The values of p that satisfy the inequality for all[tex]$q > 0$[/tex] are
[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]
Given:[tex]$$\frac{3(pq^2 p^2q 3q^2 3pq)}{p q} > 2p^2q^2$$[/tex]
Step 1: Multiply both sides by [tex]$\frac{pq}{3}$[/tex] to get: [tex]$$pq^3 p^2q 3q^2 3pq > 2p^2q^3$$[/tex]
Step 2: Simplify the left side to get: [tex]$$3p^2q^3+3pq^3+3q^2 > 2p^2q^3$$[/tex]
Step 3: Divide both sides by [tex]$q^2$[/tex] to get: [tex]$$3p^2q+3pq+3 > 2p^2$$[/tex]
Step 4: This is a quadratic inequality in[tex]$p$[/tex]with solution[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all [tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]
the given inequality can be simplified to a quadratic inequality in p by multiplying both sides by[tex]$\frac{pq}{3}$[/tex], simplifying the left side, and dividing both sides by[tex]$q^2$[/tex] The solution of the quadratic inequality is
[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and
[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all [tex]$q > 0$[/tex] are
[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and
[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex], which means that any value of p that is greater than[tex]$\frac{3+\sqrt{21}}{2}$[/tex] or less than
[tex]$-\frac{3+\sqrt{21}}{2}$[/tex]will satisfy the inequality for all [tex]$q > 0$[/tex]
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What is the product of the complex numbers below?
(4-2i) (1 +7i)
Answer:
B
Step-by-step explanation:
Note that i² = - 1
Given
(4 - 2i)(1 + 7i) ← expand factors using FOIL
= 4 + 28i - 2i - 14i²
= 4 + 26i + 14
= 18 + 26i → B
You roll a 6-sided die.
What is P(even)?
Write your answer as a percentage rounded to the nearest tenth.
%
P(even) is 50%
It is simple to calculate the likelihood of one die roll.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%
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would anyone know the answer to this?
Answer: The mystery number is 5.5
5.5 converts to the fraction 11/2.
=================================================
Explanation:
The phrasing "subtract 10 from the number, then square the result" leads to the expression [tex](\text{x}-10)^2[/tex]
The phrasing "Square the number, then subtract 10 from the result" means we have [tex]\text{x}^2-10[/tex]
Set those expressions equal to one another so we can solve for x like shown in the steps below.
[tex](\text{x}-10)^2 = \text{x}^2-10\\\\\text{x}^2-20\text{x}+100 = \text{x}^2-10\\\\-20\text{x}+100 = -10\\\\-20\text{x} = -10-100\\\\\text{x} = -110/(-20)\\\\\text{x}=11/2\\\\\text{x} = 5.5[/tex]
The x^2 terms cancel out in the third step (since we subtract x^2 from both sides).
--------------
Check:
[tex](\text{x}-10)^2 = \text{x}^2-10\\\\(5.5-10)^2 = (5.5)^2-10\\\\(-4.5)^2 = (5.5)^2-10\\\\20.25 = 30.25-10\\\\20.25 = 20.25[/tex]
The answer is confirmed.
pleaseeeeeeeeeeeeeeeeeeee help
Answer:
0
Step-by-step explanation:
Well, since the line has the same y coordinates, you know it's a horizontal line.
All slopes of horizontal lines are 0.
What is the measure of m?
Answer:
m=10
Step-by-step explanation:
hypotenuse is 15+5=20
to find shorter leg m divide the hypotenuse by 2
20÷2=10
Represent - 16/5 on a number line
NO links or files
Plz attach a photo or type it out
I need it today ASAP
Answer:
3.1 is the answer.
xy^4 Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.
How to determine the concavity?(b) To find the second derivative of y with respect to x, we can use the chain rule. Since y is a function of x, we have [tex]dy/dx = f(x) and d^2y/dx^2 = d/dx(dy/dx) = d/dx(f(x)) = f'(x).[/tex]
To find f'(x), we can use the product rule and the given differential equation:
[tex]f'(x) = d/dx(xy^4) = y^4 + xy^4dy/dx = y^4 + xy^4f(x)[/tex]
Now, to determine the concavity of the solution curves, we need to find the sign of f'(x).
In Quadrant II, x and y are both positive, so [tex]x*y^4[/tex] is positive. Therefore, f'(x) is positive as well.
A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.
(c) To find a particular solution to the differential equation with the given initial condition, we can use separation of variables.
The equation can be rewritten as [tex]dy/y^4 = x dx[/tex]
Integrating both sides gives:
[tex]\int\limits^ {} \,dy/y^4 = \int\limits^ {} \, dx* dx\\-1/y^3 = (x^2)/2 + C\\y^3 = -1/(x^2/2 + C)\\y = (-1/(x^2/2 + C))^(1/3)[/tex]
Using the initial condition f(4) = -1, we can find the value of C:
[tex](-1) = (-1/(4^2/2 + C))^(1/3)\\(-1)^3 = -1/(4^2/2 + C)\\-1 = -1/(16/2 + C)\\C = 15/2[/tex]
So the particular solution is:
[tex]y = (-1/(x^2/2 + 15/2))^(1/3)[/tex]
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Complete question is: Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.
Please I need help with all four who or whom
Answer: 2=who
3=who
4=whom
5=I
Step-by-step explanation:
The question is in the picture I would appreciate if you could explain how to get the answer thank you.
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
The slope of an equation:
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.
The slope intercept form of a line is y = mx + c
Where, c - y-intercept and m - the slope of the line
Given that
The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.
4 minutes of internet costs $ 3
8 minutes of internet costs $ 4
[ We can represent the given situation as given below ]
And the coordinates formed are (4, 3) and (8, 4)
The slope of the line formed = (4 - 3)/(8 - 4) = 1/4
Let y = mx + c be the equation to the model situation
=> y = (1/2)x + c
=> 2y = x + c ---- (1)
As we know (1) will pass through (4, 3)
=> 2(3) = 4 + c
=> 6 = 4 + c
=> c = 6 - 4
=> c = 2
=> 2y = x + 2
=> x - 2y + 2 = 0
Therefore,
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
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What is the sum of the following equation?
Ill mark brainly if its correct. :) a,b,c, or d. answer quick please
Answer:
C. Is the answer
Question 13
Find the area of the (gray) shaded region. (2 tangent circles inscribed in a rectangle):
20
Answer:
42.92 square
Step-by-step explanation:
The radius of the circles is 5m
So, area of 1 circle is π(5×5)=78.54 square
Two areas will (78.54+78.54)=157.08 square
Rectangles height is ( 5+5)=10m
Rectangles area is (10×20)=200 square
Shaded region=(200-157.08) square =42.92 square
What's the answers I'm insanely bad at reorganizing the y=mx+b equations (Possibly a brainliest if I learn a lot)
Answer:
x = 2, y = 0
Step-by-step explanation:
find y in terms of x:
8x - 4y = 16
4y = 8x - 16
y = 2x - 4
substitute y:
8x + 4y = 16
8x + 4(2x - 4) = 16
8x + 8x - 16 = 16
16x = 32
x = 2
find y:
8x + 4y = 16
16 + 4y = 16
y = 0
what is the circumference of the circle that circumscribes a triangle with side lengths 3, 4 , and 5?
Answer:
Circumference of the circle = 15.70 units.
Step-by-step explanation:
In this question three sides of a triangle has been given as 3, 4 and 5 units.
These are the sides of a right angle triangle.
3² + 4² = 5² [By Pythagoras theorem]
9 + 16 = 25
If this triangle is inscribed in a circle then Hypotenuse of the triangle will be the diameter of the circle.
Theorem for the angle formed in the semicircle says, "angle formed by drawing the the lines from the ends of the diameter of a circle to it's circumference form a right angle."
Therefore, radius of the circle will be units
Now we know the formula of circumference of the circle = 2πr
= 2π(2.5)
= 2(3.14)(2.5)
= 15.70 units
You accepted a job for which the annual salary is $39236. This salary
includes a year-end bonus of $500. You will be paid once a month. What
will your gross pay be for each paycheck?
Answer:
$3228
Step-by-step explanation:
39236 - 500 = 38736
38736 / 12 = 3228
Can u plz help me thank you
Answer:
A) first quadrant
hope it helps.
stay safe healthy and happy.An object is launched at 39.2 meters per second (m/s) from a 42.3-meter tall platform. The equation for the objects height s at time t seconds after launch is s(t)=-4.9t^2+39.2t+42.3, where s is in meters. Create a table of values and graph the function. Approximately what is the maximum height of the object?
help again please thank you and no links! ^^
Answer:
23
Step-by-step explanation:
Angles x and 157 are linear pairs,
x + 157 = 180
x = 180 - 157
x = 23
Answer:
23°
Step-by-step explanation:
180-157= 23
What is the length of a leg of a 45 45 90 right triangle if the hypotenuse measures 5 square root of 2?
If the leg of the triangle is equal to a, then:
The second leg is also equal to a.
the given hypotenuse is a√2.
The given area is equal to a²/2; and
The perimeter equals a (2 + √2).
Now, looks easy, but from where does it come? There are various of methods to prove that equation, the most popular of them are:
By using the Pythagorean theorem, we can do that.
As you know one leg length a, then you know the length of the other as well, as both of them are equal.
The given 45 45 90 triangle shows the remaining parameters. Now you know that:
hypotenuse length is - 9 in * √2 = 12.73 in.
area is - 9 in * 9 in / 2 = 40.5 in²; and
perimeter - 9 in + 9 in + 9 in * √2 = 30.73 in.
Find the hypotenuse from the Pythagorean theorem:
a² + b² = c² => a² + a² = c² so c = √(2a²) = a√2
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Find the volume of each solid. Round to the nearest tenth if necessary. Use 3.14 for or
22/7
Answer:
half of 20 is 10
10 is your new radius so
10^2 = 100
100 x 3.14 = 314
Now we multiply by the height:
314 x 11 = 3,454 cm^3
The volume of the solid is option (a) 3454 cm³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given is a cylinder.
Volume of a cylinder = π r² h
Here r is the radius of the circular base and h is the height of the cylinder.
Given,
Diameter of circular base = 20 cm
Radius = Diameter / 2 = 20/2 = 10 cm
Height = 11 cm
Substituting,
Volume = π r² h
= (3.14) (10²) (11)
= 3454 cm³
Hence the volume of the cylinder shown is 3454 cm³.
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What is 78,400,000 expressed in scientific notation?
Answer:
7.84 × 10 ^7
Step-by-step explanation:
Write the formula to find the length of the rectangle and then solve.
Formula:___________
Length:____________
Answer:
Formula-W=A/L
Legnth-17
Step-by-step explanation:
Using the formula to find width of a rectangle, (width= area divided by legnth), you get 17. You can check by multiplying 26 by 17 to get 442. Hope this helps (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
Answer:
Formula : L x W
Length : 17.
Step-by-step explanation:
26 times 17 is 442
35 cubes with a length of 7 meters, height of 1 meter, and width of 5 meters.
What is the length of the figure?
7 m
What is the width?
5 m
What is the height?
1 m
What is the number of cubes?
What is the volume?
Answer:
35 cubic meters along with 35 cubes.
Answer:
The Answer is length 7m Width 5 m Height 1 m number of cubes 35 and volume 35
Step-by-step explanation:
help meeeeeeeeeeeeee
I don't see the image. Can you send it in the message.
explaination with steps
Answer:
50
Step-by-step explanation:
angleQPR=50
becauseQR=RP
so angleRQP=RPQ
x=50
Answer:
50
Step-by-step explanation:
angle QPR = 50 because QR= rp
[tex]3 \ \frac{2}{5} \times 3 \times \frac{1}{3} [/tex]
answer in fraction plz
Answer:
[tex] \displaystyle \frac{17}{5} [/tex]
Step-by-step explanation:
we are given
[tex] \displaystyle3 \frac{2}{5} \times 3 \times \frac{1}{3} [/tex]
since ⅓ is a reciprocal of 3 therefore if we multiply it we'd get 1
[tex] \displaystyle3 \frac{2}{5} \times \cancel{ \: 3} \times \frac{1}{ \cancel{ \: 3}} [/tex]
[tex] \displaystyle 3\frac{2}{5} [/tex]
remember that
[tex] \displaystyle \rm c\frac{a}{b} \xrightarrow{ \text{improper fraction}} \frac{b \times c + a}{b} [/tex]
so,
[tex] \displaystyle \frac{17}{5} [/tex]
Help ASAP!!!!
Which of the following statements is NOT true?
In the figure below, side AC of ABC lies on line l.
A. 25
B. 30
C. 22
D. 24
As you can see, 5y is an external angle of triangle ABC
we know that 5y=180-x
since angle B is 40, and angle A=x and C=x, we have
x%2Bx%2B40=180
2x=180-40
x=140%2F2
x=70
so, angle A=70 and C=70
then
5y=180-70
5y=110
y=110%2F5
y=22
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Help please, i have been stuck on this question for 20 minutes AND I DONT GET IT. Please help me.
Answer:
d
Step-by-step explanation:
sorry if im wrong
20. Kim works on commission. If her monthly earnings for the first
four months of the year were $1625, $960, $1235, and $1420,
estimate what her annual earnings will be.
A) $14,240 B) $15,390 C) $15,720 D) $16,150 E) $16,280
O A
OB
OC
OD
ΟΕ
Since, Kim works on commission and her trend of monthly earnings are not constant, Calculate the average from the data and estimate for the whole year , The answer is C) $15,720
What is statistics?Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It helps to make sense of large amount of data and use it to draw conclusions and make informed decisions. It provides methods to summarize, describe and analyze data, as well as techniques to infer characteristics of a population from a sample.
What is mean of the data?The mean is a measure of central tendency and a way to describe the average value of a dataset. It is calculated by adding up all the values in a dataset and then dividing by the number of values. The resulting value is the mean of the dataset, also known as the arithmetic average. Mean is commonly used to describe a large data set, while median is used to describe data with values have outliers.
salary for four months = $1625, $960, $1235, and $1420.
Average = ($1625 + $960+ $1235+$1420) /4 = $1310
for whole year = $1310 * 12 = $15,720
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