Answer:
3*∑ (1/2)^n = 6
Step-by-step explanation:
We have the summation from n = 1 to n = ∞, for:
∑ 3/(2)^(n - 1)
We know that the summation between k = 0, and k = N - 1 for:
∑ r^k = (1 - r^N)/(1 - r)
if we have the summation between k = 0 and k = ∞ - 1 = ∞
(here we used that ∞ is really big, then ∞ - 1 = ∞)
In the numerator we will have the term r^∞, if 0 < r < 1, then r^∞ = 0.
Then if we assume that 0 < r < 1 we can write:
∑ r^k = 1/(1 - r)
In our case, we can rewrite our summation as:
3*∑ (1/2)^n
for n = 0 to n = ∞
You can see that i changed the limits for n, this does not really matter because we are summing between a number and infinity, the only thing you need to take care is that now the power is n, instead of (n - 1)
Then we have r = (1/2) which is clearly smaller than 1.
then (1/2)
Then this summation is equal to:
3*∑ (1/2)^n = 3*( 1/(1 - 1/2)) = 3*( 1/( 2/2 - 1/2)) = 3*( 1/(1/2)) = 3*2 = 6
3*∑ (1/2)^n = 6
La diferencia de dos numero es 3.su suma es 13 cuáles son los dos numero
Answer: Los dos números son 8 y 5
Explanation:
Considere los dos números como
x
and
y
A partir de los datos dados, escribimos:
x
−
y
=
3
x
+
y
=
13
A partir de la primera ecuación, determinamos un valor para
x
.
x
−
y
=
3
agregar
y
a ambos lados.
x
=
y
+
3
En la segunda ecuación, sustituya
x
with
(
y
+
3
)
.
x
+
y
=
13
(
y
+
3
)
+
y
=
13
Abra los corchetes y simplifique.
y
+
3
+
y
=
13
2
y
+
3
=
13
Sustraer
3
de cada lado.
2
y
=
10
Divide ambos lados por
2
.
y
=
5
En la primera ecuación, sustituya
y
con
5
.
x
−
y
=
3
x
−
5
=
3
Agregar
5
a cada lado.
x
=
8
Step-by-step explanation:
Let a be a rational number and b be an irrational number. Is a+b rational or irrational?
Please HALP
a rational number m is called a perfect square if and only if for some positive rational number, m equals
50a+80
GIVING BRAINLEST
Answer:
180
Step-by-step explanation:
Two lines, a and b, are parallel. If both of the lines are rotated 90° in the same direction and then translated to the right by the same number of units, which statement about the lines resulting from these transformations is true? They will be parallel. They will be the same line. They will be perpendicular. They will intersect, but they won't be perpendicular.
Answer:
They will be parallel.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Translation is the movement of a point up, down, left or right. Rotation is the turning of a point about a fixed point.
If two parallel lines a and b are rotated 90° in the same direction, they would still be parallel. If they are then translated to the right by the same number of units, they would still remain parallel to each other.
the square on the right is a scaled copy of the square on the left identify the scale factor
The shape of a patio is triangle without hight of 8 ft and base of 17 ft what is the cost of out door carpeting to cover the patio of the carpeting costs 6.50 per ft
Answer:
$442
Step-by-step explanation:
Given :
Height of patio, h = 8ft
Base of patio = 17 ft
Cost of carpeting = $6.50 per ft²
Area of triangular patio :
Area = 1/2 * base * height
Area = 0.5 * 17 * 8
Area of patio = 4 * 17
Area of patio = 68 ft²
Cost of carpeting :
Area of patio * contains st per ft²
68 * 6.50
= $442
A regular 13-gon is inscribed in a circle. Find the measure of each are intercepted by the sides of the polygon. Round your answer to the nearest hundreth of a degree.
Answer:
The measure of the angle subtended by each arc intercepted by the sides of the reh13-gon is approximately 27.69°
Step-by-step explanation:
The number of of equal sides in a regular 13-gon = 13 sides
The measure of the angle, 'θ', subtended by each arc intercepted by the sides of the 13-gon is given as follows;
θ = 360°/13 = [tex]27\dfrac{9}{13} ^{\circ}[/tex]
By rounding rounding the answer to the nearest 10th, we have that the measure of the angle subtended by each arc intercepted by the sides of the 13-gon, θ = [tex]27\dfrac{9}{13} ^{\circ}[/tex] ≈ 27.69°
In the following equation, which number is the slope (rate of change) and which is the y-intercept?
y = 32 - 4
Slope:
Y-Intercept:
Answer: Slope: 3z
Y intercept: -4
Step-by-step explanation:
Andre runs for 35 seconds at a velocity of -8 meters per second. He is running west. What is his finishing position?
Answer:
d = -280 m
Step-by-step explanation:
Given that,
Velocity of Andre, v = -8 m/s
Time taken, t = 35 seconds
We need to find his finishing position. Let the finishing position be x.
We know that,
Velocity = distance/time
So,
[tex]d=v\times t\\\\d=-8\times 35\\\\=-280\ m[/tex]
so, he was at a distance of 280 m in west.
What is the range of (-5, 2), (-2, 4), (2, -7), (4, 8)?
Which is the graph of y= 3/4x-3?
Graph C
Graph B
Graph A
Help I'm not sure if this is the answer?
(This question is about trigonometric ratios)
9514 1404 393
Answer:
(b) 15.32
Step-by-step explanation:
You can use your triangle sense to answer this.
The side x will always be shorter than the hypotenuse, 20. This eliminates the last two choices.
If the angle is 45°, then the sides are equal at about 0.707 times the length of the hypotenuse. That would make them 0.707×20 = 14.14. Since the angle is greater than 45°, the opposite side will be greater than 14.14. Only one answer choice fits between 14 and 20: the second choice -- 15.32.
__
The mnemonic SOH CAH TOA reminds you of the relation ...
Sin = Opposite/Hypotenuse
sin(50°) = x/20
x = 20×sin(50°) . . . . multiply by 20 to find x
x ≈ 15.32 . . . . . . . . . use your calculator to evaluate
__
The attachment is intended to show how the triangle side lengths change with angle.
This statement shows the ______ property.
Answer:
besti you didnt put the statement
Find the inverse of the given function.
y = log2(4x)
Answer:
f^−1(x)=2^x/4
Step-by-step explanation:
The inverse of the function will be;
⇒ [tex]f ^{-1} (x) = \frac{2^{x}}{4}[/tex]
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The function is,
⇒ y = log₂ (4x)
Now,
Since, The function is,
⇒ y = log₂ (4x)
Find the inverse of the function as;
⇒ y = log₂ (4x)
⇒ [tex]2^{y} = 4x[/tex]
⇒ [tex]\frac{2^{y}}{4} = x[/tex]
⇒ [tex]f ^{-1} (x) = \frac{2^{x}}{4}[/tex]
Thus, The inverse of the function y = log₂ (4x) is,
⇒ [tex]f ^{-1} (x) = \frac{2^{x}}{4}[/tex]
Learn more about the function visit:
https://brainly.com/question/28361556
#SPJ2
The distance a train travels between 2 cities is 540 miles. The train travels at a speed of 80 miles per hour. Matt set up these rates to find the time it took the train to travel between the 2 cities.
Answer:
it takes 6 hours 40 minutes
Answer: 6.75 hours
Step-by-step explanation:
540%80=6.75
Simplify: 3x + 6y - (4x - 2y)
Answer:
-x + 8y
Step-by-step explanation:
Jackson invested $140 in an account paying an interest rate of 3 3/4% compounded
quarterly. Lucy invested $140 in an account paying an interest rate of 3 1/2%
compounded daily. After 10 years, how much more money would Jackson have in his
account than Lucy, to the nearest dollar?
Answer: $5
Step-by-step explanation:
24% of 40
I need it worked out pls thank uuu:)
Step-by-step explanation:
24% is the same as 6/25
[tex] \frac{6}{25} \times 40 \\ = \frac{48}{5} = 9.6[/tex]
Answer:
9.6
Step-by-step explanation:
24% of 40 = 0.24 × 40 = 9.6
Help me please thanks
Replace x any with the given values:
x/y = 9/3 = 3
The answer is 3
Which rule describes the translation below? On a coordinate plane, triangle S T U is shifted 3 units down and 5 units to the left to form triangle S prime T prime U prime.
Answer:
(x, y) ⇒ (x - 5, y - 3)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Translation is the movement of a point up, down, left or right. If a point A(x, y) is translated a units left and b units down, the new point is at A(x - a, y - b), while If a point A(x, y) is translated a units right and b units up, the new point is at A(x + a, y + b).
Given that triangle S T U is shifted 3 units down and 5 units to the left to form triangle S prime T prime U prime. The rule that describes this translation is given as:
(x, y) ⇒ (x - 5, y - 3)
If y=2x and 3x – 3y = 2, then x
Answer:
x = - 2/3
Step-by-step explanation:
2x = y
3x - 6x = 2
- 3x = 2
- 3x ÷ - 3 = 2 ÷ - 3
x = 2 ÷ - 3
x = - 2/3
The value of x is_____and the value of y is ___.
Answer:
x=60 y=50
Step-by-step explanation:
60+y=110
y=50
My sister is 11 years old. My brother say that his age minus thirteen is equal to my sister age . How old is my brother
Answer:
24
Step-by-step explanation:
13+11=24
Change 22 metres per second to a speed in kilometres per hour.
Show your working clearly.
Answer:
79.2 km/hour
Step-by-step explanation:
1 m/sec= 3.6 km/hour 22m/sec= ? so just multiply 22 m/sec by 3.6 km/hour then the answer will be :- 79.2 km/hour
I really need help...Will mark brainiest
Answer:
[tex]x^{2} -1[/tex]
Step-by-step explanation:
You will need to multiply and distribute out the equation.
[tex](x-1)(x+1)\\x^{2} - x + x -1\\x^{2} - 1[/tex]
Explain how you use a net to find the surface area of a prism.
Answer:
Nets of rectangular prisms are made up of rectangles and squares. Finding the areas of each of the rectangles and squares of the net of a rectangular prism and adding up those areas gives the surface area or total surface area of the prism.
Step-by-step explanation:
Answer:
By drawing a net, you can see each face of the prism. You can find the areas of each face and then add them together to find the total surface area.
Step-by-step explanation:
This is edges sample resopnse
A and B are independent events. Find P(A and B). P(A)=1/5, P(B)=3/7
Answer:
Step-by-step explanation:
I’m stuck lol pls help
Answer:
x=90
Step-by-step explanation:
So, since x-20 is the vertical angle directly near 70, we can say:
x-20=70.
if we solve x is 90.
HOPE IT HELPS!!!!!!!!!!!
Find C.
Round to the nearest tenth
Answer:
Step-by-step explanation:
c^2=a^2+b^2-2abcosC
cosC= (a^2+b^2-c^2)/(2ab)
C=arccos[(a^2+b^2-c^2)/(2ab)]
C=arccos(90^2+55^2-50^2)/(2(90)55)
C=arccos(8625)/(9900)
C=29.4 degrees