step-by-step explanation:
Price of meal before discount: $78.31
They leave a 20% tip that applies to the cost of the meal before the discount, so the tip is 20% of $78.31.
Now we calculate the amount of the tip.
20% of $78.31 =
= 0.2 * $78.31
= $15.66
The tip is $15.66. We will apply it later after we use the discount.
The meal's original price was $78.31 before the discount.
The discount is 15%. Now we find the amount of the discount.
15% of $78.31 =
= 0.15 * $78.31
= $11.75
The discount due to the coupon is $11.75
The final price of the meal is the original price, minus the discount, plus the tax.
final price = $78.31 - $11.75 + $15.66 = $82.22
If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, what is the perimeter of A'B'C'D?
A)
30 units
B)
60 units
C)
90 units
D)
120 units
Answer:
90
Step-by-step explanation:
What is the midpoint for CD given the coordinates C (-4,8) and D (8,-4).
A. (0,0)
B. (2,2)
C. (4,4)
D. (6,6)
Find the x- and y-intercepts of the equation x – 5y = –15. Question 16 options: A) x-intercept: (0,3), y-intercept: (–15,0) B) x-intercept: (0,–15), y-intercept: (3,0) C) x-intercept: (–15,0), y-intercept: (0,3) D) x-intercept: (3,0), y-intercept: (0,–15)
Answer:
y-intercept: (3,0) C) x-intercept: (–15,0)Step-by-step explanation:
Given the expression x - 5y = -15
x intercept occurs at y = 0
Substituting y = 0 into the expression
x - 5(0) = -15
x - 0 = -15
x = -15
Hence the x-intercept occurs at (-15, 0)
y intercept occurs at x = 0
Substituting x = 0 into the expression
0 - 5y = -15
-5y = -15
y = -15/-5
y = 3
Hence the y-intercept is at (0, 3)
Two side length of a triangle are given as 9 cm and 5 cm. What could be the length of its third side?
Answer: Two sides are given 5 cm and 9 cm. .Therefore, the third side can not be greater than or equal to (9+5)=14 cm and it can not be less than or equal to (9–5)=4 cm
Step-by-step explanation:
Please Give me brainliest
Answer:
Step-by-step explanation:
the length to the third side can be
a) a^2+b^2=c^2
a=9, b=5
c^2=81+25=106
c=sqrt106=10.29
or
a=5, c=9
b^2=c^2-a^2
b^2=81-25=56
b=sqrt56=7.48
which is a multiple of 6?
3?
16?
39?
54?
Answer:
54 is a multiple of 6
Step-by-step explanation:
Step-by-step explanation:
54..
_______________________
Help if your good at math please!
Answer:
40% apples
train going 80 miles per hour
Evaluate -7 1/3 - (-2/5)=
Answer:
-6 14/15
Step-by-step explanation:
An 8-oz can of orange juice contains about 97 mg of vitamin C. About how
many milligrams of vitamin C are there in a 12-oz can of orange juice?
Answer:
Step-by-step explanation:
12/8=1.5
1.5*97=145.5mg
Determine whether each quadrilateral is a parallelogram. Justify your answer. Yes/No? Reason... opposite side congruent, opposite angles congruent, opposite sides parallel, diagonals bisect each other, one pair of parallel and congruent sides, not enough information? (look at the image)
Answer:
yes it is a parallelogram because diagonals bisect each other.
what order do I put it in?
Answer:
circle is pir^2. Triangle is 1/2b*h and rec is B*H
Step-by-step explanation:
At the gym, Jasper was able to bench press 224 pounds, which was StartFraction 7 over 8 EndFraction of the weight that Balin was able to bench press. Which shows the correct equation and value of x, the weight that Balin could bench press
Answer:
Balin could bench press 256 pounds.
Step-by-step explanation:
Jasper was able to bench press 224 pounds, which is 7/8 of x, which is the weight that Balin was able to bench press. So, mathematically:
[tex]\frac{7}{8}x = 224[/tex]
[tex]7x = 224*8[/tex]
[tex]x = \frac{224*8}{7} = 256[/tex]
Balin could bench press 256 pounds.
Answer:
d
Step-by-step explanation:
Kim paid 3/7 of a bill, Sherri paid 35% of the bill, and Judy paid the rest.
Which of the following statements is true?
a.Kim paid the most.
b.Sherri paid the most.
c.Judy paid the most.
d.They all paid the same amount.
find exact value sin^2 40° + cos^2 40°
Answer:
1 i think i looked it up on mathaway
Step-by-step explanation:
1
Find the value of x.
Answer:
x = 18°
Step-by-step explanation:
The sum of interior angles of any polygon is given by:
180(n -2) , where n is the number of sides of that polygon.
So for this pentagon;
The sum of its interior angles = 540°
∴
90 + (9x -6) + (3x + 23) + 95 + (7x - 4) = 540
19x + 198 = 540
19x = 540 - 198 = 342
x = 342 ÷ 19 = 18°
Solve the question
Show work
Answer:
Step-by-step explanation:
Given functions are,
f(x) = 2x - 3
g(x) = x³ - 2
h(x) = x² - 3x + 5
(10). f(4) = 2(4) - 3
= 5
g(-2) = (-2)³ - 2
= -8 - 2
= -10
f(4) + g(-2) = 5 -10 = -5
(11). g(3) = 3³ - 2 = 25
h(1) = 1² - 3(1) + 5
= 1 - 3 + 5
= 3
g(3) - h(1) = 25 - 3 = 22
(12). f(2) = 2(2) - 2 = 2
h(-3) = (-3)² - 3(-3) + 5
= -27 + 9 + 5
= -13
f(2).h(-3) = 2(-13) = -26
A borrower has a monthly payment of $1,980 on a loan with a monthly constant of 6.45. What is the loan amount (to the nearest hundred)
Answer:
loan amount = $307,000
Step-by-step explanation:
given data
monthly payment = $1,980
monthly loan constant = 6.45
to find out
loan amount
solution
we get here loan amount that is express as
loan amount = ( monthly payment ÷ monthly loan constant ) × 1000 .........1
put here value
loan amount = ( 1980 ÷ 6.45 ) × 1000
loan amount = $307,000
8. Write the missing symbol (+,-, or =) to
make the equation true. Use precise math
language to explain how you chose the symbol.
16 = 4 + 8 ⚪️ 4
What is the approximate area of the circle shown below
Pls help grades close today I’ll brainlest for the right answer
Answer:
decrease 40%
Step-by-step explanation:
20/50 * 100 = 40
Find the equivalent expression.
8(2x−3y)+4(y−3x
Liz flips a coin 50 times. The coin lands heads up 24 times and tails 26 times. Based on Liz’s results, what is the experimental probability of the coin landing on heads?
Answer:
48%
Step-by-step explanation:
First, lets start with what we know.
Coin was flipped 50 times. Landed Heads 24 times, and landed tails 26 times.
Now, we want this in a percentage. So:
24 = x
50 = 100
We know that 50 is 100/2. So, we can multiply both of the numbers to get a percentage.
24 × 2 = 48
26 × 2 = 52
In conclusion, the experimental probability for the coin landing on heads is:
48/100 OR 48%
Simplify 5(4x-2)-5(2x-10)
Answer:
Step-by-step explanation:
20x - 10 - 10x + 10
Solving like terms
10x
I want to know the exact height of the big column