According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
The surface area of a sphere is 320 square centimeters. what is the radius of the sphere? round your answer to 2 decimals places. the radius is centimeters.
Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.
What is the radius of the sphere?The surface area of a sphere is simply the total area that covers its outer surface.
The surface area of a sphere is expressed as;
A = 4πr²
Where r is radius and π is pi. ( π = 3.14 )
Given the data in the question;
Area A = 320cm²Radius r = ?We substitutes the given values into the equation above.
A = 4πr²
320cm² = 4 × 3.14 × r²
320cm² = 12.56 × r²
r² = 320cm² / 12.56
r² = 25.477707cm²
r = √25.477707cm²
r = 5.05cm
Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.
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Answer:
The radius is 5.05 centimeters.
Hope this helps!
Step-by-step explanation:
find the missing length 25 and 65
Answer: 60.
Step-by-step explanation:
Let in a right triangle one of the legs is 25, and the hypotenuse is 65.
Hence, the other leg is: [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]
Find a power series representation for the function
Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].
[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]
By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have
[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]
Then the series expansion of [tex]f(x)[/tex] is
[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]
[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.
Find the power series representation for the function:In the question the given function is,
⇒ f(x) = x³sin(x) + e³ˣ⁺²
We know that series representation of sin x and eˣ are:
[tex]sin x = \sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1}[/tex][tex]e^{x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]
= [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
Substituting the series representation in the function we get,
⇒ f(x) = x³sin(x) + e³ˣ⁺²
⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².
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Is there anyone who help me in my math work
Answer:
LCM=72
Step-by-step explanation:
l.c.m by prime factorization
a)18,24
factor of 18=2*3*3
factor of 24=2*2*2*3
common and remaining factor=2*3*3*2*2= 72
Evaluate the line integral
6 integral yzcosx ds x = t, y = cost, z = sint 0 < t < pi
It looks like the integral is
[tex]\displaystyle 6 \int yz\cos(x) \, ds[/tex]
With [tex]x=t[/tex], [tex]y=\cos(t)[/tex], and [tex]z=\sin(t)[/tex], the line element is
[tex]ds = \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt}\right)^2 + \left(\dfrac{dz}{dt}\right)^2} \, dt = \sqrt2 \, dt[/tex]
and so
[tex]\displaystyle 6 \int yz\cos(x) \, ds = 6\sqrt2 \int_0^\pi \cos^2(t) \sin(t) \, dt[/tex]
Substitute [tex]u = \cos(t)[/tex] and [tex]du=-\sin(t)\,dt[/tex], then
[tex]\displaystyle 6 \int yz\cos(x) \, ds = -6\sqrt2 \int_1^{-1} u^2 \, du = 12\sqrt2 \int_0^1 u^2 \, du = \boxed{4\sqrt2}[/tex]
where in the second-to-last equality, we have
[tex]\displaystyle -\int_1^{-1} = \int_{-1}^1[/tex]
and
[tex]\displaystyle \int_{-1}^1 u^2 \, du = 2 \int_0^1 u^2\,du[/tex]
by symmetry.
find the exepted value of the random varible with the following probability distribution x=2,3,4,5,6,7,8,9,10,11,12 Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36
The expected value of the random variable is 7
How to determine the expected value of the random variable?The probability distribution is given as:
x=2,3,4,5,6,7,8,9,10,11,12
Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36
The expected value of the random variable is calculated using
E(X) = ∑xP(x)
Using the above formula, we have
E(x) = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9+ 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18+ 12 * 1/36
Evaluate the sum of products
E(x) = 7
Hence, the expected value of the random variable is 7
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Marcus had $50 in the bank and deposited
$x a week. At the end of 15 weeks, he had
$1,010 in the bank. Write and solve an
equation to determine how much money he
deposited each week.
13)
Answer:
$64
Step-by-step explanation:
Equation: 50 + 15x = 1010
x = (1010 - 50) ÷ 15 = 64
Since x is the total amount of money deposited in the bank per week, the answer is $64.
Calling out to anyone who knows this. Seeking assistance!
Answer: someone already answered this check the link out
Step-by-step explanation. https://brainly.com/question/11711784
What is the value of y?
Z
Y
60 degrees
70 degrees
50 degrees
Using proportions, the value of y is of 100º.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:
y = 2 x 50º = 100º.
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Briefly describe each of the eight guidelines for evaluating statistical studies.
8 Guidelines for Critically Evaluating a Statistical Study
1. Identify the Goal, Population, and Type of Study
2. Consider the Source
3. Examine the Sampling Method
4. Look for Problems in Defining or Measuring the Variables of
Interest
5. Watch Out for Confounding Variables
6. Consider the Setting and Wording of Any Survey
7. Check That Results Are Fairly Represented in Graphics or
Concluding Statements
8. Stand Back and Consider the Conclusions
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algebra 2: graph question
what is the value of a?
what is the value of b?
(graph attached)
Answer:
a = 3.14
b = 6.28
Step-by-step explanation:
The interval where the function is decreasing is where increasing x values result in decreasing y values. The y values peak at the point (3.14, 2) and decrease until the point (6.28, 0) where the function starts increasing again.
What is the directrix of a parabola whose equation is (y+3)^3=8(x-3)?
Considering the equation of the parabola, the directrix is: x = 1.
What is the equation of a parabola given it’s vertex?The equation of an horizontal parabola, of vertex (h,k), is given by:
(y - k)² = 4p(x - h).
The directrix is at x = h - p.
For this problem, the equation is:
(y + 3)² = 8(x - 3).
The relevant coefficients for this problem are:
4p = 8 -> p = 2, h = 3.
Hence the directrix is:
x = h - p = 3 - 2 = 1.
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The equation of the parabola whose equation [tex](y + 3)^3 = 8(x - 3).[/tex], the directrix exists x = 1.
What is the equation of a parabola given its vertex?The equation of a horizontal parabola, of vertex (h, k), exists given by:
(y - k)² = 4p(x - h).
The directrix exists at x = h - p.
For this problem, the equation exists:
[tex](y + 3)^3 = 8(x - 3).[/tex]
The appropriate coefficients for this problem exist:
4p = 8
p = 8/4 = 2 and h = 3.
Hence the directrix exists:
x = h - p = 3 - 2 = 1.
Therefore, the directrix exists at x = 1.
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Which expression is equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0.
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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What is the range of the data? 6 7 9 10
Answer:
4
Step-by-step explanation:
10 - 6 = 4
Select the correct answer.
Which equation represents the vertical line passing through (14.-16)?
OA
OB. y=-16
OC
X= 14
OD.
y=14
X=-16
Check the picture below.
A video game shop is analyzing its sales performance using matrices. matrix a contains the unit sales data for each product category (horizontally) per week (vertically). matrix b contains the unit sales data for weekends for each category (horizontally) per week (vertically). to find the number of games in each product category that were sold each week only on weekdays, which matrix operation must be performed? a. add matrix a to the inverse of matrix b. b. more data is needed to calculate the sales during weekdays. c. subtract matrix b from matrix a. d. add matrix b to matrix a.
Answer:
Matrix B should be subtracted from Matrix A.
Step-by-step explanation:
Build Your Math Skills 2A, Round decimals to the nearest hundredth (0.01): 42.988
Answer: 42.99
Step-by-step explanation:
42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.
a) Solve
4(x-7)= 14
(2)
Answer:
x=14
Step-by-step explanation:
4(x-7)= 14(2)
4x - 28 = 28
4x = 56
x = 14
Instructions: Find the missing side length in the image below.
? =
10/
7
?
14.
Using proportions, the missing side length in the image below is of 20.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the side lengths are proportional, being related by the rule of three given as follows:
x/10 = 14/7
Applying cross multiplication:
7x = 14 x 10
7x = 140
x = 140/7
x = 20.
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please answer this question I f0ll0w u and mark brainiest and give many thanks
Answer:
look above
Step-by-step explanation:
hope it helps
please answer quickly
will give brainliest for right answer
Slope-Intercept Form: y = mx + b
---Where m is the slope and b is the y-intercept
Correct Answer: y = -5/4x + 2
---Option A
Hope this helps!
While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2. 4 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 18-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 32 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?.
The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.
How to estimate the speed of the moving walkway relative to the airport terminal?Let x be the speed of the walkway.
(2.8 + x) = speed of child moving in direction of the walkway
(2.8 - x) = speed of child moving against the direction of the walkway
Travel time = distance/speed
Travel time of child moving in direction of walkway = 23/(2.8+x)
Total elapsed time given = 29s
23/(2.8 + x)+ 23 / (2.8-x) = 29
LCD = (2.8 + x)(2.8 - x)
[tex]23(2.8 - x) + 23(2.8 + x) = 29(2.8 + x)(2.8 -x)[/tex]
simplifying the equation, we get
[tex]23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)[/tex]
[tex]23(2.8+2.8)/29=2.8^2-x^2[/tex]
[tex]x^2=(2.8)^2-(23*5.6)/29)=3.4[/tex]
[tex]x=\sqrt{3.4}=1.84m/s[/tex]
Speed of walkway = 1.84 m/s
The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.
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write 3 ratios equivalent to 2:5. Show your work
Answer: 4/10, 6/15, 8/20
Hope this helps!
The table of ordered pairs (x,y) gives an exponential function.
Write an equation for the function.
The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
At point (0, 8):
8 = ab⁰
a = 8
At point (1, 32):
32 = 8b
b = 4
The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ
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Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0, and x y≤6
For function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
For given question,
We have been given a function k(x, y) = -x² - y² + 4x + 4y
We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
First we find the partial derivative of function k(x, y) with respect to x.
⇒ [tex]k_x=-2x+4[/tex]
Now, we find the partial derivative of function k(x, y) with respect to y.
[tex]\Rightarrow k_y=-2y+4[/tex]
To find the critical point:
consider [tex]k_x=0[/tex] and [tex]k_y=0[/tex]
⇒ -2x + 4 = 0 and -2y + 4 = 0
⇒ x = 2 and y = 2
This means, the critical point of function is (2, 2)
We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
Consider k(0, 0)
⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)
⇒ k(0, 0) = 0
Consider k(3, 3)
⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)
⇒ k(3, 3) = -9 - 9 + 12 + 12
⇒ k(3, 3) = -18 + 24
⇒ k(3, 3) = 6
Therefore, for function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
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Russell has $38 and is saving $2 per day. cornelius has $64 and is spending $2 per day. after how many days will russell have more money than cornelius?
The equation be 38 + 2x - (64 - 2x) = 0 then the value of x = 6.5.
How to find the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Let the day be x
38 + 2x - (64 - 2x) = 0
Subtract 38 from both sides
38 + 2x - (64 - 2x) - 38 = 0 - 38
Simplifying the above equation, we get
2x - (64 - 2 x) = -38
Expanding the above equation, 2x - (64 - 2x) = 4x - 64
4x - 64 = -38
Add 64 to both sides
4x - 64 + 64 = -38 + 64
Simplify
4x = 26
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{26}{4}[/tex]
Simplifying the equation
[tex]$x=\frac{13}{2}[/tex]
The value of x = 6.5.
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A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?
The dart player throws a dart horizontally at a speed of 24.75 m/s.
In this question,
The horizontal distance traveled by the dart, x = 2.5 m
The dart hits the board 5 cm below the height from which it was thrown.
⇒ 5 cm = 0.05 m
Let the time taken by the dart to hit the board is t.
The time taken can be calculated using the Newton's second law of motion,
[tex]y = ut+\frac{1}{2}at^{2}[/tex]
Put, u = 0, a = -g and g = 9.8
On substituting the above values, we get
⇒ [tex]-0.05 = 0-\frac{1}{2}(9.8)t^{2}[/tex]
⇒ [tex]0.05(\frac{2}{9.8}) = t^{2}[/tex]
⇒ [tex]t^{2} =0.0102[/tex]
⇒ [tex]t=\sqrt{0.0102}[/tex]
⇒ t = 0.1010 s
Now, the velocity (speed) can be calculated as
displacement = speed × time
⇒ 2.5 = speed × 0.1010
⇒ speed = [tex]\frac{2.5}{0.1010}[/tex]
⇒ speed = 24.7524 m/s
Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.
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When navigating the maze, the robot will only need to go north, south, east, and west. it can be useful to use the complex plane to represent these directions. when using the complex plane this way, we use numbers such that their magnitude is equal to 1. if we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?
The values represent the robot facing east, south, and west are 1, -i, -1.
What was the meaning of puzzle?To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.
given that,
The robot can only go north, south, east and west.
Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.
Now,
It is provided that the ' i ' represent that robot is facing north.
So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.
Since, the values on y-axis are negative in that direction.
Hence, South will be represented by ' - i ' .
Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.
So, the value that represents East will be 1.
(as it is on the positive x-axis ).
Since, west is in the opposite direction of east.
So, West will be represented by -1.
Hence,The values represent the robot facing east, south, and west are 1, -i, -1.
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I need help asap please help me
Answer:
8
Step-by-step explanation:
I belive what they mean is how many dots thier are i am not complety sure though but just by counting them up i came up with 8.
hope this helped
solve for x in x²+8x+15=0 in factorisation method
Answer: [tex]x=-5, -3[/tex]
Step-by-step explanation:
[tex]x^2 +8x+15=0\\\\(x+5)(x+3)=0\\\\x=-5, -3[/tex]
