The sum 4 + 8 + 16 + 32 + 64 + 128 + 256 can be rewritten using sigma notation as:
∑k=1^7 2k-1; where n = 7 and ak = 2k-1.
To understand this notation, ∑ is the symbol for sum, k is the index variable that starts at 1 and goes up to n, and ak is the term in the sum that depends on the index variable k. In this case, ak = 2k-1 means that the k-th term in the sum is obtained by raising 2 to the power of (k-1).
So, for example, when k = 1, we have a1 = 2^0 = 1, and when k = 2, we have a2 = 2^1 = 2, and so on, up to k = 7, which gives a7 = 2^6 = 64. Adding up all the terms gives the original sum: 4 + 8 + 16 + 32 + 64 + 128 + 256 = 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
The sum 4 + 8 + 16 + 32 + 64 + 128 + 256 can be rewritten as ∑(from k=1 to n) a_k, where a_k = 2^(k+1). In this case, n=7 because there are 7 terms in the sum, and a_k follows the formula a_k=2^(k+1).
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Your math teacher tells you that the next week's test is worth 100 points and contains 28 problems. Each problem is worth either 5 or 3 points. How many of each type of problem are on the test?
Therefore , equation problem answer is there will be six 5 mark problem and twenty two 3 mark problem.
How do you quickly solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.
Here,
Given :
Since the total number of points is 28, we can create the Let Statements:
Let x= one type of question
Let 28-x= the other type of questions
Create an equation to relate the number of questions to the price
100=5x+3(28-x) Distribute
100=5x+82-3x Subtract 76 from both sides of the equation
100-82=5x-3x Combine like terms
18=3x Divide both sides by 3
x=6
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if each quadrilateral below is a kite, find the missing measures
please hurry
A quadrilateral shape called a trapezoid that has exactly one set of parallel sides. Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.
What are angles in a quadrilateral?A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed by two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle.
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. A quadrilateral's internal angles add up to 360 degrees in all cases. The four angles found at each vertex of a four-sided form are referred to as the interior angles of a quadrilateral and are the only angles in a quadrilateral. Every quadrilateral's internal angles add up to 360 degrees.
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How do you convert base 10 to base E?
To convert from base 10 to base e, we need to split down a number in base e into the powers of e.
When we convert from base 10 to base e, the pattern will be exactly the same. It will be just with e instead of 10.
For example, to see how many digits (before the decimal point) of ln(12) = 2.4849...
It means that the first digit will be on the e^2 position. Now lets find:
12 / e^2 = 1.624…
So, there will only be a 1 in the e^2 position. The remaining is 12 – e^2. The next position is e^1 position. To find out what’s on this position, we need to do the following calculation:
(12 – e^2) / e = 1.696…
The next digit will also be a 1.
Now we do the 1’s position:
(12 – e^2 – e) / 1 = 1.892…
Next digit’s a 1.
We can continue for a few more decimal places:
(12 – e^2 – e – 1) / e – 1 = 2.426…
Next digit’s a 2.
(12 – e^2 – e – 1 – 2 * e – 1) / e – 2 = 1.159…
Next’s digit a 1.
So, 12 in base e is 111.21…
Since e is irrational and 12 is not, this will be never ending. But there will only can be 0’s, 1’s, and 2’s, since e is less than 3.
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PLSSS HELP ME LAST ONE AND I PASS PLEASEEEEEE HELP
Answer: D
Step-by-step explanation:
Answer:
D) 320 pi
Step-by-step explanation:
pi*r^2*h is the equation for the volume of a cylinder.
If you plug in the given values, then you get 320pi.
The answer is D) 320 pi.
Hope this helped! :)
There are 8 squares and 2 triangles. What is the simplest ratio of triangles to total shapes?
Answer:
2:10 or 1:5
Step-by-step explanation:
Answer: 4 squares to 1 triangle
Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into
Term 4
1/7
Gustavo is driving a bus along a motorway with a
speed limit of 70 miles per hour. In 30 minutes, he
travels 36 miles. Is his average speed during this
period exceeding the speed limit? And what is his average speed
Yes, his average speed during this time exceeded the posted speed limit; it was 35 miles per hour.
what is equation ?Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations. Algebra is used in many equations. When it comes to arithmetic, algebra is used when it's difficult to compute an exact amount.
given
His average speed throughout this time was 35 miles per 30 minutes (average speed = 70 / 2 = 35 miles per 30 minutes),
which is over the speed limit because he traveled 36 miles during that time.
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Find the measure of angle “x” in degrees. Round to two decimals places as necessary!! HELPP PLS
The value of x is 0.01
What is the measure of a degrees?Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees. We'll just take into account angles between 0° and 360° for the time being; however, we'll take into account angles higher than 360° and negative angles later, in the section on trigonometric functions.
Minutes and seconds can be used to further split degrees, but this separation is less common than it once was. Minutes are the 60 equal pieces that make up each degree. Thus, seven and a half degrees can also be written as seven degrees and thirty minutes, or seven°30'. Additionally, each minute is divided into 60 equal seconds.
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someone help
f(-3x)
-3f(x)
f(3x)
3f(x)
Answer:
Step-by-step explanation:
f(-3x) = -3f(x)
f(3x) = 3f(x)
This is assuming that f is an existing function and it follows this rule for any input. If not, it will not necessarily be true for all inputs.
given segment CE and point D that lies on CE, find CD =27, CD=76-7x, and ED=39-4x
Answer:
use c and d
Step-by-step explanation:
What is the third quartile of this data set?
14, 18, 20, 21, 25, 32, 40, 44, 48
Answer: 42
Step-by-step explanation:
Math
What is the value of x? round to the nearest tenth, if necessary. Responses x = 4 x, = 4 x = 5 x, = 5 x = 6. 2 x, = 6. 2 x = 9. 4.
The value of x is 6.2 units.
Now by using the Pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
Now in the Δ ABD
As given DB² = DA² + AB²
As given
DB = 13 units
AB = 9 units
Putting values in the above
13² = 9²+ DA²
169 - 81 = DA²
88 = DA²
DA=√88
In ΔABC
AB² = AC² + CB²
(As given AB = 9 units , CB = x)
9² = AC² + x²
AC ² = 81 - x²
Now in ΔADC.
AD² = AC² + DC ²
As AC ² = 81 - x²
DC = 13 - x
AD=√88
(√88)²=81-x²+(13-x)²
(By using the formula (a + b)² = a² + b² + 2ab )
88=81-x²+13²-2*13*x+x²
88=81-x²+13²-26x+x²
88-81 - 169 = -26x
88-250 =-26x
-162 = - 26x
x=162/26
x = 6.2 (Approx)
Therefore the value of x is 6.2 units.
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42 POINTS!!!
Better Cable Company must provide service to a customer whose house is located 2 miles from the main highway. The nearest connection box for the cable is located 5 miles down the highway from the customer's driveway. The installation cost is $14/mile for any cable that is laid from the house to the highway. (The cable must be laid along the driveway to the house or across the field). The cost is $10/mile when the cable is laid along the highway. Determine where the cable should be laid so that the installation cost is as low as possible.
Please show work!
The required point is 0.25 miles away from the nearest point on the shore.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = lim h--> 0 (f(x + h) - f(x)) /(x + h - x).
here, we have,
It can be applied to minimize or maximize a function.
The given problem can be shown in the form of a diagram as follows
Suppose the underwater cable meet the shore at a distance x from the nearest point.
Then, the distance of cable in water is x² + 3.5² = x² + 12.25
And, the distance of cable in the ground is 10 - x.
As per the question, the cost of the laying cable can be represented as follows,
C(x) = 1200(10 - x) + 2400(x² + 12.25)
In order to minimize the cost the above function can be differentiated and equated to zero as,
C'(x) = -1200 + 4800x = 0
=> x = 1200/4800
= 1/4
= 0.25
Hence, in order to minimize the cost of the entire project the underwater cable should meet the shore at 0.25 miles away from the nearest point.
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Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is isosceles.
The quadrilateral MNPQ is trapezoid but not an isosceles trapezoid .
What is a trapezoid?A trapezoid, as well known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.
Here given points,
M(-2,0), N(0,4), P(5,4), and Q(8,0) are given.
We are familiar with the slope formula,
Slope = y2 - y1 / x2 - x1
So here,
Slope of MN = 4 - 0 / 0 - (-2)
= 4/2
= 2
Slope of NP = 4 - 4 / 5 - 0
= 0/5
= 0
Slope of PQ = 0 - 4 / 8 - 5
= -4/3
Slope of QM = 0 - 0 / -2 -(-8)
= 0/10
= 0
Therefore we can see, NP||QM and MN∦PQ.
Therefore MNPQ is a trapezoid because it has two parallel sides.
By using distance formula,
MN = [tex]\sqrt{0-(-2)^{2} +(4-0)^{2} }[/tex]
= √20
= 2√5 units
PQ = [tex]\sqrt{(8-5)^{2} +(0-4)^{2} }[/tex]
= √25
= 5 units
Here MN ≠ PQ , MN and PQ are not congruent to each other.
Therefore MNPQ not is a isosceles trapezoid.
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How do you find the sides of a triangle given the vertices?
So on solving the provided question we can say that - all angles of triangle - 180; x = 60
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
all angles of 180
x +90+30 = 180
x = 60
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The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
If the equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books. The number of books is 4.
How to find the number of books?Given data:
Equation: 3.95m + 8.95b = 47.65
Where:
Magazine, m = 3
Now let find the number of book by using the equation to solve for b
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
Collect like terms
8.95b = 35.8
Divide both side by 8.95b
b = 35.8/8.95
b = 4 books
Therefore we can conclude that the number of books is 4.
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The complete question is;
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
Briana estimates the length of a living room to be 24 feet. Ariane estimates it to be 9 yards. If the actual length is 26 feet, which is the better estimate explain
Answer:
9 yards is a better estimate.
Step-by-step explanation:
This is because it is closer to the actual answer. 9 yards is only 1 foot off while the other is 2.
Yoo can someone help me please and show the work
A triangle is a polygon with three sides and three vertices. The triangle's interior angle, which is 180 degrees, is formed.
What is a triangle definition?Three sides and three vertices make up a triangle, which is a polygon. There is a 180 degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.
A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is a triangle that is depicted in the previous illustration.
An "opposite" side in a right triangle is the one that is across from a specific angle, while a "adjacent" side is the one that is next to a specific angle. The hypotenuse is the longest side in a right triangle.
Therefore, the answer is:
Side LN = 4.33013 = 5√3/2
Side MN = 5
Side c = 2.5
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What is the solution to the system that is created by the equation y = negative x + 6 and the graph shown below?
On a coordinate plane, a line goes through (0, 0) and (4, 2).
What is the solution to the system that is created by the equation y = negative x + 6 and the graph shown below?
On a coordinate plane, a line goes through (0, 0) and (4, 2).
(4, 2)
(–4, –2)
(–8, –4)
(6, 3)
The solution of system of equations are (4, 2). Therefore, option A is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given equation is y=-x+6 ---------(I)
On a coordinate plane, a line goes through (0, 0) and (4, 2).
Here, slope m=(2-0)/(4-0)
= 1/2
Substitute m=1/2 and (4, 2) in y=mx+c, we get
2=1/2 (4)+c
c=0
y=1/2 x ---------(II)
Substitute equation (II) in equation (I), we get
1/2 x=-x+6
x=-2x+12
x+2x=12
3x=12
x=4
Substitute x=4 in equation (II), we get
y=2
Then, solution of system of equations is (4, 2)
Therefore, option A is the correct answer.
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You can complete 40 push-ups in 2 minutes. Your friend can complete 57 push-ups in 3 minutes. Do these rates form a proportion? Explain by finding the unit rates.
_____ (yes or no), the rates _____(are or are not) equivalent. I can complete _____ push-ups per minute and my friend can complete _____ push-ups per minute.
Response:
---------------------------------------------
----------------------------------------------
----------------------------------------------
----------------------------------------------
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.2=6
6=40
Find the length of the indicated
side of the similar figure.
12
X
x = [?]
X
8
4
The length of the side indicated in the similar figure can be found using the concept of similarity.
Find the length of the indicated side?The length of the side indicated in the similar figure can be found using the concept of similarity.When two figures are similar, the corresponding sides are proportional.In this case, the side indicated in the figure is 8, and the side we are looking for is X.To find the length of X, we can set up a proportion and solve for X. The proportion would be 8/X = 12/8, which simplifies to X = 12.Therefore, the length of the side indicated in the similar figure is 12.The length of the indicated side of the similar figure is 4.This is because the two figures are similar, meaning they have the same shape and ratio of sides.This means that if one side is 8, the other will be 4, since 8/4 = 2.This theory is called the Proportionality Rule and states that if two figures are similar, the corresponding sides are proportional.To learn more about Proportionality Rule refer to:
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What is the volume of a box shape of a right rectangular prism with height 10 inches, length 7 inches, and width 4 inches?
The volume of a box shape of a right rectangular prism with height 10 inches, length 7 inches, and width 4 inches would be 280 cubic inches.
What is Volume?
Volume can be defined as the amount of space occupied by any three-dimensional solid. These solids can be anything from a cube to a cuboid, a cone, a cylinder or a sphere.
It is also the measure of the capacity that an object holds.
Volume = h x l x w
where
h = 10 inches
l = 7 inches
w = 4 inches
Volume = 10 x 7 x 4
Volume = 280 cubic meters
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what is the measure of the length of a rectangle with a perimeter of 10 inches and a width of 2 inches?
Answer:
3 inches
Step-by-step explanation:
The perimeter is the sum of all the sides of a shape. A rectangle has 4 sides.
2 * 2 = 4
One side is 2 in., so the parallel side is also 2 in.
10 - 4 = 6
Subtract the sum from the perimeter.
6 / 2 = 3
Since there are two sides left, divide by 2.
Reggie made a cale drawing of a houe. In real life, the garage i 3 meter wide. It i 6 millimeter wide in the drawing. What i the drawing' cale factor?
The scale factor of Reggie's drawing is 1/500.
The scale factor of a drawing is the ratio of the size of the drawing to the size of the real object.
To find the scale factor of Reggie's drawing, we can use the information given: in real life, the garage is 3 meters wide, and in the drawing, it is 6 millimetres wide.
We know that:
Scale factor = size of drawing/size of the real object
We can use this equation to find the scale factor of Reggie's drawing:
Scale factor = 6 millimetres / 3 meters
To make the units consistent, we need to convert 3 meters to millimetres.
1 meter = 1000 millimeters
So, 3 meters = 3 * 1000 millimeters = 3000 millimeters
Now we can substitute this value into the scale factor equation:
Scale factor = 6 millimetres / 3000 millimetres
Simplifying the fraction: Scale factor = 1/500
Therefore, the scale factor of Reggie's drawing is 1/500. This means that every 1 millimetre on the drawing represents 500 millimetres (or 0.5 meters) in real life.
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What is the value of x?. round to the nearest tenth, if necessary. responses x = 6 x, = 6 x = 6.3 x, = 6.3 x = 7 x, = 7 x = 9.2
Round to the nearest tenth , if necessary the value of x is 6.3.
What is right triangle ?
A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.
To find the value of x ,
⇒ [tex]\frac{10}{x}=\frac{x}{4}[/tex]
⇒ [tex]x^{2} = 40[/tex]
⇒ x = 6.3
Hence , Round to the nearest tenth , if necessary the value of x is 6.3.
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What is 50% dilated?
Dilation is a process of changing the size of an object or shape by decreasing or increasing its dimensions by some scaling factors.
What is Dilation ?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape. This transformation is expressed by the term “scale factor.The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor , k . The value of k determines whether the dilation is an enlargement or a reduction. If |k|>1 , the dilation is an enlargement. If |k|<1 , the dilation is a reduction.To learn more about Dilation refers to:
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Dilation is the practice of altering an object's or shape's size by either enlarging or decreasing its dimensions by a certain amount.
Dilation: What is it?A transform called dilation is used to alter an object's size. Dilation is a technique for enlarging or contracting objects.
The result of this transformation is an image that has the same shape as the original. A stretched figure can be enlarged by using given formula:
Scale is equal to the difference between the original and new shapes' sizes.
Stretch transformations (similarity transformations) enlarge or shrink shapes. You require a scale factor of k and a central point. Depending on the value of k, the expansion either grows or shrinks. Elongation is elongation for |k| > 1. If 1 is stretched, for |k|.
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in 1988, I paid$8450 brand new car, but boy, did that car depreciate. by 1993, it was only worth $2200
write an equation that will model this situation. round your rate the nearest 4 places
y = 8450(0.7640)ˣ is the equation that will model this situation
How to write an equation that will model this situation?The general form of exponential equation is given by:
y = abˣ
Where a is the initial value of the car, b is the depreciation rate and x is the number of years
When x = 0, y = $8450:
y = abˣ
8450 = ab⁰
a = 8450
In 1993, x = 1993 - 1988 = 5 years and y = $2200:
y = abˣ
2200 = 8450b⁵
b⁵ = 2200/8450
b = [tex]\sqrt[5]{}[/tex](2200/8450)
b = 0.7640
Thus, the equation that model the situation is y = 8450(0.7640)ˣ
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A 1. 50-kilogram ball is attached to the end of a 0. 520-meter string and swung in a circle. The velocity of the ball is 9. 78 m/s. What is the tension in the string? do not round your answer during any of your calculations until the end and then round to the nearest whole number. 3. 39 n 28. 2 n 276 n 74. 6 n.
The the tension in the string is 276 N. Thus, the correct answer is B.
The tension in the string provides the centripetal force needed to keep the ball moving in a circular motion. As the tension in the string increases, the centripetal force increases as well, and the ball will move in a smaller circle (the radius will decrease). Therefore, if the tension increases, the radius decreases and the velocity increases, and if the tension decreases, the radius increases and the velocity decreases.
To determine the tension in the string, we can use the equation:
Tension = m * v^2 / rWhere m is the mass of the ball, v is the velocity of the ball, and r is the radius of the circle.
In this problem:
m = 1.50 kgv = 9.78 m/sr = 0.520 mSo, tension:
= (1.50 kg) * (9.78 m/s)^2 / (0.520 m) = (1.50 kg) * 96.0864 m^2/s^2 / (0.520 m)= 276 NThe tension in the string is 276 N. Hence, the correct answer is B.
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help me pleaseeeeeeee dont guess
The inequalities given are 9) "And inequality, 10) "Or" inequality.
What are Compound Inequalities?Compound inequalities are inequalities which consist of two or more simple inequalities.
"And" compound inequality has both the inequalities true.
"Or" compound inequalities have any one of them as true.
9. |5 + m| < 13
This can be written as,
-13 < 5 + m < 13
-13 - 5 < m < 13 - 5
-18 < m < 8
This is an "and" inequality. Because m can lie between -18 and 8.
10. 4 |y + 6| ≥ 3
|y + 6| ≥ 3/4
-3/4 ≥ y + 6 ≥ 3/4
-3/4 - 6 ≥ y ≥ 3/4 - 6
-6.75 ≥ y ≥ -5.25
The value of y can be either ≤ -6.75 or y ≥ -5.25. y cannot be both.
So this is an "or" inequality.
Hence the first one is and inequality and the second one is or inequality.
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Evaluate (-6)^8/(-6)^5.
Answer:
[tex] \sf \: {( - 6)}^{3} = - 216[/tex]
Step-by-step explanation:
Given problem,
→ (-6)⁸/(-6)⁵
Let's evaluate the problem,
→ (-6)⁸/(-6)⁵
→ 1679616/-7776
→ (1679616) ÷ (-7776)
→ -216
→ (-6)³
Hence, the answer is (-6)³.
3. A skydiver started his jump from the airplane. He fell 4.9 m in the 1st second, 14.7 m
in the 2nd second, 24,5 m in the 3rd second. How far did he fall between the 7th and the
10th seconds?
Arithmetic or geometric
The distance between the 7th seconds and the 10th seconds is 29.4 m.
It is arithmetic.
How to determine how far did he fall between the 7th and the 10th seconds?An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is always the same, called the common difference.
Since the height in the 1st second, 2nd second and 3rd second are 4.9m, 14.7 and 24.5 respectively.
They have a common difference (d) of 9.8. That is:
d = 14.7 - 4.9 = 9.8
Thus, it is arithmetic
The formula for determining nth of an AP is given by:
nth = a + (n-1)d
where a is the first term, d is the common difference and n is the number of terms
7th seconds:
nth = a + (n-1)d
nth = 4.9 + (7-1)9.8 = 63.7 m
10th seconds:
nth = a + (n-1)d
nth = 4.9 + (10-1)9.8 = 93.1 m
distance between the 7th and the 10th seconds:
10th seconds - 7th seconds = 93.1 - 63.7 = 29.4 m
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