Given:
[tex]\dfrac{dr}{dt}=1.4\text{ in/s}[/tex]
[tex]\dfrac{dh}{dt}=-2.1\text{ in/s}[/tex]
To find:
The rate of change in volume at [tex]r=120\text{ in. and }175\text{ in.}[/tex]
Solution:
We know that, volume of a cone is
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Differentiate with respect to t.
[tex]\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right][/tex]
Substitute the given values.
[tex]\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right][/tex]
[tex]\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right][/tex]
[tex]\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560[/tex]
[tex]\dfrac{dV}{dt}=29920[/tex]
Therefore, the volume of decreased by 29920 cubic inches per second.
A corporation worth 40 million is expected to grow 8% per year compounded annually for 5 years. (A) find the future value to the nearest million. (B)
Answer:
$56 million
Step-by-step explanation:
8% x 5 = 40%
40% of 40 = 16
40 + 16 = 56
Troy has to order 8 pounds of ham, 15 pounds of cheese, and 12 pounds of turkey. What is the toatal cost of troys order?
Answer:
93.75
Step-by-step explanation:
Answer:
The answer is $93.75
Step-by-step explanation:
In a large human population, cranial length is approximately normally distributed with a mean of 185.6 mm and a standard deviation of 12.7 mm. What is the probability that a random sample of size 10 from this population will have a mean less than than 180? a. 0.0174 b. 0.1357 c. 0.0823 d. -1.39
Answer:
The correct option is c
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 185.6 \ mm[/tex]
The standard deviation is [tex]\sigma = 12.7 \ mm[/tex]
The sample size is n = 10
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{ 12.7}{\sqrt{ 10 } }[/tex]
=> [tex]\sigma_{x} = 4.016[/tex]
Generally the probability that a random sample of size 10 from this population will have a mean less than than 180 is mathematically represented as
[tex]P(X < 180 ) = P(\frac{ X - \mu }{\sigma_{x} } < \frac{180 - 185.6}{4.016} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(X < 180 ) = P(Z < - 1.394 )[/tex]
From the z table the area under the normal curve to the left corresponding to -1.394 is
[tex]P(X < 180 ) = P(Z < - 1.394 ) = 0.081659[/tex]
=> [tex]P(X < 180 ) = 0.0823[/tex]
A car travels at a constant speed.
What is the car's speed between checkpoints, expressed as a unit rate?
Use the information given in the picture.
Answer:
Step-by-step explanation:
Checkpoint A-> time being 1:00pm total miles driven being 120 and
checkpoint B-> time being 3:00pm and the total miles being 208
The distance between two checkpoint A and B is 208 - 120 = 88 miles
Now the time between the two checkpoints = 3.00 - 1.00 = 2 hours
We need to find car speed between the checkpoints
We know Distance = speed * time
Speed = 44 miles per hour
Answer:
The answer is 1 miles
Step-by-step explanation:
1+1=2
Are these ratios equivalent? 38:19 and 2:1 *
Answer:
Yes
Step-by-step explanation:
2 times 19=38
1 times 19=19
Answer:
yep it is equivalent by decreased orchard Harvick hdiwbxgcysnabudnd
Skip and Jena are selling raffle tickets to raise money for new basketball uniforms. Skip sold 2 tickets for every 7 tickets that Jena sold. If Jena sold 63 tickets how many did Skip sell? Use a double number line and equivalent ratios to justify your answer.
PLEASE HELP ANSWER THIS QUESTION RIGHT I WILL GIVE YOU 1000 PIONTS!!!
Why is Thomas Nast famous?
He took photographs of immigrants to bring attention to their plight.
He wrote articles calling for an end to segregation in the South.
He helped bring down Boss Tweed and Tammany Hall with his political cartoons.
He campaigned tirelessly for women's right to vote.
Answer:
C. He helped bring down boss tweed and tammany hall with his political cartoons.
I believe that is the correct answer.
Answer: C.
Step-by-step explanation: Took the test.
Find the value of y
Will give brainliest
And brainless lol
Answer:
155
Step-by-step explanation:
- because of the angle rules, (6x+1) = (2x+17)
- with this, you can now solve to get x = 4
- also because of the angle rules, y = 180 - (2x+17)
- replace the x with 4 and calculate and you'll get y = 155
What is the distance between z1 = 5 - 2i and z2 = 8 + i?
3√2
13.3
2√3
18
Answer:
d=2√10
Step-by-step explanation:
The distance between the two points will be given by:
d=√[(x-x1)^2+(y-y1)^2]
point z1=(3-2i) has the coordinates of (3,-2)
point z2=(5-8i) has the coordinates of (5,-8)
thus the distance between them will be:
d=√[(-8-(-2)²+(5-3)²)]
d=√[(-6)²+2²]
d=√(36+4)
d=√40
d=2√10
Answer:
3√2
Step-by-step explanation:
distance formula: d = √(a₁ - a₂)² + (b₁ - b₂)²
a = x, b = y
d = √(x₁ - x₂)² + (y₁ - y₂)²
(Pls help me ASAP i will give brainliest!! Also, pls write at least 3 sentences to explain your reasoning :) )
12,400 x one and one fifth = ________. Will the product of this equation be less than or greater than 12,400? Explain your reasoning.
Answer:
the answer is 14,880 and its bigger :D 14880>12400
Step-by-step explanation:
Answer:
14880
Step-by-step explanation: I think that it would be greater to me because 14 is bigger than 12.
what are all the angles?
1) 137 degrees
2) 43 degrees
3) 137 degrees
4) 43 degrees
5) 43 degrees
6) 137 degrees
7) 43 degrees
8) 137 degrees
180-137= 43
My mother likes _____ milk at the store.
nadar
aceptar
comprar
enseñar
Answer:
comprar makes the most sense
what is 4901 and 75 estimated to
Answer:
5000 and 100
Step-by-step explanation:
1. A jet travelled 640 miles in 2.5 hours. How far does it travel in 1 hour?
2. Renee as 20 days to read a book with 250 pages. How many pages should she read per day to finish the book on time?
plsssssss help i will mark u brainliest if possible
Answer:
1.) 256 miles
2.) 2 1/2 ( 2.5 ) pages a day
Step-by-step explanation:
1.) ( 256 * 2.4 = 640 )
2.) 250 / 20 = 2.5
11 points please help and give a small explanation I’ll mark brainliest
Answer:
what are we looking at
Step-by-step explanation:
Answer:
31.5 IS YOUR ANSWER
2in=7m. 3in=10 1/2. 4in=14m. 6in=21m. 8in=28. 9in=31.5
TO GET THE METERS ADD 31/2 WHICH IS HALF OF 7.
Form a polynomial whose zeros and degree are given.
Zeros: -2, 2, 9; degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
Answer:
the polynomial is: [tex]\mathbf{x^3-9x^2-4x+36=0}[/tex]
Step-by-step explanation:
We need to form a polynomial whose zeros are:
-2,2,9
We can write them as: x=-2, x=2 and x=9
x+2=0, x-2=0 , x-9=0
(x+2)(x-2)(x-9)=0
Now multiplying all terms:
[tex](x(x-2)+2(x-2))(x-9)=0\\(x^2-2x+2x-4)(x-9)=0\\(x^2-4)(x-9)=0\\x^2(x-9)-4(x-9)=0\\x^3-9x^2-4x+36=0[/tex]
So, the polynomial is: [tex]\mathbf{x^3-9x^2-4x+36=0}[/tex]
Blank divided by 7 = 4 Remainder 5
Answer:
21
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
7 x 4 = 28
33 - 5 = 28
Please help! Brainliest!!!!! 50 points!
Answer:
your answer is 5,0 on the x-axis, 0,6 on the y-axis, 8. 7,2. 3 on Q1, -1,10 on Q2, -1/4, -6 1/2 on Q3, 5, -2 on Q4.
Step-by-step explanation:
Answer:
5,0 on the x-axis, 0,6 on the y-axis, 8. 7,2. 3 on Q1, -1,10 on Q2, -1/4, -6 1/2 on Q3, 5, -2 on Q4.
Step-by-step explanation:
need fast plz anwers right plz
Answer:
it's the 1st one he was nervous
Answer:
The first option
Step-by-step explanation:
First of all he had butterflies I his stomach but it did not say he forgot his whole speech he was just nervous
Find the slope between the points (4, -2) and (6, -6)!
please help
Mr. Washington purchased three cell phones. Each cell phone cost one hundred fifty dollars. What is the total she paid for the cell phones?
Answer:
The answer is $450
Step-by-step explanation:
You need to do 150+150+150=450
or
150x3=450
two fifth of a certain number plus two is equal to ten
Answer:
that no. is 20
Step-by-step explanation:
let us take that certain no. as x
so
2/5. x +2=10
2x/5 = 10-2
2x = 8×5
x= 40/2
x= 20
Here is a number in expanded form. (6 x 100) + (1 x 10) + (7 x 1) + (9 x 1/10) + (2 x 1/1000) Write it in standard form. (Using Decimals)
Answer:
617.902
Step-by-step explanation:
(6 * 100) + (1 * 10) + (7 * 1) + (9 *1/10) + (2 *1/1000)=308951/500
308951/500=617.902
The standard form of given number is 6.17 ×10².
What is standard form?
Standard form is a way of writing down in easy form of very large or very small numbers.
Let E is the standard form of given number
E = (6 × 100) + (1 × 10) + (7 × 1) + (9 ×1/10) + (2 ×1/1000)
E =600+10+7+0.9+0.002
E =617.902
E =0.617 × 10³ = 6.17 ×10²
E = 6.17 ×10²
Hence, the standard form of given number is 6.17 ×10²
Learn more about Standard form
https://brainly.com/question/13139379
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PLEASE I NEED HELP I WILL MARK BRAINLYEST!!!!!!!!!!!!!!!!
PLEASE ANSWER NOWW!!!!!!!!!!!!!!
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 10,125(1.83)
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year?
Answer:
The amount is increasing and is increasing by 3.34% each year?
Step-by-step explanation:
Anything times a number higher than 1 will increase. 10125×1.83=18528.75.
And again....thank you!
Answer:
The second one to the left
Step-by-step explanation:
PLS GIVE BRAINLIEST
Answer:
the second graph id the correct one
Step-by-step explanation:
because he asked about the type of the of the food and the number of lunches sold
i hope i helped :)
The sum of two square numbers is 15 square. What are the square numbers?
what is 5 1/2 plus 5 1/4
Answer 10.75
......................................
Answer:
10 and 3/4
Step-by-step explanation:
For the fractions, get a common denominator (bottom number): 1/2=2/4
So 2/4 plus 1/4 equals 3/4 and 5+5 equals ten.
10+3/4=10 3/4
Decimal form: 10.75
A cylindrical mass has a radius of 5 cm and a height of 6 cm. If the mass of the cylinder is 900 grams, what is the density of the cylinder?
Approximately 1.9 grams per cubic centimeter.
First you calculate the size of the cylinder in centimeters by taking the area of the base and multiplying it by the height, and then you divide the mass of the cylinder by the volume.
Are 6 + 10 and 2(3) + 2(5) equivalent expressions? How do you know?
Can someone help with this? You dont really have to solve it (I mean you can if you want to....) But if not, can someone explain how to solve it? Thanks!
Answer:
43
Step-by-step explanation:
