To find how many terms of this sequence must be added to get 1440, we must know the arithmetic sequence equation to find any term in the sequence:
⇒ [tex]a_{n}=a_{1} +(n-1)d[/tex]
[tex]a_{n}[/tex] --> value of the nth number of the sequence[tex]a_{1}[/tex] --> first term of the sequencen --> position of the nth termd --> common differenceLet's examine the information given:
first term a = 5⇒ [tex]a_{1} =5[/tex]
common difference d = 2⇒ d = 2
Therefore the equation for finding the nth term of the sequence so far is:
[tex]a_{n}=5+(n-1)*2=5+2n-2=3+2n[/tex]
Now we want to find how many terms this sequence must be added to get 1440
General equation for adding all the terms = [tex]\frac{n(a_{1}+a_{n} ) }{2}[/tex]
[tex]a_{1}[/tex]: first term of the sequence[tex]a_{n}[/tex]: last term of the sequencen: number of terms in the sequence.Using all the information given, let's plug in the all the values:
[tex]1440=\frac{n*(5+(3+2n))}{2} \\1440=\frac{n*(8+2n)}{2} \\2880=8n+2n^2\\2n^2+8n-2880=0\\(2n+80)(n-36)=0[/tex]
To solve this we set (2n + 80) = 0 and (n-36) = 0
[tex]2n+80=0\\ 2n = -80\\n= -40[/tex] [tex]n - 36 =0\\n = 36[/tex]
In this case, n can only equal 36 since n cannot be negative.
Answer: 36 terms of this sequence must be added to get 1440.
Hope that helps!
General formula
a_n=a+(n-1)ds_n=n/2[2a+(n-1)dWe need n
n/2[2(5)+2(n-1)]=1440n[10+2n-2]=2880n[2n+8]=28802n²+8n-2880=0n²+4n-1440=0(n+40)(n-36)=0Take it positive
n=36paid well, HELP I need someone with tangent knowledge...
[tex]tan (M) = \frac{side-opposite-angle-M}{side-adjacent-angle-M} =\frac{8\sqrt{2} }{4} =2\sqrt{2}[/tex]
Hope that helps!
ps. I attached a sheet of trigonometry identities
TODAY'S BRAIN TEASER
Solve it and gain 50 points plus BRAINLIEST
Solve any two questions out of three
WRONG COPIED OR SPAM WILL BE INTOLERABLE
SO SO SO NOT WASTE TIME IF YOU DON'T KNOW
GOOD LUCK
Answer:
Question 3
Find the range of the function for the domain 2 < x < 3
[tex]f(2)=(2)^2-1=3[/tex]
[tex]f(3)=(3)^2-1=8[/tex]
Therefore, the range of [tex]f(x)=x^2-1[/tex] is [tex]3 < f(x) < 8[/tex] with domain 2 < x < 3
This means that for the function to be continuous, when the domain is x=3, f(x) = 8
[tex]f(3)=2a(3)=6a[/tex]
[tex]\implies 6a=8\implies a=\dfrac43[/tex]
Similarly, when the domain is x > 3, f(x) > 8
[tex]f(3)=b(3)-4=3b-4[/tex]
[tex]\implies 3b-4 > 8 \implies b = 4[/tex]
Therefore, [tex]a=\dfrac43[/tex] and b = 4
Question 5
[tex]\textsf{let}\:u=\ln (x)[/tex]
[tex]\implies \dfrac{du}{dx}=\dfrac{1}{x}\implies dx=x\:du[/tex]
[tex]x=1\implies u=0[/tex]
[tex]x=3 \implies u=\ln 3[/tex]
[tex]\implies \displaystyle \int\limits_{1}^{3} \dfrac{\ln x \sin (\ln x)}{x} \,\:dx=\displaystyle \int\limits_{0}^{\ln 3} \dfrac{u \sin u}{x} \, \cdot x\:du=\displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du[/tex]
Use integration by parts:
[tex]\displaystyle \int u\dfrac{dv}{dx} \, dx=uv- \displaystyle \int v \dfrac{du}{dx} \, dx[/tex]
[tex]\textsf{where}\:u=u\:\textsf{and}\:\dfrac{dv}{dx}=\sin u[/tex]
[tex]\implies \dfrac{du}{dx}=1\:\textsf{and}\:v=\int \sin u=-\cos u[/tex]
[tex]\implies \displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du=-u \cos u- \int\limits_{0}^{\ln 3}-\cos u \,\:du[/tex]
[tex]\begin{aligned}\implies \displaystyle \int\limits_{0}^{\ln 3} (u \sin u) \, \:du & =\left[-u \cos u+ \sin u\right]_{0}^{\ln 3}\\ & =[- (\ln 3) \cos (\ln 3)+ \sin (\ln 3)]-[-0 \cos (0)+ \sin (0)]\\\\ & =[- (\ln 3) \cos (\ln 3)+ \sin (\ln 3)]-0\\\\ & = 0.3908925527...\end{aligned}[/tex]
Part A
The distance that Eric can travel by driving to work can be represented by a linear equation because he sets his cruise control and is moving at a constant rate. He drives at a rate of 75 mph on the interstate for a total of 1.5 hours.
What is the linear equation that can be used to find the distance that Eric travels each day? In the equations d = distance traveled, r = rate and t = time taken.
A. d = rt
B. d = t/r
C. d = r/t
D. d = r + t
E. d = r/75
Part B
What is the total distance that Eric travels each day?
A. 37.5 miles
B. 75 miles
C. 112.5 miles
D. 150 miles
E. 187.5 miles
WILL GIVE BRAINLIEST AND 40 POINTS
Answer:
Step-by-step explanation:
There's a saying to this kind of equation: Rate + Time = Distance and B best fits the saying, so B must be right (Don't quote me on that, it may be wrong)
the linear equation that can be used to find the distance that Eric travels each day is A. d = rt & the total distance that Eric travels each day is C. 112.5 miles.
What is speed?Speed is measured as distance moved over time.
here, given that,
He drives at a rate of 75 mph on the interstate for a total of 1.5 hours.
so, the linear equation that can be used to find the distance that Eric travels each day is A. d = rt
i.e. d= 75*1.5
=112.5
& the total distance that Eric travels each day is C. 112.5 miles.
To learn more on speed click:
brainly.com/question/28224010
#SPJ2
Jorge went to Target to buy a Lego Kit. The Lego Kit is worth $25.00 plus a 8.5% sales tax. How much is Jorge paying in sales tax?
Answer:
Price before Taxes: $ 25.00
Sales Tax (8.5%): $ 2.13
Total Price with Tax: $ 27.1
Step-by-step explanation:
If 14 g of a radioactive substance are present initially and 4 yrs later only 7 g remain, how much of the substance will be present after 8 yrs?
5.25 g
Step-by-step explanation:
The half-life of a radioactive substance is the amount of time it takes for half the mass of the substance to decay.
In this question no calculations are required to get half-life. This is because it is given that it took 3 years for the 14g to halve to 7g.
To find amount of the substance after a further 4 years, we’ll use the formula;
Final amount = initial amount / 2ⁿ
Where n = elapse time / half-life
We begin by finding n;
n = 4 years / 3 years
= 4/3
Final amount;
= initial amount / 2ⁿ
= 7 / 2 ^ (4/3)
= 5.25 g
Learn More:
For more on half-lives calculations check out;
brainly.in/question/3080737
https://brainly.com/question/1831303
https://brainly.com/question/2674699
find the area sector of AOB
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=12\\ \theta = 70 \end{cases}\implies \begin{array}{llll} A=\cfrac{(70)\pi (12)^2}{360}\implies A=28\pi \\\\\\ A\approx 87.96~cm^2 \end{array}[/tex]
HELP / 100 POINTS
This shape has _______ faces.
This shape has 5 vertices.
This shape has 8 edges.
Answer:
5 faces
Step-by-step explanation:
A traingular prism has 5 faces. The square on the bottom and the four traingles that make up the sides.
hope this helps :)
Answer:
5
8
5
step by step
Love your pfp
If a rectangle has a base of 6 units, and a helght of 8 units, what Is Its area?
Answer:
Answer is 48
Step-by-step explanation:
6x8 = 48
Hope it helps!
Answer:
area=b•h
6 units • 8 units = 48 units²
Classify Two-Dimensional Figures question 5
Answer:
Examples of 2D shapes
2D Shape Properties
Pentagon A shape with five sides and five equal angles.
Kite A quadrilateral with two pairs of sides of the same length.
Rhombus A quadrilateral with both pairs of opposite sides parallel and all sides of the same length. Unlike a square, however, its angles are not all 90˚.
Step-by-step explanation:
By rewriting the formula for the multiplication rules you can write a formula for finding conditional probabilities. The conditional probability of event b Occurring giving that event a has occurred is
The probability that an airplane flight departs on time is 0.91
The probability that a flight arrives on time is 0.89.
The probability that a flight departs and arrives on time is 0.84
The probability that a flight departed on time given that it arrives or
(Round to the nearest thousandth as needed
The probability that a flight departed on time given that it arrives is 0.92
Conditional ProbabilityThe conditional probability of event B occurring giving that event A has occurred is expressed as
P(B|A) = P(A and B)/P(A)
Given the following parameters
P(A and B) = The probability that a flight departs and arrives on time = 0.84
P(A) = The probability that an airplane flight departs on time = 0.91
P(B | A) = 0.84/0.91
P(B | A) = 0.92
Hence the probability that a flight departed on time given that it arrives is 0.92
Learn more on conditional probability here: https://brainly.com/question/25870256
#SPJ1
Find the exact value of the trigonometric expression when
sin(u) = − /13 and cos(v) = − 4/5. (Both u and v are in Quadrant III.)
tan(u+v)
Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.
Expand the tan expression using the angle sum identities for sin and cos :
tan(u + v) = sin(u + v) / cos(u + v)
tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]
Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.
Recall that for all x,
cos²(x) + sin²(x) = 1
and it follows that
cos(u) = - √(1 - sin²(u)) = -12/13
sin(v) = - √(1 - cos²(v)) = -3/5
Then putting everything together, we have
tan(u + v)
= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]
= 56/33
(or, if sin(u) = -12/13, then tan(u + v) = -63/16)
IRIS BULBS
First half-dozen
Second half-dozen
Each additional bulb
$5 per bulb
$4 per bulb
$3 per bulb
Which of the following calculations represents the
cost of 2 dozen iris bulbs?
A. 24 x $3
B. $5 + (2 x $4) + (12 x $3)
C. (6 x $5) + (6 x $4) + (12 $3)
D. (12 x $5) + (12 $4)
E.
(3 x 85) + (3 x sa) + (12 x $3)
+
$3
The calculation that represents the cost of 2 dozen iris bulbs is ($5 * 6) + ($4 * 6) + ($3 * 12)
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
The cost of 2 dozens of iris bulbs is given by the equation:
Cost = ($5 * 6) + ($4 * 6) + ($3 * 12)
The calculation that represents the cost of 2 dozen iris bulbs is ($5 * 6) + ($4 * 6) + ($3 * 12)
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Solve.
2 What is the volume of this rectangular prism?
Show your work.
Step-by-step explanation:
if width = 3 length = 5 hight = 10
Volume of rectangular prism = 3×5×10
= 150
Sarah is designing a triangular pyramid made of all glass to go on top of a building. All of the faces of the pyramid have a height of 17 feet and a base of 20 feet.
How much glass is needed?
A.
680 sq ft
B.
340 sq ft
C.
2,040 sq ft
D.
1,360 sq ft
Answer:
Area of a triangle is 1/2 x base x height.
area of triangle = 1/2 x 20 x 17 = 170 square feet.
the image shows 4 triangles, total area = 170 x 4 = 680 square feet.
the answer is A. 680 sq. ft.
Hope this helps you!!
Please Mark me as Brainleast!!!!!!!!!!!!!
Answer: the answer is a which is 680 ft²
Step-by-step explanation: we will make 17 Times 220 divided by 2 equals 170 times by 4 equals 680 . Hope it helps you buddy .
Using each digit once, list all the
3-digit numbers that can be made
From 1, 4, and 7.
Answer:
1,4,7 1,74. 4,7,1 ,4,1,7 ,7,4,1
Please help !
∆ABC is similar to ∆DEF. The measure of AB = 6, the measure of DE = 18, the measure of BC = 12, and the measure of DF = 15.
Find the measures of AC and EF.
AC =
_______________
EF =
[tex] \frac{ab}{de} = \frac{bc}{ef} = \frac{ac}{df} [/tex]=k
[tex] \frac{6}{18} = \frac{12}{ef} [/tex]
[tex]ef = 36[/tex]
from this[tex] \frac{12}{36} = \frac{ac}{15} [/tex]
[tex]ac = 5[/tex]
[tex] \frac{6}{18} = \frac{12}{36} = \frac{5}{15} = \frac{1}{3} [/tex]
I hope it helps
Help me please please!!!!!!
Answer:
And great great the owner is 44
Step-by-step explanation:
or 36 because you have to add all sides
35) Use a formula to find the area of the figure.
a
15 in.
7 in.
20 in.
Answer:
c:) 150 in²
Step-by-step explanation:
It's basically and SAS triangle
SAS is Side, Angle, Side
side 15 in angle 90° and 20 in
a = 20 in
b = 25 in
c = 15 in
Angles:
A = 53.1301 °
B = 90 °
C = 36.8699 °
Other:
P = 60 in
s = 30 in
K = 150 in2
r = 5 in
R = 12.5 in
Agenda:
A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
5x+5=3x+4 solve as a fraction
Answer:
[tex] \hookrightarrow \sf \bold{ - \frac{1}{2} }[/tex]
Step-by-step explanation:
⇢ [tex] \bold{5x+5=3x+4} [/tex]
⇢ - 3x + 5x = 4 - 5
⇢ 2x = -1
⇢ 2x/2.= -1/2
⇢ x = -1/2
5x+5=3x+4
5x-3x=4-5
2x=-1
2x/2=-1/2
x=-1/2
Ryan's mother recorded how many donuts he has eaten over the past few months. cake donuts 3 chocolate frosted donuts 48 maple donuts 7 cream-filled donuts 12 glazed donuts 20 Considering this data, how many of the next 45 donuts Ryan eats would you expect to be cream-filled donuts?
Answer:
6
out of the total donuts (90), Ryan ate 12 cream filled donuts. 45 is half of that, therefore he should eat half the cream filled donuts
Please Help
Solve for x.
3/5x+5=4/5
Enter your answer in the box.
X=
Answer:
x = -1/7
Step-by-step explanation:
3/5x + 5 = 4/5
3/5x + 5/1 = 4/5
3 + 25x/5x = 4/5
4(5x) = 5(3 + 25x)
20x = 15 + 125x
-15 = 125x - 20x
-15 = 105x
-15/105 = x
-1/7 = x
What are the coordinates of A?
factor completely. Be sure to show all of your work.
g(x)=x3-x2-4x+4
Find the zeros of the function. Be sure to show all of your work.
Find the y-intercept of the chosen function. Be sure to show all of your work.
Describe the end behavior of the graph.
The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The zeros of the function is at:
g(x) = 0, hence:
x³ - x² - 4x + 4 = 0
(x - 1)(x² - 4) = 0
(x - 1)(x + 2)(x - 2) = 0
x = 1, x = -2 and x = 2
The y intercept is at x = 0, hence:
g(0) = 0³ - 0² - 4(0) + 4 = 4
The function g(x) = x³ - x² - 4x + 4 has zeros at 1, 2 and -2. The y intercept is at 4.
Find out more on equation at: https://brainly.com/question/2972832
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
Answer:f θ =2sin θ + square root of 3.
Step-by-step explanation: I think this is right
Which statement describes the transformation of figure 2 into figure 3?
Answer:
2 reflection across the y axis
PLEASE HELP PLEASE PLEASE
Answer:
True! We can tell that it is still there through weight becuase weight is a method of evidence/measurement. Hope this helps!
Find the area of the figure (Explain it please)
Check the picture below.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(160)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(90)(120)}}\implies 3200~~ + ~~5400\implies 8600[/tex]
what is the reciporcal of 7/6
Answer:
6/7
Step-by-step explanation:
you juts switch the top and bottom
Brainleist please
ABC
Question 2
A helicopter landing pad is built on the roof of a hospital. Helicopters land inside the circular part of the pad. This part has a diameter of 50 feet.
What is the area inside the circle on the landing pad to the nearest whole number?
A
1963 feet2
B
3927 feet2
C
7854 feet2
D
15,708 feet2
Answer:
A
Step-by-step explanation:
If 50 is the diameter that thr radius is 25 and the equation to find the area of a circle is pi(r^2). So you would do pi(25^2) and that is 1963
HELP!
You own a square plot of land and you want to determine its surface area. You know that one side of land measures 10 longer than what the appraisers estimated, but you lost the paperwork with the information. Write an expression to represent the area of your land.
What is the area of the property if x = 12?
The area of the property is the product of its dimensions, and the expression for the area is (x + 10)²
How to determine the expression for area?The area of the land is the product of its dimensions.
Let the length and the width of the land be x.
So, the area measured by the appraisal is:
Area = x²
One side of the land is 10 more than the measured length.
So, we have:
Area = (x + 10)²
Substitute 12 for x
Area = (12 + 10)²
Evaluate
Area = 484
Hence, the area of the property is 484
Read more about area at:
https://brainly.com/question/14137384