The question is incomplete. The complete question is :
The volume of a right circular cone with radius r and height h is V = pir^2h/3. a. Approximate the change in the volume of the cone when the radius changes from r = 5.9 to r = 6.8 and the height changes from h = 4.00 to h = 3.96.
b. Approximate the change in the volume of the cone when the radius changes from r = 6.47 to r = 6.45 and the height changes from h = 10.0 to h = 9.92.
a. The approximate change in volume is dV = _______. (Type an integer or decimal rounded to two decimal places as needed.)
b. The approximate change in volume is dV = ___________ (Type an integer or decimal rounded to two decimal places as needed.)
Solution :
Given :
The volume of the right circular cone with a radius r and height h is
[tex]$V=\frac{1}{3} \pi r^2 h$[/tex]
[tex]$dV = d\left(\frac{1}{3} \pi r^2 h\right)$[/tex]
[tex]$dV = \frac{1}{3} \pi h \times d(r^2)+\frac{1}{3} \pi r^2 dh$[/tex]
[tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]
a). The radius is changed from r = 5.9 to r = 6.8 and the height is changed from h = 4 to h = 3.96
So, r = 5.9 and dr = 6.8 - 5.9 = 0.9
h = 4 and dh = 3.96 - 4 = -0.04
Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]
[tex]$dV = \frac{2}{3} \pi (5.9)(4)(0.9)+\frac{1}{3} \pi (5.9)^2 (-0.04)$[/tex]
[tex]$dV=44.484951 - 1.458117$[/tex]
[tex]$dV=43.03$[/tex]
Therefore, the approximate change in volume is dV = 43.03 cubic units.
b). The radius is changed from r = 6.47 to r = 6.45 and the height is changed from h = 10 to h = 9.92
So, r = 6.47 and dr = 6.45 - 6.47 = -0.02
h = 10 and dh = 9.92 - 10 = -0.08
Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]
[tex]$dV = \frac{2}{3} \pi (6.47)(10)(-0.02)+\frac{1}{3} \pi (6.47)^2 (-0.08)$[/tex]
[tex]$dV=-2.710147-3.506930$[/tex]
[tex]$dV= -6.22$[/tex]
Hence, the approximate change in volume is dV = -6.22 cubic units
Which graph represents y as a function of x?
Answer:
b
Step-by-step explanation:
In a class of 7, there are 3 students who have done their homework.
If the teacher chooses 3 students, what is the probability that none of the three of them have done their
homework?
Choose 1 answer:
2/37
6/41
ОООО
5/29
4/35
Answer:
4/35
Step-by-step explanation:
Probability of 1 student having no hw is 4/7, then 3/6, then 2/5
4/7 x 3/6 x 2/5 reduces to 4/35
A function is shown in the table below. What equation represents this function?
y = -32 + 12
3r – 6
1
2
1
1
4
y
12
9
3
0
y = -30 + 6
+6
Answer:
y=-30+6+6 I hope it helps
have a good night
Someone please help me answer this!!
Answer:
c = 53 miles
Step-by-step explanation:
a^2 + b^2 = c^2
45^2 + 28^2 = c^2
2,025 + 784 = c^2
2809 = c^2
c = 53
ASAP SHOW WORK PLEASE
Answer:
1) 5 in, 12 in, 13 inStep-by-step explanation:
1)
5² + 12² = 13²25 + 144 = 169169 = 169Yes2)
5² + 7² = 9²25 + 49 = 8174 ≠ 81No3)
10 + 12 < 30, there is no possible triangle with given sides as per triangle inequality theoremgive the correct triangle congruence theorem
Find the measure of x
Answer:
13°
Step-by-step explanation:
1. the two angles are equal
2. the sum of all the angles of a triangle is equal to 180°
so X+13+154=180
X+167=180
X= 180-167
X=13°
What is the answer no links please
9514 1404 393
Answer:
B 550 tickets
Step-by-step explanation:
50% of 1100 tickets were sold the first two days.
0.50 × 1100 = 550
550 tickets were sold the first two days.
Answer:
B. 550 TicketsStep-by-step explanation:
#CarryOnLearningI know it small but can someone help me. It says The table below shows customers' favorite ice cream flavors at a popular ice cream shop, The North Pole. Which relative frequency table and percent bar graph best represents the favorite ice cream flavors for customers at The North Pole ice cream shop?
Answer:
Graph AStep-by-step explanation:
We know it must be graph A because when finding the most popularly bought item, the percentages only can go to 100%
So graphs C and D are eliminated.
Also since it never said any flavors were unknown, all the percents have to add up to 100%
So graph B is eliminated.
Only graph A follows the requirements
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
Angle HGD and HGI are adjacent angle
hope it helps
Please help very urgent
Answer:
all sides are equal so the x is 50.1 degree and nearest 100 will be 100
please mark me as brainliest
A decimal that stops (like 2.48) is which type of number?
A.rational
B.whole number
C.irrational
D.integer
Answer: B rational
Step-by-step explanation:
If you do this for me you get Brainlyist
Answer:
v - √19
Step-by-step explanation:
the answer is v - √19
What is 1/2 + 2/3?, what is 2/3 multiplied by 3/4?
Answer:
Hi! The answer to your question is 1. [tex]7/6[/tex] and 2. [tex]1/2[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
6. Find the distance between the points (-2,-3) and (-4,4).
Answer:
Step-by-step explanation:
10. Type in the correct Inequality
Answer:
x > 8
Step-by-step explanation:
The open circle means that 8 is not included in the solution.
All values greater than 8 are included.
Answer: x > 8
What is the scale factor of the dilation shown?
Answer:
A) [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
What size is a standard margin?
a.
1.5 inches
c.
.5 inches
b.
2 inches
d.
1 inch
Please select the best answer from the choices provided
A
B
C
D
Answer: D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
(Photo is part one)Malik also adds the following ingredients. How many cups of each
did he add? Show each step of your solution.
• 28 tablespoons of sugar
• 6 tablespoons of cocoa powder
Answer:
Step-by-step explanation:
what are we looking for?/
4. What type of sequence is this? *
6.6, 7.2, 7.8, 8.4, 9, ...
lArthimetic
Geometric
Neither
Answer:
Arithmetic
Step-by-step explanation:
We are given the sequence :
6.6, 7.2, 7.8, 8.4, 9, ...
We need to determine whether it is arithmetic, geometric, or neither.
Arithmetic sequences are a bunch of numbers that gradually increase or decrease through equal amounts of adding or subtracting.
Geometric are the same thing but the numbers are gradually increasing or decreasing through multiplication or dividing.
Looking at the sequence, we notice that 0.6 is added into every single number to reach the one next to it.
It fits the description of an arithmetic sequence, therefore the sequence is arithmetic.
A cube or cuboid has _______ sides .
Answer:
6 sides
Step-by-step explanation:
Fill in the boxes to make a true statement. (_-3i)-(15+_i)=7-12i
Answer:
blank space=[tex]\frac{31}{2}[/tex]+[tex]\frac{13i}{2}[/tex]
The empty boxes which make the equation true are (22 -3i) - (15 + 9i)
= 7 - 12i.
What are complex numbers?As the name suggests it is a combination of real numbers and imaginary numbers.
A complex number (a + ib) where a is the real part and b is the imaginary part.
'i' here is called iota and i = √-1, i² = - 1, i³ = - i and i⁴ = 1.
Given, (_ -3i) - (15+_i) = 7 - 12i.
Assuming the real number to be 'a' and the imaginary number to be 'b'.
∴ (a - 3i) - (15 + bi) = 7 - 12i.
a - 3i - 15 - bi = 7 - 12i.
On comparing the real and imaginary parts we get,
a - 15 = 7.
a = 22,
- 3i - bi = - 12i.
- bi = - 9i.
b = 9.
learn more about complex numbers here :
https://brainly.com/question/10251853
#SPJ2
Enter the number that makes this equation true. 4.20 + 12/100 = _/100 + 12/100
If 200 customers buy 45 desserts at your store, how
many desserts can you expect to sell to
500 people?
NO LINKS
Answer:
113
Step-by-step explanation:
200 Customers = 45 Desserts
1 Customer = 45/200= 0.225 Desserts(Approx)
500 Customers= 0.225*500 = 113 Desserts(Approx)
Omar is born weighing 8 pounds,3 ounces.The doctor says he should gain a about 5 ounces each week for the next 4 weeks.How much should Omar weigh after 4 weeks?
Can someone please help me I will mark u brilliant
Answer:
The volume is : 63
Step-by-step explanation:
Volume = Length x width x height
The volume for this rectangular prism is : 8 x 2 1/4 x 3 1/2 which equals 63
Answer:
C, 63 cm cubed
Step-by-step explanation:
To the the volume of a rectangular prism you do this equation: l x w x h = v
fill in the measurements:
8 x 2.25 x 3.5 = 63
Which of the following best describes ABC – DEF?
A. ABC is a dilation of DEF.
B. ABC is similar to DEF.
C. ABC is a reflection of DEF.
D. ABC is congruent to DEF
Please help I will give brainliest.
Answer:
A. ABC is a dialtion of DEF
Please answer as soon as you can.
Solve each system by eliminating one of the variables by addition or
subtraction.
Answer:
(=^w^=) hope this helps
Step-by-step explanation:
1. (10,2)
2. (2,0)
3. (6,2)
4. (0.5,7.5)
5. (3.3, 0.36)
6. (3.5, 2.5)
someone help me answer this
Answer:
c = 53 yd is the answer.
Step-by-step explanation:
a = 45 yd
b = 28 yd
c = ?
According to the Pythagorean Theorem,
a² + b² = c²
45² + 28² = c²
2025 + 784 = c²
c² = 2809
c = 53 yd
∴ The dog runs 53 yd