Answer:
The series converges as any two consecutive elements of the sum are monotonically decreasing.
Step-by-step explanation:
The series converges since the consecutive element is monotonically decreasing. That is:
[tex]\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}[/tex] (1)
Where:
[tex]a_{i}[/tex] - The i-th component of the sum.
[tex]a_{i+1}[/tex] - The (i+1)-th component of the sum.
A steamer travels 36 km upstream and 32 km downstream in 6.5 hours. The same steamer travels 4 km upstream and 40 km downstream in 180 minutes. Determine the steamer's speed in still water and the stream's speed.
Answer:
The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Step-by-step explanation:
Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.
Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').
he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')
The total time is thus t + t' = 36/(v + v') + 32/(v - v')
Since the whole trip takes 6,5 hours,
36/(v + v') + 32/(v - v') = 6.5 (1)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v') (1)
(v - v')36 + (v + v')32 = 6.5(v + v')(v - v') (1)
36v - 36v' + 32v + 32v' = 6.5(v² + v'²)
68v - 4v' = 6.5(v² + v'²) (2)
Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').
he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')
The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')
Since the whole trip takes 180 minutes = 3 hours,
4/(v + v') + 40/(v - v') = 3 (3)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v') (1)
(v - v')4 + (v + v')40 = 3(v + v')(v - v') (1)
4v - 4v' + 40v + 40v' = 3(v² + v'²)
44v - 36v' = 3(v² + v'²) (4)
Dividing (2) by (4), we have
(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)
(68v - 4v')/(44v - 36v') = 6.5/3
3(68v - 4v') = 6.5(44v - 36v')
204v - 12v' = 286v - 234v'
204v - 286v = 12v' - 234v'
-82v = -222v'
v = -222v'/82
v = 111v'/41
Substituting v into (2), we have
68v - 4v' = 6.5(v² + v'²)
68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²
[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²
[7384/41]v' = 6.5[14002/1681]v'²
[7384/41]v' = [91013/1681]v'²
[91013/1681]v'² - [7384/41]v' = 0
([91013/1681]v' - [7384/41])v' = 0
⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or v' = 7384/41 × 16841/91013
⇒ v' = 0 or v' = 180.097 × 0.185
⇒ v' = 0 or v' = 33.33 km/h
Since v' ≠ 0, v' = 33.33 km/h
Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h
So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Daine simplified the expression below.
8(1 + 2i) – (7 – 3i) = 1 + 5i
What mistake did Daine make?
Answer:
Step-by-step explanation:
8(1 + 2i) - (7 - 3i) = 8*1 + 8*2i + 7*(-1) - 3i*(-1)
= 8 + 16i -7 + 3i
= 8 - 7 + 16i + 3i
= 1 + 19i
Daniel forgot to multiply 2i by 8
Answer:
A , He did not apply the distributive property correctly for 8(1 + 2i).
on edge
Step-by-step explanation:
Which equation models the data in the table?
Which of the following does (square root f^2) simplify to, for any nonnegative real number f?
Answer:A
Step-by-step explanation:
En una granja hay 26 corrales con una capacidad para 68 gallinas cada uno. Sí cada gallina pone un huevo cada día ¿cuántos huevos recolectan en una semana (7 días )?
Answer:
12376 huevos
Step-by-step explanation:
Son 68 gallinas en 26 corrales por tanta se multiplicaría
26 x 68=1768 estas serian el total de las gallinas en todos los corrales, aparte te dicen que cada pone un huevo al día, entonces como te piden cuantos huevos serán en 7 días sería:
1768 x 7= 12376
1768= a los huevos de cada gallina en un día ya que te dice que cada una pone un huevo en cada día.
Danielle has test scores of 92, 86, 83, 90 and 91 in her math class. What score does she need on the next test to have an overall class average of 90%?
Answer:
98
Step-by-step explanation:
An average score can be calculated by finding the sum of all scores and then dividing by the number of tests. So we can create an equation like this:
[tex]\frac{(92+86+83+90+91+x)}{6}=90[/tex]
The numerator is the sum of her scores, where x represents the score of her next test (which is what we're trying to find).
The denominator is the total number of tests, which is 6 - this includes the 5 she has taken already and the next test that she hasn't taken yet.
Furthermore, we know all of this has to equal 90 because that's the average we're looking for.
Now we just solve for x.
Step 1) Multiply by 6:
[tex]92+86+83+90+91+x=90 \times 6[/tex]
Step 2) Simplify equation:
[tex]442+x=540[/tex]
Step 3) Subtract 442:
[tex]x=540-442=98[/tex]
Therefore, x = 98, so Danielle must achieve a score of 98 to have an overall class average of 90.
Simplity
-1|2/3-4|
÷ 5/6
Answer:
-4
Step-by-step explanation:
Simplify. You can do this with what I've provided below.
[tex]\frac{-(\frac{2}{3}+4)}{\frac{5}{6} }[/tex]
Billy looks through holiday brochure in Spain, Greece,Italy and UK.
1/3 in Spain, 1/6 in Greece,1/8in Italy the remainder in uk
Answer:
Assuming you want to know there was for UK it was [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
Let's add the fractions together
[tex]\frac{1}{3} +\frac{1}{6}+\frac{1}{8\\}\\\frac{8}{24} +\frac{4}{24} +\frac{3}{24} =\frac{15}{24}[/tex]
The remainder is the amount in UK so
[tex]\frac{24}{24} -\frac{15}{24} =\frac{9}{24} \\[/tex]
Simplified it's [tex]\frac{3}{8}[/tex]
PLEASE HELP ME
PLEASE HELP ME
Find the lateral surface area of
the following square pyramid:
4 cm
6 cm
LA = [?] cm2
Answer:
Surrounding area of pyramid = area of a side face multiplied by 4
Step-by-step explanation:
The area of a side face is the area of the triangle:
[tex]\frac{1}{2} *6*4[/tex] = 12
So the perimeter of the pyramid is:
12×4=48
Explanation: because the side faces have the same area.
Can someone please help me, this is for summer school and I need fast replies, I have 29 other question like these, please help.
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: A. \:- 8 {v}^{4} + 3 {v}^{3} + v + 5}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex](4 + 6v + 3 {v}^{3} ) - (5v + 8 {v}^{4} - 1)[/tex]
➼[tex] \: 4 + 6v + 3 {v}^{3} - 5v - 8 {v}^{4} + 1[/tex]
Combining like terms, we have
➼[tex] \: - 8 {v}^{4} + 3 {v}^{3} + 6v - 5v + 4 + 1[/tex]
➼[tex] \: - 8 {v}^{4} + 3 {v}^{3} + v + 5[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?
Answer:
x = 9
Step-by-step explanation:
24x - 18 - 8x - 30 = 96
add or subtract like terms
16x - 48 = 96
shift - 48 to right hand side . when it goes to other side minus changes to plus
16x = 96 + 48
16x = 144
x = 144/16
x = 9
to prove that the value of x satisfy the given equation or not.
to prove that the value of x is 9 substitute 9 inplace of x and if it gives 96 then it satisfy
24x - 18 - 8x - 30 = 96
24*9 - 18 - 8*9 - 30 = 96
216 - 18 - 72 - 30 = 96
216 - 120 = 96
96 = 96
since both sides is equal to 96 it can be concluded that the value of x is 9.
Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?
AnswerX = 9Step by Step Explanation24x - 18 - 8x - 30 = 96
First let's just add/subract the following terms.
16x - 48 = 96
Second.. shift the 48 to the right side. after that change the minus sign into plus sign.
16x = 48 + 96
16x = 44
x = 144/16
x = 9
Explanation:
So we just prove that the value of x satisfy the equation true or not.To prove that the value of x is 9.. we just substitute the 9 in place of x and if it was 96 the result of the equation the problem must be true.So we begin to solve it!
24x - 18 - 8x - 30 = 96
24*9 - 18 - 8*9 - 30 = 96
216 - 18 - 72 - 30 = 96
216 - 120 = 96
Since that all both sides are equal to 96 it can be concluded that the value of x is 9.
#LearnwithBrainly
Find the area of the shape.
17 m
4 m
7 m
9 m
What is the area
Step-by-step explanation:
Area squares the unit of length. in this case, none of these are area
(By the way is this question tagged with a picture)
MCQ type questions.
[tex]1) \sqrt{ - 1 } = [/tex]
[tex]i) \: i \\ ii) \: {i}^{2} \\ iii) {i}^{3} \\ iv) \: {i}^{4} [/tex]
Answer: Option one i.
Explanation:
Just rewrite √-1 as i.
! Task 1. Bookwork code: G24 Calculator X not allowed Anthony has three number cards, as shown below. The minimum of the three cards is 6. The range of the three cards is 5. What is the mean of Anthony's three cards? Cards are 6, 7 and unknown
Answer:
8
Step-by-step explanation:
In order to find the range you need to subtract maximum card number from the minimum card number. We know that the range is 5 and that the minimum card is 6 so we can set up the equation like this to find the maximum shown as x.
[tex]5=x-6[/tex]
Add 6 to both sides
[tex]11=x[/tex]
Now we know all the the numbers of the three cards Anthony has since we were given the minimum = 6, 7, and solved for the last card which was the maximum = 11. In order to find the mean we have to add all of the numbers then divide by how many numbers there are (in this case it will be 3):
[tex]mean=\frac{6+7+11}{3}[/tex]
Add 6+7+11
[tex]mean=\frac{24}{3}[/tex]
Divide by 3
[tex]mean=8[/tex]
(6x+15)°
63° triangle
Answer:
x = 2
Step-by-step explanation:
The sum of the 3 angles in the triangle = 180°
Sum the 3 angles and equate to 180
6x + 15 + 90 + 63 = 180
6x + 168 = 180 ( subtract 168 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
the perimeter of a rectangle is 56 meters. Find the dimensions of the rectangle if they are in the ratio 1:3
Answer:
length= 7m and breadth= 21m
Step-by-step explanation:
Perimeter=56m
Perimeter of a rectangle= 2(l+ b)
Dimensions in the ratio 1:3
1:3= 1x and 3x
Take length as 1x and breadth as 3x
2(1x+3x)= 56m
2(4x)= 56
8x=56
x= 56/8 = 7m
length= 1x= 7m
breadth= 3x= 3*7 = 21m
Please mark me as brainliest
Find the missing interior angle in a triangle when one angle is 48 degrees, a second angle is Y+2 degrees, and the exterior angle is 2Y - 3 degrees?
Answer:
61°
Step-by-step explanation:
Angles in a straight line add up to 180°.
Also angles in a triangle add up to 180°.
See the image above.
Factorise a² - b²
.......
[tex]\longrightarrow{\green{ (a + b)(a - b) }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] ={a}^{2} - {b}^{2} [/tex]
[tex] = (a + b)(a - b)[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Determine the mean, median, and mode of the data set.
37, 12, 32, 23, 12, 40, 11, 12, 10, 23, 27
a.
C.
mean=22
median=40
mode=23
mean=21.7
median=23
mode=12
b. mean=20
d. mean=22
median=20
median=12
mode=12
mode=23
Answer:
mean=21.7
median=23
mode=12
Step-by-step explanation:
Mean=37+12+32+23+12+40+11+12+10+23+27/11
=21.7(3 s.f)
Median: 10,11,12,12,12,23,23,27,32,37,40
Median=23
Mode=12
There are a total of 40 red, yellow or blue balls in a box. Each ball is marked with a number out of 1, 2, 3 and 4 on the side. The figure in the shaded area below each shows the number of balls in that category. For example, the number of red balls marked with the number "1" is 12. What is the minimum number of balls to be taken out of the box to ensure that you have at least one ball of each color and each marked number?
Answer:
9
Step-by-step explanation:
Question:
Minimum number of balls to ensure there is at least one ball of each colour marked with each number.
The quantity of distinct numbers are:
red: 4
Yellow 3
Blue 2
So the minimum number of balls to satisfy the given requirements is
4+3+2= 9
Please explain the answer and show your work
Answer:
6
Step-by-step explanation:
Arc length ACB = 6 pi
The arc length = fraction of a circle times the circumference
6 pi = 180/360 * 2 * pi *r
6 pi = 1/2 * 2 * pi*r
6 pi = pi r
The radius is 6
If a number is chosen at random from the numbers 1 to
20 inclusive, what is the probability that a single-digit
number will be picked? ( give your answer in simplified
fractions eg. 2/5 when necessary)
Answer:
1/20
Step-by-step explanation:
only a single number can be chosen out of 20. And 1/20 is the most simplified it can get.
a rectangle is twice as long as it is wide and its perimeter is 432cm
a) work out the dimensions of the rectangle.
b) work out the area of the rectangle.
Let
Width of rectangle=xLength of rectangle=2xPerimeter=432cmWe know that in a rectangle
☆ Perimeter=2(Length+Breadth)
[tex]\\ \sf\longmapsto 2(x+2x)=432[/tex]
[tex]\\ \sf\longmapsto 2x+4x=432[/tex]
[tex]\\ \sf\longmapsto 6x=432[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{432}{6}[/tex]
[tex]\\ \sf\longmapsto x=72[/tex]
[tex]\\ \sf\longmapsto 2x=2(72)=144[/tex]
Length=144cmBreadth=72cm☆Area=Length×Breadth
[tex]\\ \sf\longmapsto Area=144\times 72[/tex]
[tex]\\ \sf\longmapsto Area=10368cm^2[/tex]
please show me the steps of to do this
DON"T GIVE ME THE ANSWER
ASAP
Answer:
B
Step-by-step explanation:
The number [tex]a . 10^{-2}[/tex] is 8 times greater than [tex]b . 10^{-3}[/tex]
thus, [tex]a . 10^{-2} = 8b. 10^{-3}[/tex]
multiply both sides by [tex]10^{2}[/tex]
we get [tex]a = 8b. 10^{-1} \\a = 0.8 b[/tex]
if we take a = 2.5 and b = 3.1 we get 2.5/3.1 = 0.8
then B is the answer
what is 18 7/8 -14 7/9
Answer:
295/72
Step-by-step explanation:
Find the missing side. Round to the nearest tenth.
A.7.4
B.4.4
C.6.4
D.5.4
Answer:
option D
Step-by-step explanation:
take 39 degree as reference angle
using cos rule
cos 39 = adjacent / hypotenuse
0.77 = x / 7
x = 7*0.77
x = 5.39
x = 5.4
Answer:
D. 5.4
Step-by-step explanation:
Using trigonometric ratio
cos 39 = x/7
cross multiple
x = cos39(7)
x=5.4
Does anyone know the answer to this ?!? ( links and answers that have nothing to do with the question will be reported.)
Answer:
the triangle was 2x scale (*2)
it was reflected across y=0
and translated x +2
Step-by-step explanation:
Complete the work to calculate the scale factor. 1. Scale factor = StartFraction Scale drawing dimension over original dimension EndFraction. 2. Enter the corresponding lengths: StartFraction 24 over 3 EndFraction. What is the scale factor?
Answer:
8
Step-by-step explanation:
To obtain scale factor of a particular drawing:
We use the relation:
Scale factor = Scale drawing dimension / original dimension
Given :
Scale drawing dimension = 24
Original dimension = 3
Scale factor = 24 / 3
Scale factor = 8
Answer:
an enlargement
Step-by-step explanation:
PLEASE HELP 25 POINTS. If you apply the changes below to the quadratic parent function, fx) = x2,
what is the equation of the new function?
.
Shift 1 unit left.
.
Vertically stretch by a factor of 3.
• Reflect over the x-axis.
Answer:
[tex]f(x) = 3 (x+1)^{2}[/tex]
Step-by-step explanation:
I need help with this can someone help me please!!! I will give brainlist, no links!!
Leo is visiting New York City to see the Empire State building. He knows that the Empire State building is 1,484 feet tall. When he spots it, he stops and has to look up at an angle of 84.7 degrees to see the top. How far away from the base of the Empire State building is he?
Answer:
Leo stop at 1339. 3 feet tall and Leo almost reach the top of the building
