Answer:
This is verry easy! Is 105.56,do u need expabation?
The sum of n terms of the AP √3, √8, √18, √32,.... is
S = √2+√8+√18+√32+……………… n terms.
or, S = √2 + 2√2 +3√2 +4√2.+………………….+ n terms.
This is an A.P. in which a = √2. , d = √2.
Sn = n/2.[2.a +(n-1).d].
or, Sn = n/2.[ 2√2 +(n-1).√2].
or, Sn = (n/2).√2.[ 2 +n-1].
or, Sn = n.(n+1)/√2. Answer.
Given AP :√2,√8,√18,√32,...
First term = √2
Common difference = √8-√2
⇛ √(2×2×2)-√2
⇛ 2√2-√2
⇛√2
We know that
Sum of first n terms of an AP
⇛ Sn = (n/2)[2a+(n-1)d]
⇛ Sn = (n/2)[2√2+(n-1)(√2)]
⇛ Sn = (n/2)[2√2+√2 n -√2]
⇛ Sn = (n/2)[√2 n +√2)
⇛ Sn = (n/2)×(√2)(n+1)
⇛Sn = (n/√2)(n+1)
⇛ Sn = n(n+1)/√2
Additional comment:
nth term of an AP = a+(n-1)d
Sum of first n terms of an AP
Sn = (n/2)[2a+(n-1)d]
Sum of the first n terms = Sn =
(n/2)(a+an)
If a,b,c are the three consecutive terms in an AP then b = (a+c)/2
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The sum of the 8th & 4th of an Ap is 24 and sum of and sum of 6th & 10th term is 44 Find the Ap
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Find the solution of the differential equation that satisfies the given initial condition.
The first equation is separable:
dy/dx = x/y ⇒ y dy = x dx
(provided that y ≠ 0)
Integrating both sides yields
1/2 y² = 1/2 x² + C
Given that y(0) = -8, we find
1/2 • (-8)² = 1/2 • 0² + C ⇒ C = 32
so that the particular solution is
1/2 y² = 1/2 x² + 32
Solving for y explicitly, we have
y² = x² + 64
y = ± √(x² + 64)
but since y(0) is negative, we take the negative solution:
y = - √(x² + 64)
The second equation is also separable:
du/dt = (2t + sec²(t)) / (2u) ⇒ 2u du = (2t + sec²(t)) dt
Integrate both sides:
u² = t² + tan(t) + C
Given u(0) = -6, we have
(-6)² = 0² + tan(0) + C ⇒ C = 36
and so
u² = t² + tan(t) + 36
u = ± √(t² + tan(t) + 36)
but again we take the negative root here to agree with the initial condition, so
u = - √(t² + tan(t) + 36)
Mrs. Nisbet had 97 books in her classroom library. She received a grant to expand her classroom library. After spending the money, she had 213 books. What is the percent increase? *
Answer: 219
Step-by-step explanation:
An object starts from rest with a constant acceleration of 2m/s^2 along a straight line. Find the distance travelled for the interval of 10 s.
Answer:
Distance is 100 m
Step-by-step explanation:
From second equation of motion;
[tex]{ \rm{s = ut + \frac{1}{2} {at}^{2} }} \\ [/tex]
s is displacementu is initial velocity, u = 0 [ from rest ]a is acceleration, a = 2 m/s²t is time, t = 10s[tex]{ \rm{s = (0 \times 10) + ( \frac{1}{2} \times 2 \times {10}^{2}) }} \\ \\ { \rm{s = {10}^{2} }} \\ \\ { \rm{s = 100 \: {m} }}[/tex]
The distance covered is 200m
Data;
acceleration = 2m/s^2time = 10sdistance = ?Distance CoveredTo find the distance covered by the object, we have to use the formula
of velocity. But we are not given the velocity or speed of the object here.
[tex]v = s/t[/tex]
where s and t are the distance and time respectively.
But from acceleration,
[tex]a = v/t\\v = a*t\\v = 2 * 10 \\v = 20m/s[/tex]
The velocity of the object is 20m/s
let's use this to find the distance covered.
[tex]v = s/t\\20 = s/10\\s = 20*10\\s= 200m\\[/tex]
The distance covered is 200m
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–3 2/6 ÷ 1 1/2=
A. 9/20
B. -3 2/3
C. -2 2/9
D. -5
Answer:
its C
1.convert the mixed number to an improper fraction
([tex]\frac{-20}{6\\}[/tex] x [tex]\frac{2}{3}[/tex] )
2. reduce the numbers with the greatest common factor (2)
[tex]\frac{-20}{3}[/tex] x [tex]\frac{1}{3}[/tex]
3. then multiply and get
[tex]\frac{-20}{9}[/tex]
4. then reduce to get
-2[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
Two numbers multiply to be 0 and add to be -81?
Answer:
0 and -81
Step-by-step explanation:
So, we know anything times zero is zero, and anything added or subtracted to zero would give you that number, meaning one of these numbers is zero.
Zero plus -81 will give you the same number, -81, and zero times -81 will give you zero since anything added to or subtracted to zero is that number.
The sum of two numbers is 20. The greater number is 4 more than three times the smaller number.
Answer:
And x=12 are the two numbers.
Step-by-step explanation:
x+y=20-----(1)
Let x be the larger number of the two.
x=2y-4
Hence 4=2y-x------(2)
Adding (1) and (2) we get 3y=24 so y=8
And x=12 are the two numbers.
PLEASE LAST FEW SETS OF QUESTIONS FOR SEMESTER PLEASE HELP 2
Problem 1
Answer: C) 132.6--------------------
Explanation:
a1 = 1.7 = amount of concrete for the first step
a4 = x = amount of concrete for the fourth step
Sn = sum of the first n terms of an arithmetic sequence
Sn = (n/2)*(a1 + an)
S4 = (4/2)*(a1 + a4)
S4 = 2(1.7+x)
S4 = 2x+3.4
S4 = 17
2x+3.4 = 17
2x = 17-3.4
2x = 13.6
x = (13.6)/2
x = 6.8
We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d
an = nth term of an arithmetic sequence
an = a1 + d(n-1)
a4 = a1 + d(4-1)
a4 = a1 + 3d
6.8 = 1.7 + 3d
6.8-1.7 = 3d
5.1 = 3d
(5.1)/3 = d
1.7 = d
d = 1.7
Coincidentally, the common difference is the same as the first term. This won't always happen.
Now we can compute the 12th term
an = a1 + d(n-1)
a12 = 1.7 + 1.7(12-1)
a12 = 20.4
which is then used to find the sum of the first 12 terms
Sn = (n/2)*(a1 + an)
S12 = (12/2)*(a1 + a12)
S12 = 6(1.7 + 20.4)
S12 = 132.6
=============================================================
Problem 2
Answer: C) [tex]x^2 + (y-10)^2 = 225\\\\[/tex]--------------------
Explanation:
The center is (h,k) = (0,10) which is where the nozzle is located.
The distance from (0,10) to (0,25) is 15 units, so r = 15.
Also, the distance from (0,10) to (0,-5) is also 15 units.
Plug those values into the equation below.
[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]
That equation represents the boundary of the circle, which is where the water can reach.
=============================================================
Problem 3
Answer: B) 2.336 ft--------------------
Explanation:
a1 = height 1st bounce = 6.7 fta2 = height 2nd bounce = 81% of a1 = 81% of 6.7 = 0.81*6.7 = 5.427a3 = height 3rd bounce = 81% of a2 = 81% of 5.427 = 0.81*5.427 = 4.39587Or note that,
a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 = 4.39587
which must mean,
a4 = a1*(0.81)^3a5 = a1*(0.81)^4a6 = a1*(0.81)^5This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]
So,
a6 = a1*(0.81)^5
a6 = 6.7*(0.81)^5
a6 = 2.33614554867
a6 = 2.336
6(31)+6(4)-6(15) mental math form
[tex]6(31)+6(4)-6(15)=6(31+4-15)=6(20)=120[/tex]
ok done. Thank to me :>
I need the answer for this ASAP
Answer:
Y is cookies x is cupcakes
for the first birthday party: 20x + 40y = 61
For the second party 30x + 30y = 64.50
There aren't any other constraints
20x + 40y = 61
30x + 30y = 64.50
Step-by-step explanation:
An angle measures 136°. What is the measure of its supplement?
Answer:
44⁰.
Step-by-step explanation:
Its supplement = 180 - 136
= 44 degrees.
HELP ME FAST PLZZ
Wendy has 5 1/3 of ribbon.
Part A: How many 2/3 -foot pieces can Wendy cut from the 5 1/3 feet of ribbon? Show your work. (5 points)
Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
Answer:
Part A: 8 ribbons
Part B: see below
Step-by-step explanation:
first 5 1/3 = 16/3
[tex] \frac{16}{3} \div \frac{2}{3} \\ = \frac{16}{3} \times \frac{3}{2} \\ = \frac{48}{6} = 8[/tex]
the answer is 8 dude!
I need help asap!! pls pls PLS help
Answer:
Step-by-step explanation:
It's the third choice. Since the triangles are given as similar and they are right triangles, points A, B, and D are all on the hypotenuses of those 2 triangles and are co-linear. The slope between all points on a single line is constant.
How can the equation of a parabola be derived when given the focus and the directrix?
Answer:
If the focus is to the right of the directrix, then the parabola opens to the right and p>0 . If the focus is to the left of the directrix, then the parabola opens to the left and p<0 .HOPE ITS HELP
1. Which of the following is the remainder when the polynomial x^2-5x+3 is divided by (x -8)?
(1) 107
(3) 3
(2) 27
(4) 9
Answer:
27
Step-by-step explanation:
Use synthetic division:
8 | 1 -5 3
__8_24
1 3 | 27
Therefore, (x²-5x+3)/(x-8) = x+3 R27
discuss the criteria of a good test
At noon, a tank contained 8 in. of water. After several hours, it contained 6 in. of water. What is the percent decrease of water in the tank?
Answer:
25%
Step-by-step explanation:
8-6=2
2/8=0.25
0.25×100=25%
Find the future value of $124,357 deposited at 8% compounded quarterly for 4 years
Answer:
Future value, $63,398.79; Interest, $16,798.79
Step-by-step explanation:
The cost C to produce x number of tennis rackets is C = 190 + 18. The tennis rackets are sold wholesale for $23
each, so revenue R is given by R = 23x. Find how many tennis rackets the manufacturer needs to produce and
sell to break even.
38 tennis rackets or
43 tennis rackets or
19 tennis rackets or
33 tennis rackets
Answer:
19 tennis rackets
Step-by-step explanation:
Pls help I’ll brainlest
Complete the activities below
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
rate of change or slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]
y = mx + b
"b" is y-intercept
~~~~~~~~~~~~~~~~~~~
3 to the power of -2 as a fraction
From the power rules, the power [tex]3^{-2}[/tex] is equal to the fraction [tex](\frac{1}{3})^{-2}[/tex].
Power RulesThere are different power rules one of them is the negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent. See the examples:
[tex]5^{-3}=(\frac{1}{5})^3=\frac{1}{125} \\ \\ \\ {\frac{4}{6} }^{-2}={\frac{6}{4} }^2=\frac{36}{16}[/tex]
Then, the question gives:
[tex]3^{-2}=({\frac{1}{3}})^2[/tex]
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Tara wants to put a white fence aroung the yard including the garden. Write an
expression for the perimeter of her yard (including the garden).
Then simply the expression.
The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.
The amount of fencing needed is 2(6) + 2(12) = 12 + 24 = 36 ft of fencing
3) Choose the graph which represents the solution to the inequality:
XS-4x + 15
A)
B)
CS
Answer: x has to be less than 5 i can’t read it but it is starting from positive 5 with the arrow going to the left
Step-by-step explanation:
a family buys 6 airline tickets online. the family buys travel insurance that costs 18 per ticket. the total cost is 1,044
Answer:
936
Step-by-step explanation:
Therefore you multiply 6 by 18 = 6×18= 108
1,044 - 108 = 936
So therefore the total is 936
Select the equation that has a = 112 as its solution.
a−114=35
a+358=434
416+a=523
a×38=214
Answer:
none
Step-by-step explanation:
a-114=35 ⇒ a= 149
a+358=434⇒ a=76
416+a=523⇒ a=107
ax38=214⇒ a=5.63
The equation that has 112 as it's solution is not existing in the options.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given are four linear equations.
Check the solution of each equation.
a - 114 = 35
Adding both sides of the equation with 114,
⇒ a = 35 + 114 = 149
a + 358 = 434
Subtracting both sides of the equation with 358,
⇒ a = 434 - 358 = 76
416 + a = 523
Subtracting both sides of the equation with 416,
a = 523 - 416 = 107
a × 38 = 214
Dividing both sides of the equation with 38,
a = 214/38 = 5.63
Hence none of the equations have 112 as it's solution.
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PLEASE HELP ME WITH THIS QUESTION
Answer:It’s money so use the $ symbol. You got this
Step-by-step explanation:
Answer plzzz!!!!!!!!!!!
Answer:
110
Step-by-step explanation:
Know the angle for BCD which is 130.
Subtract 180 from 130 and you get angle c for the triangle which is 50
Already knowing B and C, add them both which comes up to 70
All triangle angles equal 180 so subtract 70 for 180 and you get 110
Find the slope and the y-intercept of the line with the equation 8y - x + 7 = 0.
if (a+b)^2=54, and (a-b)^=46, then a^2+b^2=?
[tex](a+b)^2 =a^2 +b^2 + 2ab = 54~~~.....(i)\\\\(a-b)^2 = a^2 +b^2 -2ab = 46~~~.....(i)\\\\\\(i)+(ii):\\\\(a+b)^2 +(a-b)^2 = 54+46\\\\\implies a^2 +b^2 + 2ab + a^2 +b^2 - 2ab =100\\\\\implies 2a^2 +2b^2 =100\\\\ \\\implies 2(a^2 +b^2) =100\\\\\implies a^2 +b^2 = \dfrac{100}2 = 50[/tex]
What is the equation of the line that passes through
(-5, 0) and (4, 3)?
Answer:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]
Step-by-step explanation:
The point-slope form of an equation for a line is y = mx + b (m is the slope; b is the y-intercept).
First, find the slope using the two given points.
[tex]m=\frac{y_2 - y_1}{x_2-x_1}=\frac{3-0}{4-(-5)}=\frac{3}{9}=\frac{1}{3}[/tex]
At this stage, you know the slope and need to find the y-intercept. Plug in one of the points (either one) into the equation. Let's use (-5, 0).
[tex]y=\frac{1}{3}x+b\\0=\frac{1}{3}(-5)+b\\0=-\frac{5}{3}+b\\\frac{5}{3}=b[/tex]
The equation for the line is [tex]y=\frac{1}{3}x+\frac{5}{3}[/tex].
You can check for errors by putting in the point you didn't use...
Check to make sure the point (4, 3) satisfies the equation.
[tex]3=\frac{1}{3}(4)+\frac{5}{3}\\3=\frac{4}{3}+\frac{5}{3}\\3=\frac{9}{3}[/tex] True!