Answer:
[tex]\sum\limits_{i=1}^{n} c \cdot a_i \ is \ equal \ to \ c = \ c \cdot \sum\limits_{i=1}^{n} a_i[/tex]
[tex]\sum\limits_{i=1}^{n} i \ is \ equal \ to \ b = \dfrac{n \cdot (n + 1)}{2}[/tex]
[tex]\sum\limits_{i=1}^{n} c \ is \ equal \ to \ d = c \cdot n[/tex]
[tex]\sum\limits_{i=1}^{n} i^3 \ is \ equal \ to \ e = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2[/tex]
[tex]\sum\limits_{i=1}^{n} i^2 \ is \ equal \ to \ a = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6}[/tex]
Step-by-step explanation:
1) The sum of a series of the cubes of numbers 'i' is given as follows;
Sₙ = n/2 × (1st term + Last term)
∴ Sₙ = n/2 × (1 + n) = n·(n + 1)/2
It can be shown that the sum of a series of the cubes of numbers 'i²' is given as follows;
Sₙ = (n·(n + 1)·(2·n + 1))/6
It can be also be shown that the sum of a series of the cubes of numbers 'i³' is given as follows;
Sₙ = (n·(n + 1)/2)²
Therefore, we have;
[tex]\sum\limits_{i=1}^{n} c \cdot a_i= c \cdot \sum\limits_{i=1}^{n} a_i = c[/tex]
[tex]\sum\limits_{i=1}^{n} i = \dfrac{n \cdot (n + 1)}{2} = b[/tex]
[tex]\sum\limits_{i=1}^{n} c = c \cdot n = d[/tex]
[tex]\sum\limits_{i=1}^{n} i^3 = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2 = e[/tex]
[tex]\sum\limits_{i=1}^{n} i^2 = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6} = a[/tex].
Answer:
c, b, d, e, a
Step-by-step explanation:
verify the following
1. (-3/4)3 = -27/64
Choose the equation that is not a linear function.
A
8x + 12 = 2y
B
y =
x
5
+ 20
C
x = 12y
D
y = (2x)x
Answer:
The answer is D
Step-by-step explanation:
D, y=(2x)x
y=2x^2
this is a parabola, not a linear equation
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9514 1404 393
Answer:
BC ≈ 17.0 (neither Crow nor Toad is correct)
Step-by-step explanation:
The left-side ratio of (2+4)/4 = 3/2 suggests BC is 3/2 times the length DE. If that were the case, BC = (3/2)(11) = 16.5, as Crow says.
The right-side ratio of (5+9)/9 = 14/9 suggests that BC 9 is 14/9 times the length DE. If that were the case, BC = (14/9)(11) = 154/9 = 17 1/9 ≈ 17.1, as Toad says.
The different ratios of the two sides (3/2 vs 14/9) tell you that the triangles are NOT similar, so the length of BC cannot be found by referring to the ratios of the given sides.
Rather, the Law of Cosines must be invoked, first to find angle A (109.471°), then to use that angle to compute the length of BC given the side lengths AB and AC. That computation gives BC ≈ 16.971. (See the second attachment.)
Find the mean of 9, 1, 3, 9, 3 graphically
Answer:
The mean is 3
Step-by-step explanation:
9+ 1+ 3+ 9+ 3= 15
15/5= 3
In the figure,Line x is parallel to line y. identify the angles congruent to angle 3
Answer:
For example, slide ∠ 1 down the transversal and it will coincide with ∠2. are equal in measure. If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.
Step-by-step explanation:
How to do it
Step by step
Step-by-step explanation:
23.35......is answer.......
Solve 4(b−3)=64(b−3)=6
24 foot wire is tied from a stake in the ground to the top of flagpole. If the angle elevation from the stake to the top of the flagpole is 53 degrees how far is the stake from the base of the flagpole? Round to the nearest tenth
Answer:14.44 ft
Step-by-step explanation:
Given
Length of wire [tex]l=24\ ft[/tex]
Angle of elevation [tex]53^{\circ}[/tex]
from the figure
[tex]\Rightarrow \cos 53=\dfrac{b}{24}\\\\\Rightarrow b=24\cos 53=14.44\ ft[/tex]
The answer is, [tex]14.44 ft[/tex]
Definition of angle of evevation:
The angle between the horizontal and a line of sight from the observer to a place of interest that is "upwards."
An Angle of Depression occurs when the angle moves "downwards."
Given,
Wire's length [tex]l=24ft[/tex]
The elevation angle [tex]53^{0}[/tex]
[tex]cos 53= \frac{b}{24} \\b=24 cos53\\=14.44ft[/tex]
Learn more about angle of elevation here, https://brainly.com/question/88158
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Whats a Factor tree?
One endpoint of a line segment has coordinates represented by (x + 2, 3y). The midpoint of the line segment is (6, -3). How are the coordinates of the other endpoint expressed in terms of x and y? O (10 – r, y) O (10 - 1,-6-y) (12 - 2,6 - 3y) (14 – 1,3 - y) 1 2 3 4 5 Next
HELP!!!! Put the following in order from greatest to least.
Answer:
A
Step-by-step explanation:
A = 9, 7, 5, -2, -6, -8
The radius of a cylindrical water tank is 6.5 ft, and its height is 12 ft. What is the volume of the tank?
Answer:
.............. just for filling 20 characters
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Answer:
number 8 is $0
number 9 is D
Answer:
number 8 is $0
number 9 is D
the radius of a circle is 13 find its area un terms of pi
Answer:
530.66
Step-by-step explanation:
A = πr²
13 x 13 = 169
169 x 3.14 = 530.66
Let me know if this helps!
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Answer:
x = 11 , y = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
The opposite sides of a parallelogram are congruent
For the figure to be a parallelogram , then
ON = LM, that is
5x - 7 = 4x + 4 ( subtract 4x from both sides )
x - 7 = 4 ( add 7 to both sides )
x = 11
and
OL = NM , that is
3y - 4 = x - 7 = 11 - 7 = 4 ( add 4 to both sides )
3y = 8 ( divide both sides by 3 )
y = [tex]\frac{8}{3}[/tex]
The total weight of the shape blocks on both sides of Michael's pan balance equals 30 grams. Circles weigh 5 grams, squares weigh 10 grams, and triangles weigh 3 grams. The right side has a circle and a square. How many triangles are on the left side?
Answer:
There would be 5 triangles on the other side
Step-by-step explanation:
If the right side has 1 circle and 1 square, that would mean that there is 5g+10g=15g weight on the right side
In total, there is 30g, and we already have 15
We can use the equation 15+3x=30, and by solving, the answer would be 5 triangles.
Hope this helps!
I need help my mind don’t proses right.! f(x) = x2. What is g(x)?
Answer:
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On a map, Haven Rd and Pine Rd are parallel, and Mills Rd is a transversal. How can the
value of x be determined?
Answer:
B: Corresponding angles are congruent, so x = 43
Answer:
B: Corresponding angles are congruent, so x = 43
Step-by-step explanation:
Complete the equations below. please only if you know
Answer:
153, 51, 5.1
Step-by-step explanation:
15.3÷3= 153 tenths÷315.3÷3=51 tenths15.3÷3=5.1Use a formula to find the surface area of the cylinder. Use 3.14 for pi
Answer:
A = 376.99
Step-by-step explanation:
A=2πrh+2πr2
Just plug in and solve:
A=2πrh+2πr2
A = 376.99
Pls help with c. and d. Plssss I will give bonus if you answer it correctly.
Answer:
Austing needs 160 boxes to complete the rack.
Step-by-step explanation:
Givens
12 cereral boxes occupies 60 centimeters of shelving.
The rack has 10 meters of shelving, equivalent to 1000 centimeters.
2 meters are already used.
There are 800 centimeters of shelving remaining.
To find the total number of cereal boxes needed to use the whole rack, we just need to use the rule of three: If 12 cereal boxes occupies 60 centimeters of shelving, 800 centimeters would require how many cereal boxes
Therefore, Austing needs 160 boxes to complete the rack.
Answer: C. Y=(1000-200)/5
D. 160 boxes of cereal
Step-by-step explanation: To create the equation I changed the measurements all to centimeters by scaling up the meters by 100 since there are 100 centimeters in a meter.
What is the surface area of this Square Pyramid?
10 in
5 in
5 in.
Answer:
Base Surface Area: 25 in^2
Total surface area A = 128.07764064044 in^2
(PLEASE NOTE THIS IS BASED ON THE HEIGHT BEING 10 IN AND SIDE LENGTH A BEING 5 IN (IF THIS IS INCORRECT COMMENT AND ILL FLIP IT)
Step-by-step explanation:
Jimmy and his friends want to sign up for a game rental service. They have information on game rental plans from four different companies. The friends plan to rent 15 games per month. Which plan is the BEST? Use substitution to determine the best price.
A-GameStop; pay $5 for each game ordered. (5g)
B-Level-up Games; pay $25 to join and $2 for each game ordered (2g + 25)
C-Game Changer; pay $20 to join and $2.50 for each game ordered (2.5g + 20)
D-Game Land; pay $60 per month for unlimited amount of game rentals (60)
Answer: A
Step-by-step explanation:
It’s the cheapest
PLEASE ANSWER QUICKLY.
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Answer:
options (c) is right answer
Answer: B
Step-by-step explanation:
The farmer is not correct. She sold _% of the onions and _ % of the turnips by noon on Saturday. If she had sold 4 more pounds of onions she will have sold _% of the onions. This percentage of onions sold ___ equal to the percentage of turnips sold. *: 20 25 :: 28 :: 32 :: 35 .: 40 :: 50 :: 56 :: 80 :: is .! is not
Answer:
28 32 35 50
Step-by-step explanation:
Which expression is equivalent to
Answer:
i think is b
Step-by-step explanation:
Answer:
C: 2
Step-by-step explanation:
the numerator equals 8 and the denominator equals 2, so its (8/2)^1/2
which all equals 2
which of the following points is the solution of the quadratic equation : 3x² - 5x-2=0
Answer:
answer in the file
Step-by-step explanation:
The Flying Dutchman, located in St. Martin, is the steepest zipline in the world. While sailing downhill at 56 miles per hour, you lose 1,050 feet of elevation across 2,800 feet of cable. If you are at the top getting strapped in, what is the angle of depression between you and a safe landing at the bottom? (Drawing a diagram may help.)
Answer:
Sine angle A = 1,050 / 2,800
Sine angle A = .375
arc sine (.375) = Angle A
Angle A = 22.024 Degrees
(THIS REPLACES THE PREVIOUS ANSWER.)
Step-by-step explanation:
Araine borrows $400 on a 4-year loan. She is charged 5% simple interest per year. How much interest is she charged for 4 years? What is the total amount she has to pay back?
Answer:
Interest Charged = $80
Total payback = $480
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Present Value (PV) = $400
Time period (n) = 4 years
Interest rate (r) = 5%
So, we can calculate the future value(FV), by using following formula,
FV = PV ( 1 + n × r)
By putting the value, we get
FV = $400 ( 1 + 4 × 0.05)
= $480
Hence total amount she has to pay back = $480.
Interest charged = FV - PV
= $480 - $400
=$80
if possible, verify sin^2(x)/1 + cos(x) = 1 - cos(x) by rewriting the left hand side of the equation.
I really really don't understand identities, and I'm not getting replies from my teacher. Thank you for any help I do get!!
sin^2(x)/1 + cos(x) = 1 - cos(x)
We know that sin^2 x = 1 - cos^2 x. It is one of our trig identities.
We now have this:
(1 - cos^2 x)/(1 + cos x) = 1 - cos x
Take note:
1 - cos^2 x is a perfect square difference in terms of cosine.
So, (1 - cos^2 x) = (1 + cos x)(1 - cos x).
We now have this:
[(1 + cos x)(1 - cos x)]/(1 + cos x) = 1 - cos x
Do you see what happens on theft side?
On the left side, (1 + cos x) cancels out on the top and bottom.
We are now left with this:
1 - cos x = 1 - cos x
Done!!