Answers
See the attachment for the table values.
Obviously, the patterns are similar in that each row is multiplied by some constant to get the next row. They are different in that the constants are different. 2 is used for the left column, so the reward grows less fast than in the right column where 3 is used.
The King's Plan 2 will only be cheaper if the number of squares being filled is less than about 5/8 of the number of squares in the original Plan 1.
Related Questions
An inscribed angle has a measure of 48°. Determine the measure of the intercepted arc.
24° 48° 72° 96°
Answers
[tex]\frac{48}{\frac{1}{2}}=\frac{\frac{1}{2}x}{\frac{1}{2}} \\ 48 \div \frac{1}{2} = x \\ \frac{48}{1} \div \frac{1}{2} = x \\ \frac{48}{1}*\frac{2}{1} = x \\ \frac{96}{1}=x \\ 96=x[/tex]
The measure of the intercepted arc is 96°.
The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.
After about how many seconds is the acorn 5 m above the ground?
Answers
We look for a height of 5 meters on the vertical axis.
When finding the height of 5 meters we must observe for what time value this height belongs.
For this, we observe the horizontal axis.
The value of time is approximately:
t = 1.7 seconds
Answer:
t = 1.7 seconds
option 3
The equation of the parabola is y = – 5x² + 20. The time when an acorn is 5 m above the ground in 1.7 seconds. Then the correct option is C.
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.
We know that the equation of the parabola will be given as
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a is the constant.
We have
(h, k) = (0, 20)
Then
y = ax² + 20
The parabola is passing through (2, 0), then we have
0 = 4a + 20
a = -5
Then we have
y = – 5x² + 20
The time in seconds when the acorn is 5 m above the ground.
–5x² + 20 = 5
–5x² = –15
x = 1.7
More about the parabola link is given below.
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if you received an annual salary of 33500 paid monthly what would your gross pay be each pay period
Answers
PLEASE HELP ME ASAP 40 POINTS AND BRAINLIEST SHOW WORK
Find the variables and the lengths of the sides of this kite
Answers
Y = 16
Since we know that the bottom two sides are congruent we can make an equation to solve for that X first [2x + 5 = x + 12] . (since we cannot make an equation with the two congruent sides at the top because there are different variables).
Now that we've solved for X which is 7, we can plug it into the top equation [y - 4 = x + 5] which would simplify to [ y - 4 = 12] which would give us 16 for Y
solve for t. use the quadratic formula.
d=−16t^2+12t
Answers
Answer:
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Step-by-step explanation:
Given: d = -16t² + 12t
To find: t using quadratic formula
If we have quadratic equation in form ax² + bx + c = 0
then, by quadratic formula we have
[tex]x\,=\,\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Rewrite the given equation,
-16t² + 12t - d = 0
from this equation we have,
a = -16 , b = 12 , c = d
now using quadratic formula we get,
[tex]t\,=\,\frac{-12\pm\sqrt{12^2-4\times(-16)\times d}}{2\times(-16)}[/tex]
[tex]t\,=\,\frac{-12\pm\sqrt{144+64d}}{-32}[/tex]
[tex]t\,=\,\frac{-12\pm\sqrt{16(9+4d)}}{-32}[/tex]
[tex]t\,=\,\frac{-12\pm4\sqrt{9+4d}}{-32}[/tex]
[tex]t\,=\,\frac{4(-3\pm\sqrt{9+4d})}{-32}[/tex]
[tex]t\,=\,\frac{-3\pm\sqrt{9+4d}}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:,\:\:\frac{-3-\sqrt{9+4d}}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{-(3+\sqrt{9+4d})}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Therefore, [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Answer:
[tex]\frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]
Step-by-step explanation:
Here, the given expression,
[tex]d= -16t^2+12t[/tex]
[tex]\implies -16x^2+12t-d=0[/tex] ------(1)
Since, if a quadratic equation is,
[tex]ax^2+bx+c=0[/tex] ------(2)
By using quadratic formula,
We can write,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
By comparing equation (1) and (2),
We get, a = -16, b = 12, c = -d,
[tex]t=\frac{-12\pm \sqrt{12^2-4\times -16\times -d}}{2\times -16}[/tex]
[tex]t = \frac{-12\pm \sqrt{16\times 9-16\times d}}{-32}[/tex]
[tex]t = \frac{-12\pm \sqrt{16}\times \sqrt{9-d}} {-32}[/tex]
[tex]t = \frac{-12\pm 4\sqrt{9-d}} {-32}[/tex]
[tex]t = \frac{4(-3\pm \sqrt{9-d})} {4(-8)}[/tex]
[tex]t = \frac{-3\pm \sqrt{9-d}} {-8}[/tex]
[tex]t = \frac{-3+\sqrt{9-d}} {-8}\text{ or }t=\frac{-3-\sqrt{9-d}} {-8}[/tex]
[tex]\implies t = \frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]
Which is the required solution.
The formula used to find the length of a line segment in space.
Answers
length = √((∆x)^2 +(∆y)^2 +(∆z)^2)
.. where ∆x, ∆y, ∆z are the differences between the end-point coordinates in the x-, y-, and z-directions, respectively.
if youre doing the vocab thing -- Distance
Which expression represents the number of sides in the polygon for the nth member of the pattern? A) n + 3 B) n3 C) n + 2 D) 3n
Answers
2nd member has 6 sides (3x2)
3rd member has 9 sides' (3x3)
Therefore, i think for nth member
the appropriate expression for n th member will be 3n
Joan has 45 marbles . MARY HAS m marbles if Joan has 15 times as many marbles , write an equation that shows how many marbles mary has
Answers
Mary has 3 marbles.
Explanation:To find out how many marbles Mary has, we can use the information that Joan has 45 marbles and Joan has 15 times as many marbles as Mary. So, we can set up an equation:
45 = 15m
To solve for m, we divide both sides of the equation by 15:
m = 45/15
Simplifying the expression, we get:
m = 3
Therefore, Mary has 3 marbles.
A car travels 3 times around a traffic circle whose radius is 80 feet. What is the distance the car will travel? Use 3.14 for π . Enter your answer in the box. ft
Answers
Answer : Distance will be 1507.2 feet .
Explanation :
Since we have given that
Radius of circle = 80 feet
So,
Circumference of circle is given by
[tex]2\pi r=2\times 3.14\times 80=502.4 \text{ feet}[/tex]
Since , a car travels 3 times around a traffic circle.
So,
[tex]\text{ Distance covered by the car will travel}= 3\times 502.4= 1507.2 \text{ feet }[/tex]
So, Distance will be 1507.2 feet .
Is .8/100 equal to .8%
Answers
but is also equal to 2/25, the simplest form of .8/100
Look at the data in the table below
X Y
4. 9
12. 28
7. 14
9. 20
5. 9
12. 30
10. 22
Which graph shows the best fit for this data
Answers
I hope this helps.
Ben and Marge are purchasing a house with a 20-year, 5/1 ARM for $265,000 at 5.25% with a 3/12 cap structure. What will the difference in payments be from year 5 to year 6?
A. $925.81
B. $880.29
C. $369.32
D. $234.39
Answers
The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.
To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.
1. Initial Mortgage Parameters :
- Loan Amount: $265,000
- Interest Rate: 5.25%
- Term: 20 years
2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.
3. Cap Structure :
- Initial Adjustment Cap: 3%
- Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.
4. Calculation Steps :
a. Calculate the initial monthly payment using the loan amount, interest rate, and term.
b. Determine the new interest rate for year 6 based on the cap structure.
c. Calculate the monthly payment for year 6 with the new interest rate.
d. Find the difference between the payments from year 5 to year 6.
Let's start the calculations:
a. Calculate the initial monthly payment using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:
[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] = Monthly Payment
- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)
- [tex]\( A \)[/tex] = Loan Amount
- [tex]\( r \)[/tex] = Periodic Interest Rate
- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)
For the initial fixed period of 5 years:
[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]
[tex]\[ n = 20 \times 12 = 240 \][/tex]
Plugging these values into the formula:
[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]
[tex]\[ P \approx 1645.80 \][/tex]
So, the initial monthly payment is approximately $1,645.80.
b. Determine the new interest rate for year 6 :
- The initial rate can adjust up to 3% in year 6.
- So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).
c. Calculate the monthly payment for year 6 :
- Use the formula for the monthly payment again with the new interest rate:
[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]
Plugging into the formula:
[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]
[tex]\[ P \approx 1985.09 \][/tex]
So, the monthly payment for year 6 is approximately $1,985.09.
d. Find the difference in payments from year 5 to year 6:
[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]
[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]
[tex]\[ Difference \approx 339.29 \][/tex]
So, the difference in payments from year 5 to year 6 is approximately $339.29.
Therefore, the closest answer is C. $369.32 .
Check my answers? GIving medal:
7. What is the slope of the line that passes throught the pair of points (1, 7) and (10, 1)?
a. 3/2
b. -2/3
c. -3/2
d. 2/3 <--
8. What is the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1)?
a. -1
b. 1
c. -3 <--
d. d
9. what is the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2)?
a. 6/22 <--
b. -6/22
c. 22/6
d. -22/6,
Answers
Number seven Is B. -2/3
A small plane leaves an airport at a speed of 252 miles per hour. A jet leaves the airport 2 hours later traveling at 672 miles per hour. How long will the small plane be flying before the jet catches up to it? What unit will you use for your answer?
Answers
the small plane runs at a rate of 252 mph, the jet runs at 672 mph, but the jet takes off 2 hours later.
if the jet plane say has been traveling for "t" hours by the time they meet, the small plane was already rolling before the jet, actually 2 hours earlier, so if the jet has gone for "t" hours, the small plane has been going for "t+2" hours.
now, by the time they both meet, the distance covered by say the small plane is "d" miles, but the distance covered by the jet is also the same "d" miles, since they're meeting.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{small plane}&d&252&t+2\\ \textit{jet plane}&d&672&t \end{array} \\\\\\ \begin{cases} d=252(t+2)\\ d=672t\\ --------\\ 252(t+2)=672t \end{cases} \\\\\\ 252t+504=672t\implies 504=420t\implies \cfrac{504}{420}=t\implies \cfrac{6}{5}=t \\\\\\ \textit{an hour and 12 minutes}=t[/tex]
No, thanks to you, I got the question wrong it was hours.
need help so much ...
Answers
The die in this problem is not fair. The sides are coming up with frequencies that are far from being equal. In an actual experiment with a fair die, you would expect each face to come up a NEARLY equal number of times. You would not expect the frequencies to be so different that one of them is 20 and another one is 2.
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
Answers
we know that
the side of square=2*[r*√2/2]=r*√2
r=14 ft
the side of square=14*√2=19.80 ft
[area of the remaining portion of the circle]=[ area of a circle]-[area of a square]
[area of a square]=(14√2)²=392 ft²
[ area of a circle]=pi*14²=615.75 ft²
therefore
[area of the remaining portion of the circle]=615.75-392=223.75 ft²
the answer is 223.75 ft²
A square is cut from a circle with a 14-foot diameter. Remaining circle area ≈ 53.86 sq ft here nearest round off option is c. 50 square feet.
To find the area of the remaining portion of the circle after a square with a side of 10 feet is cut out,
Find the area of the square:
Area of square
= side × side
= 10 feet × 10 feet
= 100 square feet
Find the radius of the circle:
The diameter is approximately 14 feet, so the radius is half of that:
Radius = 14 feet / 2 = 7 feet
Find the area of the entire circle:
Area of circle = π × radius²
Area of circle
= π × (7 feet)²
≈ 153.86 square feet (using π ≈ 3.14)
Subtract the area of the square from the area of the circle to find the remaining portion:
Remaining area = Area of circle - Area of square
Remaining area
≈ 153.86 square feet - 100 square feet
≈ 53.86 square feet
Therefore, the approximate area of the remaining portion of the circle is approximately 53.86 square feet nearest option is c. 50 square feet.
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The above question is incomplete , the complete question is:
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
Attached figure
Which foundation drawing matches this orthographic drawing? ( just tell me what picture)
Answers
Which is the ratio for sin a written as a fraction in simplest form
Answers
your Answer issss:
√3/2
An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.
Answers
now, the center is half-way between the vertices, therefore it'd be at 0, -4, like in the picture in red.
the distance from the center to either foci, is "c", and that's c = 3.
the "a" component of the major axis is 5 units, now let's find the "b" component,
[tex]\bf \textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases}\\\\ -------------------------------[/tex]
[tex]\bf \begin{cases} a=5\\ c=3 \end{cases}\implies c=\sqrt{a^2-b^2}\implies c^2=a^2-b^2\implies b^2=a^2-c^2 \\\\\\ b=\sqrt{a^2-c^2}\implies b=\sqrt{5^2-3^2}\implies b=4\\\\ -------------------------------\\\\ \begin{cases} h=0\\ k=-4\\ a=5\\ b=4 \end{cases}\implies \cfrac{(x- 0)^2}{ 4^2}+\cfrac{[y-(-4)]^2}{ 5^2}=1 \\\\\\ \cfrac{(x- 0)^2}{ 16}+\cfrac{(y+4)^2}{25}=1[/tex]
The equation of the ellipse is required.
The required equation is [tex]\dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]
It can be see that the major axis is parallel to the y axis.
The major axis points are
[tex](h,k+a)=(0,1)[/tex]
[tex](h,k-a)=(0,-9)[/tex]
[tex]k+a=1[/tex]
[tex]k-a=-9[/tex]
Subtracting the equations
[tex]2a=10\\\Rightarrow a=5[/tex]
The foci are
[tex](h,k+c)=(0,-1)[/tex]
[tex](h,k-c)=(0,-7)[/tex]
[tex]k+c=-1[/tex]
[tex]k-c=-7[/tex]
Subtracting the equations
[tex]2c=6\\\Rightarrow c=3[/tex]
[tex]k+c=-1\\\Rightarrow k=-1-c\\\Rightarrow k=-1-3\\\Rightarrow k=-4[/tex]
Foci is given by
[tex]c^2=a^2-b^2\\\Rightarrow b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{5^2-3^2}=4[/tex]
The equation is
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-0)^2}{4^2}+\dfrac{(y+4)^2}{5^2}=1\\\Rightarrow \dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]
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What is the area of the composite figure whose vertices have the following coordinates? (−1, 5) , (3, 5) , (7, 3) , (3, 0) , (−1, 1)
Answers
Answer:
28
Step-by-step explanation:
Square: 4 * 4 = 16
Small Triangle: 1 * 4 = 4 / 2 = 2
Large Triangle: 5 * 4 = 20 / 2 = 10
16 + 2 + 10 = 28
Use the Remainder Theorem to find the remainder: (–6x3 + 3x2 – 4) ÷ (2x – 3).
23
-17.5
-4.4444444...
-0.8888888...
Answers
(–6x³ + 3x² – 4) ÷ (2x – 3)
----------------------║--------------------------
+6x³+9x² -3x²+6x+9
---------------------
12x²-4
-------------------
-12x²+18x
-------------------
18x-4
-----------------
-18x+27
----------------
23-----------------> the remainder
the answer is 23
The remainder obtained when we carry out the operation (-6x³ + 3x² - 4) ÷ (2x - 3) is -17.5 (2nd option)
How do i determine the remainder?The following data were obtained from the question:
Expression = (-6x³ + 3x² - 4) ÷ (2x - 3)Remainder =?Using the remainder theorem, we can obtain the remainder as illustrated below:
Let
f(x) = -6x³ + 3x² - 4
2x - 3 = 0
From 2x - 3 = 0, make x the subject as shown below:
2x - 3 = 0
x = 3/2
Substitute the value of x into f(x). We have:
f(x) = -6x³ + 3x² - 4
f(3/2) = -6(3/2)³ + 3(3/2)² - 4
= -6(27/8) + 3(9/4) - 4
= -20.25 + 6.75 - 4
= -17.5
Thus, we can conclude that the remainder obtained when (-6x³ + 3x² - 4) is divided by (2x - 3) is -17.5 (2nd option)
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Which linear inequality is represented by the graph? y > 2/3x – 1/5 y ≥ 3/2x + 1/5 y ≤ 2/3x + 1/5 y < 3/2x – 1/5
Answers
We have then that by substituting the values of x = 0 and x = 3 we obtain:
y = 0.2
y = 2.2
Respectively.
So, the line is:
y = 2 / 3x + 1/5
Then, the points that satisfy the inequality are all those of the shaded region.
Answer:
The inequality is:
y ≤ 2 / 3x + 1/5
Answer: The correct option is third, i.e., [tex]y\geq \frac{3}{2} x+\frac{1}{5}[/tex].
Explanation:
From the figure it is noticed that the line passing through the points (0,0.2) and (3,2.2).
The equation of line passing through two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]y-0.2=\frac{2.2-0.2}{3-0}(x-0)[/tex]
[tex]y-\frac{1}{5} =\frac{2}{3} x[/tex]
[tex]y =\frac{2}{3} x+\frac{1}{5}[/tex]
The equation of the line is [tex]y =\frac{2}{3} x+\frac{1}{5}[/tex].
From the figure it is noticed that as the value of x increases the value of y is less.
he point (1,0) lies on the shaded reason it means this point must satisfy the equation.
[tex](0)=\frac{2}{3} (1)+\frac{1}{5}[/tex]
[tex](0)=\frac{2}{3} +\frac{1}{5}[/tex]
[tex](0)=\frac{10+3}{15}[/tex]
[tex](0)=\frac{13}{15}[/tex]
It is true of the sign is less than or equal to instead of equal.
[tex]y \leq \frac{2}{3} x+\frac{1}{5}[/tex]
Therefore, option third is correct.
Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?
Answers
Let X be the number of minutes
Bill*Minutes +Greg*Minutes +20 = total distnce between
45x + 75x +20 = d
Plug in 2.5 for both values of x
45(2.5) + 75(2.5) + 20 =d
Multiply values by 2.5
112.5 + 165 + 20 = d
add together
Distance = 297.5 feet apart
Answer:
320 ft
Step-by-step explanation:
I'm not sure how the other person was awarded brainliest answer because that answer is pretty far off. But the work was good just they messed up. Also kinda sad he is a brainly teacher and still has incorrect answers.
PLEASE HELP ASAP
EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.
The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.
Write an equation for the area of the photo in terms of x.
Answers
A=LxW
A is the area of the photograph (A=54 in²).
L is the lenght of the photograph (L=12-4x).
W is the widht of the photograph (W=12-2x)
2. When you substitute these values into the formula A=LxW, you obtain:
A=LxW
54=(12-4x)(12-2x)
3. When you apply the distributive property, you have:
54=144-24x-48x+8x²
8x²-72x+144-54=0
4. Finally, you obtain a quadratic equation for the area of the photo:
8x²-72x+90=0
5. Therefore, the answer is:
8x²-72x+90=0
If the expected adult of a 2 week old puppy is 20 pounds how many grams per day should they gain?
Answers
Dominik paid three-quarters of a dollar for a newspaper. Which amount is equivalent to the cost of the newspaper?
Answers
If a < 0 and b > 0, then the point (a, b) is in Quadrant A) I. B) II. C) III. D) IV.
Answers
Answer:
The actual answer is D
The point (a, b) lies in the second quadrant. Then the correct option is B.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
If a < 0 and b > 0.
Then the point (a, b) is in Quadrant will be given as,
If a > 0 and b > 0, then the points is in first quadrant.If a < 0 and b > 0, then the points is in second quadrant.If a < 0 and b < 0, then the points is in third quadrant.If a > 0 and b < 0, then the points is in fourth quadrant.Thus, the point (a, b) lies in the second quadrant.
Then the correct option is B.
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Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
Answers
Answer: The answer is 5, 10, 20, 40 and 80.
Step-by-step explanation: We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.
Let the first five terms of a sequence be 5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term [tex]a_1 5[/tex] and common ratio [tex]r=2.[/tex]
Therefore, we have
[tex]a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots[/tex]
Therefore, the recursive formula is
[tex]a_{n+1}=2a_n,~~a_1=5.[/tex]
And explicit formula is
[tex]a_n=a_1r^{n-1}.[/tex]
Answer:
Let the first five terms of a sequence be, 4,8,12,20,24
Ok, let me explain the meaning of term explicit and Recursive formula.
Explicit formula ,is the general formula to find any term of the sequence.
And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.
So,the explicit formula for the sequence is,
y = 4 n, where , n is any natural number.
And the recursive formula is .
y = 4 (n-1), with the help of (n-1)th term we can find nth term.
First term =4=4 × 1
Second term =8 =4 × 2
Third term =12=4×3
Fourth term =16 =4 × 4
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(n-1) th term =4 × (n-1)
nth term =4 × n
Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.
As, you said you don't want simpler sequence
Consider the first five terms of the sequence, 0, 3,8,15, 24.
Explicit formula =n² + 2 n
Recursive formula=(n-1)²+2(n-1)
If,you will look at the sequence, it is neither Arithmetic nor geometric .
First term =0=0²+0×0
Second term =3=1+2=1²+2 × 1
Third term =8=4+4=2²+2×2
Fourth term =15=9+6=3²+2×3
Fifth term =24=16 +8=4²+2×4
So, Explicit formula= n²+ 2 n, where n is a whole number.
if the remainder on division of x^3+2x^2+kx+3 by x-3 is 21,find the quotient and the value of k. Hence,find the zeroes of the cubic polynomial x^3+2x^2+kx-18.
Answers
On dividing p(x) by x-3, the remainder is 21. Therefore,
P(3)=21
Substituting x=3 in p(x)
P(3)=3^3 +2*(3)^2+k*3+3
=27+18+3k+3
=48+3k
We know that, p(3)=21.
So, 48+3k=21
3k=21-48
3k=-27
k=-27/3 =-9
now, p(x) =x^3+2x^2-9x-18
-2 is a factor of p(x) on inspection. Therefore, divide p(x) by x+2 to find the
zeroes of the polynomial.
On dividing, we get the factors to be, (x^2-9)(x+2)
(x^2-3^2)(x+2)
Factorizing using the identity a^2-b^2=(a+b)(a-b) we get,
(x+3)(x-3)(x+2)
Therefore, the zeroes of the polynomials are -3,+3 and -2.
What is the circumference of a circle with a radius of 6.1 centimeters? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. cm
Answers
C = 2 * pi × r
Substitute:
C = 3.14 × 6.1 × 2
C = 38.303
Round to the nearest tenth:
38.3.
ANSWER:
The circumference of the circle is about 38.3 centimetres.
:D