Answers
In the picture we have to solve the individual variables A=2πr²+2πrh. We got function with r as subject is\(\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }\)
Given that,
In the picture we have to solve the individual variables
A=2πr²+2πrh
We have to find function with r as subject.
Taking A to left side we get
2πr²+2πrh-A=0
We can see the equation is in the form of quadratic equation with variable r.
So, The factor we find by using the formula
That is \(\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}\)
Here, a=2π,b=2πh and c=-A
r=\(\frac{-2\pi h\pm\sqrt{(2\pi h)^{2}-4(2\pi)(-a) } }{2(2\pi)}\)
r=\(\frac{-2\pi h\pm\sqrt{(4\pi^{2}h^{2} +8\pi a) } }{4\pi}\)
r=\(\frac{-h}{2} \pm\frac{\sqrt{(4\pi^{2}h^{2} +8\pi a )} }{4\pi}\)
r=\(\frac{-h}{2} \pm\sqrt{\frac{4\pi^{2}h^{2}+8\pi a }{16\pi^{2} } }\)
r=\(\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }\)
Therefore, We got function with r as subject is\(\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }\)
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Related Questions
plss do the working
Answers
Answer:
1386
Step-by-step explanation:
V=πr²*h
V=22/7*7²*9
V=1386
The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answers
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
Help ASAP!
Question 1:
Check attached file for question 1
Question 2:
A new lake was populated with a small number of trout. The number of trout in the lake can be modeled by the function: P(t)=740 / 1+73e^−0.07 where t is the number of months since the population of trout was first introduced. Round all answers to the nearest whole number
A. what is P(0)= I got 10
B. What does the answer from part A tell us about the trout population?
C. How many trout were in the lake after 1 year?
D. How many trout were in the lake after 10 years?
E. lim t→∞P(t)= I got 740
F. What does the answer from part E tell us about the trout population?
Answers
The answer from part A tells us that the trout population was 10 in the first month after it was introduced.
How solve the problem?A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.
B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.
C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.
D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.
E. lim t→∞ P(t) = 740, so the answer is 740.
F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.
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Solve for ? To make a no solution problem
Answers
Please help..........
Answers
Answer:
1178 inches
Step-by-step explanation:
Using the triangle I drew (assuming n is across from ∠N), we can conclude that ∠O = 180-97-32 = 51 as the angles in a triangle add up to 180.
Using the law of sines, we can conclude that
\(\frac{o}{sinO} = \frac{n}{sinN} \\\)
Plugging our values in, we get
\(\frac{o}{0.78} = \frac{800}{0.53}\)
Multiply both sides by 0.78 to get
\(o = \frac{800*0.78}{0.53} = around 1177.5\)
round up to get 1178 as our answer
james earns $3,129 a month. He is saving 1/3 of his income each month for a down payment on his home at the end of the year. How much money will james be saving each month?
Answers
Answer:
1,043
Step-by-step explanation:
To find this, multiply 1/3 x the monthly income.
1/3(3,129)
1,043
-Xax
$1043 money will james be saving each month.
what is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
James earns $3,129 a month.
He is saving 1/3 of his income each month.
So, money will james be saving each month
= 3129 x 1/3
= 1043
Hence, $1043 money will james be saving each month.
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The test statistic of zequals2.31is obtained when testing the claim that pgreater than0.9.a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.b. Find the P-value.c. Using a significance level of alphaequals0.10,should we reject Upper H 0or should we fail to reject Upper H 0?
Answers
Answer:
Step-by-step explanation:
a) From the information given, we can state the hypothesis as follows:
For null hypothesis,
p = 0.9
Or
p ≤ 0.9
For alternative hypothesis,
p > 0.9
Because of the greater than inequality symbol in the alternative hypothesis, it means that it is a right tailed test.
b) Since z = 2.31, we would determine the p value by looking at the probability corresponding to the area above the z score from the normal distribution table. Thus
P value = 1 - 0.9896 = 0.0104
Using a significance level of alpha equals 0.10, since alpha, 0.10 is > p value, 0.0104, then we would reject the null hypothesis.
I need help right now!!!
Answers
1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.
2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.
What does it mean for figures to be congruent?When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.
Similar figures have the same shape, but they may have different sizes and be located in different positions.
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(c) Ben changes £800 to Euros before he goes on holiday.
£1 = 1.25 Euro
He spends 895 Euros.
He changes the Euros that he has left to Pounds (£).
The exchange rate is now £1 = 1.40 Euro
How many Pounds does he get back?
Answers
Amount of pounds that Ben get back is £75.
What is Exchange Rate?Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.
Ben changes £800 to Euros before he goes on holiday.
Before holiday, exchange rate is, £1 = 1.25 Euro
£800 = 800 × 1.25 Euros = 1000 Euros
He spends 895 Euros.
Euros left = 1000 - 895 = 105 Euros
Now, the exchange rate is £1 = 1.40 Euro.
or 1.40 Euro = £1
⇒ 1 Euro = £ 1/1.40
⇒ 105 Euros = £ (1/1.40) × 105 = £75
Hence Ben got £75 of pounds back.
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11. Given that the function graphed is f(x), what
is f(-5)?
Answers
Answer:
f(-5) =5
Step-by-step explanation:
We want to find the output value when x = -5
Looking at the graph when x = -5 the graph is at 5
f(-5) =5
Solve the simultaneous equations using elimination method= x+2y-3z=0 3x+3y-z = 5 x-2y = 2z=1
Answers
Answer:
[1;1;1]
Step-by-step explanation:
try this option; all the details are in the attachment.
use the gas prices data below to calculate a 3-month simple moving average (sma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. round your answer to two decimal places, if necessary.
Answers
Three- month simple moving average (sma) forecast for the average gas prices are $3.08
$3.16 , $3.29 and predict the average retail gasoline price for june 2020 is $3.54.
What Is a Simple Moving Average (SMA)?A simple moving average (SMA) is defined as an arithmetic moving average calculated by adding recent prices and then dividing that figure by the number of time periods in the calculation average. The formula for SMA is:
SMA = (A₁ + A₂ + ------+ Aₙ )/n
where, Aₙ = the price of object at nth period
n = the number of total periods
We have, a average gas prices for different months. Calculate the three-month moving average, add together the first three sets of data, for this example it would be Dec, January, and February. This gives a total of $9.25 , then calculate the average of this total, by dividing this figure by 3 we get 3-month simple moving average. We have to predict the 3-month simple moving average for June 2020. As we seen in above table we calculate the 3-month simple moving average for different months.
The 3-month simple moving average for June 2020 is ( $3.29 + $3.51 + $3.82 )/3 = $3.54
So, required value is $3.54..
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Complete question:
use the gas prices data below to calculate a 3-month simple moving average (sma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. round your answer to two decimal places, if necessary.
Year - month Averge gas price
19-Dec $3.07
20-Jan $3.10
20-Feb $3.08
20-Mar $3.29
20-Apr $3.51
20-May $3.82
20-Jun
3(4x - 6) - 2x + 1 = 3 - (3x - 6)?
Answers
10x - 17 = -3x + 9
13x = 26
x = 2
I hope this helps
Vector v is shown in the graph.
vector v with initial point at 0 comma 0 and terminal point at negative 8 comma 6
Which are the component form and magnitude of v?
v = ❬–8, 6❭; ||v|| = –10
v = ❬8, 6❭; ||v|| = –10
v = ❬8, 6❭; ||v|| = 10
v = ❬–8, 6❭; ||v|| = 10
Question 5
Vector v is shown in the graph.
vector v with initial point at 2 comma 5 and terminal point at negative 3 comma negative 2
Which are the magnitude and direction of v? Round the answers to the thousandths place.
||v|| = 8.602; θ = 54.462°
||v|| = 8.602; θ = 234.462°
||v|| = 9.220; θ = 54.462°
||v|| = 9.220; θ = 234.462°
Answers
Question 4
Answer: Choice DExplanation:
If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.
We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.
===========================================================
Question 5
Answer: Choice BExplanation:
Vector v starts at (2,5) and ends at (-3,-2).
The x component of the vector is x2-x1 = -3-2 = -5 meaning we move 5 units to the left when going from the start point to the endpoint.
At the same time we move 7 units down because y2-y1 = -2-5 = -7 which is the y component of the vector.
The component form of vector v is
v = <-5, -7>
it says "move 5 units left, 7 units down".
Apply the pythagorean theorem to find the length of the vector.
a^2+b^2 = c^2
c = sqrt(a^2 + b^2)
||v|| = sqrt( (-5)^2 + (-7)^2 )
||v|| = 8.602 which is approximate.
Now let's use the arctangent function to find the angle
theta = arctan(b/a)
theta = arctan(-7/(-5))
theta = 54.462 which is also approximate.
There's a problem however. This angle is in Q1 but the vector <-5,-7> is in Q3. An easy fix is to add on 180 to rotate to the proper quadrant.
54.462+180 = 234.462
which is the proper approximate angle for theta.
Factor to write an equivalent expression: 360 – 16
Answers
Answer:
360 - 16 = 8(45 - 2) = 344
Step-by-step explanation:
360 - 16
4(90 - 4)
8(45 - 2)
344
Please help I have to be at 100% in Khan :( Look at the Image I give Brainliest
Answers
Answer:
Look below
Step-by-step explanation:
2/3 - 1/4 = m
Hope this Helps!
(a+b)^3 ///////////////////////////
Answers
Answer:
What is the question you are asking?
Answer:
(a+b)³ = a³+b³+3ab(a+b)
Step-by-step explanation:
hope it's helpful to you ☺️
Your mother bought a three-liter bottle of water. When she got home, she discovered a small leak in the bottom and asked you to find a container to transfer the water into. All you could find were two half-gallon jugs. Part 1 out of 2 Will your containers hold all of the water? Complete the explanation. Two half gallons containers (select) hold one gallon, which is about liters.
Answers
Answer:
1
Step-by-step explanation:
A bag contains 15 red candies, 15 yellow candies, and 15 blue candies. What is the probability of randomly
choosing two candies of the same color, without replacement?
Answers
\(|\Omega|=45\cdot44=1980\\|A|=15\cdot14\cdot3=630\\\\P(A)=\dfrac{630}{1980}=\dfrac{7}{22}\approx31.8\%\)
Given: AB=BC,AM=MC
BM IAC , EF I BC
EC
FC
Prove:
AB
MA
B
F
с
A
EM
Answers
Answer:
AB=BC,AM=MC
BM IAC , EF I BC
Step-by-step explanation:
AB
MA
B
F
с
A
Find the probability of spinning red on every spin
Answers
y’all can get banned.... so yeah okay 623
Please help this is timed!!!!
Answers
Answer:
C and D
89 _> 12.50t -14
+14 +14
103 _> 12.5t
/12.5 /12.5
8.24 _> t
A national grocery store chain designed a study to determine whether its customers would be interested in home delivery. The
chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who
hopped in the chain's stores were interested in the service. What is the sample in the study?
Answers
The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.
The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.
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The average winter snowfall for Syracuse, New York, for December, January, February is 27.5 inches per month. If Syracuse receives 24 inches of snow in December and 32 inches in Januar how much snow is required in February to exceed the 3 month average?
Answers
Answer: More than 26.5 inches
Step-by-step explanation:
Solve this equation :
\(\frac{32+24+x}{3} \geq 27.5\)
x>26.5
Consider the system of equations. 20 POINTS NEED HELP ASAP
y = –5x – 1
y = 2x + 6
Choose the correct answer to each question.
What is the slope of the first line?
What is the slope of the second line?
How many times do the lines intersect?
How many solutions does the system have.
Answers
- 5x - 1 = 2x + 6
- 7x = 7
7x = -7
x = -1
Which line contains an error?
Line 1: 6x – 2 (x – 5) = 12
Line 2: 6x – 2x – 10 = 12
Line 3: 4x – 10 = 12
Line 4: 4x = 32
Line 5: x = 8
Answers
Answer:
this is how to correctly do it:
6x – 2 (x – 5) = 12
6x-2x+10=12
4x-10=12
4x=22
x=5.5
so the error is in line 4
Select all expressions that are equivalent to -2x - (x+5) + 3
-2x - x -5 + 3
-X + 8
-X-2
-3x-2
2x - x + 5+ 3
Answers
Emily's score for a Mathematics test was 5% higher than her score for an English test. If Emily scored 84 points for the Mathematics test, how many points did she score for the English test?
Answers
Answer:
80 points
Step-by-step explanation:
If score in English is x points and score in math is 5% higher then score in math
y = x + 0.05x
where 0.05 = 5% expressed as decimal
0.05x refers to the 5% increase in score
y = math score
y = x(1 + 0.05)
y = 1.05x
Given score in math = 84 this becomes
84 = 1.05x
x = 84/1.05
x = 80
So Emily's score in English was 80 points
Simplify the following expressions:
10x + 6 + 2(x + 5)
6 - 5(x + 2)
-2x - 10(2 + 4x)
6 - (x + 3)
3x - (x + 10) + 12
Answers
10x + 6 + 2(x + 5) =
= 10x + 6 + 2x + 10 = 12x + 16
6 - 5(x + 2) = 6 - 5x - 10 = -5x - 4
-2x - 10(2 + 4x) =
= -2x - 20 - 40x = -42x - 20
6 - (x + 3) = 6 - x - 3 = -x + 3
3x - (x + 10) + 12 =
= 3x - x - 10 + 12 = 2x + 2
nequality
Imagine the polynomial function shown represents the
profits, in y dollars, earned by the production of x
widgets.
What is the minimum number of widgets for the
company to earn more than 50 dollars?
widgets
Answers
Answer:
The minimum number of widgets for the company to earn more than 50 dollars = 104 widgets.
Step-by-step explanation:
Complete Question
Inequality
Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.
y = -0.04x² + 40x - 3600
What is the minimum number of widgets for the company to earn more than 50 dollars?
Solution
For the profit to be more than 50
y > 50
-0.04x² + 40x - 3600 > 50
-0.04x² + 40x - 3650 > 0
0.04x² - 40x + 3650 < 0
(x - 898.4) (x - 101.6) < 0
Using the inequality table to obtain the required solution to this inequality
Eqn | x < 101.6 | 101.6 < x < 898.4 | x > 898.4
(x - 898.4) | -ve | - ve | + ve
(x - 101.6) | -ve | + ve | + ve
(x-898.4)(x-101.6) | +ve | - ve | +ve
Hence, the inequality that satisfies the equation of (x - 898.4) (x - 101.6) < 0, that is, negative, is 101.6 < x < 898.4.
And from this range, the minimum number of widgets for the company to earn more than 50 dollars = 102 widgets.
But 102 widgets give a profit of 13 dollars, 103 widgets give a profit of 47 dollars and it is until 104 widgets that the profits exceed 50 dollars truly.
Hope this Helps!!!
Answer:4
Step-by-step explanation: