Given:
The sequence is:
[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]
To find:
The formula for the nth term in the given sequence.
Solution:
We have,
[tex]17,-\dfrac{17}{8},\dfrac{17}{27},-\dfrac{17}{64},\dfrac{17}{125},...[/tex]
The given sequence can be written as
[tex]\dfrac{17}{1^3},-\dfrac{17}{2^3},\dfrac{17}{3^3},-\dfrac{17}{4^3},\dfrac{17}{5^3},...[/tex]
The sign are alternative and the absolute value of each term can be defined by the expression [tex]\dfrac{17}{n^3}[/tex], where n is a natural number.
So, the required formula is:
[tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex]
Therefore, the formula for nth term in the given sequence is [tex]a_n=(-1)^{n+1}\dfrac{17}{n^3}[/tex].
1. Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.
Answer:
So we'll use trig to solve this because it's a right triangle. The hypotenuse is the ladder (h) and the two smaller sides are the ground and the vertical wall (w).
That angle ladder makes with the ground = €
SOH: sin € = opposite/hypotenuse
No the ladder won't be safe!!!
Now let's make it safe:
The ladder's length (w) is constant, so stays 12
So now let's ask in an inequality what height will be safe (75° or less)
what does that mean?? well as long as you put the ladder against the wall so that the height from ground to top of the ladder is < 11.6 ft!!
Hope that helps! :-D
Step-by-step explanation:
Answer:
not safe it is 78.5 degrees
Step-by-step explanation:
Consider the point on the polar graph below.
Represent the point's location in the polar form (r,θ) where 0≤r<50 and 0≤θ<2π.
(r,θ)=
Represent the point's location in the polar form (r,θ) where 0≤r<50and 2π≤θ<4π.
(r,θ)=
Represent the point's location in the polar form (r,θ) where 0≤r<50and −2π≤θ<0.
(r,θ)=
J0IN G00GLE MEET GIRL$
wnp-hxru-ipf
What is the graph of the function f(x) = the quantity of x squared plus 4 x minus 12, all over x plus 6 ? (1 point)
Solve for x in the equation x2 + 4x-4-8.
O x= -6 or x = 2
O x--2+/- 2_/2
O x=-2 or x = 6
O x-2+/-2_/3
The solution of the equation is x= -6 or x = 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
We have the Equation x²+ 4x -4 - 8 or x² + 4x - 12.
Now Factorizing the equation we get
x² + 4x - 12
= x² + 6x - 2x - 12.
= x (x+ 6) - 2( x+ 6)
= (x -2) (x+ 6)
So, x-2 = 0 or x+ 6= 0
x= 2 or x= -6
Thus, the solution of the equation is x= -6 or x = 2.
Learn more about Equation here:
https://brainly.com/question/29657992
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Can someone please explain the answer step by step pls.
Answer:
a) x= 29, y= 87
b) x= 19, y= 45
Step-by-step explanation:
Q5. a) Let the first number be x and the second number be y.
The sum of 2 integers is 116.
x +y= 116 -----(1)
The second number is three times the first number.
y= 3x -----(2)
Substitute (2) into (1):
x +3x= 116
4x= 116
x= 116 ÷4
x= 29
Substitute x= 29 into (2):
y= 3(29)
y= 87
b) Let the smaller number be x and the larger number be y.
x +y= 64 -----(1)
y -x= 26 -----(2)
Since we have to use substitution to solve the equations, let's first rewrite an equation to make one of the variables the subject of the equation.
From (1):
x= 64 -y -----(3)
Substitute (3) into (2):
y -(64 -y)= 26
y -64 +y= 26 (expand bracket)
2y= 26 +64 (simplify, +64 on both sides)
2y= 90
y= 90 ÷2
y= 45
Substitute y= 45 into (3):
x= 64 -45
x= 19
The bottom of a swimming pool is 10 feet below the surface of the water in the pool. The surface of the water is represented by the number 0, and the bottom of the pool is represented by the number -10. The pool’s diving board is the same distance above the surface of the water as the bottom of the pool is below the surface of the water. HELP I WLL GIVE THE CROWN THNG AND MORE POINTS
Answer:
I think its +10 above surface
Amir bought a camera 5 year ago for RM1500. He plans to sell his camera at a price of RM1800. What percentage of the profit or loss?
Answer:
20% profit
Step-by-step explanation:
Hope this helps
Pattern A follows the rule "subtract 3" and Pattern B follows the rule "subtract 4." Pattern A 20 17 14 11 8 Pattern B 24 20 16 12 8 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. (17, 20) (20, 24) (12, 11) (8, 8) (14, 20) (20, 16)
Answer:
(20,24) (17,20) and (8,8)
Hope this helps
Step-by-step explanation:
PLEASE HURRY PLEASE :(
Answer:
Step-by-step explanation:
height after x seconds = -16x² - 2x + 600
-16x² - 2x + 600 = 450
16x² + 2x - 150 = 0
8x² + x - 75 = 0
Quadratic formula
x = [-1 ± √(1² – 4·8(-75))] / [2·8]
= [-1 ± √2401] / 16
= [-1 ± 49] /16
= 3, -3⅛
-3⅛ is an extraneous solution, so x = 3 seconds.
help please! by what fraction would you multiply 8 1/2 so that the proudct is about 5 explain your reasiong
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Answer:
5/8 or 5/9
Step-by-step explanation:
The fraction will be exactly ...
5/(8 1/2) = 10/17 ⇒ (8 1/2)×(10/17) = 5
__
The fraction will be approximately ...
5/8 or 5/9
The denominator will be a number that makes (8 1/2)/(denominator) ≈ 1. For that denominator, the numerator will be 5, so that we have ...
(8 1/2) × (5/denominator) ≈ 5
(8 1/2)/(denominator) ≈ 1 . . . . . . . . divide by 5
If we want the denominator to be an integer, we could choose either 8 or 9. If we choose 8, the result will be slightly more than 5; if we choose 9, the result will be slightly less.
(8 1/2) × (5/8) = 5.3125 ≈ 5
(8 1/2) × (5/9) = 4.722... ≈ 5
Either 5/8 or 5/9 will give a product of about 5.
Answer:
Step-by-step explanation:
the 20% tip on a $8 sandwich
Answer:
Tip of $1.60
The total is $9.60
Step-by-step explanation:
(20% × $8) + $8
$1.60 + $8
$9.60
Which line shown appears to have a Y-intercept of 3?
A. I
B. II
C. III
D. IV
E. none of the above
What is the answer for B
Please help and use the proper theorem!
2. Jason can put his money in a savings account and earn about 12 cents in interest this month, or he can
loan it to Matt, who says he'll return the money plus $20 at the end of the month. He loans it to Matt.
a. The opportunity cost is
Answer:
12 cents
Step-by-step explanation:
opportunity cost of the next best option forgone when one alternative is chosen over other alternatives
by loaning matt the money he forgoes the opportunity to earn 12 cents in interest. this is his opportunity cost
Graph the function f(x)= -³√x+2.
Answer:
Step-by-step explanation:
a bag contains 1 red beads,2 yellow beads,2 green beads and 1 blue beads
a bead is chosen at random
a)what is probability that it is green ?
b)what probability that it is green or yellow
Answer:
a) 2/6 b) 4/6
Step-by-step explanation:
You add the amount of beads: 1+2+2+1= 6
And take the amount of green beads and put it over the total amount so 2/6
For b you do the same but add the green and yellow beads and put that over the total amount 4/6
Answer:
Step-by-step explanation:
a) 2/6 = 1/3
b) green or yellow = (2/6 x 1/5) + (2/6 x 1/5) = 1/15 x 1/15 = 1/225
im not sure if my answers are correct
please help!!!
i would really apreciate it
Answer:
it should be the graph on the bottom right
Step-by-step explanation:
The income should be more than the cost in order to make a profit and that happens for Leanne when she sells 8 quilts, so the 8 should be on the x-axis (the axis named "Quilts Sold")
The income should be 0 in the beginning bc when she sells 0 quilts she will be earning 0.
after selling 8 quilts her income will be higher than her costs
(Though naming the y-axis as "profit" is not accurate bc when she sells 0 quilts she will lose money since she will be spend money to make the quilts but not earn the money to compensate for the cost).
with all of these reasons combined the correct should be the one on the bottom right
solve 9x-10÷2=x+9
explain how
Answer:
x = 4
Step-by-step explanation:
profesor de Educación Física Oriente y occidente hacer Cada día los siguientes recorridos lunes 5,12 y kilómetros más de 6 koma 23 kilómetros miércoles 7,0 2 km y jueves 12,0 7 km y el viernes 15,0 1 kilómetros Cuántos kilómetros recorre cada estudiante a final de la semana datos operacion
Answer:
ask in English then only I will answer
[tex]533 {?}^{2} \times \frac{?}{?} [/tex]
Answer:
53
Step-by-step explanation:
jddhhevehevevegejwkwveehjebebsjsbs
Find the value of x
Answer:
x=80
Step-by-step explanation:
(x+30)=110 because they are vertically opposite angles.
x+30=110
x=110-30
x=80
Answer:
x = 80 degrees
Step-by-step explanation:
x + 30 = 110
- 30 = -30
x = 80 degrees
please please help me I will mark brainlist !!
Answer:
9. B. 32 millimeters
10. C. 7 inches
11. C. 56.24 millimeters
13. B. 14.13 square feet
Step-by-step explanation:
9. Radius of a circle or any circular shape = ½ of its diameter
Diameter of the disk = 64 millimeters
Radius of the disk = ½(64) = 32 millimeters
10. Width of the cooler = 6 in.
Length = 8 in.
Volume = 336 in.³
Height = ?
Formula for volume of a rectangular prism = L*W*H
Plug in the values
336 = 8*6*H
336 = 48*H
Divide both sides by 48
336/48 = H
H = 7 inches
11. A dime has a circular shape
The circumference of the dime = circumference of a circle = πd
Where,
d = 17.91 millimeters
π = 3.14
Plug in the values
C = 3.14 × 17.91 = 56.2374
≈ 56.24 millimeters (nearest hundredth)
12. Area of the top of the desk = area of semicircle = ½ × πr²
Where,
r = ½(6) = 3 ft
π = 3.14
Plug in the values
Area = ½ × 3.14 × 3² = ½ × 3.14 × 9
Area = 14.13 square feet
Can anyone help! I can’t figure out the answer.
what
is the quistion cause can't nobody see that
PLZ HELP ASAP (BRAINLIEST + 30 POINTS (show all work)
(7.03) Determine the missing term from the perfect square trinomial. Show ALL work.
x2 − ______+ 36
Write in factored form: ( )2
Answer:
x² - 12x + 36
factored: (x - 6)(x - 6)
Rachel received a monthly raise of $105.25. If this represented a 5.5% increase, what is her monthly salary after the raise?
A. $1,913.64
B. $1,964.13
С. $2,018.89
D. $2.089.18
Answer:
C
Step-by-step explanation:
105,25:5,5*105.5=2018,89
A store gives customers a markup of 13%. If the store sells a belt for $25, what was the wholesale price paid for the belt by the store?
Answer:
$22.12
Step-by-step explanation:
Let x be the wholesale price (the price before adding the markup).
The markup is 13%, so 13% of x is added to x.
x + 13%x = $25
x + 0.13x = 25
1.13x = 25
x = 25/1.13
x = 22.12
you deposit $1600 in a bank account. find the balance after 3 years if the account pays 1.75% annual interest compounded quarterly
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Answer:
$1686.05
Step-by-step explanation:
The amount with compound interest is ...
A = P(1 +r/n)^(nt)
for principal P earning annual rate r compounded n times per year for t years.
A = $1600(1 +0.0175/4)^(4·3) = $1686.05
The balance after 3 years is $1686.05.
Answer:
the answer is $1686.05
Step-by-step explanation:
:))
PLEASE HELP!!
Solve for m
m+7=3+m+4
Answer:
M = -7
Step-by-step explanation:
It makes sense if you replace it in for M! Hope this helps and have a great day!
What is the range of this function?
{(-2,3), (0,1), (1, -2), (2,5)}
Answer:
3,1,-2,5
Step-by-step explanation:
The range means the y number of the domain (x)
Answer:
Hi! The answer to your question is {3,1,-2,5)
Step-by-step explanation:
The Domain is a set of all the values of x. The Range is a set of all the values of y.
Hope this helps **™
- Brooklynn Deka
❣❣❣
The scatterplot below shows a data set
and an approximate trend line for the
data.
7
6
5
3
1
0 10 20 30 40 50 60 70
Which is the best estimate of the value of
x that corresponds to y = 3? (8.18, 8.10,
SIE, SIF)
Where does
F 35
the line y = 3
G 25
intersect the
trend ine?
H 50
10
Pls help I don’t know hot to multiply the last part 8 2
Answer:
8^2 = 64
Step-by-step explanation:
Hi! Okay, let's get started!
[tex]8^{2}[/tex] is what you need help with right?
So, that equals to 8 x 8.
8 x 8 = 64, so it would be 64
Hope that helps!
-Aphrodite :)