Answer:
For F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
a. [tex]M = \frac{Fr^{2} }{Gm}[/tex]
b. [tex]r = \sqrt{\frac{GMm}{F}}[/tex]
M=kxa^3/p^2
[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]
a. [tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]
b. [tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]
Step-by-step explanation:
To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.
For F=GMm/r^2
a. M =
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
The first thing to do is cross multiply, so that the equation gives
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides of the equation by [tex]Gm[/tex], we then get
[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm}[/tex]
Then, [tex]\frac{Fr^{2} }{Gm} = M[/tex]
Hence,
[tex]M = \frac{Fr^{2} }{Gm}[/tex]
b. r =
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
Likewise, we will first cross multiply, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]F[/tex], so that the equation becomes
[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]
∴ [tex]r^{2} = \frac{GMm}{F} \\[/tex]
Then,
[tex]r = \sqrt{\frac{GMm}{F}}[/tex]
For M=kxa^3/p^2
a. P =
M=kxa^3/p^2
[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]
The first thing to do is cross multiply, so that the equation becomes
[tex]Mp^{2} = kxa^{3} \\[/tex]
Now, divide both sides by M, we then get
[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3} }{M}[/tex]
∴ [tex]p^{2} = \frac{kxa^{3} }{M}[/tex]
Then,
[tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]
b. a =
M=kxa^3/p^2
[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]
Also, we will first cross multiply to get
[tex]Mp^{2} = kxa^{3} \\[/tex]
Then, divide both sides of the equation by [tex]kx[/tex] to get
[tex]\frac{Mp^{2} }{kx}= \frac{kxa^{3} }{kx}\\[/tex]
[tex]\frac{Mp^{2} }{kx}= a^{3}[/tex]
∴ [tex]a^{3} = \frac{Mp^{2} }{kx}[/tex]
Then,
[tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]
−6x+14<−28 AND 3x+28≤25
Answer: -1≥ x > 7 or x>7 and x ≤ -1
Step-by-step explanation:
-6x + 14 < -28
-14 -14
-6x < -42
x> 7
AND
3x + 28 ≤ 25
-28 -28
3x ≤ -3
x ≤ -1
x>7 and x≤ -1
Answer
x>7 and x<-1
Step-by-step explanation:
1a.) -6x+14<-28
2a.) subtract 14 from 14 and -28 (what you do to one you do to other)
3a.) you are left with -6x<-42
4a.) divide by -6 eache side of "<"
5a.) you HAVE to flip the sign when you divide by a negative
6a.) x>7
1b.) 3x+28<25
2b.) subtract 28 from 28 and 25 (what you do to one you do to other)
3b.) 3x<-3
4b.) divide both sides by 3
5b.) x<-1
Use the distributive property to remove the parentheses.
-2(5u - 3x-6)
Answer:
I think it would be: -10u - 6x 12
Step-by-step explanation:
(step 1) -2(5u - 3x-6) "First you need to times -2 by 5, 3 and -6"
that should give you -10u - 6x 12
Directions: Danny earns $12.25 per hour. He works 27 hours in a week. What is his
weekly wage? Round your answer to the nearest dollar.
Answer:
$331
Step-by-step explanation:
$12.25 per hour
27 hours
$12.25 • 27 = $330.75
What is the value oft in the easton below
--3-(-8)-(-2)
Answer:
-13
Step-by-step explanation:
What the Answer please?
Answer:
x = 151
Step-by-step explanation:
In the figure given, x is an exterior angle of the ∆.
According to the exterior angle theorem, x = the sum of the two opposite interior angles of the ∆.
One of the opposite angles measures 101°, while the second opposite angle equal 50°, since line l is parallel to m, alternate interior angles are equal.
Therefore, x = 101 + 50 = 151°
Write a literal equation that represents x% of z is equal to y.
Answer:
zx - 100y = 0
Step-by-step explanation:
Since, x% of z is equal to y
[tex] \therefore \: \frac{x}{100} \times z = y \\ \therefore \: \frac{xz}{100} = y \\ \therefore \: zx = 100y \\ \therefore \: zx - 100y = 0[/tex]
The literal equation that represents x% of z is equal to y will be xz = 100y.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
x% of z is equal to y.
Then the literal equation that represents x% of z is equal to y will be given as,
x% of z = y
xz / 100 = y
xz = 100y
The literal equation that represents x% of z is equal to y will be xz = 100y.
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Over the past several months, the water level of a lake has been decreasing by 3% each week. If the highest water level before the decrease started was 520 ft, what was the level at the end of 8 weeks?
Answer:
y= 407.54654 ft
Step-by-step explanation:
This is an exponential decay functions
y = ab^x where a is the initial value and b is ( 1 - rate of decay)
a = 520
b = 1- 3%
y = 520 ( 1- .3) ^x
y = 520 ( .97) ^x
We want x to be 8 weeks
y = 520 ( .97) ^8
y= 407.54654 ft
I need to transform this into a expression with a rational exponent but how?
Answer:
x^ (21/5)
Step-by-step explanation:
[tex]\sqrt[5]{x ^7}[/tex] ^ 3
Rewriting as a fraction
x ^ 7/5 ^3
We know that a ^b^c = a^ ( b*c)
x ^ ( 7/5 *3)
x^ (21/5)
Answer: That would be x and 21/5 ths
Step-by-step explanation:
what’s 63.55+31.99+2
Answer:97.54
Step-by-step explanation:
Answer:
97.54
Step-by-step explanation:
1 1
63.55
31.99
+ 2.00
________
97.54
Last year Frankie deli made an 11 foot 6 inch submarine this year they plan to make another one 2 feet and 3 inches longer how many feet long will this sandwich be?
Answer:
13 feet 9 inches
Step-by-step explanation:
11ft+2ft=13
6in+3in=9in
what is fifty five plus seventy two divided by three
Hey There!!~
Answer: 42
Because, 55 + 72 = 127. After you should do 3 ÷ 127. The divisor (3) goes into the first digit of the dividend (1), 0 times. Therefore, put 0 on top. Then you should Multiply the divisor by the result in the previous step (3 × 0 = 0) and write that answer below the dividend. After that Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below. Move down the 2nd digit of the dividend in the below. The divisor (3) goes into the bottom number (12), 4 time(s). Therefore, put 4 on top... Subtract the result in the previous step from the number written above it. (12 - 12 = 0) and write the answer at the bottom. Move down the last digit of the dividend in the below. The divisor (3) goes into the bottom number (7), 2 time(s). Therefore put 2 on top, Multiply the divisor by the result in the previous step (3 x 2 = 6) and write the answer at the bottom... Subtract the result in the previous step from the number written above it. (7 - 6 = 1) and write the answer at the bottom. The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 127 divided by 3 calculated using Long Division is
Answer: 42 and Remainder 1.
Hope This Helps!!~
[tex]Itsbrazts[/tex]
Hey There!! ~
The answer to this is: 79. Because, First you need to add fiifty five and seventy two which that will be 127 Then, Add fifity five and seventy two Plus, Divide three Then. you should get the answer 79.
Hope It Helps!~ [tex]ItsNobody[/tex]~
Y+v=w, for V
Please help me
Answer:
v=w/y
Step-by-step explanation:
If w=y+v, and solving for v, then simply just divide both sides by y, and you get v=w/y.
ONLY NEED TO DO 6, 8, 10, 12, 14.
Answer:
6 = (2,2)8 = (0, -6)10 =(13,-6)Step-by-step explanation:
[tex]Midpoint = (\frac{x_2+x_1}{2} , \frac{y_2+y_1}{2} )\\[/tex]
6.
[tex](5.8) =(x_1,y_1)\\(-1,-4) =(x_2,y_2)\\\\Midpoint =\left(\frac{-1+5}{2},\:\frac{-4+8}{2}\right)\\\\Midpoint =( \frac{4}{2} , \frac{4}{2} )\\\\Midpoint = ( 2 , 2)[/tex]
8.
[tex](-3 ,-7) =(x_1 ,y_1)\\(3,-5)=(x_2,y_2)\\\\\left(\frac{3-3}{2},\:\frac{-5-7}{2}\right)\\ \\Midpoint = (\frac{0}{2} , \frac{-12}{2} )\\\\Midpoint = ( 0, -6)[/tex]
10.
[tex]L(-9 ,4) =(x_1 ,y_1)\\K(2 , -1 ) = (x ,y )\\M(x_2 ,y_2 )=?\\ \\x = \frac{x_2+x_1}{2}\\ 2 = \frac{x_2 +(-9)}{2}\\ 2 = \frac{x_2-9}{2}\\ Cross\:Multiply\\\\4 =x_2-9\\4+9=x_2\\13 =x_2\\\\y = \frac{y_2+y_1}{2}\\ -1 = \frac{y_2 +4}{2} \\-1 \times 2= y_2+4\\-2 =y_2+4\\-2-4 =y_2\\-6 =y_2\\\\(x_2 ,y_2) = (13 , -6)\\[/tex]
what type of number is -1.48298
6x + 3x =
combine like terms
Answer:
9x
Step-by-step explanation:
6x + 3x
6 + 3 = 9
add the x and you get 9x
i hope this helps
Answer:
6x + 3x = 9x
Step-by-step explanation:
6 and 3 have the same coefficient meaning you can combine them and add them to get 9x.
Ali and Steve share some sweets in the ratio 2:7
Steve gets 30 more sweets than Ali.
Work out how many sweets Steve gets.
Answer:
Step-by-step explanation:Let Ali's number of sweets be x
so let Steve's number of sweet be x + 30
hence the equation is x/(x + 30)= 2/7
or, 7x = 2(x + 30)
or, 7x= 2x +60
or,7x-2x=60
or, 5x=60
or, x=60/5
or, x=12
Alif gets 12 sweets
x+30
or, 12+30
=42
Ans:Steve gets 42 sweets.
Solve by graphing. Round each answer to the nearest tenth. 6x2 + 31x = 12
Answer:
-5.5 and 0.4 (first option in your list)
Step-by-step explanation:
Please see attached image where we have graphed the expression [tex]y=6x^2+31x\\[/tex] and the expression [tex]y=12[/tex] and looked for the two points of intersection of the parabola (representing the first expression) with the horizontal line (second expression)
From the graphing we extract that one solution for "x" is approximately -5.5, and the other one around 0.36, which can be rounded to one decimal to: 0.4. then the closest solution is that one shown as the first option in your list.
can someone help me find this answer?
Answer:
(0, - 23 )
Step-by-step explanation:
Find the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 72, 25) and (x₂, y₂ ) = (- 36, 1) ← 2 ordered pairs from the table
m = [tex]\frac{1-25}{-36+72}[/tex] = [tex]\frac{-24}{36}[/tex] = - [tex]\frac{2}{3}[/tex] , thus
y = - [tex]\frac{2}{3}[/tex] + c
To find c substitute any ordered pair into the equation
Using (- 54, 13 ) , then
13 = 36 + c ⇒ c = 13 - 36 = - 23 ← y- intercept
Thus coordinates of y- intercept = (0, - 23 )
Try to calculate the arc elasticity percentage change from 80 to 100. Input your answer in percent form.
Answer: the arc elasticity percentage change from 80 to 100 is 22%
Step-by-step explanation:
formula for arc-elasticity percentage change is given as;
{ [Xₙ - X₀] / [ (X₀+Xₙ) / 2] } × 100
X₀ is old value, Xₙis new value
Now from our question
old value X₀ = 80
new value Xₙ = 100
WE SUBSTITUTE
Arc-Elasticity = { [100 - 80] / [ (80+100) / 2] } × 100
Arc-Elasticity = { [20] / [ 180 / 2] } × 100
Arc-Elasticity = (20/90) × 100
Arc-Elasticity = 22.22 ≈ 22%
Therefore the arc elasticity percentage change from 80 to 100 is 22%
In this exercise we have to use the percentage knowledge, in order to calculate the arc elasticity, so:
the arc elasticity percentage is 22%
First, we have that the formula for the elastic arc is:
[tex]([X_n - X_0] / [ (X_0+X_n) / 2] } * 100[/tex]
X₀ is old value, Xₙis new value
Informed the exercise data as:
old value X₀ = 80 new value Xₙ = 100
Substituting the values in the formula given above, we find that:
[tex]Arc-Elasticity = { [100 - 80] / [ (80+100) / 2] } * 100\\Arc-Elasticity = { [20] / [ 180 / 2] } * 100\\Arc-Elasticity = (20/90) *100\\Arc-Elasticity = 22%[/tex]
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X and Y are modeled inflation rates, in terms of %, for two different countries at the end of a five-year period. X is uniformly distributed on the interval (0, 10). Y, given X = x is uniformly distributed on the interval (0, x). Calculate Cov(X, Y).
Answer:
The value of Cov (X, Y) is 25/6.
Step-by-step explanation:
It is provided that:
[tex]X\sim U(0,10)\\\\Y|X\sim U(0,x)[/tex]
The probability density functions are as follows:
[tex]f_{X}(x)=\left \{ {{\frac{1}{10};\ 0<X<10} \atop {0;\ \text{otherwise}}} \right. \\\\f_{Y|X}(y|x)=\left \{ {{\frac{1}{x};\ 0<Y<x} \atop {0;\ \text{otherwise}}} \right.[/tex]
Then the value of f (x, y) will be:
[tex]f_{X,Y}(x,y)=\left \{ {{\frac{1}{10x};\ 0<X<10,\ 0<Y<x} \atop {0;\ \text{Otherwise}}} \right.[/tex]
Then f (y) is:
[tex]f_{Y}(y)=\int\limits^{10}_{y} {\frac{1}{10x}} \, dx[/tex]
[tex]=\frac{1}{10}\times [\log x]^{10}_{y}\\\\=\frac{1}{10}[\log 10-\log y][/tex]
Compute the value of E (X) as follows:
[tex]E(X)=\frac{b+a}{2}=\frac{10+0}{2}=5[/tex]
Compute the value of E (Y) as follows:
[tex]E(Y|X)=\frac{b+a}{2}=\frac{x+0}{2}=\frac{x}{2}\\\\\text{Then,}\\\\E(E(Y|X))=E(\frac{x}{2})\\\\E(Y)=\frac{1}{2}\times E(X)\\\\E(Y)=\frac{5}{2}[/tex]
Compute the value of E (XY) as follows:
[tex]E(XY)=\int\limits^{10}_{0}\int\limits^{x}_{0} {xy\cdot \frac{1}{10x}} \, dx dy[/tex]
[tex]=\int\limits^{10}_{0}\int\limits^{x}_{0} {\frac{y}{10}} \, dx dy\\\\=\frac{1}{10}\times \int\limits^{10}_{0}{\frac{y^{2}}{2}}|^{x}_{0} \, dx \\\\=\frac{1}{10}\times \int\limits^{10}_{0}{\frac{x^{2}}{2}}\, dx\\\\=\frac{1}{10}\times [\frac{x^{3}}{6}]^{10}_{0}\\\\=\frac{100}{6}\\\\=\frac{50}{3}[/tex]
Compute the value of Cov (X, Y) as follows:
[tex]Cov (X, Y)=E(XY)-E(X)E(Y)[/tex]
[tex]=\frac{50}{3}-[5\times\frac{5}{2}]\\\\=\frac{50}{3}-\frac{25}{2}\\\\=\frac{100-75}{6}\\\\=\frac{25}{6}[/tex]
Thus, the value of Cov (X, Y) is 25/6.
Simplify 9v + 9 + v + v when v=5
[tex]11v+9=11\cdot5+9=55+9=64[/tex].
Hope this helps.
Answer:
64
Step-by-step explanation:
9v + 9 + v + v
Combine like terms
11v+9
Let v = 5
11*5+9
55+9
64
I have one half of a circle and I want to divide it by 1/6 how many pieces would I have
2
How can the additive inverse be used to evaluate the problem below?
Vx
-3-(-6)
Because 3+(-6) is an equivalent expression, the answer is –3.
Because 3+(-6) is an equivalent expression, the answer is 3.
O Because -3+6 is an equivalent expression, the answer is -3.
Because -3+6 is an equivalent expression, the answer is 3.
An additive inverse of a number (x) is a number which when added to x results in being 0.
The given problem is -3 - (-6)
The additive inverse of -6 is 6
-3 -(-6) = -3 + 6 = 3
Communities property: 6-3 = 3
The answer is:
Because -3+6 is an equivalent expression, the answer is 3
As a person cycling increases speed, the rate of calorie burned, distance traveled, and energy expended also increase. Which of the following is the independent variable?Please explain why you chose this answer to better understand.
a. Calories
b. Energy
c. Distance
d. Speed
Answer:
d
Step-by-step explanation:
The speed is the independent variable because when it changes all the others change because it changed
The correct option is D. speed.
Given, As a person increases cycling speed, the rate of calorie burned, distance traveled, and energy also increase.
We have to find the Independent variable.
Since, Calories burned, distance traveled and Energy generated all are dependent on the speed of cycling. As the speed increases calories burned will be more.So speed is the independent variable here and the other variables all are dependent variable.
Hence the correct option is D. speed.
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Graph the line whose x-intercept is 5 and whose y-intercept is -6.
Answer:
See attached image
Step-by-step explanation:
We can easily graph the equation if we know it’s y and x intercepts. We can plot these points on a coordinate plane then connect them using a ruler, then extend these further.
Mathematically, we can find the slope which is rise over run. Every time x increases by 5, y increases by 6. This means the slope is [tex]\frac{6}{5}[/tex]. We also know the y-intercept is -6, so the equation is [tex]y=\frac{6}{5}x - 6[/tex].
Hope this helped!
there is a box in your attic with 3 books 4 dolls and 16 candles what is the ratio of candles to books
Answer:
the answer would be 16 to 3 which can also be shown as 16:3
Step-by-step explanation:
this is because it is asking for candles first so you put 16 next they ask for books so that is why you put 3 next
suppose point p(4,-9) is translated accoring to the rule (x,y). (X+3,Y-2) what are the coordinates of p? explain
Answer:
(7,-11)
Step-by-step explanation:
We are given the rule of: [tex](x,y)\rightarrow(x+3,y-2)[/tex].
Apply the rule to point P:
[tex](4,-9)\rightarrow(4+3,-9-2)\rightarrow\boxed{(7,-11)}[/tex]
P' should be (7,-11).
Hope this helps.
What is the new coordinate for point S' when the figure is reflected over the line y=x HINT: (just switch the x and y coordinates of the points)
Answer: (1, -2)
Step-by-step explanation:
The original coordinate of S is (-2, 1)
As mentioned, also in the hint, exchange the position of x and y coordinate to get the new coordinate that is reflected after y=x
(basically in the 4th quadrant)
The new coordinate of S' is (1, -2)
Hope this helps!! :)
Please let me know if you have any question
Elias completely covered a square canvas using 77.8 in.² of fabric without any overlap. Which measurement is closest to the side length of this canvas in inches? 8 in. 9 in. 19 in. 39 in.
The area of a 2D form is the amount of space within its perimeter. The measure of the side of the canvas is closest to 9 inches. The correct option is B.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given that Elias completely covered a square canvas using 77.8 in.² of fabric without any overlap. Therefore, the area of the canvas will be equal to the area of the fabric. Thus, we can write,
Area of the canvas = Area of the fabric
Since the area is square, therefore,
Area of the canvas = Area of the fabric
Area of the canvas = 77.8 in.²
Side of the canvas = √(77.8 in.²)
Side of the canvas = 8.82 inches ≈ 9 inches
Hence, the measure of the side of the canvas is closest to 9 inches.
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James ate 4/5 of his banana and Eric ate 7/9 of his banana. Who ate more of their banana?
actually it will be easier for you to know it if you convert it into decimal.
So
James = 4/5 = 0.8
Eric = 7/9 = 0.78
So James ate more
Answer:
James ate more of his banana
Step-by-step explanation: You would convert the fractions into the same denominator. And then you can compare.
36/45 35/45