Using implicit differentiation, it is found that she must blow air at a rate of 251.33 cm³/sec.
A balloon has a spherical format.The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
The radius is half the diameter, hence:
[tex]r = \frac{d}{2}[/tex]
[tex]r^3 = \frac{d^3}{8}[/tex]
[tex]V = \frac{4\pi d^3}{24} = \frac{\pi d^3}{6}[/tex]
Applying implicit differentiation, the rate of change of the volume is:
[tex]\frac{dV}{dt} = \frac{d^2 \pi}{2}\frac{dd}{dt}[/tex]
The diameter increases at the rate of 10 cm/sec, hence [tex]\frac{dd}{dt} = 10[/tex].It is of 4 cm, hence [tex]d = 4[/tex]The rate that she must blow air is:
[tex]\frac{dV}{dt} = \frac{d^2 \pi}{2}\frac{dd}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{4^2 \pi}{2}(10)[/tex]
[tex]\frac{dV}{dt} = 251.33[/tex]
She must blow air at a rate of 251.33 cm³/sec.
A similar problem is given at https://brainly.com/question/25581404
The length of a rectangle is 10 times its width. If the area of the rectangle is 52 yd2, find its approximate width.
Answer: approximate width= 5.2 yd
Step-by-step explanation:
Help this is due today!!!!!!!
Does anyone know this?
Answers:
A. b=4/3, c=12
B. b=4/3, c=2/3
C. b=8/3, c=16/3
D. b=8/3, c=16
Answer:
the answer will be choice D
as we can see that the triangle have angles measuring 30 60 and 90 so we will use the 30-60-90 rule
you can look up the explantion about the rule online
2x² - x + 6 is subtracted from x² + 3x - 2, the result is
Answer:
-x² + 4x - 8
Step-by-step explanation:
Given: 2x² - x + 6 is subtracted from x² + 3x - 2
Rewriting: (x² + 3x - 2) - (2x² - x + 6)
Distrubte negative: x² + 3x - 2 - 2x² + x - 6
Combine like terms: -x² + 4x - 8
Answer: -x² + 4x - 8
Hope this helps, have a nice day :D
how to convert fraction in time
Answer:
give an example
Step-by-step explanation:
Identify the factors of the following numbers 1. 40- 2. 54- 3 63 - 4.70 - 6. 85 -
Which of the following fraction below is an IMPROPER FRACTION?
a. 1/3
b. 16/5
c. 2/3
d. 4/27
Juanita has saved 10% of the money that she needs to buy a new bicycle.
If she has saved $22, how much money does the bicycle cost?
There were 5 7/10 of water in a bucket. Mollie spilled some of the water. Then she added an additional 1 5/10 liters of water to the bucket. After that, there was 6 4/10 liters of water in the bucket. How much did Mollie spill?
Answer:
8/10
Step-by-step explanation:
57/10 add 15/10=72/1072/10 subtract 64/10=8/10Which logarithmic equation is equivalent to the exponential equation below?
e^4x = 5
Step-by-step explanation:
e^4x = 5
x = 1/4 × ln(5)
x ÷ 1/4 = ln(5)
x.4 = ln(5)
4x = ln(5)
ln(5) = 4x
Option → D
Marcus works at a clothing store and gets an employee discount. The price
he pays can be modeled by the function d(c) = C -0.10c, where c is the original price
of the item. Find d(32) and describe what this means in the context of the problem.
(please answer i need asap)
9514 1404 393
Answer:
d(32) = 28.80
the price Marcus pays on an item with an original price of 32
Step-by-step explanation:
d(32) = 32 -0.1(32)
d(32) = 28.8
The problem statement tells you d(32) is the price Marcus pays when the original price is 32.
SOMEONE HELP ME PLEASE!
AND IF YOU ANSWER FIRST YOU GET BRAINLIST
AND YOU GET 10 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
How to find the GCF 2x-4y+6z
Answer:
inding the Greatest Common Factor (GCF): To find the GCF of two expressions:
Factor each coefficient into primes. Write all variables with exponents in expanded form.
List all factors—matching common factors in a column. ...
Bring down the common factors that all expressions share.
Multiply the factors
Answer:
Step-by-step explanation:
2x = 2*x
4y = 2 *2 *y
6z = 2* 3 * z
GCF = 2
GCF is the greatest common factor. Here 2 is common factor
2x - 4y + 6z = 2*(x - 2y + 3z)
Which of the following expressions are equivalent?
Answer:
all of the expressions are equivalent
Step-by-step explanation:
if you simplify each expression, you get the same answer for all of them
If it takes 2.5 gallons of milk to make 2 pounds of cheese. How many pounds of cheese can John make with 50 gallons of milk?
Answer:
21 pounds
tell me if it helped :P
Step-by-step explanation:
Whiskers the cat weighs 2 and 2 over 3 kg.piglio weighs 4 kg. How many times as heavy as whiskers is piglio
Answer:1.33 kg
Step-by-step explanation:
2 2/3= 8/3
8÷3= 2.66 kg
2.66-4= 1.33 kg
HELP I NEED HELP ON THIS QUESTION ITS TIMED
Answer:
The answer is A
Step-by-step explanation:
When you reflect something over the x-axis all of the negative y coordinates become positive.
A U.S. Coast Guard survey of 500 small boats in the Cape Cod area found 195 in violation of one or more
safety regulations.
a. What is the value of the point estimate?
b. What is the critical value you will use for a 95% confidence interval?
C.
What is the value of the standard error?
d. What is the value of the margin of error?
e. State the lower and upper bounds for a 95% confidence interval.
f. State a conclusion, in context.
Using the information given, it is found that:
a) 0.39
b) z = 1.96
c) s = 0.0218
d) M = 0.0428
e)
The lower bound is 0.3472.The upper bound is 0.4328.f) The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more safety regulations is (0.3472, 0.4328).
Item a:
The point estimate is the sample proportion, hence:
[tex]\pi = \frac{195}{500} = 0.39[/tex]
Item b:
95% confidence level, hence [tex]\alpha = 0.95[/tex], the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
Item c:
The standard error is:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For this problem, [tex]\pi = 0.39, n = 500[/tex], hence:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]s = \sqrt{\frac{0.39(0.61)}{500}}[/tex]
[tex]s = 0.0218[/tex]
Item d:
The margin of error is:
[tex]M = zs[/tex]
In this problem, [tex]z = 1.96, s = 0.0218[/tex], hence:
[tex]M = zs = 1.96(0.0218) = 0.0428[/tex]
Item e:
The lower bound is:
[tex]\pi - M = 0.39 - 0.0428 = 0.3472[/tex]
The upper bound is:
[tex]\pi + M = 0.39 + 0.0428 = 0.4328[/tex]
The lower bound is 0.3472.
The upper bound is 0.4328.
Item f:
The 95% confidence interval is (0.3472, 0.4328), which means that we are 95% sure that the true proportion of boats who are in violation of one or more safety regulations is (0.3472, 0.4328).
A similar problem is given at https://brainly.com/question/15136737
In one jar, I have two balls labelled 1 and 2 respectively. In a second jar, I have three balls labelled 0, 1 and 2 respectively. I draw one ball from each jar, multiply the numbers on the two balls together, and then calculate three to the power of that product, e.g. if I draw 1 and 2, I calculate 3^2=9. Let’s call this number X. What is the probability that the number 1,024 is an exact multiple of X?
Step-by-step explanation:
this is a kind of trick question, actually.
with whatever we draw, we produce X values as power of 3.
to be precise, we can have only
3⁰ = 1
3¹ = 3
3² = 9
3⁴ = 81
due to the possible combinations of drawn numbers (e.g. 3 cannot be created by a multiplication of 0s, 1s and 2s).
so, mostly, these results cannot be exact factors of 1024.
1024 cannot be divided by 3, nor by 9 nor by 81.
but 1024 is a multiple of 1 (as is every number).
so, we are looking at the probability to get 0 as multiplication result of the numbers on the 2 drawn balls.
the only possibilities are
1 and 0
2 and 0
out of in total 6 (2×3) different outcomes
1 and 0
1 and 1
1 and 2
2 and 0
2 and 1
2 and 2
the probability of this "0" event is again
number of desired outcomes / number of possible outcomes = 2/6 = 1/3
please help me thank you
Answer:
3
Step-by-step explanation:
The slope is 3. It's the correct answer.
3.
Which of the following is the graph of y = 5x2 + 2?
Answer:
Graph A
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: ( 0 , 2 )
Focus:
( 0 , 41 /20 )
Axis of Symmetry: x = 0
Directrix: y = 39 /20
x y
− 2 22
− 1 7
0 2
1 7
2 22
May i have some help please?
Answer:
yes
Step-by-step explanation:
someone please help me due in an hour
Answer:
9 players rushed 20 or more yards this season
Step-by-step explanation:
What is 5/8÷1 and 1/3
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{8}\div 1\frac{1}{3}\implies \cfrac{5}{8}\div \cfrac{4}{3}\implies \cfrac{5}{8}\cdot \cfrac{3}{4}\implies \cfrac{15}{32}[/tex]
on the last 5 quizzes, marco has earned a total of 21 out of 25 possible points. if he has a perfect score on the next several quizzes, exactly how many points will he need to bring up his average up to 90%
Using the mean concept, it is found that we will need 15 more points to bring up his average up to 90%.
The mean of a data-set is the sum of all observations divided by the number of observations.
In this problem:
In the first 5 observations, total of 21 out of 25 points, hence the mean for these observations is [tex]\frac{21}{25} = 0.84[/tex].In the next n observations, mean of 1.Hence, the mean is:
[tex]M = \frac{0.84(5) + n}{5 + n} = \frac{4.2 + n}{5 + n}[/tex]
We want the mean to be of 0.9, thus:
[tex]M = 0.9[/tex]
[tex]\frac{4.2 + n}{5 + n} = 0.9[/tex]
[tex]4.2 + n = 0.9n + 4.5[/tex]
[tex]0.1n = 0.3[/tex]
[tex]n = \frac{0.3}{0.1}[/tex]
[tex]n = 3[/tex]
3 more testes are need, each worth 5 points, hence, 15 more points are needed to bring up his average up to 90%.
A similar problem is given at https://brainly.com/question/25323941
The function f(x)=bx^2+x-7 has a remainder of 3 when divided by (x-2), where b is a real constant.Find the value of b
Step-by-step explanation:
f(x) = bx² + x - 7
g(x) = x — 2
Remainder is 3.
Let us find the zero of g(x).
→ g(x) = 0
→ g(x) = x - 2
→ 0 = x - 2
→ x = 2
Now, as when f(x) is divided by g(x), then remainder is 3. So,
→ f(2) = 2
→ b(2)² + 2 - 7 = 2
→ 4b - 5 = 2
→ 4b = 7
→ b = 7/4
Therefore, the answer is 7/4.Find 5(-12). Thanks I just needed help real quick
Answer:
-60 ? At least that's if you meant like
[tex]5 \times ( - 12) = - 60[/tex]
Answer:
Cannot simplify As a decimal 0.41.6 Explanation: 512 does not cancel down
Step-by-step explanation:
8(-b-4) distributive property
Answer:
-8b - 32
Step-by-step explanation:
8(-b-4)
Distribute
8 *(-b) + 8 * (-4)
-8b - 32
Answer:
-8b-32
Step-by-step explanation:
8(-b-4) next it would be -8b-32
Need help with this please
Answer:
slope: 2y-intercept: -1Step-by-step explanation:
The slope is most easily found using two grid intersections. We know that the line crosses the grid intersection (0, -1) at the y-axis. (That is the y-intercept.) And it crosses another one at (1, 1), just above the x-axis in the first quadrant.
The slope of the line between these points can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -(-1))/(1 -0) = 2/1 = 2
The slope can also be found by counting the grid squares of "rise" (2) for each grid square of "run" (1) between those two points or any other convenient points on the line.
m = rise/run = 2/1 = 2
The slope of the line is 2.
__
The y-intercept is the point where the line crosses the y-axis. That point is on an unmarked grid line between y = 0 and y = -2. That is, it is halfway between the values 0 and -2, so is y = -1.
The y-intercept is (0, -1).
A car is travelling at an average speed of 110 km/hr. Each trip the car must stop for gas
which takes 15 minutes. Write an equation to determine the amount of time (T) in
hours it takes the car to travel x distance.
Answer:
1 minute every mile
Step-by-step explanation:
just divide
