The rate of change of the radius is 1.32cm²/s
The formula for calculating the volume of a sphere is expressed as:
[tex]v = \frac{4}{3} \pi r^3[/tex]The rate of change of the volume is given as:
[tex]\frac{dv}{dt} = \frac{dv}{dr} \cdot \frac{dr}{dt} \\\frac{dv}{dt} = =4 \pi r^2 \cdot \frac{dr}{dt} \\[/tex]Given the following paramters;
dv/dt = 23cm³/s
Volume = 7cm³
Get the radius of the sphere:
7 = 4/3 πr³\
21 = 4πr³
r³ = 21/4π
r = 1.18 cm
Get the rate of change of the radius to have:
[tex]23 = 4(3.14)(1.18)^2 \frac{dr}{dt} \\23 = 17.48 \frac{dr}{dt} \\\frac{dr}{dt}=1.32cm^2/s[/tex]
Hence the rate of change of the radius is 1.32cm²/s
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4000 families were randomly selected for a survey. 50% of them read the newspaper in nepali language, 45% read it in English language and 25% read in neither of these languages. How many families read the newspaper in both the languages? Also find the number of families who read exactly one of these papers.
Answer:
2000 families read the newspaper in the Nepali language.
1800 families read it in the English language.
3800 families read the newspaper in both.
Step-by-step explanation:
#1. individual
convert % to decimal ( x ÷ 100 )
0.5 x 4000 = 2000
0.45 x 4000 = 1800
#2. together
2000 + 1800 = 3800
OR
50 + 45 = 95
95 ÷ 100 = 0.95
0.95 x 4000 = 3800
Evaluate the determinate:
I 5 3 3 I
I -4 -5 1 I
I 5 3 0 I
Please show work... I will give Brainliest.!
Answer:
39
Step-by-step explanation:
detailed explanation showed in the diagram above
How is the key event in this paragraph illustrated?
The area of a square depends on the length of its sides. This can be written in function notation as a(s). What is the best interpretation of a(4) = 16?
A. The area of a square is always one-fourth of the side length.
B. The area of a square is always four times the side length.
C. A square with sides 4 units long has an area of 16 square units.
D. A square with sides 16 units long has an area of 4 square units.
Answer:
option d is the right answer
what is the number of terms for 1000z + 800y
Answer:
2 terms
Step-by-step explanation:
hope this helps! :D
have a MIRACULOUS day!! <3
4. Match these equation balancing steps with the description of what was done in each step.
Step 1:
12x−6 =10 6x−3 =5
Step 2:
6x−3 =5 6x =8
Step 3:
6x =8 x =43
Descriptions to match with each step:
A: Add 3 to both sides
B: Multiply both sides by 16
C: Divide both sides by 2
Answer:
step 1 - C.
step 2 - A.
step 3 - B.
3x^3-4x^2-28x-16 divided by 3x+2
Help help help help help
You have to show work
Answer:
your answer is right -2/3
Step-by-step explanation:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{10 - 4}{ - 6 - 3} = \frac{6}{ - 9} = - \frac{2}{3} [/tex]
Karen's mother gets a restaurant bill for $25 she has a coupon for 15% off after the discount is applied she adds 20% as a tip what is the total after the discount and tax
Answer:
$25.50
Step-by-step explanation:
with a 15% off coupon she is paying 85% of the $25 bill, which is:
.85 x 25 = 21.25
if she adds a 20% tip on 21.25 then we can do the following:
1.2 x 21.25 to get the total after the discount and with tax:
$25.50
If I have a 68 in a class and I get 295 out of 300 points on a test, how much will the grade improve and what percentage would result?
Answer:
Use calculator
Step-by-step explanation:
Answer:
your grade would improve by a lot and if im not mistaken the resulting percentage would probably be between 80%-90%
Step-by-step explanation:
Drag the numbers below to put them in order from least to greatest:
-9 -12 -4
–4 20 -1 -6
Answer:
-12, -6, -4, -1, 9, 20
Step-by-step explanation:
9, -12, -4, 20 -1, -6
putting them in order from least to greatest means that negatives should go to the left (1st), largest should go to the right (last).
The number -9, -12, -4, 20, -6, -1 in the order from least to greatest is -12, -9, -6, -4, -4, -1, 20.
Given data: -9, -12, -4, 20, -6, -1
Starting from the smallest number:
-12 is the smallest number.
Next is -9, which is larger than -12 but smaller than -6.
Then comes -6, larger than -9 but smaller than -4.
After that, we have two occurrences of -4.
Following that is -1, greater than -4.
Finally, the largest number is 20.
So, the numbers in ascending order are: -12, -9, -6, -4, -4, -1, 20.
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please help me !!! omaths student see the attached question
Answer:
34.64m
Step-by-step explanation:
Tan30= x(height) /60
x=60tan30
=34.64m
Help me on 5 and 6 plssssss
write an expression describing all the angles that are coterminal with 266°
Answer:
-814°, -454°, -94°, 266°, 626°. Did you mean like that?
Ok here’s another question
Answer:
20 necklaces
Step-by-step explanation:
If Elizebeth is starting off w/10 necklaces we can find on the graph that $10 buys an additional 10 necklaces. Now knowing that information we can add 10 necklaces to our original necklaces and get 20 necklaces. We can also find that our unit rate of change is 10 dollars : 10 necklaces or 1 dollar : 1 necklace. Knowing this can help us solve future problems like how many necklaces can Elizebeth get for x dollars.
Burt ran the length of the trail in his town’s park. There are 9 parts to the trail, and each part is the same length. Burt ran a total of 1.8 kilometers.
What is the length of each part of the trail?
Answer:
.2 kilometers
Step-by-step explanation:
Since there are 9 parts to the trail and the total is 1.8 kilometers, just divide the total by how many parts. 1.8 divided by 9 is .2 so the length of each part of the trail is .2 kilometers
Which table represents a linear function?
Answer:
First Graph (1-5 2-10)
Step-by-step explanation:
10÷2=5
3÷15=5
4÷20=5
5÷25=5
(Topic: Vectors) - Prove that ADE is a straight line
Answer:
Because the angle is a 180 degree angle.
Step-by-step explanation:
Answer:
If it looks straight, well then i would guess that it would be straight. You can also put it against a ruler and see if it matches up. if it does not then it is not a line.
Step-by-step explanation:
hope this helps
pls brainliest
hellp plsssss
I would love it if you did!
Answer:
1050
Step-by-step explanation:
bylon 3 x 68 =204
wool (3x3) x 94 =846
204 + 846 = 1050
he spent 1050 $ on materials
Answer:
$846
Step-by-step explanation:
I think it is sry if u got it wrong
a large bottle of juice contains 500 milliliters of juice. a medium bottle contains 70% as much juice as the large bottle. how many milliliters of juice are in the medium bottle.(can you include a number line? thanks!)
Answer:
350 millilitres
Step-by-step explanation:
70/100×500=350
Carl placed $2,600 in a savings account that compounds interest annually at a rate of 0.5%. How much will he have in the account after 7 years
Answer:
$2,691
Step-by-step explanation:
Interest (I) = Principal x Rate x Time
Total Amount (A) = Interest + Principal
I = 2600(.005)(7)
I = 91
A = 2600 + 91
A = 2691
What is the greatest common factor of 3 and 33?
Answer:
3
Step-by-step explanation:
Step 1: Find the factors of 3 and 33.
3: 1, 333: 1, 3, 11, 33Step 2: Find the largest common factor they share.
As you can see, the largest common factor they share is 3.Therefore, the GCF of 3 and 33 is 3.
What are two equivalent fractions for 1/2 ?
The fractions which are equivalent to 1/2 are 2/4, 3/6, 4/8, 6/12 etc. Equivalent fractions have same value in reduced form.
how much would it cost for a 9-hour repair
what is y-2=4(x+1) in slope intercept form
Answer: y=4x+3
Step-by-step explanation: First, lets clean this expression up.
y - 2 = 4(x+1)
Multiply 4 times x and 4 x 1.
y-2=4x+1
add 2 to both sides.
Finally, you get y=4x+3.
Remember that 4 is your m (slope), and b (y-intercept). If you were graph this, it would increase to the right. You graph your intercept 3 on the positive y-axis at (0,3) and since your slope is 4x, you go 4 units up and 1 unit to the right and from there, you get the graph of the given equation.
Hope this explanation helps.
Divide 120ml into the ratio 3:7
Answer:
Step-by-step explanation:
sum of ratio=3+7=10
total=120 ml
first part=3/10×120=36 ml
second part=7/10×120=84 ml
IF ANYONE CAN ANSWER THESE 2 QUESTIONS I WILL GIVE YOU BRAINLIEST AND LOVE YOU FOREVER. SERIOUSLY, ILL NEVER FORGET U <3
Answer:
3. 314 student and 226 adult
4. x = 6.5, y = -0.5
Step-by-step explanation:
3. First we will take our information and make a system of equations:
[tex]2.4a+1.25s=934.9[/tex]
[tex]a+s=540[/tex]
[tex]a[/tex] is the number of adult tickets sold and [tex]s[/tex] is the number of student tickets sold.
From the second equation we can rearange it to be:
[tex]a=540-s[/tex]
Then we can plug in our new value of [tex]a[/tex] to our first equation
[tex]2.4(540-s)+1.25s=934.9[/tex]
[tex]1296-2.4s+1.25s=934.9[/tex]
[tex]1.15s=361.1[/tex]
[tex]s=314[/tex]
We can then find [tex]a[/tex] by plugging in s to our second equation
[tex]a+314=540[/tex]
[tex]a=226[/tex]
4. It is mostly solved already. We can take the value of y from the first equation and plug it into the second to get:
[tex]3x -5(-5x+32)=22[/tex]
[tex]3x+25x-160=22[/tex]
[tex]28x=182[/tex]
[tex]x=6.5[/tex]
Then plug our value of x into the first equation to get:
[tex]3(6.5)-5y=22[/tex]
[tex]19.5-5y=22[/tex]
[tex]5y=-2.5[/tex]
[tex]y=-0.5[/tex]
A jacket costs $80. it is on sale for 35% off. what is the discount?
Answer:
$52
Step-by-step explanation:
35% off
100% - 35% = 65%
65/100 = 0.65 ( multiplier)
0.65 x 80 = 52
Answer:
$28
Step-by-step explanation:
35/100 = x/800
0.35 * 800 = $28
One angle of a right triangle measures 36. 5 degrees. What is the measure of the other small angle?.
Answer:
The other small angle is 53.5 degrees
Step-by-step explanation:
We know that a right triangle has to have a 90 degree angle and 2 other small angles.
All triangles when adding up all of their "degrees" has tp equal 180 degrees.
Since we know that there is a 90 degree angle and a 36.5 degree angle.
All we have to do is add 90 plus 36.5, then subtract that sum onto 180.
90 + 36.5 = 126.5
180 - 126.5 = 53.5
So the answer is 53.5 degrees.
Hope this helps! :)
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A right triangle is a triangle in which the angles sum up to 180 degrees. It is made up of three sides : the height, the base and the hypotenuse. One of the angles in a right triangle has a value of 90 degrees.
Missing angle = sum of angles in a triangle - (sum of the two given angles)
Missing angle = 180 - ( 90 + 36.5)
180 - 126.50
= 53.5 degrees
Please find attached an image of a right triangle. A similar question was answered here: https://brainly.com/question/24353342
