The three geometric mean between 2 and 512 are
When r = 4 , 8,32, 128When r = -4, -8, 32, -128The first term = 2
Consider the common ratio as r
Then the second term = 2r
The third term = [tex]2r^2[/tex]
The fourth term is = [tex]2r^3[/tex]
The fifth term is given that 512
The fifth term = [tex]2r^4[/tex]
Then the equation will be
[tex]2r^4[/tex] = 512
[tex]r^4[/tex] = 512 / 2
[tex]r^4[/tex] = 256
r = ±4
When r = 4
The three geometric mean between 2 and 512 are
2r = 2×4 = 8
[tex]2r^2[/tex] = 2×4×4 = 32
[tex]2r^3[/tex] = 2×4×4×4 = 128
When r = -4
The three geometric mean between 2 and 512 are
2r = 2×-4 = -8
[tex]2r^2[/tex] = 2×-4×-4 = 32
[tex]2r^3[/tex] = 2×-4×-4×-4 = -128
Hence, the three geometric mean between 2 and 512 are
When r = 4 , 8,32, 128When r = -4, -8, 32, -128The complete question is :
Find the three geometric means between 2 and 512.
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To find the local extrema of a polynomial function f(x) = anxn + an-1xn-1 + … + a2x2 + a1x + a0 (or any other function), you would apply the equation f ’(x) = 0. Consider the basic form of a quadratic equation: f(x) = ax2 + bx + c. Apply the equation above to this quadratic function and solve for x. The resulting equation should be familiar from algebra/pre-calculus. What did you call this equation and how is it related to the location of a local extrema on a quadratic function?
The resulting equation is the x-coordinate of the point of local extrema of a quadratic function.
To find the local extrema of a polynomial function f(x), we apply the equation f'(x) = 0. We are given the basic form of a quadratic equation. The equation is given below.
f(x) = ax² + bx + c
We need to find the differentiation of the above equation.
f'(x) = 2ax + b
Now, we will equate the obtained equation to zero and solve for the value of the variable "x".
f'(x) = 0
2ax + b = 0
2ax = -b
x = -b/2a
This resulting equation is familiar from algebra/pre-calculus. This is the x-coordinate of the point of local extrema of a quadratic function.
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Write a linear function $f$ with $f\left(0\right)=7$ and $f\left(3\right)=1$ .
A linear function will have the form f(x) = mx + b.
f(0)=7 means the point (0,7) is on this line.
f(3)=1 means the point (3,1) is on the line as well.
Using those two points, we can find the slope:
m = (1-7)/(3-0) = -6/3 = -2
Since we were given f(0)=7, we also know the y-intercept.
So our function is f(x) = -2x+7
what is the volume of the recycling box shown in the diagram , 20cm, 40cm, 60cm can someone please help asap
write answers and working out.
Answer:
i got 48000
Step-by-step explanation:
20x40x60
when solving volume you multiply the length times width times height.
The function
h
(
x
)
=
(
x
+
3
)
5
can be expressed in the form
f
(
g
(
x
)
)
where
f
(
x
)
=
x
5
, and
g
(
x
)
is defined below:
The auxiliary function used in the composition between the two functions f(x) and g(x) is equal to linear function g(x) = x + 3.
How to derive the auxiliary function in a composition function
Herein we find the result of a composition between two functions, where the variable x of the parent function f(x) is substituted by the auxiliary function g(x). The composition between the two functions is defined below:
h(x) = f ° g (x) = f [g (x)]
If we know that the parent function f(x) = x⁵, then the auxiliary function within the composition is the linear function g(x) = x + 3.
Remark
The statement is poorly formatted, the correct form is shown below: The function h(x) = (x + 3)⁵ can be expressed in the form f[g(x)] where f(x) = x⁵ and g(x) is defined below.
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it Question 3 Sandra draws a graph representing the relationship between time and distance on her morning run. She wants to show her coach that her rate in minutes per mile was the same for the entire run. Sandra chose two points on the line and drew vertical line segments from the points to the x-axis. How can she use these segments to prove that her speed was constant? Explain your reasoning.
Using the two points on the graph, Sandra can prove that her speed was constant using: Slope (m) = (18 - 6) / (3 - 1).
What is the Slope of a Graph?The slope of a graph is the ratio of the vertical distance along the line to the horizontal distance across the line, which is given as, m = change in y / change in x.
For a proportional graph, the slope is always constant, for whichever points we choose to use on the line.
Given two points on the line that Sandra chose, (3, 18) and (1, 6), therefore:
Slope (m) = change in y / change in x
Slope (m) = (18 - 6) / (3 - 1)
Slope (m) = 12/2
Slope (m) = 6
Therefore, to show her speed, which is the slope of the line, is constant, she can use the equation below:
Slope (m) = (18 - 6) / (3 - 1).
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compare 5.9 and 152 using <, > or =
Answer:
Step-by-step explanation:
Assume the radius of a certain planet is 4790 km and the planet is a sphere. What is its surface area?
Answer:
A ≈ 2.88×108km²
Step-by-step explanation:
A= 4 π r² = 4·π· 47902 ≈ 2.88324×10 power 8 km²
I need help in answering this question
Answer:
2 6 12 20,000
6 18 36 60,000
Step-by-step explanation:
The bottom number is 3 times the top number.
Shayla is tracking the weight of the smallest puppy in a liter. use the table to write a linear function that model’s the puppy’s growth
The linear function that models the puppy's growth is written as: y = 3x + 3.
How to Write the Equation of a Linear Function?The values we need to find before we can write he linear function that models a situation, are:
The slope = mThe y-intercept = bThe linear function would be expressed as y = mx + b, which is in the slope-intercept form.
The table of the puppy's growth that Shayla is tracking is shown below. Using two points on the table, say, (0, 3) and (1, 6):
Slope (m) = change in y / change in x = (6 - 3)/(1 - 0)
Slope (m) = 3/1 = 3
Substitute m = 3 and (0, 3) into y = mx + b to find b:
3 = 3(0) + b
3 = 0 + b
3 = b
b = 3
To write the linear function, substitute m = 3 and b = 3 into the equation, y = mx + b:
y = 3x + 3
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Answer: A
Step-by-step explanation: FLVS question the answer is A
HELP PLS AND HURRY!!!
Answer:
1. 5√7
2. (√15)/6
Step-by-step explanation:
1. √175
= √(25) * √(7)
= 5√7
2. √(5/12)
= (√5)/(√12)
= (√5)/(√(4) * √(3))
= (√5)/(2√3)
Radicals can't be in the denominator:
(√5)/(2√3)
(√5 * 2√3)/(2√3 * 2√3)
(2√15)/12
(√15)/6
1. Find the y-intercept of the line passing through the points A (3, -2) and B (-1, 3). (5 pts)
Answer:
-1.25
Step-by-step explanation:
m=
[tex]y2 - y1 \div x2 - x1[/tex]
3- (-2)÷ -1-3
5/-4
m=-1.25
How many more white squares are there than black squares in the 47th term? Explain how you know.
Expression (White Squares):
Expression: (Black Squares):
There are 9216 more white squares than black squares in the 47th term with it's an odd number of 97
How to calculate the 47th termThe terms are generated with the square of odd numbers with the black squares being the addition of the odd number and one subtracted from it.
For the 47th term:
Given that the first term is consists of 25 squares with 9 black and 16 white squares
first term has odd number 5
the square of 5; 5² = 25
black squares = 5 + (5-1) = 9
white squares = 25 - 9 = 16
Therefore, for the 47th term:
47th term has odd number 97
the square of 97; 97² = 9409
black squares = 97 + (97-1) = 193
white squares = 9409 - 193 = 9216
Hence, the 47th term has an odd number 97 with 9216 more black squares than the white squares,
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What is the standard form of the quadratic function y=ax^2+bx+c shown in the graph below? a=_ b=_ c=_
The standard form of the quadratic function y=ax² + bx + c = a (x - h)² + k
How to find the standard for of a quadratic function?By definition, quadratic function is a function in the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.
ax² + bx + c = a (x² - 2xh + h²) + kax² + bx + c
= ax² - 2ah x + (ah² + k)
Comparing the coefficients of x on both sides,b = -2ah ⇒ h = -b/2a .............................................(i)
Comparing the constants on both sides,c = ah² + kc = a (-b/2a)² + k (From (1))
c = b²/(4a) + kk = c - (b²/4a)k = (4ac - b²) / (4a)
Therefore, we can use the formulas h = -b/2a and k = (4ac - b²) / (4a) to convert the standard form to its vertex form.
the vertex form of the parabola is y = a (x - h)² + k
The standard form of the parabola is y = ax² + bx + c
The standard form of the quadratic function y=ax²+bx+c is x=-b± [tex]\frac{\sqrt{b^{2}- } 4ac}{2a}[/tex]
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PLEASE HELP MEEE!!!
Which point is located on the line represented by the equation y+8=3/7(x-5)
a. (3/7, 5)
b. (-5, 8)
c. (8, -5)
d. (5, -8)
e. (-8, 5)
Answer:
D, (5,-8)
Step-by-step explanation:
On the graph in the image, you can see option D's only point on the line.
Answer: D
Step-by-step explanation:
You will plug every value into the equation; if they are true, that is the correct option.
A.
5+8=3/7(3/7-5)
13=3/7(-32/7)
13=(-96/49)
A is INCORRECT
B.
8+8=3/7(-5-5)
16=3/7(-10)
16=-30/7
B is INCORRECT
C.
-5+8=3/7(8-5)
3=3/7(3)
3=9/7
C is INCORRECT
D.
-8+8=3/7(5-5)
0=3/7(0)
0=0
D IS CORRECT
Darren planted sunflowers in the community garden. During his last visit to the garden, the plants were 60 inches tall. Today, Darren found them to be 10% taller. How tall are the sunflowers now?
please due tommroe
Answer:
66 inches
Step-by-step explanation:
60 + .1(60)
60 + 6
66
Answer:
66 inches
Step-by-step explanation:
60 x .10 = 6
60 +6 =66
Let f(x) = 1 / 2+3x and point P = (2 , 1/8)
a.) Use the following definition of the slope of the tangent line at x = a to find the slope of the line tangent to the graph of f at P.
m = lim f(a+h) - f(a) / h
tan h --> 0
b.) Determine an equation of the tangent line at P.
The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
f(x) = 1 / 2+3x and point P = (2 , 1/8)
f(x+h) = 1/(2 + 3a + 3h)
f(a) = 1/(2 + 3a)
m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h
After simplifying:
m(tan) = -3/[(2+3a)(2+3a+3h)]
h = 0
m(tan) = -3/(2+3a)²
The equation of the line:
y - 1/8 = [-3/(2+3a)²](x - 2)
Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
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The length of one parallel side of a trapezium measures 24 m and the distance between parallel sides measures 28 m. The area of the trapezium is 756 m2. What is the measure of the other parallel side?
Answer:
30 m
Step-by-step explanation:
Given a trapezium with area 756 m², height 28 m, and one base of length 24 m, you want to know the length of the other base.
Area formulaThe formula for the area of a trapezium is ...
A = 1/2(b1 +b2)h
ApplicationUsing the given values, we have ...
756 = 1/2(24 +b2)(28)
54 = 24 +b2 . . . . . . . . . . . divide by 14
30 = b2 . . . . . . . . . . . . subtract 24
The measure of the other parallel side is 30 m.
i need help what is the ancer to 7+7
Answer: 14 is the ancer
Step-by-step explanation:
Answer:
its 14
Step-by-step explanation:
subtract -2x^2+5x+10 and -7x-3
The difference of the given algebraic expressions is -2x²+12x+13.
The given algebraic expressions are -2x²+5x+10 and -7x-3.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
The subtraction of given expressions is as follows
-2x²+5x+10-(-7x-3)
= -2x²+5x+10+7x+3
= -2x²+12x+13
Hence, the difference of the given algebraic expressions is -2x²+12x+13.
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Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(25,F1), (−30,F2)
The corresponding values of F1 and F2 in the ordered pairs are 77 degrees Fahrenheit and -22 degrees Fahrenheit
How to use the equation to convert from degrees Celsius to degrees Fahrenheit?
Given: the equation F=9/5C+32 and ordered pairs: (25, F1), (−30, F2)
In order to convert the given values to degrees Fahrenheit, substitute the given values into the equation to get F1 and F2 respectively:
For (25, F1):
F = 9/5 C+32 (put C= 25 in the equation)
F1 = 9/5(25) + 32
F1 = 45 +22
F1 = 77 degrees Fahrenheit
For (−30, F2):
F = 9/5 C+32 (put C= -30 in the equation)
F2 = 9/5(-30) + 32
F2 = -54 + 32
F2 = -22 degrees Fahrenheit
Therefore, the values of F1 and F2 are 77 degrees Fahrenheit and -22 degrees Fahrenheit respectively
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please help me ..............................!!!
Answer:
I hope this will be helpful for you.
0 (zero)
Step-by-step explanation:
[tex]{ \blue{ \sf{ {5}^{ - 3} \times {2}^{4} \times {5}^{3} \times {2}^{ - 5}}}} [/tex]
Arrange the like terms in order
[tex]{ \blue{ \sf{ {5}^{ - 3} \times {5}^{3} \times {2}^{4} \times {2}^{ - 5}}}} [/tex]
This is in the form of [tex]{ \red{ \sf{ {a}^{m} \times {a}^{n} = {a}^{m + n}}}} [/tex]
[tex]{ \blue{ \sf{ {5}^{ - 3 + 3} \times {2}^{4 + ( - 5)}}}} [/tex]
[tex]{ \blue{ \sf{ {5}^{0} \times {2}^{4 - 5}}}} [/tex]
[tex] { \blue{ \sf{0 \times {2}^{ - 1}}}} [/tex]
[tex]{ = \blue{ \sf{0}}}[/tex]
Any number which is multiplied with zero is zero itself.
Solve the equation 32 = v + 27 for v.
−5
5
−59
59
Answer:
Step-by-step explanation: 32=v + 27
V= 5
how:
32-27=5
v=5
I don"t know what you meant for at the bottom, if that is included please explain what you mean.
Answer:
5
Step-by-step explanation:
32 = v + 27
Subtract 27 from both sides and make v the subject.
32 - 27 = v
5 = v
Let
U
be the universal set, where:
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
Let sets
A
and
B
be subsets of
U
, where:
A
=
{
4
,
8
,
9
,
10
}
and
B
=
{
2
,
3
,
4
,
6
,
7
}
Find
(
A
∩
B
)
c
:
{
}
Find
A
c
∪
B
c
:
{
}
Enter the elements as a list, separated by commas in order from smallest to largest. If the result is the empty set, enter DNE
The elements of set (AnB)' = {1,2,3,5,6,7,8,9,10} and The elements of A'uB' = {1,2,3,5,6,7,8,9,10}
What is complement of a set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. For example, if A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
Therefore if U={1,2,3,5,6,7,8,9,10} and A={4,8,9,10} B= {2,3,4,6,7} then,
(AnB) = {4}
(AnB)' = {1,2,3,5,6,7,8,9,10}
A' = {1,2,3,5,6,7} and B' = {1,5,8,9,10}
therefore A'uB'= {1,2,3,5,6,7,8,9,10}
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Okay I think I'm going on to see if ur in
Answer:
21y-7/11
Step-by-step explanation:
First you would multiply everything outside of the prhthises to the inside. Second multiply 7 times 3y that would equal 21y. Third multiply 7 times - 1/11 that would equal to 21y-7/11
PLEASE HELP ASAP!!! Find the volume of a cube with the given side length.
1/5b^3
The volume of the cube is 1/125b⁹
How to determine the volume of the cube?From the question, we understand that
Shape = Cube
Side length = 1/5b³
Rewrite the side length as
a = 1/5b³
The volume of a cube can be expressed as V = a³
where a is the length of any side
And v is the volume
Substitute the known values in the above equation So, we have the following equation
V = (1/5b³)³
Evaluate
V = 1/125b⁹
Hence, the volume is V = 1/125b⁹
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3, 12, 27, 64, 75, 108
a) give the next number in this pattern
b) what is the rule to find the nth term?
c) what is the 20th term?
Please help + explain!
The third term from the sequence should be 48 so that (a) the next term is 147 (b) the rule to find the nth term is 3×n² and (c) the 20th term is 1200.
How to find the next term of the sequenceFrom the question, 3, 12, 27, 64, 75, 108 the third term 64 is supposed to be 48. hence the terms are derived as follows:
1st term; 3 × 1² = 3
2nd term;3 × 2² = 12
3rd term; 3 × 3² = 27
4th term; 3 × 4² = 48
5th term; 3 × 5² = 75
6th term; 3 × 6² = 108
Therefore, the next term which the 7th term is 3 × 7² = 147, the rule for the sequence is 3×n² and the 20th term is 3 × 20² = 1200.
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Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second – by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face.
Answer:
I 728.Two beetles sit at the verticesAandHof a cubeABCDEFGHwith edge length40√110 units. The beetles start moving simultaneously alongACandHFwiththe speed of the first beetle twice that of the other one.....ADCBEFGH✈s✈s. . . . . . . . . . . . . . . . . . . . . . . . ......................................................................What will be the shortest distance between the beetles?29.In the diagram,4PQRhas an area of 960 square units. The pointsS,TandUare the midpoints of the sidesQR,RPandPQ, respectively, and the linesPS,QTandRUintersect atW.......PQRSUTNMLW✓✓✼. . . . . . . . . . . . . . .....................The pointsL,MandNlie onPS,QTandRU, respectively, such thatPL:LS= 1 : 1,QM:MT= 1 : 2 andRN:NU= 5 : 4.What is the area, in square units, of4LMN?30.A 40×40 white square is divided into 1×1 squares by lines parallel to its sides.Some of these 1×1 squares are coloured red so that each of the 1×1 squares,regardless of whether it is coloured red or not, shares a side with at most one redsquare (not counting itself). What is the largest possible number of red squares?
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
3 to the second power times 3 to the third power
Judging by the appearance, name a acute angle, an obtuse angle, and a right angle
Answer:
acute angle - UVW
obtuse angle - VWX
right angle - UYX
A square with sides length x are cut out of each corner of a rectangular piece of cardboard measuring 5ft by 8ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed this way.
The volume of the largest box that can be made from the rectangular cardboard obtained by using the value of the derivative of the function for the volume at the extremum point is 18 cubic feet
What is an extremum point in mathematics?An extremum of a function is the point where the value of the function is a maximum or a minimum.
The side length of the cut out squares = x
The width of the rectangular cardboard = 5 feet
The length of the rectangular cardboard = 8 feet
The length of the side of the cut square = 8 - 2·x
Width of the side of the cut square = 5 - 2·x
Height of the cut square = x
Volume of the cut square, V = (8 - 2·x) × (5 - 2·x) × x = 4·x³ - 26·x² + 40·x
When the volume of the box is largest, we have;[tex]V' = \dfrac{d}{dx} \left(4\cdot x^3 - 26\cdot x^2 + 40\cdot x\right) = 12\cdot x^2 - 52\cdot x + 40=0[/tex]
12·x² - 52·x + 40 = 0
3·x² - 13·x + 10 = 0
Which gives;
(3·x - 10)·(x - 1) = 0
The dimensions of the cut square that gives the maximum volume are therefore;
x = 1 or x = 10/3
When x = 10/3, we have;
V = (8 - 2×(10/3)) × (5 - 2×(10/3)) × (10/3) ≈ -200/27 < 0
When x = 1, we have;
V = (8 - 2×1) × (5 - 2×1) × 1 = 18
The value of x that gives the maximum volume is therefore, x = 1
The dimensions of the box that give the maximum volume are therefore;
Height = x = 1
Length = 8 - 2×1 = 6
Width = 5 - 2 × 1 = 3
The dimensions of the box that gives the maximum volume are;
Height = 1 ft
Length = 6 ft
Width = 3 ft
The volume of the largest box that can be formed is 18 cubic feet
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