Given:
The explicit function is:
[tex]f(n)=1000\left(\dfrac{1}{4}\right)^{n-1}[/tex]
To find:
[tex]f(1)=?,r=?[/tex] and first 5 terms.
Solution:
The explicit formula a geometric sequence is:
[tex]f(n)=ar^{n-1}[/tex] ...(i)
Where, a is the first term and r is the common ratio.
We have,
[tex]f(n)=1000\left(\dfrac{1}{4}\right)^{n-1}[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1000[/tex]
[tex]f(1)=1000[/tex]
And,
[tex]r=\dfrac{1}{4}[/tex]
For [tex]n=1[/tex],
[tex]f(1)=1000\left(\dfrac{1}{4}\right)^{1-1}[/tex]
[tex]f(1)=1000\left(\dfrac{1}{4}\right)^{0}[/tex]
[tex]f(1)=1000(1)[/tex]
[tex]f(1)=1000[/tex]
For [tex]n=2[/tex],
[tex]f(2)=1000\left(\dfrac{1}{4}\right)^{2-1}[/tex]
[tex]f(2)=1000\left(\dfrac{1}{4}\right)^{1}[/tex]
[tex]f(2)=1000\times \dfrac{1}{4}[/tex]
[tex]f(2)=250[/tex]
Similarly, substituting [tex]n=3,4,5[/tex], we get
[tex]f(3)=62.5[/tex]
[tex]f(4)=15.625[/tex]
[tex]f(5)=3.90625[/tex]
Therefore, [tex]f(1)=1000,r=\dfrac{1}{4}[/tex] and the first five terms are [tex]1000,250,62.5,15.625,3.90625[/tex].
Given:
The explicit function is:
To find:
and first 5 terms.
Solution:
The explicit formula a geometric sequence is:
...(i)
Where, a is the first term and r is the common ratio.
We have,
...(ii)
On comparing (i) and (ii), we get
And,
For ,
For ,
Similarly, substituting , we get
Therefore, and the first five terms are .
A curve is given the equation xy=25 and the equation of a line y=mx+b.
i. Express m in terms of b given that the line and the curve have one and only one point of intersection.
ii. If the line intersects the curve in two distinct points, find the set of values of b, given m=-5
Answer:
Below in bold.
Step-by-step explanation:
i, This is a rectangular hyperbola with symmetry about the line y = -x
If it touches the graph at one point only then
y = 25/x
y = mx + b so
25/x = mx + b
mx^2 + bx + 25 = 0
Using the quadratic formula:
x = (-b + sqrt(b^2 - 25*4*m)) / 2m
Now there's only one value of x so
b^2 - 25*4*m = 0
b^2 = 100m
m = b^2/100.
m = +/-b/10.
ii In this case b^2 > 100m
If m = |-5|
b^2 > 500
b > +/-√500
So b > √500 or b < -√500.
A rectangular tank with length 50 cm and width 30 cm contains 36 litres of water. Find the depth of the water.
Answer:
24cm
Step-by-step explanation:
Given data
Length=50cm
Width= 30cm
Volume = 36liters
=36000cm^3
We know that the expression for volume is
V= L*W*H
substitute
36000=50*30*H
36000= 1500*H
H= 36000/1500
H= 24cm
Hence the height is 24cm
WILL GIVE BRAINLIEST IF BOTH QUESTIONS ARE CORRECT!!!
Answer:
69824.21
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＼＼ Λ＿Λ This is Memecat. Help
＼( 'ㅅ' ) memecat take over
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o(*≧□≦)o
Step-by-step explanation:
find the value of x in the triangle shown below
Answer:
nice
Step-by-step explanation:
Answer:
x=32
Step-by-step explanation:
So a triangles angles add up to 180 degrees. . .
2x+116=180
64=2x
x=32
I completely forgot how to do this, so if you can answer and give an explanation, I’d really appreciate it!
Answer:
C
Step-by-step explanation:
Well to do this we can eliminate answers that seem unreasonable and just calculate the ones we think might be it
We know it can't be the first one or the second since its perimeter isn't 32
It could be the third one so we can check the perimeter
3+3+16+16=38
so it is the third one
WILL GIVE BRAINLIEST!!!
Question 5(Multiple Choice Worth 1 points)
(07.01 MC)
A box has 6 beads of the same size, but all are different colors. Tania draws a bead randomly from the box, notes its color, and then puts the bead back in the box. She repeats this 3 times. What is the probability that Tania would pick a yellow bead on the first draw, then a blue bead, and finally a yellow bead again?
1 over 216
1 over 36
1 over 6
1 over 2
Answer:
multiply 1/6 by 1/6 by 1/6 essentially
(1/6)^3
1/216
Step-by-step explanation:
Each specific bead color has (each time) a probability of being drawn.
Hence the final probability is 1/216
Answer:
1 over 216
Step-by-step explanation:
Plz help!!!!!
ctc math
Answer:
7,13,37,55,103
Step-by-step explanation:
y = 5 + 2x^2
if x =1
y = 5 + 2(1)^2
1^2 = 1
2 x 1 = 2
y=5 + 2 or y = 7
you substatute each one in for x to solve for y
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h ( t ) = − 16 t 2 + 16 t + 480 h(t)=−16t 2 +16t+480, where t is the time in seconds and h is the height in feet. What is the maximum height that Jason reaches?
Answer:
484feet
Step-by-step explanation:
If the height as a function of time could be modeled by the function h(t)=−16t^2 +16t+480, where t is the time in seconds and h is the height in feet.
The maximum height of Jason occurs when dh/dt = 0 (velocity is zero)
dh/dt = -32t + 16
0 = -32t + 16
32t = 16
t = 16/32
t = 1/2
t = 0.5secs
Get the maximum height
Recall that h(t)=−16t^2 +16t+480
Substitute t = 0.5
h(0.5)=−16(0.5)^2 +16(0.5)+480
h(0.5) = -4 + 8 + 480
h(0.5) = 4 + 480
h(0.5) = 484
Hence the maximum height reached by Jason is 484feet
The maximum height that Jason reaches is h = 484 feet and it will be reached at t = 0.5 sec.
How to find the maximum of a polynomial function?Let the function be denoted by [tex]y = f(x)[/tex]
If it is twice differentiable, then, firstly, we differentiate it with respect to x and equate with 0 to find the critical values.
Let the obtained critical values be [tex]x_1, x_2, ... x_n[/tex]
The second derivative of that function is then evaluated on those critical values.
The [tex]i^{th}[/tex] critical value has got the maximum if [tex]f''(x_i) < 0[/tex]
That means, if at [tex]x = x_i[/tex] , we get
[tex]f'(x-i) = 0\\and\\f''(x_i) < 0[/tex]
Then that point is where function will have maximum.
If [tex]f''(x_i) > 0[/tex], then the point where the function will have minimum
If value of second rate at point [tex]x_i[/tex] is 0, then we go for third rate of function and check the same facts so on for upper rate(if they exist).
For the given case, we're given the height function as:
[tex]h(t) = - 16t^2 + 16t + 480[/tex]
The function is infinitely differentiable as its polynomial(by a theorem).
Its first and second rate with respect to 't', we get;
[tex]h(t) = - 16t^2 + 16t + 480\\h'(t) = -32t + 16\\h''(t) = -32 < 0[/tex]
Thus, all critical points will be maximum points.
The critical points are evaluated by [tex]h'(t) = 0[/tex]
They are calculated as:
[tex]h'(t) = 0\\-32t + 16 = 0\\t = 0.5 \: \rm sec[/tex]
The height at t = 0.5 s is evaluated as:
[tex]h(0.5) = - 16(0.5)^2 + 16(0.5) + 480 = 484 \: \rm feet[/tex]
Thus, at time 0.5, the height function will be at its maximum value(484 feet). That means, the height of Jason will be maximum when time will be 0.5 seconds from initial time.
Learn more about maximum and minimum values here:
https://brainly.com/question/13333267
Ellen is drawing two polygons. One of the polygons has 3 more angels then the other. What shapes could she be drawing?
Answer:
Step-by-step explanation:
This is quite and easy one, but also vague at the same time.
A polygon is a shape with 5 or more sides, so, if she were drawing a pentagon, then the second polygon has to be an octagon. A pentagon has 5 sides, and an octagon has 5 + 3 sides
In the same vein, if she were drawing a hexagon, with 6 sides, the other polygon has to be monsoon, with 6 + 3 sides.
A heptagon also gives us a 7 + 3 polygon, in decagon.
All in all, it depends on the first polygon she's drawing as the question is vague in that aspect.
F(x)=400-4/5x find the function and intercepts
Answer:
The x-intercept is (500, 0); the y-intercept is (0, 400).
Step-by-step explanation:
F(x)=400-4/5x is already a function: a function of x.
To find the y-intercept, set x = 0 and calculate F(0):
F(0) = 400 - 0 = 400; the y-intercept is (0, 400).
To find the x-intercept, set F(x) = y = 0 and solve for x:
0 = F(x) = 400 - (4/5)x, or (4/5)x = 400. To isolate x, multiply both
sides by (5/4): x = (5/4)(400) = 500. The x-intercept is (500, 0).
Find the slope of the line y= -2/3x
Combine like terms. Which Pokemon has the correct answer?
-17x + 13x = ?
Answer:
-4x
Step-by-step explanation:
You add -17x and 13x and you get -4x.
Some of answers use 3,14 as a substitute for pi.
Some use the symbol for pi. which type of answers
more accurate? The more accurate value is
is
Personally i think that if you use the pi symbol it would be more accurate because on a calculator there is an pi symbol √ which is the same it will give you an answer closer to an whole number.
Simplify the following expression by combining like terms: *
-2g - 8 +5g - 5
Answer:
3g -13
Step-by-step explanation:
Choose the expression that represents a quadratic expression.
A.) 6x4 − 5x3 + 3x2 −7x − 8
B.) 5x3 + 3x2 −7x − 8
C.) 2x2 + 3x − 1
D.) 3x − 1
Answer:
C. 2x^2 + 3x - 1
is the answer
Dog food bad contains 18 cups to fill it up his friend dog eats 1 1/2 each day he says he'll be able to feed his dog for 27 days that true?
Answer:
It's not true because 18 cups will only last 12 days, not 27 days.
Step-by-step explanation:
1 1/2 = 3/2
3/2(27) = 40.5 cups
18 = 3/2c
c = 12
If Greg Has 15 Jars of Cookies, and there are 143 cookies IN TOTAL how many cookies are left over after EQUALLY distributing them.
WILL GIVE BRAINLIEST!!!!!!
Answer:
8 cookies left over
Step-by-step explanation:
use long division.
divide 143 by 15.the remainder is 8
On a coordinate plane, a rectangle is shown. It has points (2, 3), (4, 9), (7, 8), and (5, 2).
A rectangular table is positioned in a 10-foot by 10-foot room as shown.
How long is the longer edge of the table?
Square root of
feet
What is the area of the tabletop?
square feet
Answer:
the answer is 40 for the first one and 20 for the second one
Step-by-step explanation:
just did it and it was right
Answer:
40, 20
Source:
Trust me bro
a line is reflected. Which of these could be the result? Pls help
Answer:
A
Step-by-step explanation:
Answer:
The answer is A.
Step-by-step explanation:
AP EX
Shelley's Cupcakes recently sold 8 cupcakes, of which 4 were coconut cupcakes. Considering this data, how many of the next 20 cupcakes sold would you expect to be coconut cupcakes?
Answer:
10 coconut cupcakes.
Step-by-step explanation:
3 5⁄7 + 1 9⁄14
helppppppppppppppppppppp
1-point free throw 2-point field goal he made 35 shots he scored 62 points how many of each shot does he make in 1 minute write the two equations for the problem
Answer:
x + y = 35 equation 1
x + 2y = 62 equation 2
He made 8 1 point free throw
He made 27 2 point field goal
Step-by-step explanation:
let x = 1 point free throw
y = 2 point field goal
two equations can be derived from the question
x + y = 35 equation 1
x + 2y = 62 equation 2
Subtract equation 1 from 2
y = 27
Substitute for x in equation 1
x = 35 - 27 = 8
He made 8 1 point free throw
He made 27 2 point field goal
Kaylee read 19 1/2 pages in 3/4 of an hour. If she continues reading at the same rate,
how many pages will she read in an hour?
Answer: The answer is 26.
Step-by-step explanation:
Simple, find the unit rate. That's 19.5 / 0.75 = 26.
or using fractions:
19 2/4 divided by 3/4
78/4 divided by 3/4
78 / 3 = 26
4 / 4 = 1
Unit rate = 26books/1 hour
(a) Calculate 8% of £3.25.
Answer:
8÷100×3.25
=£0.26
hope it is helpful to you
Step-by-step explanation:
8÷100×3.25
=0.26
espero ter te ajudado
In a class of 30 students, 6 play an instrument and 17 play a sport. There are 9 students who do not play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument?
Find the distance between the points (1,0) and (2,-2)
Distance = ?
please help!!!!
Answer:
√5
Step-by-step explanation:
use distance formula
can some one give me a hand here???????
A line that passes through the point (-3,-6) has a slope of 4/3. What is another point on this line
Answer:
3,3
Step-by-step explanation:
help please i don’t get it
Alice found the area of the figure by breaking apart it apart where the dashed line is drawn. Her work is shown below. area of rectangle = bh = 6(2) = 12 mm2 area of triangle = bh = 2(2) = 4 mm2 area of figure = 12 + 4 = 16 mm2 A figure can be broken into a rectangle and triangle. The rectangle has a base of 6 millimeters and height of 2 millimeters. The triangle has a base of 2 millimeters an height of 2 millimeters. What error did Alice make? She didn’t use the correct formula for area of a triangle. She didn’t use the correct formula for area of a rectangle. She didn’t find the height of the triangle correctly. She didn’t add the areas of the triangle and rectangle correctly.
Answer:
She didn’t use the correct formula for area of a triangle.
Step-by-step explanation:
edg 2021 Sorry for the late answer.