Answer:
Step-by-step explanation:
uhhh i think so its 84 is abc but adc is missing try 48 i dont know but i try
A function y(t) satisfies the differential equation dy dt = y4 − 10y3 + 24y2. (a) What are the constant solutions of the equation? (Enter your answers as a comma-separated list.) y = (b) For what values of y is y increasing? (Enter your answer in interval notation.) y (c) For what values of y is y decreasing? (Enter your answer in interval notation.) y
Answer:
[tex](a)\ y =0\ or\ y=4\ or\ y=6[/tex]
[tex](b) \ (-\infty,4)\ u\ (6,\infty)[/tex]
[tex](c)\ (4,6)[/tex]
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
Solving (a): The constants
This implies that:
[tex]\frac{dy}{dt} = 0[/tex]
So, we have:
[tex]y^4 - 10y^3 + 24y^2 = 0[/tex]
Factorize:
[tex]y^2(y^2 - 10y + 24) = 0[/tex]
Expand and Factorize the expression in bracket
[tex]y^2(y^2 - 6y - 4y + 24) = 0[/tex]
[tex]y^2(y(y - 6) - 4(y - 6)) = 0[/tex]
[tex]y^2(y - 4)(y - 6) = 0[/tex]
Split
[tex]y^2 =0\ or\ y-4=0\ or\ y-6=0[/tex]
Solve for y
[tex]y =0\ or\ y=4\ or\ y=6[/tex]
The above represents the constants
Solving (b): Increasing values
Here
[tex]\frac{dy}{dx} > 0[/tex]
Follow the same process in (a) but replace all = with >
i.e.
[tex]y^2(y - 4)(y - 6) > 0[/tex]
[tex]y >0\ or\ y>4\ or\ y>6[/tex]
Test the values of each inequality
For [tex]y > 6[/tex]; say [tex]y = 7[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 7^4 - 10*7^3 + 24*7^2[/tex]
[tex]\frac{dy}{dt} = 147[/tex]
[tex]147 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]; This implies that: [tex](6, \infty)[/tex]
For [tex]y > 4[/tex] Say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is false:
Say [tex]y = 3[/tex] i.e. [tex]y < 4[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
[tex]27 > 0[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that: [tex](0,4)[/tex]
For [tex]y > 0[/tex]
[tex]y > 0[/tex] implies that: [tex]y < 4[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is true for [tex]\frac{dy}{dx} > 0[/tex]. This implies that [tex](-\infty, 0)[/tex]
We have: [tex](-\infty,0), (0,4)\ and\ (6,\infty)[/tex]
[tex](-\infty,0)\ and\ (0,4)[/tex] can be combined to give: [tex](-\infty,4)[/tex]
So, the interval is: [tex](-\infty,4)\ u\ (6,\infty)[/tex]
Solving (c): Decreasing values
Here
[tex]\frac{dy}{dx} < 0[/tex]
i.e.
[tex]y^2(y - 4)(y - 6) < 0[/tex]
[tex]y <0\ or\ y<4\ or\ y<6[/tex]
Test the values of each inequality
For [tex]y < 6[/tex]; say [tex]y = 5[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 5^4 - 10*5^3 + 24*5^2[/tex]
[tex]\frac{dy}{dt} = -25[/tex]
This is true for [tex]\frac{dy}{dx} < 0[/tex]; This implies that: [tex](\infty,6)[/tex]
For [tex]y < 4[/tex]; say [tex]y = 3[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 3^4 - 10*3^3 + 24*3^2[/tex]
[tex]\frac{dy}{dt} = 27[/tex]
This is false
Say [tex]y = 5[/tex] i.e. [tex]y > 4[/tex]
This is the same as: [tex]y < 6[/tex]
So, we have the interval to be: [tex](4,\infty)[/tex]
For [tex]y < 0[/tex] say [tex]y = -1[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = (-1)^4 - 10*(-1)^3 + 24*(-1)^2[/tex]
[tex]\frac{dy}{dt} = 35[/tex]
This is false
Say [tex]y = 2[/tex] i.e [tex]y > 0[/tex]
[tex]\frac{dy}{dt} = y^4 - 10y^3 + 24y^2[/tex]
[tex]\frac{dy}{dt} = 2^4 - 10*2^3 + 24*2^2[/tex]
[tex]\frac{dy}{dt} = 32[/tex]
This is also false
So, the intervals are: [tex](4,\infty)[/tex] and [tex](\infty,6)[/tex].
This can be merged as: [tex](4,6)[/tex]
Hence, the interval for [tex]\frac{dy}{dt} < 0[/tex] is [tex](4,6)[/tex]
Can someoneee please help me
9514 1404 393
Answer:
37°
Step-by-step explanation:
The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.
∠1 = 37°
__
Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.
The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? (a) 20% of all adult Americans support the changes (b) 25% of all adult Americans support the changes
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
What is proportionality ?In mathematics, proportionality is the connection between two factors that maintains a fixed ratio called scale factor. Or, to put it another way, if one variable is increased or divided by a specific number, the second variable will also be doubled or divided by that identical number, maintaining their proportionality. Calculus, algebra, and geometry are three areas of mathematics where this idea is frequently applied.
given
(a) If 20% of adult Americans favour the suggested reforms, the sample size needed at the very least is:
n = [(zα/2)² * p * (1-p)] / E²
where z/2 is the standard normal distribution's critical value for the chosen degree of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.2 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.2 * (1-0.2)] / 0.05²
n = 1536.64
Thus, the study would require at least 1537 more adult Americans to be sampled.
(b) The minimal sample size needed if the proposed modifications are
supported by 25% of all adult Americans is:
n = [(zα/2)² * p * (1-p)] / E²
where:
The standard normal distribution's critical value, z/2, depends on the desired level of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.25 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.25 * (1-0.25)] / 0.05² \sn = 384.16
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
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9.3+b=−42 , you would subtract 9.3 to isolate the variable.
Answer:
yeh you are correct so it will be b is equal to minus 42 minus 9.3 that will be equal to -51.3 so that is the value of b
Jamie placed $2800 in a savings account which earns 4.3% interest, compounded continuously. How much will she have in the account after 9 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answer:
4123
Step-by-step explanation:
A=Pert,
where A is the balance of the account, P is the principal, r is the annual interest rate (as a decimal), and t is the time (in years). We are given that P=2800, r=0.043, and t=9. Substituting the values into the formula and using a calculator to evaluate, we find
A=Pert=2800e(0.043)(9)≈4123.16
Pls help me solve this
1. Find the slope of the graph. Slope:
Answer:
I think the answer is 5 down and over to the left 3.
Step-by-step explanation:
I just counted from the point on the (4,3) and counted down until it was line up with the other point. Next, I counted from there to the other point.
Question
Sam sells orange juice by the glass and each glass contains 250 milliliters of orange juice. Sam has 10
cartons that each contain 3.5 liters of orange juice. What is the greatest number of glasses of orange juice
that Sam can sell? (1 liter = 1,000 milliliters)
Answer:
14 glasses
Step-by-step explanation:
3.5 (liters) times 10 (cartons) = 35 (liters)
(1 liter = 1,000 milliliters)
(35 liters = 3,500 milliliters)
3,500 (liters) divided by 250 (milliliters) = 14 glasses
The greatest number of glasses of orange juice that Sam can sell will be 140 glass.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Sam sells orange juice by the glass, and each glass contains 250 milliliters of orange juice.
Sam has 10 cartons that each contain 3.5 liters of orange juice.
Then the total amount of orange juice will be
Total amount = 10 x 3.5
Total amount = 35 liters
We know that one liter is equal to 1000 milliliters.
Then the total amount of the orange juice in milliliters will be
Total amount = 35 x 1000
Total amount = 35,000 milliliters
Then the greatest number of glasses of orange juice that Sam can sell will be
Total number of glass = 35,000 / 250
Total number of glass = 140 glass
The greatest number of glasses of orange juice that Sam can sell will be 140 glass.
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Six years ago Matt was four times as old as Brown, and in 3 years the sum of their
ages will be 43 years. Find their present ages.
Answer:
Matt=26
Brown=11
Step-by-step explanation:
Just trust me!!!
The present age of Matt given the information in the question is 26.
The present age of Brown given the information in the question is 8.
What are the linear equations that represent the question?4y - 6 = x equation 1
x + y + 6 = 43 equation 2
Where:
x = Matt's agey = Brown's ageWhat is Brown's age?Subsistute for x in equation 2
4y - 6 + y + 3 = 43
Combine similar terms
5y = 40
y = 8
What is Matt's age?
Subsitute for y in equation 1
4(8) - 6 = x
32 - 6 = 26
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The cost of an item is $75. What will the total cost be with 9% tax?
Answer:
81.75
Step-by-step explanation:
75*1.09 = 81.75
Answer:$81.75
Step-by-step explanation:
9% of 75 is 6.15, add that to 75 and the answer is 81.75
twenty subtract from 28
Answer:
8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
20-28= -8
PLEASE HELp ME U GET ALOT OF POINTS 97points
circumference and Area of circles
7. Demi measured the wheels on her brother's wagon. The diameter of each
wheel is 15 inches. To the nearest inch, how far will the wagon travel each
time the wheels make a complete turn?
8.The radius of circle A is 6 ft. The diameter of circle B is 6 ft. To the nearest
foot, how much greater is the circumference of circle A as compared to the circumference of circle B?
9. The larger circle in the design at the right has a radius of 40 in.
What is the area of the shaded part of the design?
30 in.
10. Max knows that the circumference of a circular pool is 12 ft.
He estimates that the diameter of the pool is between 3 ft and 4 ft. Is this reasonable? Explain.
Answer:
#7
C = πd = 3.14*15 in = 47 in (rounded)#8
C₁ = 2πr = 2*3..14*6 ft = 37.68 ftC₂ = πd = 3.14*6 ft = 18.84 ftThe difference:
C₁ - C₂ = 37.68 - 18.84 = 19 ft (rounded)#9
No picture attached#10
C = 12 ftd = C/πd = 12/3.14 = 3.82 ft3 ft < 3.82 ft < 4 ftMax is right
You moved 7 units left, 8 units up, and ended at point W
Where did you begin?
OA) (1.8)
OB) (9.1)
OC) (81)
OD) (9.8)
Please help me I’m tired
Answer:
C. (8,1)
Step-by-step explanation:
Li’s family is saving money for their summer vacation. Their vacation savings account currently has a balance of $2,764. The family would like to have at least $5,000.
The inequality 2764 + x Greater-than-or-equal-to 5000 can be used to determine the amount of money the family still needs to save. What is the solution to the inequality?
x Greater-than-or-equal-to 2236
x Greater-than-or-equal-to 7764
x Less-than-or-equal-to 2236
x Less-than-or-equal-to 7764?
Answer: x greater-than or equal-to 2,236
Step-by-step explanation:
5,000-2,764= 2,236
so Li's family still needs to save at least $2,236
Answer:
A
Step-by-step explanation:
bc
What is the range of the function on the graph?
Range is the output values which are the y values.
The dot is at y = 2 and the line moves upward to the right off the graph. This means the line will continue to infinity.
The range would be 2 to infinity.
(2, infinity)
PLEASE HURRY! FIRST PERSON GETS BRAINLIST!!!!!!
Hank is throwing a surprise party. The party costs $20 per person. Create an equation and graph to represent the relationship between the cost of the party and the number of friends attending.
The independent variable is ____.
A. Number of friends (f)
B. Cost of party (c)
Answer:
B
Step-by-step explanation:
−8≤2/5(k−2) negative 8 is greater than/equal to 2/ fifths (k minus 2)
Answer:60
Step-by-step explanation:
Please help ! Please help!
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9 What is the confidence interval for the population mean μ? <μ
Answer:
Confidence Interval = ( 5.6 < μ < 8.2 )
The interval shows that the mean attractiveness is Above average on a scale of 1 to 10
Step-by-step explanation:
Data Given : 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9
a) construct a confidence interval at a 95% confidence level
confidence interval = x ± tcritical ( s / √ n ) ------ ( 1 )
n = 12
μ (mean) = ( 5+8+2+8+7+6+6+8+9+9+6+9 ) / 12 ≈ 6.92
std ( s ) = √ 1/11 *∑( xi- X )^2
= √ 1/11 * ( 5 - 6.92)^2 + ( 8 - 6.92)^2 + ( 2 - 6.92)^2 + ( 8 - 6.92)^2 + ( 7-6.92)^2 + ( 6 - 6.92)^2 + (6 - 6.92 )^2 + ( 8 - 6.92 )^2 + ( 9 - 6.92)^2 + ( 9 - 6.92)^2 + ( 6 - 6.92 )^2 + ( 9 - 6.92 )^2
= √ 1/11 * 46.92 = 2.07
tcritical at ∝ 0.05 , df = 11 = 2.20
Back to equation 1
6.92 ± 2.2 ( 2.07 / √ 12 )
( 6.92 ± 1.31 )
Confidence Interval = ( 5.6 < μ < 8.2 )
Which of the following is NOT an example of a right angle?
Ο Α.The corner of a door
O B.The corner of a book
C.The point of a pencil
D.The corner of a piece of notebook paper
Answer:
The point of a pencil
Step-by-step explanation:
all other three mesure 90 the point of pencil is not square shape in order for it to be right angle its gotta be square shape hope this helps! may i be marked brainliest?
find the HCF of 12;28 and 32
Answer:
4
Step-by-step explanation:
28 = 22 • 7
12 = 22 • 3
32 = 25
I NEED HELP PLEASE ASAP!
Answer:
Step-by-step explanation:
Can you help me thanks!
A box contains 3 black pens, 7 blue pens and 5 red pens. Without replacing the first pen,
what is the probability of pulling a red or blue pen?
Answer:12/15
Step-by-step explanation: first you add 7+5=12
then add 12+3=15
Carl paid $40 for 12.5 gallons of gas.After calculating,he said that the cost per gallon was about 31 cents per gallon.Is there anything wrong with Carl's thinking?.
Answer:
Well yes, because it should have cost $3.2 PER gallon
Step-by-step explanation:
Divide 40 by 12.5 to find out how much of a per gallon costs! Hope it helps.
Solve for the following by
FACTORING:
x2 + 15x + 56 = 0
Answer:
17x + 56 = 0
Step-by-step explanation:
add 2x and 15x
Please help :) Giving brainliest.
Answer:
D
Step-by-step explanation:
MUST HELP!!!! (+50 POINTS +BRANILEST +5 STARS +THANKS ON PROFILE)
Answer:
Personification is your answer.
Hope it helps!!!
David invests $7000 in two different accounts. The first account paid 2 %, the second account paid 5
% in interest. At the end of the first year he had earned $182 in interest. How much was in each
account?
Answer:
3,990
Step-by-step explanation:
Find the exact value of x. Do the side lengths form a Pythagorean triple?
Answer: Square root (52), No
Step-by-step explanation:
Answer:
Step-by-step explanation:
4^2 + 6^2 = x^2
sqrt 52 = x
x= 7.211
No, it is not a pythagorean triple because x is not a whole number.