The compound interest for 5 year is $3868.7.
What is compound interest?Interest accrued on both the principal sum of money and the interest already earned.
The formula for compound interest is p(1+r/100)ⁿ - p
Where p is principal amount, r is rate and n is time.
Given that,
Principal = $20000,
Time = 5 years,
And rate of interest = 18/5 %
To find compound interest, use formula,
Compound interest = p(1+r/100)ⁿ - p
Compound interest = 20000(1+18/(5×100))⁵-20000
Compound interest = 23868.7 - 20000
= 3868.7
The compound interest for 5 years is $3868.7.
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Two planes are driving toward each other with the speeds 250 mph and 420 mph respectively. If the distance between them are 1250 miles, in how many hours they will meet?
Answer:
They will meet in 1.866 hours.
Step-by-step explanation:
This is actually quite a simple question once we think about it in a different way.
Instead of thinking of two different planes that are going at two different speeds, think of it like this: the distance between the two planes is decreasing by 670mph (250mph + 420 mph).
Note: miles per hour is equivalent to miles/hour (miles divided by hours or miles over hours)
670m/h becomes our new rate. The rate the distance between the planes is decreasing.
Now, if the distance between them is 1250 miles, how long until they meet?
If we have miles and multiply it by hours/miles, the miles cancel out and you are left with hours.
We have miles (1250) and miles/hours (670). If we multiply these we get units of miles^2 / hours which is not what we want.
we need to multiply 1250 miles by something with the units of hours/miles.
It turns out that the reciprocal of miles/hours is hours/miles
That means we need to multiply 1250 miles by the reciprocal of 670 miles/hours
Note: the reciprocal of a fraction is the fraction flipped around. 1/2 becomes 2/1, reciprocal of 3/5 is 5/3, etc...
the reciprocal of 670 miles/hours = 1/670 miles/hours
Multiplying 1250 miles by 1/670 miles/hours is the SAME as
dividing the number of miles(1250m) by the rate(670m/h)
1250m / 670m/h = 1250m x 1/670 x h/m = 1.866 h = 1.866 hours (the miles cancel out)
A power plant has 4 tons of coal. A ton of coal produces 2460 kilowatt hours of electricity. Is this enough to power 9 light bulbs for a year? Explain.
Answer:
Yes
Step-by-step explanation:
We will assume that each bulb is of 100 kW (kilowatt).
We will calculate how much energy in kilowatt-hours the light bulb will use per year in kilowatts, by the number of hours in a year.
We have,
100 kW = 0.1 kW so the energy consumed in one year is,
[tex]0.1 \times 8760=876.0\text {kWh}[/tex]
Since there are 8760 hours in one year.
It is given that there are 9 bulbs so we need to have,
[tex]876 \times 9 = 7884 \text {kWh}[/tex]
It is given that 1 ton of coal produces 2460 kWh, so 4 tons of coal will produce,
[tex]4\times 2460= 9840 \text {kWh}[/tex]
We can observe that 4 tons of coal is producing 9840 kWh which is mroe than 7884 kWh. So, yes, 4 tons of coal can produce enough power to light 9 bulbs for a year.
The 4 tons of coal from the power plant will produce 9840 kilowatt hours of electricity. A single 60 watt light bulb consumes around 526 kilowatt hours in a year. Thus, the energy produced by the coal would be enough to power 9 light bulbs for a year.
Explanation:The power plant has 4 tons of coal, with each ton producing 2460 kilowatt hours of electricity, resulting in a total production of 9840 kilowatt hours (4 tons * 2460 kilowatt hours/ton).
To discover if this can power 9 light bulbs for a year, we must first understand the energy consumption of a single bulb. A typical light bulb uses around 60 watts, and there are 8760 hours in a year. Therefore, a light bulb consumes 60 watts * 8760 hours = 525,600 watt-hours or about 526 kilowatt hours in a year.
For 9 light bulbs, the total energy consumption in a year would be 9 * 526 = 4734 kilowatt hours. Therefore, the 9840 kilowatt hours produced by the coal power plant is more than enough to power 9 light bulbs for a year.
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ΔABC is an equilateral triangle. m∠A = (3x - 12)°. Solve for x. A) 14 B) 19 C) 20 D) 24
Answer:
option (d)
Step-by-step explanation:
An equilateral triangle is a triangle whose all the sides are equal and all the angles are same.
There are three angles in a triangle and the according to the property of the angles of a triangle, the angle sum of a triangle is 180°.
So, in an equilateral triangle, the measure of each angle is 60°.
[tex]3x-12= 60[/tex]
3x = 60 + 12
3x = 72
x = 24
option (d)
IF YOU THINK YOUR SMART OR AT A HIGH RANK THEN ANSWER 3 QUESTIONS FOR ME....BTW I'LL GIVE YOU BRAINLIEST.
1. Ronald is making hats and scarves for charity. He has enough yarn to make 5 hats and 8 scarves. It takes him 12 hours to knit a hat and 6 hours to knit a scarf; he has 20 hours to knit.
Let x represent the number of hats made. Let y represent the number of scarves made.
Which inequalities are among the constraints for this situation?
Select each correct answer.
A) y≤8
B) 12x+6y≤20
C) x≤5
D) 5x+8y≤20
E) x+y≤20
2. Which ordered pairs lie on the graph of the exponential function f(x)=2^(x+4) −8?
Select each correct answer.
A) (−2,−4)
B) (2, 56)
C) (8, 0)
D) (24, 1)
3. The expression 15.85(1+x) gives the total cost of a toy, where x is the sales tax written in decimal form.
What does 1 + x represent in the expression?
A) percent of original price being paid in tax
B) cost of toy
C) percent of tax
D) amount of tax
Answer:
B, D, E- 12 per hat so 12x / 6 per scarf 6x
A - Graph then find the order pair on the line
?
Problem 1
Answer: Choice A, Choice B, and choice C
---------
Explanation:
x = number of hats made,
12*x = total time to knit just hats (12 hrs to do 1 hat)
y = number of scarves made
6*y = total time to knit just scarves (6 hrs to do 1 scarf)
In total, it takes 12x+6y hours to knit everything (scarves+hats) and we want this total time to be 20 or less, so this means choice B is one of the answers
Choice A and choice C are also answers because they restrict how many scarves and hats we can make. Choice A says we can make at most 8 scarves. Choice C says the max number of hats we can make is 5.
The other inequalities won't apply so they can be crossed off the list.
=============================
Problem 2
Answer: choice A and choice B
---------
Explanation:
If you plug in x = -2 and simplify, you'll end up with f(x) = -4, so that helps confirm A is one of the answers. Choice B is the other answer because x = 2 leads to f(x) = 56
In contrast, if you plugged in x = 8, you'd end up with 4088 which is way off of the y coordinate 0 listed. The same story happens with x = 24 but the result is much much larger.
=============================
Problem 3
To be honest, I'm not sure what to make of this problem. If x is the decimal form of the sales tax, then 1+x would be the multiplier to help get the total cost. For example, if x = 0.02 then 1+x = 1+0.02 = 1.02, meaning that the final cost (after tax) is 102% of the original cost (before tax)
1+x isn't the amount of tax as that would be 15.85*x
The percent of tax would be 100*x (eg: x = 0.02 so 100*x = 100*0.02 = 2% tax rate)
The cost of the toy is given to be 15.85 so that answer is out as well.
=============================
Consider the scatter plot.
Consider the scatter plot. The line of best fit is
The line of best fit is y = 0.75x + 5.
Choose the best representation for the y-intercept.
The y-intercept of the line of best fit shows that when time started, the distance was 0.75 feet.
The y-intercept of the line of best fit shows that after 0.75 minutes, the distance was 5 feet.
The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
The y-intercept of the line of best fit shows that when time started, the distance was 0 feet.
Answer:
The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Step-by-step explanation:
We are given a scatter plot with a best fit line as shown on the given graph.
The equation of the best fit line is given by:
y = 0.75x + 5
So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.
Since the distance shown on the y axis is already 5 when the time started at 0 minutes.
(r3 +6r2 −21r−18)÷(r−3) solve using synthetic division
Answer:
y = x^2 + 9x + 6 No remainder.
Step-by-step explanation:
The divisor will be 3 The sign on the divisor switches.
3 || 1 + 6 - 21 - 18 ||
3 27 + 18
================================
1 9 6 0
The answser is x^2 + 9x + 6
I need help with #8 and #9 Please! :)
I will mark as brainliest!
Answer:
see explanation
Step-by-step explanation:
(8)
the common ratio r, of a geometric sequence is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = ......
r = [tex]\frac{\frac{1}{32} }{\frac{1}{256} }[/tex] = [tex]\frac{\frac{1}{4} }{\frac{1}{32} }[/tex] = 8
(9)
The simplest way to evaluate the sum is to substitute k = 3, 4, 5, 6 into each term and sum them
(- 9 + 20) + (- 12 + 20) + (- 15 + 20) + (- 18 + 20)
= 11 + 8 + 5 + 2 = 26
What is the solution of the system?
Use the substitution method.
{3x+2y=11x−2=−4y
The only solution is (12, −52) .
The only solution is (4, −12) .
There is no solution.
There are an infinite number of solutions.
Answer: [tex]\bold{\text{b.}\bigg(4,-\dfrac{1}{2}\bigg)}[/tex]
Step-by-step explanation:
x - 2 = -4y → x = 2 - 4y
3x + 2y = 11
3(2 - 4y) + 2y = 11 replaced "x" with (2 - 4y)
6 - 12y + 2y = 11 distributed "3" on left side
6 - 10y = 11 added like terms (-12y + 2y)
- 10y = 5 subtracted "6" from both sides
y [tex]= -\dfrac{1}{2}[/tex] divided both sides by -10
Next, solve for x:
x = 2 - 4y
[tex]= 2 - 4(-\frac{1}{2} )[/tex]
= 2 + 2
= 4
Answer:
your answer would be b
Step-by-step explanation:
The cone shown has a diameter of 18 m and a slant height of 15 m which choice is closest to the lateral surface area
Answer:
[tex]423.9 m^2[/tex] is the required lateral surface area of the cone.
Step-by-step explanation:
The lateral surface area of cone is:
[tex]\pi\cdot r\sqrt{h^2+r^2}[/tex]
Slant height is l which is [tex]l=\sqrt{h^2+r^2}[/tex]
We have given diameter 18 m
Since, radius is half of diameter so r=18/2 =9
Slant height l =15
[tex]\pi=3.14[/tex]
On substituting the values in the formula we get:
[tex]3.14\cdot 9\cdot 15[/tex]
On simplification we get:
[tex]3.14\cdot 135[/tex]
Further simplification will give:
[tex]423.9 m^2[/tex] is the required lateral surface area of the cone.
HelllPPPP
What is the measure of ABC
Answer:
B 46
Step-by-step explanation:
Using the formula for tangents, arcs and angles
< ABC = 1/2 (CDA - CA)
<ABC = 1/2 (226-134)
<ABC = 1/2(92)
<ABC = 46
Six friends equally share the cost of a gift. They pay $90 and receive $42 in charge . How much does each friend pay?
Answer:
$8.00
Step-by-step explanation:
Let's set up the equation first.
What do we know:
1. We have 6 friends spliting the costs of the gifts
2. After purchasing the gifts they have $42 in change
3. They originally had $90 to spend.
Equation:
6f + $42 = $90
Next: Subtract the $42 from each side and we are left with:
6f = $48
Divide both sides by 6 and we are left with
f = $8
Since f represented the cost each friend spent our answer is $8.00
Each friend will pay $8.
What are the fundamental mathematical operations?The Fundamental mathematical operation are Addition,Subtraction
Multiplication and Division.
Given,
Six friends will equally share the cost.
they paid $90 and received $42 in change.
The money they will pay = $90 -$42
= $48.
As they will equally share the cost.
the individual cost will be = $48/6
=$8.
Therefore, Each friend will pay $8.
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What is 15 x 11? Bjnsjxjscjsnjsnjcnsjncjsncj
Answer:
165
Step-by-step explanation:
Dina and Masha started out on a 10 km bike path at the same time. When Dina reached the end of the 10 km, Masha still had 2 km to bike. If Dina's biking speed was 5km/h, find Masha's biking speed
Answer:
4 km/h
Step-by-step explanation:
We are told that Dina and Masha started out on a 10 km bike path at the same time.
Dina's biking speed is 5 km/h.
Let us find taken by Dina to cover 10 kn distance.
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
[tex]\text{Time taken by Dina to cover 10 km}=\frac{10km}{5\frac{km}{hr}}[/tex]
[tex]\text{Time taken by Dina to cover 10 km}=\frac{10km}{5}\times \frac{hr}{km}}[/tex]
[tex]\text{Time taken by Dina to cover 10 km}=2hr[/tex]
Therefore, Dina took 2 hours to complete 10 km.
Since both started at the same time, therefore, Masha also took 2 hours to complete 2 km less than Dina.
Let us find distance covered by Masha.
[tex]\text{Distance covered by Masha}=10\text{ km}-2\text{ km}=8\text{ km}[/tex]
Now let us find Masha's biking speed.
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Masha's biking speed}=\frac{8\text{ km}}{2\text{ hour}}[/tex]
[tex]\text{Masha's biking speed}=4\frac{\text{ km}}{\text{ hour}}[/tex]
Therefore, Masha's biking speed is 4 km per hour.
Will mark you as brainiest
if right!! Please Please answer this question! I need it done by 4 P.M. Eastern Time
Which answers describe the end behaviors of the function modeled by the graph?
f(x)=−3^(x+2)−2
Select each correct answer.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) approaches the line y=−2.
As x increases without bound, f(x) approaches the line y=−2.
As x increases without bound, f(x) decreases without bound.
This is a multiple choice question, so there might be 2 answers.
Answer:
Option B and D are correct.
Step-by-step explanation:
Given the function: [tex]y=f(x) = -3^{x+2}-2[/tex]
End behavior states that a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity.
As [tex]x \rightarrow \infty[/tex] in the given function, then [tex]f(x) \rightarrow -\infty[/tex]
and
As [tex]x \rightarrow -\infty[/tex] in the given function, then [tex]y=-2[/tex]
Therefore, as x increases without bound , f(x) decreases without bound
and as x decreases without bound , f(x) approaches the line y =-2
20 large plastic bottles can be recycled to make 1 fleece jacket. How may fleeces can be made with 280 large plastic bottles?
Answer:
14 Fleece jackets could be made.
Hope this helped:)
Step-by-step explanation:
280/20=14
Answer:
14 fleece jackets
Step-by-step explanation:
Lanette drove 248 miles in 4 hours. At the rate, how many hours will it take her to drive a additional 93miles.
Answer:
1.5 hours
Step-by-step explanation:
using the relationship between distance/ speed / time
distance = speed × time
speed = [tex]\frac{distance}{time}[/tex] = [tex]\frac{248}{4}[/tex] = 62 mph
travelling at this rate then
time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{93}{62}[/tex] = 1.5 hours
PLEASE HELP!!
A sequenced is defined by an=-3/4an-1, and a3=9/16. What is the seventh term?
Answer:
[tex]a_{7}[/tex] = [tex]\frac{729}{4096}[/tex]
Step-by-step explanation:
To obtain the next term in the sequence multiply the previous term by - [tex]\frac{3}{4}[/tex]
given [tex]a_{3}[/tex] = [tex]\frac{9}{16}[/tex], then
[tex]a_{4}[/tex] = - [tex]\frac{3}{4}[/tex] × [tex]\frac{9}{16}[/tex] = - [tex]\frac{27}{64}[/tex]
[tex]a_{5}[/tex] = - [tex]\frac{3}{4}[/tex] × - [tex]\frac{27}{64}[/tex] = [tex]\frac{81}{256}[/tex]
[tex]a_{6}[/tex] = - [tex]\frac{3}{4}[/tex] × [tex]\frac{81}{256}[/tex] = - [tex]\frac{243}{1024}[/tex]
[tex]a_{7}[/tex] = - [tex]\frac{3}{4}[/tex] × - [tex]\frac{243}{1024}[/tex] = [tex]\frac{729}{4096}[/tex]
Answer:
D
Step-by-step explanation:
E2020
a skateboard rises 2ft for every 7ft, measured horizontally. what is the slope?
In two hours holden completed 3 fouths of his race how long will holden take to complete the entire race
If xy= -20 -2y= -6. What's the value of x
Answer:
x = -6 2/3 or -20/3
Step-by-step explanation:
So we know:
-2y = -6
Divide -2 on both sides
y = 3
Plug that into the other equation:
3x = -20
divide 3 on both sides
x = -20/3 or -6 2/3
You plan to put anti-theft devices on each garment in your store. You have 1,320 garments, and it takes an employee 20 seconds to tag a garment. How long will it take TWO employees to tag all the garments?
Answer:
13,200 Seconds, or 220 Minutes
Step-by-step explanation:
Since there are 2 employees working at the same time, so in 20 seconds, they will be tagging a total of 2 garments. So we can say the rate is:
rate = [tex]\frac{20 Seconds}{2 Garments}[/tex]
So how long would it take to tag 1320 garments?
We set up the ratio, cross multiply, and solve.
[tex]\frac{TimeInSeconds}{NumberOfGarments}=\frac{20}{2}=\frac{x}{1320}}\\\frac{20}{2}=\frac{x}{1320}\\20*1320=2x\\x=\frac{26400}{2}=13,200[/tex] seconds
Or in minutes, we divide by 60, so we have:
[tex]\frac{13,200}{60}=220[/tex] Minutes
Answer:
3 hours 40 minutes.
Step-by-step explanation:
We are told that we have 1320 garments and it takes an employee 20 seconds to tag a garment.
1 employee tags one garment in 20 seconds.
So garments tagged by 1 employees in 1 minute will be [tex]\frac{60}{20} =3[/tex] garments.
2 employees will tag 3*2=6 garments in 1 minute.
To find the total time it will take two employees to tag all the garments we will divide total number of garments by 6.
[tex]\text{Time taken by two employees to tag 1320 garments}=\frac{1320}{6}[/tex]
[tex]\text{Time taken by two employees to tag 1320 garments}=220[/tex]
Therefore, it will take 220 minutes or 3 hours and 40 minutes for 2 employees to tag 1320 garments.
Select all that apply.
Solve for x , 0 < x < 360. 1/sin^2x = 4
answer choices (choose all that apply)
30
150
210
330
Answer:
30,150, 210 ,330
Step-by-step explanation:
1/sin^2x = 4
Multiply each side by sin^2x
1 = 4 sin^2 x
Divide each side by 4
1/4 = sin^2 x
Take the square root of each side
sqrt(1/4) = sqrt(sin^2 x)
±sqrt(1/4) = sin x
±1/2 = sinx
Take the inverse sin of each side
arcsin (1/2) = arcsin (sin x) and arcsin(-1/2) = arcsin (sin x)
30 = x -30 = x
But this is not between 0 and 360,
so we add 360
-30+360 = 330
We also have to look at the other locations where sin x = 1/2
Taking the arcsin only gives values between -90 and 90
Since we are looking at the sin value, we take 180 - the value given
180 -30 = 150
180 --30
180+30 = 210
So our values are 30, 150,210,330
Cedric can buy 3 songs for $3.60 or 4 songs for $4.80. How much do you think he would pay for 5 songs?
A) $5.80
B) $6.00
C) $6.20
D) $6.40
Answer:
B) $6.00
Step-by-step explanation:
well divide 3.60 and you get 1.20
and the same for 4.80 divided by 4
so it be 1.20 times 5= he pays
To find out how much Cedric would pay for 5 songs, we divide the total cost by the number of songs and then multiply it by 5. Cedric would pay $6.00 for 5 songs.
Explanation:To find out how much Cedric would pay for 5 songs, we first need to determine the cost per song. From the given information, we can see that the cost of 3 songs is $3.60 and the cost of 4 songs is $4.80. To find the cost per song, we can divide the total cost by the number of songs.
Cost per song = Total cost / Number of songsCost per song for the 3 songs = $3.60 / 3 = $1.20Cost per song for the 4 songs = $4.80 / 4 = $1.20Since the cost per song is the same for both sets of songs, we can conclude that Cedric would pay $1.20 for each song. Therefore, for 5 songs, he would pay 5 x $1.20 = $6.00.
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PLEASE HELP!! Algebra 2 Review !!
1. What is the equation, in standard form, of a parabola that models the values in the table?
x | -2 0 4
f(x) | 2.5 1.5 -60.5
(I used STAT on the calculator, and found the answer, nevermind on this one)
2. Simplify the expression.
[tex] \frac{5 + 6i}{4 + 6i} [/tex]
Answer:
[tex]\frac{28-3i}{26}[/tex]
Step-by-step explanation:
For #2, remember that [tex]i=\sqrt{-1}[/tex], so [tex]i^{2}=-1[/tex] Also, (a+b)(a-b), where a and b are any numbers, (a+b)(a-b)=[tex]a^2-b^2[/tex]. Now, to simplify, or radicalize, a number with surds in the denominator, you have to multiply the denominator by its conjugate. If there is a complex number [tex]a+bi[/tex], where a and b are any numbers, the conjugate is always [tex]a-bi[/tex]. Lets apply these rules. The conjugate of 4+6i is 4-6i, so do this:
[tex]\frac{5+6i}{4+6i}=\frac{(5+6i)(4-6i)}{(4+6i)(4-6i)}=\frac{20+24i-30i+36}{16+36}=\frac{56-6i}{52}=\frac{2(28-3i)}{2(26)}=\frac{28-3i}{26}[/tex]
Our answer is (28-3i)/(26)!
I have tryed to find this problem and I can't everytime I try the numbers that are to high for the answer what I'm I doing wrong the problem is 51/2*21/3=
Answer:
1071/2
when you multiply the top you get 1071 and when you multiply the bottom you get 6. But if u want to simplify the answer could be 357/2
Plzzz give brainlest and thank me
Answer:
178.5
Step-by-step explanation:
First, Do 51/2, which is 25.5
Second do 25.5*21, which is 535.5
Third, do 535.5/5, which would be 178.5
So, the answer is 178.5
Hope this helps :)
Patrick took his parents to dinner and the bill was $70 plus 6% tax. If he left a tip of 15% of the total (food plus tax), what was the total cost of the dinner?
Answer: $85.33
Step-by-step explanation:
Bill: $70
Bill + Tax: $70 + $70(0.06)
= $70 + $4.20
= $74.20
Bill + Tax + Tip: $74.20 + $74.20(0.15)
= $74.20 + $11.13
= $85.33
Arjun can type 40 words per mintue.Dalia can type 55 words per mintue.If Arjun and dalia each type for 30 mintues,about how many more words will Dalia type
Answer: 450 words
Step-by-step explanation:
Arjun: [tex]\dfrac{40 words}{1minute} \times\dfrac{30minutes}{} = 1200 words[/tex]
Dalia: [tex]\dfrac{55 words}{1minute} \times\dfrac{30minutes}{} = 1650 words[/tex]
Dalia - Arjun
= 1650 - 1200
= 450
The period of a pendulum is the time the pendulum takes to swing back and forth. The function Upper L equals 0.81 t squared relates the length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth. A convention center has a pendulum that is 50 feet long. Find the period.
The period of a 50-foot pendulum can be found by plugging the given length into the provided pendulum function and solving for the time variable. This gives a final result after taking the square root of the division between the length and a constant.
Explanation:To find the period of a pendulum using the given length, we use the given function Upper L equals 0.81 t squared where L is the length in feet and t is the time in seconds that the pendulum takes to swing back and forth. In this case, the length of the pendulum is given as 50 feet. We plug this into the equation and solve for t:
50 = 0.81 * t^2
Rearranging this equation gives us:
t^2 = 50 / 0.81
Then we calculate the square root of this to find t:
t = sqrt(50 / 0.81)
The final answer after calculations gives the period of the pendulum.
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The period of the pendulum at the convention center, which is the time it takes to swing back and forth, is approximately 7.862 seconds. This is calculated using the given mathematical function relating length to swing time.
Explanation:The given function that relates the length L of the pendulum to the swinging time t is Upper L = 0.81 t squared. If the pendulum at the convention center is 50 feet long (L = 50), we can substitute that into the equation to find the time it takes to swing (t), which in other words is the period we are trying to determine.
So, 50 = 0.81 * t squared. Solving this equation for t, we divide both sides of the equation by 0.81 to isolate t squared. This will give us t squared = 50/0.81
t = sqrt(50/0.81) ≈ 7.862. This means that the period of the convention center's pendulum is approximately 7.862 seconds.
It’s important to note that the only factors that affect the period of a simple pendulum are its length and the acceleration due to gravity, and the pendulum performs simple harmonic motion.
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Tickets to a baseball game cost $22 each and parking costs $10. What is the equation of the line that represents the cost of attending the game?
x - number of games
22x - cost of x tickets
10 - parking cost
The equation:
[tex]y=22x+10[/tex]
Answer:
y = 22x + 10
Step-by-step explanation:
Given,
The cost of each ticket = $ 22,
Let x be the number of tickets,
Then, the cost of x tickets = x × cost of each ticket
= 22x dollars,
Now, parking cost = $ 10,
So, the total cost of attending the game ( say y ) = cost of all tickets + parking cost
⇒ y = 22x + 10
Which is the required equation.
The product of the roots of $2x^2 - 7x + N = 0$ is $-5.$ Find $N.$
By the fundamental theorem of algebra, we can factorize the quadratic as
[tex]2x^2-7x+N=2(x-r_1)(x-r_2)[/tex]
so that expanding the right hand side gives
[tex]2x^2-7x+N=2x^2-2(r_1+r_2)x+2r_1r_2[/tex]
[tex]\implies\begin{cases}-2(r_1+r_2)=-7\\2r_1r_2=N\end{cases}[/tex]
We're told that the product of the roots is -5, or [tex]r_1r_2=-5[/tex], so we get
[tex]2(-5)=N=-10[/tex]
The value of N for given conditions is -10. It can be calculated as shown below.
Given that:The quadratic equation given is: [tex]2x^2 -7x + N = 0[/tex]
The product of roots of given equation is: -5
To find: Value of N
Explanation for product of roots and Calculations:For quadratic equation [tex]ax^2 + bx + c = 0[/tex], we have:
[tex]\text{Product of roots} = \dfrac{c}{a}\\\\\text{Sum of roots} = \dfrac{-b}{a}[/tex]
For given quadratic equation, we have:
a = 2, b = -7, c = N
Thus, by above formula:
[tex]\text{Product of roots} = \dfrac{c}{a} = \dfrac{N}{2} = -5\\\\N = -5 \times 2 = -10[/tex]
Thus, value of N for given conditions is -10.
Learn more about roots of quadratic equations here:
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