Answer:
1. x=0 y=-20
2. x=0 y=7.5
Step-by-step explanation:
How do you determine what bn should be in a limit comparison test and a comparison test? When do you know that the series should use a limit comparison test or a comparison test to find if it is convergent/divergent? Examples would be greatly appreciated
Step-by-step explanation:
Pick a function that is the same "family". It needs to be a function that you know diverges or converges. So p-series and geometric series are common choices. Often we make the numerators the same so that it's easy to compare.
For example, if you have an = 1 / (n − 1), you would choose bn = 1 / n. Since n − 1 is less than n, we know an is greater than bn. And since we know bn diverges, that means the larger function an also diverges.
Or, if you have an = 1 / (n + 1), we again choose bn = 1 / n. However, comparison test is inconclusive here (an < bn, bn diverges), so we use limit comparison test instead.
lim(n→∞) an / bn
lim(n→∞) 1 / (n + 1) / (1 / n)
lim(n→∞) n / (n + 1)
1
The limit is greater than 0, and bn diverges, so an also diverges.
Let's try something more complicated. Let's say an = e⁻ⁿ / (n + cos²n). The numerator e⁻ⁿ is always less than 1, and the denominator is always greater than n.
If we again choose p-series bn = 1 / n, we know bn > an, and bn diverges, so comparison test is inconclusive. Limit comparison test is possible, but tricky.
But, if we choose geometric series bn = e⁻ⁿ / 1, we know bn > an, and bn converges, so by comparison test, an converges as well.
We can try one more: an = (n² + 2) / (n⁴ + 5). Let's choose bn = (n² + 2) / n⁴ = 1 / n² + 2 / n⁴.
The numerators are the same, but an has a larger denominator, so bn > an. bn is the sum of two p-series which converge, so bn converges. Therefore, an converges.
what percent of 50 is 18?
Answer:
36 %
Step-by-step explanation:
Convert the fraction to a decimal, then multiply by 100 .
Answer:
36%
Step-by-step explanation:
The same explanation as she said
A phone company charges for service according to the formula C(n) = 23 + 0.2n, where n is the number of minutes
talked, and c(n) is the monthly charge, in dollars.
Find the rate of change.
Answer:
...........................
To practice for a competition, Genevieve swam 590 meters in the pool each day for 3 weeks. How many kilometers did Genevieve swim in those 3 weeks?
Answer:
12.39km
Step-by-step explanation:
If Genevieve swam 590 meters for 3 weeks, then the equation is:
590 * 21
590 represents the number of meters Genevieve swam, and 21 is the number of days in 3 weeks.
Hope this helped!
Answer:
12.39 kilometers
Step-by-step explanation:
if she swan 590 meters each day, we know that there are 7 days in a week so multiply 7 by 3 and get 21 days. then multiply 590 by 21 and get 12390 meters. BUT the question is asking for kilometers so we are not done. from here we have to convert 12390 meters to ___ kilometers. to go from meters to kilometers divide by 1000 and we will get 12.39 kilometers.
hope this helps! brainliest please?
Write an equation for the parabola that has the
given vertex and passes through the given point.
Vertex
(0,-1)
Point
(1,-2)
f(x)= [?](x+ [ ]) ^2 + [ ]
Answer:
-1, 0, -1
f(x)=-1(x+0)^2-1
Step-by-step explanation:
vertex translated from (0,0) to (0,-1), so the function translated down by -1
f(x)=a(x-0)^2 -1
substitute (1,-2) to solve a,
a(1-0)^2 -1 = a-1 = -2
a=-1
thus, f(x)=-1 (x+0)^2 -1
Sippose there is a 1.4 drop in temperature for every thousand feet that an airplane climbs into the sky if the temperature on the ground is 53.2 what will the temperature when the plane reaches a altitude of 8,000
Answer:
whats rhe question my g
(18 - ab) + 4b (if a = -2 and b = -5)
Jayden is saving money to buy the new Jordan 11's. He
needs $220 to get them. He already has $60 saved and
he makes $20 a week doing chores around the house
Answer:
it will take Jayden 8 weeks to save money for the Jordan 11's
Step-by-step explanation:
$60 = 3 weeks
$220 = 11 weeks
subtract the three weeks from the amount of time it would take without the saved money
$220 = 8 weeks
or
subtract saved amount from total = $160 and divide by 20
solve for b
12=b/3-8
Answer:
b=60
Step-by-step explanation:
Add 8 to both sides to receive the equation of 20=b/3
Multiply all sides by 3 to get 60 as b
help me please, thank you sm
Answer:
Option B
Step-by-step explanation:
Y=3, when x value is substituted
Solve by using the quadratic formula: x^2 - 6x + 7 = 0 Please enter any square root values using "sqrt" or the decimal answer rounded to the nearest hundredth (i.e. V2 = sqrt(2) or 1.41).
Given parameters:
Quadratic expression:
x² - 6x + 7 = 0
Solve using quadratic formula;
x = [tex]\frac{-b +/- \sqrt{b^{2 } - 4ac} }{2a}[/tex]
From the equation;
a = 1, b = -6 and c = 7
Input the parameters and solve;
x = [tex]\frac{-(-6) +/- \sqrt{-6^{2 } + 4 x 1 x 7 } }{2 x 1}[/tex]
x = [tex]\frac{6 +/- \sqrt{36} +28 }{2}[/tex]
x = [tex]\frac{6 +/- \sqrt{64} }{2}[/tex]
x = [tex]\frac{6 + 8}{2 }[/tex] or [tex]\frac{6-8}{2}[/tex]
x = 7 or -1
Answer:x is 7 or -1
Step-by-step explanation: based on the quadratic expression
What is (8p - 2)(6p + 2)
answer:
48p² + 4p - 4
solution:
8p × 6p +8p × 2 - 2 × 6p - 2 × 2
48p² + 8p x 2 - 2 ×6p - 2 × 2
48p² + 16p - 12p - 4
48p² + 4p - 4
The required algebraic product is 48[tex]p^{2}[/tex] + 4p - 4.
Given the two binomial (8p - 2)(6p + 2).
To multiply two binomials, take the first term of the first binomial and multiply with the entire second binomial and positive or negative as per given in the first binomial ,take the second term of the first binomial and multiply with the entire second binomial.
Let a, b, c and d be any four variables. Consider (a - b)(c + d) gives
a(c + d) - (c + d).
That implies, (8p - 2)(6p + 2) = 8p(6p + 2) - 2(6p + 2)
Multiply by removing the brackets gives,
(8p - 2)(6p + 2) = 48[tex]p^{2}[/tex] + 16p - 12p - 4
Combining like terms and algebraic sum gives,
(8p - 2)(6p + 2) = 48[tex]p^{2}[/tex] + 4p - 4.
Hence, the required algebraic product is 48[tex]p^{2}[/tex] + 4p - 4.
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Find the value of x.
i need help
Answer:
1. x=7
2. x=6
3. x=6
4. x=4
5.x=70 degrees
6. x=75 degrees
Step-by-step explanation:
My answers may not be correct.
How many times does the quadratic function below intersect the x-axis?
y = x+3x+15
When Xander arranges his pennies into a rectangle with more than one row, he always has some leftover pennies. When he uses two equal rows or three equal rows, he has one leftover penny. When he arranges them into a rectangle with four equal rows, he has three leftover pennies. Remember he has between 10 and 40 pennies total. How many pennies does Xander have?
Answer:
20
Step-by-step explanation:
hope this was right and helpful
help meeeeee please
If it's a rectangle:
perimeter = 2F+10g
Area=g(4F+4g)
Step-by-step explanation:
Perimeter = 2×(l+b)
Area= l×b
A car with a mass of 1,250 kg travels at 2.24 m/s and bumps into a stopped car with a mass of 1,300 kg. After the collision, the two cars stick together and move forward. How fast will they both move forward? Round your answer to two decimal places.
0.57 m/s
0.55 m/s
1.10 m/s
1.14 m/s
Answer:
1.10
Step-by-step explanation:
The velocity of the combined cars after the collision is 1.10 m/s.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
The momentum of an object is equal to its mass multiplied by its velocity.
The first car has a mass of 1,250 kg and a velocity of 2.24 m/s, its momentum is 1,250 kg x 2.24 m/s = 2,800 kgm/s.
Similarly, since the second car has a mass of 1,300 kg and a velocity of 0 m/s (it is stopped), its momentum is 0 kgm/s.
Therefore, the total momentum of the two cars before the collision is:
⇒ 2,800 kgm/s + 0 kgm/s = 2,800 kg m/s.
After the collision, the two cars stick together and move forward as one unit. We can find the velocity of the combined cars by dividing their total momentum by their total mass.
The total mass of the cars is:
⇒ 1,250 kg + 1,300 kg = 2,550 kg.
So, the velocity of the combined cars after the collision is:
⇒ 2,800 kgm/s / 2,550 kg = 1.098 kgm/s.
To two decimal places, this velocity is 1.10 m/s. Therefore, the correct answer is 1.10 m/s.
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During a soccer game, Erin scored 1 of 2 goals attempted. Lauren scored 6 of 8 goals attempted. Write the fraction that represents each and compare. Who was the most successful? SHOW YOUR WORK AND EXPLAIN YOUR ANSWER.
(I KNOW THAT ERIN IS 1/2 AND LAUREN IS 6/8 BUT IM NOT SURE HOW TO COMPARE THEM)
Answer:
Lauren.
Work:
1/2 vs. 6/8
1/2 * 4/4 = 4/8
6/8 > 4/8
Answer:
One half as a percentage is 50%.
Six eighths as a percentage is 75%.
So Lauren scored 75 percent of her attempts.
Erin only scored 50% of her attempts.
Therefore, Lauren was the most successful during the game.
Work:
1/2 equals 50%.
6/8 equals 75%.
Hope this helps!
what is a polynomial
A polynomial is an expression that contains several terms.
Examples include...
5x +1
5x^(-2) +1
In order to perform the indicated operation, which are possible first steps? Check all that apply.
FREE
(7.75 x 1011) – (5.68 < 1013)
✓x
o Rewrite 7.75 x 1011 as 775 x 109.
Rewrite 7.75 x 1011 as 0.0775 x 1013
Rewrite 5.68 x 1013 as 568 x 1011
Rewrite 5.68 x 1013 as 0.568 x 1015
O Subtract 7.75 -5.68.
The Actual Answer Is B.) Rewrite 7.75 × 1011 as 0.0775 × 1013. And C.) Rewrite 5.68 × 1013 as 568 × 1011.
2020
Answer:
The answers are B and C
Step-by-step explanation:
please help me asap (picture is included) (:
Answer:
d
Step-by-step explanation:
I MARK BRAINLEIST! WHEN CONVERTING STANDARD FORM TO SCIENTIFIC FORM WITH A POSITIVE EXPONENT
YOU MOVE TO THE
O LEFT
O RIGHT
Answer:
You move the 0 to the right
Step-by-step explanation:
urgent please help !!!!!
What is the GCF of two prime numbers?
Group of answer choices
A. 1
B. The second number
C. The last number
D. 0
Answer:
A. 1
Step-by-step explanation:
prime numbers are not subject to any factors other then themselves and 1
A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet away from the player. The height y (in feet) of a second hockey puck is modeled by y=x(0.15−0.001x), where x is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.
The total distance travelled by the first and second hockey pucks before hitting the ground is 110 feet and 150 feet, respectively.
We are given that there are two hockey pucks.The height of the first hockey puck increases until it reaches a maximum height of 3 feet when it is 55 feet away from the player.This hockey puck will travel an additional 55 feet after it reaches its maximum height before it hits the ground.The total distance travelled by the first hockey puck before hitting the ground is 110 feet.The height y (in feet) of the second hockey puck is modelled by y=x(0.15−0.001x), where x is the horizontal distance (in feet).When it hits the ground, its height will be zero.0 = x(0.15−0.001x)x(0.15−0.001x) = 0A value of "x" is 0 when it is just hit by the player.When it hits the ground, the value of "x" is :0.15−0.001x = 00.001x = 0.15x = 150The total distance travelled by the second hockey puck before hitting the ground is 150 feet.To learn more about distance, visit :
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Give five elements of the following sets.
A = {different land forms}
B = {x/x is a prime number greater than 20 but less than 50}
C = {even number less than 20}
D = {fraction less than 1}
E = {noun that starts with letter "a"}
Answer:
Find the answer below.
Step-by-step explanation:
1. A = {mountain, valley, plateau, plains and hills}
A landform refers to a geomorphic or natural feature of the Earth's surface, which typically makes its terrain.2. B = {23, 29, 31, 37 and 41}
A prime number can be defined as any number that is greater than one (1) and can only be divided by itself or one (1). In this case, they are greater than 20 but less than 50.3. C = {2, 4, 8, 10 and 12}
An even number can be defined as any number that can be divided by two (2) without any remainder. In this instance, they should be between one (1) and twenty (20).4. D = {2/3, 1/2, 3/4, and 1/5}
A fraction that is less than one (1) refers to a proper fraction. Therefore, proper fractions must have the value of their numerator to be less than the value of their denominator.5. E = {ant, angel, angle, anaconda, and ark}
A noun can be defined as the name of any place, people, animal or things. In this context, the nouns should all start with the letter "a."Find the area of the polygon. Leave
your answer in exact form with proper units.
Answer:
15 square meters.
Hope this helped!
Given:QT bisects SP, SP bisects QT
Prove: QRS=SRT
Answer:
I DOnt get please more info
Step-by-step explanation:
I need hhhheeeellllpppp!!!! HURRY PLS will be thanked lol
Answer:
Just saying I LOVE THESE the slope is 3/2
Step-by-step explanation:
Answer:
-4 to -4
Step-by-step explanation:
-------------------------
-4 -4
Ninety children signed up
for a field trip to a museum
On the field trip, the ratio of
adults to children must be 1:6.
So far, 11 adults are going on
the field trip. How many
More adults are needed?
4 more adults are needed
90 ÷ 6 = 15
15 - 11 = 4
