Answer:
2.71
Step-by-step explanation:
Using this formula: Volume= 4 over 3 * π * r cubed.
then do R=(3V4π)⅓=(3·83.54·π)⅓≈2.71144
2.71144 rounded to the nearest 10 is 2.71
An arithmetic sequence is given by 20, 17, 14, 11, ...
(a) Write down the value of the common difference, d.
(b) Find a100
(c) Find s100
Answer:
The common difference equals:
[tex]-3[/tex]
The sum of the sequence equals:
[tex]62[/tex]
The explicit formula of this sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
The recursive formula of this sequence is:
[tex]a_n=a_((n-1))-3[/tex]
The nth terms:
[tex]20,17,14,11,8,5,2...[/tex]
Step-by-step explanation:
An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference.
1. Find the common difference.Find the common difference by subtracting any term in the sequence from the term that comes after it.
[tex]a_2-a_1=17-20=-3\\a_3-a_2=14-17=-3\\a_4-a_3=11-14=-3[/tex]
The difference of the sequence is constant and equals the difference between two consecutive terms.
[tex]d=-3[/tex]
2. Find the sum.Calculate the sum of the sequence using the sum formula:
Formula
[tex]Sum=\frac{(n(a_1+a_n))}{2}[/tex]
Plug in terms
[tex]Sum=(4*(a_1+a_n))/2[/tex]
[tex]Sum=(4*(20+a_n))/2[/tex]
[tex]Sum=(4*(20+11))/2[/tex]
Simplify the expression
[tex]Sum=(4*(20+11))/2[/tex]
[tex]Sum=(4*31)/2[/tex]
[tex]Sum=124/2[/tex]
[tex]Sum=62[/tex]
The sum of this sequence is [tex]62[/tex].
This series corresponds to the following straight line [tex]y=-3x+20[/tex]
3. Find the explicit form.The formula for expressing arithmetic sequences in their explicit form is:
Formula: [tex]a_n=a_1+(n-1)*d[/tex]
Plug in the terms.
[tex]a_1=20[/tex] (this is the 1st term)
[tex]d=-3[/tex] (this is the common difference)
[tex]a_n[/tex] (this is the nth term)
[tex]n[/tex] (this is the term position)
The explicit form of this arithmetic sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
4. Find the recursive form.The formula for expressing arithmetic sequences in their recursive form is:
Formula: [tex]a_n=a_((1-n))+d[/tex]
Plug in the d term.
[tex]d=-3[/tex](this is the common difference)
The recursive form of this arithmetic sequence is:
[tex]a_n=a_((n-1))-3[/tex]
5. Find the nth element.[tex]a_1=a_1+(n-1)*d=20+(1-1)*-3=20[/tex]
[tex]a_2=a_1+(n-1)*d=20+(2-1)*-3=17[/tex]
[tex]a_3=a_1+(n-1)*d=20+(3-1)*-3=14[/tex]
[tex]a_4=a_1+(n-1)*d=20+(4-1)*-3=11[/tex]
[tex]a_5=a_1+(n-1)*d=20+(5-1)*-3=8[/tex]
[tex]a_6=a_1+(n-1)*d=20+(6-1)*-3=5[/tex][tex]a_7=a_1+(n-1)*d=20+(7-1)*-3=2[/tex]
Terms and topics:
Artithmetic SequencesB3: Jill filled up her car with 15 gallons of gas for $43.35. Bill filled up his car with 22 gallons of gas for $61.82. Who got the better deal on gas?
Answer:
Bill go the better deal
Step-by-step explanation:
43.35/15=2.89
61.82/32=2.81
What is the purpose of the QUADRATIC FORMULA?
N
A Determine the distance between two points
B Determine the zeros of a quadratic function
Calculate the axis of symmetry of a quadratic function
Calculate the y-coordinate of the vertex of a parabola
for f(x)=4x+2, what value of x makes f(x)=-14
Hey there,
f(x) = 4x + 2
what value of x makes f(x) = -14?
Answer :x = -4 ✅
Explanations:f(x) = 4x + 2
>> We want f(x) to be equal to -14:
4x + 2 = -14
>> Substract 2 from both sides :
4x + 2 - 2 = -14 - 2
4x = -16
>> Divide both sides by 4:
4x/4 = -16/4
x = -4
✅
Have a good day ;)
Answer:
x = -4
Step-by-step explanation:
Given:
f(x) = 4x + 2If the value of f(x) is -14,
⇒ 4x + 2 = -14 [f(x) = 4x - 2 and -14]
To simplify the equation, we need to isolate the variable completely. Start out by subtracting 2 both sides. This will isolate "x" and the cooeficient of x.
⇒ 4x = -14 - 2⇒ 4x = -16Then, divide 4 both sides to isolate the cooeficient of x on one side and a constant on the other side. The constant will be the value of x.
⇒ 4x/4 = -16/4⇒ x = -4Thus, -4 is the value of x that makes f(x) equivalent to -14
translate the triangle 3 to the right and 2 down
Answer:
Step-by-step explanation:
There is no picture but I can give you an explanation of how to do it. You would take each point (vertice) of the triangle and move it on the x-axis 3 and on the y-axis -2. So for example, a point-like (5,4) would become (8,2) You would then repeat this for the remaining vertices.
find the volume and the surface area of the shape
Answer: 192 is the volume of the shape
Step-by-step explanation: multiply the base area which is 6 and 8 equals to 48 and times the height so 48 Times 12 Equals 576. Sorryyy I don't know the surface area . Divide by 3 equals to 192
Ejemplos: 4 x 5 = 20 -4.3 = -12 -6-9 = 54 (7) (-7) = -49 Ejercicios: 1. Resuelve 1) -6.4= 2) 4.2 = 5 3) 3 • (-4) = 4) 6 (-4) = 5) (5) (-4) = 6) (-3) (-4) = 7 -5x6= 8) -2 x 1 = 9) -8 -2 = 10) -8 • 4 =
Answer:
37
Step-by-step explanation:
it just it
Explain how you could calculate the surface area of a square pyramid
There are two different ways to find surface area of square pyramid
1st
If you are given the slant height and the side length[tex]\sf surface \ area \ = \ a^2 + 2(a)(l)[/tex]
a = side lengthl = slant height2nd
If you are given the height and the side length[tex]\sf surface \ area = a^2+2a\sqrt{\dfrac{a^2}{4}+h^2 }[/tex]
a = side lengthh = heightAnswer:
sample response
Step-by-step explanation: :)
You would first calculate the area of the base, which is length times width. You would then calculate the area of the faces, which is 1 2 (base times height) and multiply the result by 4 for the 4 faces. Finally, add the area of the base and the areas of the faces.
Please help me with this please and thank you
Answer:
Nnnnnnnnnnnn
Step-by-step explanation:
L bozo
please help me please
Answer:
its 17
Step-by-step explanation:
do 2 step Equation
Please someone help i dont understand
ill upload the rest in a second
on a number line show all the values of X that have an absolute value less than three
Answer:
x can equal 2, 1, 0, -1, -2. A line graph is shown below.
Step-by-step explanation:
The absolute value means simply changing any negative number into a positive number. In this case, anything less than three and more than -3. If it was negative 3, then it would turn into 3. Which isn't less than. This means we can do : 2, 1, 0, -1, -2.
x can equal 2, 1, 0, -1, -2.
if i gain 50 coins per 52.2 seconds how long would it take to reach 400,500 coins
Answer:
418122 seconds
Step-by-step explanation:
First divide 400,500 by 50. That is 8010.
Then multiple 8010 by 52.2 and you answer is 418122 seconds. OR
6968.7 Minutes, OR 116.145 Hours, OR 4.839375 Days
ello mate, i need help with this here question can you help a girl out and if ya do ill give you brainlist :D
Answer:
B
Step-by-step explanation:
Add the value of the dots
0 + 3/8 + 3/8 + 4/8 + 5/8 + 7/8 = 22/8 = 2 6/8
Select the correct answer.
A rubber gasket has a circumference of 3.2 cm. When placed in service, it expands by a scale factor of 2. What is the circumference of the gasket when in service?
A.
1.6 cm
B.
3.2 cm
C.
6.4 cm
D.
13.2 cm
The required circumference of the gasket after dilation with scale factor 2 is 6.4 cm. Option C is correct.
A rubber gasket with a circumference of 3.2 cm is given. After expansion by scale factor 2 the circumference of the gasket is to be determined.
The circumference is defined as the boundary length of any circular shape.
Here,
Circumference of gasket = 3.2 cm
After dilation with scale factor 2, the circumference became.
Dilated circumference of gasket = 2*3.2 = 6.4 cm
Thus, the required circumference of the gasket after dilation with a scale factor of 2 is 6.4 cm.
Learn more about circumference here:
https://brainly.com/question/9319321
#SPJ5
0.6 greater than 0.59?
Answer:
Yes, 0.6 is greater than 0.59.
Step-by-step explanation:
The easiest way to determine which is greater, 0.6 or 0.59, is to plot both values on a number line.
PLEASEEEE HELLPPPP!!!!!!!!!!!!!!!!
is y= x/2+6 linear or non-linear
If x =2/5, y=-4/3, z=8/9, then verify that : x+(y+z) = (x+y) + z
according to distributive property
x+(y+z) = (x+y) + z
hope it helps...!!!
1) Advertisement XYZ Company charges $35 for the first four lines and $5.25 per extra
line to run the ad for one week. Jacqueline plans to sell her house and places a 15-line
ad.
a. What will Jacqueline's ad cost to run for one week?
b. What will Jacqueline's ad cost to run for four weeks?
Answer:
a) $92.75, b) $371Step-by-step explanation:
Let the cost be A.
a) Cost to run ad for one week:
A = 35 + 5.25 (15 - 4) = 35 + 5.25*11 = 92.75b) Cost to run ad for four weeks:
4A = 4*92.75 = 371Answer:
See below ↓↓
Step-by-step explanation:
Cost to run one week
$35 [first 4 lines] + $5.25 x 11 [15 - 4 = 11 remaining lines]$35 + $57.75$92.75Cost to run four weeks
Cost of one week x 4$92.75 x 4$368 + $3$371what is john locke's ideas that affected government?
John Locke's ideas related to government focus on the separation of powers and respect for the individual rights of citizens.
Who was John Locke?John Locke (1632-1704) was a British philosopher who stands out as one of the most important thinkers in history in the field of political philosophy, English empiricism, and classical liberalism.
What were his outstanding ideas?Some of the most popular and important postulates of John Locke were:
The State's main mission is to protect the three natural rights: life, liberty and private property.Individuals have a fourth right, the right to defend these rights, as well as any other individual freedom of citizens.The citizen cedes some rights to the State through a written consensus or constitution.The government must be made up of a king and a parliament. Parliament is where popular sovereignty is expressed and where laws are made that must be followed by both the king and the people.He described the separation of legislative and executive power.The authority of the State is sustained by the principles of popular sovereignty and legality.Power is not absolute but must respect human rights.Learn more about John Locke in: https://brainly.com/question/13346823
2. Find the surface area of the regular pyramid shown to the nearest whole
number.
Answer:
208m^2
Step-by-step explanation:
area of hexagon = 93.53 using its equation
area of single triangle = 0.5(6*6)
area of all triangles = 6(0.5(6*6))
total area = 207.53
NWN = 208
pls help me
What is the volume of the figure?
Answer:
V = 76 ft³
Step-by-step explanation:
We can find the volume of the figure by finding the sum of volume of the small rectangular prism and big rectangular prism.
V of a rectangular prism = length*hight* width
V = V (big rectangular prism) + V (small rectangular prism)
V = (8·4·2) +(3·2·2)
V = 64 + 12
V = 76 ft³
Miguel scored 74 points in his first 5 games this season. how many points has he scored per game?
14.8
Step-by-step explanation:[tex]\frac {74}{5}[/tex]____________________________________________________
Evaluate the equation/expression:[tex]14.8[/tex]
I hope this helps you
:)
Answer:
You can divided 74 by 5. 5 fits into 7 once so you subtract 5 and you are left with 2. Then bring down the 4 and you have 24. 5 fits into 24 only 4 times so you would subtract 20 from 24 and be left with 4. Then add a decimal point and a 0. Bring down the 0 and you'll have 40. 5 fits into 40 exactly 8 times so 40 - 40 = 0. The answer is 14.8
Step-by-step explanation:
Each side of a square barn is 9 meters long. What is the barn's area?
What is the barn's perimeter?
Answer:
Perimeter = 36 meters.
Area = 81 meters.
Step-by-step explanation:
To find the perimeter of a square you have to add all sides.
To find its area you have to multiply the base by the height of a square.
4.72x 10 to the 10th power in standard form
Answer:
47,200,000,000
Step-by-step explanation:
[tex]4.72*10^{10}[/tex] is in scientific form (notation).
To change this to standard form, we must move the decimal over the amount in the exponent. In this case, that is 10.
Answer:
Step-by-step explanation:
Provide the missing reasons for the proof.
Given: (AB) || (RS)
Prove: QA/QR= QB/QS
Answer:
Step-by-step explanation:
1) Given
2) <Q is congruent to <Q by reflexive prop of congruence
3) <QBA is congruent to <QSR by alternate interior angles theorem
4) Triangle QBA is similar to triangle QSR by AA theorem
5) QA/QR=QB/QS by CPSP (corresponding parts of similar polygons are proportional)
1-4
Stan volunteered to work overtime for 6 weeks. He worked an
average
of 47 hours per week. Use the equation h = 6 = 47 to find
the total number of hours Stan worked over the 6 weeks.
Answer:
282 Hours after 6 weeks
Step-by-step explanation:
Multiply the 6 weeks and the 48 hour a week adverage and theres your answer!
What is the value of tan 0 in the circle below
Answer:
tan theta = root3/3
see image
Step-by-step explanation:
The tangent is y/x in the unit circle. Use Keep-Change-Flip to simplify. See image. You also cannot leave a radical (square root) on the bottom of a fraction, so we need to "fix" that also. Multiply to rationalize (the "fix") see image.
If PQ || SR and PQRS is an isosceles trapezoid,
find m<1
Answer: B
Step-by-step explanation:
