Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
Radius is 107 in. and the height is 151 in.
This means that [tex]r = 107, h = 151[/tex]
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that [tex]\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6[/tex]
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))[/tex]
[tex]\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}[/tex]
[tex]\frac{dV}{dt} = 1926[/tex]
Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
6 Factorise
x2 + 6x -7
Answer:
(x+7)(x-1)
Step-by-step explanation:
x^2 + 6x -7
so here we need two number that give 7 when multiplied and 6 when subtracted
7 and 1 are the numbers because
7*1=7 and ,
7-1=6 so,
x^2 + (7-1)x -7
x^2 +7x -x -7
take common from first two terms and from third and fourth term
x(x+7)-1(x+7)
take (x+7) as common
(x+7)(x*1 -1*1)
(x+7)(x-1)
Miguel went shopping for a new phone. Sales tax where he lives is 4%. What number should he multiply the price of the phone by to find the total plus tax in one step?
Answer:
miges fue y no me compro el celu
Step-by-step explanation:
mal migel
por culpa de brailyn reverg
A variable expression cannot consist of numbers or operstions. true false
Answer:
False
Step-by-step explanation:
A variable expression can contain numbers (that work alongside the variables) and operations (that describe how the numbers and variables interact)
What is the Area of the shaded portion in the square.
Step-by-step explanation:
Area of the squre is pi -360/2
Find the area of the parallelogram
A) 37.12 square units
B) 14.5 square units
C) 29 square units
D) 32 square units
Answer:
C 29 square units
Step-by-step explanation:
a = bh
a = 5.8 * 5
a = 29 square units
Answer:
C 29 square units
Step-by-step explanation:
a = bh
multiply
5.8 * 5
29 square units
hope this helps :)
Ben sold his small online business for $100,000. The purchaser will pay him $20,000 today, then $20,000 every year for the next four years. Assume that Ben could invest a lump-sum payment today in an account yielding an interest rate of 4% annually. Find the total present value of all five payments.
A.
$87,096
B.
$88,384
C.
$92,598
D.
$93,964
Answer:
c. 92,598
Step-by-step explanation:
20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08
= 92597.
= 92,598
Please help me I don’t understand this at all
Answer:
you see on the right where the ( - ) are put the dot at -3 which is on the line because y } -x (which means your on the negative side) + 3 is -6 so put the dot on 6
Can someone help me with this one?
Answer:
answer is C
Step-by-step explanation:
y intercept = -3
Answer:
ejjejjeheyreyyeueuuueuuu
!uueueuueu
Step-by-step explanation:
jejjejeujejsjjdjsjjsjsjsjsjjjjejjjejejjjjejeje
Each edge of a cube is 9 centimeters long. Find the total length of all the edges of the cube.
Answer:
108 centimeters
Step-by-step explanation:
There are 12 edges total.
9 x 12 = 108
What is the slope of the line that contains the points (-2, 5) and (6, -3)?
Answer:
-1
Step-by-step explanation:
(-2 , 5) = (x1 , y1)
(6 , -3) = (x2 , y2)
slope of a line = y2 - y1/x2 - x1
=-3 - 5/6 - (-2)
=-8/6+2
=-8/8
=-1
therefore slope of a line is -1.
7 degrees per millisecond converted to 7 degrees per second
Step-by-step explanation:
find the arithmetic mean of given data 12 15 18 20
The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years. Approximate the population of the town 5 years from now.
________ residents (round to nearest whole number)
{Answer:
3893 residents.
Step-by-step explanation:
Equation for population growth:
The equation for the size of a population, considering that it doubles every n years, is given by:
[tex]A(t) = A(0)(3)^{(\frac{t}{n})}[/tex]
In which A(0) is the initial population.
The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years.
This means that [tex]A(0) = 2463, n = 12[/tex]. So
[tex]A(t) = A(0)(3)^{(\frac{t}{n})}[/tex]
[tex]A(t) = 2463(3)^{(\frac{t}{12})}[/tex]
Approximate the population of the town 5 years from now.
This is A(5). So
[tex]A(t) = 2463(3)^{(\frac{t}{12})}[/tex]
[tex]A(5) = 2463(3)^{(\frac{5}{12})} = 3892.8[/tex]
Rounding to the nearest whole number, 3893 residents.
Elena is going to a farmer's market for fresh produce. She has two markets to
choose from and hopes to buy both cherries and asparagus. The table shows
the probability that each type of produce will be available at the markets.
North market
South market
Cherries
0.6
0.5
Asparagus
0.85
0.84
Assuming that the availability of cherries and the availability of asparagus are
independent of each other, which market should Elena choose to maximize
her chance of buying both?
A. South market. There is a 0.42 probability of both cherries and
asparagus being available.
B. North market. There is a 0.3 probability of both cherries and
asparagus being available.
c. South market. There is a 0.3 probability of both cherries and
asparagus being available.
D. North market. There is a 0.51 probability of both cherries and
asparagus being available.
Answer:
D (north, .51)
Step-by-step explanation:
since the numbers are higher for north, it is the right answer.
.6*.85=.51
D. North market. There is a 0.51 probability of both cherries and asparagus being available.
What is independent events ?If the incidence of one event does not affect the probability of the other event then the events are independent of each other and called independent events.
Now, if A and B be two events which are independent,
then P(A∩B) = P(A)×P(B)
How to find which market Elena choose to maximize her chance of buying both?In the table in given problem, the probability of cherries and asparagus are higher for north market.
For the north market,
The probability of produce cherries = P(A) = 0.6
The probability of produce asparagus = P(B) = 0.85
where A and B are the events of produce cherries and asparagus respectively.
Here, A and B are independent events.
Then probability for maximize her choice is P(A∩B) = P(A)×P(B)
= 0.6×0.85
= 0.51
∴ Elena choose north market to maximize her chance of buying both and the probability is 0.51
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A hunter is practicing his aim using a practice target. He takes 5 shots. All 5 shots hit the target, but they do not hit or surround the bullseye. In addition, all 5 shots are very spread apart on the target. Classify the hunter's accuracy and precision.
a. High accuracy and high precision
b. High accuracy and low precision
c. Low accuracy and high precision
d. Low accuracy and low precision
Answer:
D
Step-by-step explanation:
Accuracy refers to how close measurements are to the "true" value (which is the target in this case), while precision refers to how close measurements are to each other.
Since the arrows fall away from the bullseye and are spread out I would classify this as low accuracy and low precision.
- 9 times the difference between a number and 86 is equal to the number plus – 48.
Answer and Step-by-step explanation:
The equation should look like this:
-9(x - 86) = x - 48
Distribute the -9.
-9x + 774 = x - 48
Add 48 and 9x to both sides of the equation.
822 = 10x
Divide both sides of the equation by 8.
82.2 = x
[tex]\frac{411}{5}[/tex] = x -- Fraction Form
#teamtrees #PAW (Plant And Water)
a mixture of 40 liters of paint is 25% red tint, 30% yellow tint and 45% water. 6 liters of yellow tint are added to the original mixture. the percent of yellow tint in the new mixture is?
3. Simplify, 27+3]{14-3(15-5) -53-51-19
Answer:
-4170
Step-by-step explanation:
Given:
[27+3]{14-3(15-5) -53-51-19}
30{14-3(10)-123}
30{14-30-123}
30*(-139)
-4170
Answer is -4170
Write the following percents as both fractions and decimals.
Fraction Decimal
1. 25% ? ?
2. 32.5% ? ?
3. 4% ? ?
4. 75% ? ?
5. 6.5% ? ?
6. 125% ? ?
7. 12.5% ? ?
8. 0.2% ? ?
9. 0.75% ? ?
10. 107% ? ?
11. 210% ? ?
12. 22.5% ? ?
Answer:
1/4, 0.25
13/40, 0.325
1/25, 0.04
3/4, 0.75
13/200, 0.065
1 1/4, 1.25
1/8, 0.125
1/500, 0.002
3/400, 0.0075
107/100, 1.07
21/10, 2.10
9/40, 0.225
using factoring what is the solution to the equation 2x^2+3x-5=0
Answer:
Option B. ( x=1,-5/2 Or x=-5/2,1)
Step-by-step explanation:
2x2+3x−5=0
Step 1: Factor left side of equation.
(2x+5)(x−1)=0
Step 2: Set factors equal to 0.
2x+5=0 or x−1=0
x=−5/2 or x=1
(The Answer you can just switch it around but dont worry its still the same answer nothing change...)
Convert 6 qt/min to gallons per hour
Answer:
90
Step-by-step explanation:
See image below:)
Exercise 5.2
Which of the capital letters of the English alphabet are symmetrical?
Answer:
The Capital letter of English alphabet that are symmetric are B,C,D,E,H,I,K,OX
Step-by-step explanation:
hope it helps
HII TYSM IF YOU ANSWER ILL GIVE BRAINLIEST did I get some of these right? if not lmk :)
Write the equation of a line that meets all the following requirements:
Has an x-intercept at (5,0)
Has a negative slope
Write the equation in Standard Form
Write the equation is Slope-Intercept Form
Explain
How you know your line has an x-intercept of (5,0)
How you know your line has a negative slope
How you converted from one form to the other
9514 1404 393
Answer:
x + y = 5y = -x + 5Step-by-step explanation:
We can start with the point-slope form of the equation for a line. To meet the given requirements, we can use a point of (5, 0) and a slope of -1. Then the equation in that form is ...
y -0 = -1(x -5)
Simplifying gives the slope-intercept form:
y = -x +5 . . . . . . . use the distributive property to eliminate parentheses
Adding x to both sides gives the standard form:
x + y = 5
__
Explanation
We know the line has the required intercept and slope because we chose those values to put into the point-slope form. Conversion from one form to another made use of the rules of equality, the additive identity element (y-0=y), and the distributive property.
PLS HELP ASAP !!! PLSSS !!
Answer:
x=66 degree
Step-by-step explanation:
x+114 =180 degree (the relation between x and 11 degree is that they are same side interior angles and sum of same side interior angles is always 180 degree)
x=180-114
x=66
Answer:
X= 180-114
(Angles on a straight line adds up to 180°)
x= 66°
On a Ford assembly line, each worker
A.) moved from station to station.
B.) was responsible for several different tasks.
C.) performed the same task over and over.
D.) built at least one car each day.
Answer:
d
Step-by-step explanation:
A journalist releases a monthly sports column. Patrons can get either an electronic subscription or a paper subscription. The expression 325(1.03)x represents the number of electronic subscriptions after x months. The expression 345(0.97)x represents the number of paper subscriptions after x months. Which expression reveals the approximate rate of change for the ratio of the number of electronic subscriptions to the number of paper subscriptions?
(1.06)x
(1.66)x
(0.86)x
(0.94)x
Answer:(1.06^x)
Step-by-step explanation:
Translate and solve: 639 is what percent of 142?
Answer:
450
Step-by-step explanation:
639/142= 4.5 times 100
On average, the shoppers across McMaster Univerisity have 2 customers per hour and assuming that for the next hour the number of customers denoted by X, follows a Poisson Distribution. Find the probability that at least two customers are there for the next hour.
Answer:
0.5940 = 59.40% probability that at least two customers are there for the next hour.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
On average, the shoppers across McMaster Univerisity have 2 customers per hour
This means that [tex]\mu = 2[/tex]
Find the probability that at least two customers are there for the next hour.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]. So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1353 + 0.2707 = 0.4060[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4060 = 0.5940[/tex]
0.5940 = 59.40% probability that at least two customers are there for the next hour.
I need help with #2. Please help. I have to show all work so please explain
Answer:
b = 18 in.
Step-by-step explanation:
Since the triangle given is a right triangle, we can use Pythagorean Theorem to solve for b.
[tex]a^2+b^2=c^2\\7.5^2+b^2=19.5^2\\56.25+b^2=380.25\\b^2=324\\\sqrt{b^2}=\sqrt{324}\\b=18[/tex]
Therefore, b is 18 inches.
Find the volume of the prism.
Answer:
B. 864 mm³
Step-by-step explanation:
Volume = area base x height
Area base = 48
Height = 18
Multiply:
48 x 18 = 864
Units are mm³
Answer = 864 mm³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
The volume of the prism is 864 cubic units.
To calculate the volume of a prism, we use the formula: Volume = Area of Base x Height. In this case, the area of the base is given as 48 square units, and the height is given as 18 units.
To find the volume, we multiply the area of the base by the height:
Volume = 48 x 18 = 864 cubic units.
Therefore, the volume of the prism is 864 cubic units. Since the base area is given in square units and the height is given in units, the volume is expressed in cubic units. In this case, the units are mm³ (cubic millimeters).
Thus, the proper calculation yields a volume of 864 mm³.
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