Answer:
[tex]\boxed{\sf distance \: between \: the \: objects \: \: is \: 2.5 \: cm}[/tex]
Step-by-step explanation:
According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to
the product of their masses, given by standard formula.
[tex]A = G \cdot \frac{m_1.m_2}{ {d}^{2} } [/tex]
where A,d & G are force of attraction, distance of separation & proportionality constant respectively.
Given:
A1 = 2 units
d1= 5 cm
A2 = 8 units
To find:
Distance of separation when the force of attraction is 8 units d2 = ?
Solution:
Substituting the given values in above at each point,
[tex]A_1 = G \cdot \frac{m_1.m_2}{ {d_1}^{2} } \\ 2 = G \cdot \frac{m_1.m_2}{ {5}^{2} } \\ \sf similarly \: at \: second \: point \: of \: attraction \\ A_2 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ 8 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ \sf \: \: dividing \: both \: of \: the \: equation \\ \frac{2}{8} = \frac{G \cdot \frac{m_1.m_2}{ {5}^{2} }}{G \cdot \frac{m_1.m_2}{ {d_2}^{2} } } \\ \sf \: G \: m_1 and \: m_2 \: are \: \: constant \: hence \\ \sf they \: can \: be \: cancelled \: out \\ \frac{2}{8} = \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } } \\ \sf rearranging \: above \: equation \\ \frac{1}{4} = \frac{{d_2}^{2} }{ {5}^{2} } \\ {d_2}^{2} = \frac{ {5}^{2} }{4 } \\ {d_2}^{2} = \frac{25}{4} \\ {d_2}^{2} = 6.25 \\ \sqrt{{d_2}^{2} } = \sqrt{6.25} \\ \boxed{ \sf{d_2} = 2.5 \: cm}[/tex]
Answer: the distance between the two objects is 2.5 cm, if the attraction between them is 8 units.
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Is (3,-2) a solution to the system below? How do you know?
(y + 4x = 10
y +
15x - y = 13
PLEASE HELP!
Step-by-step explanation:
you know by using the x and y coordinates of the point in the equations and see, if both equations are still true.
if yes, it was a solution, and if just only one is false, then it was not a solution.
(3, -2) in
y + 4x = 10
5x - y = 13
so,
-2 + 4×3 = 10
-2 + 12 = 10
10 = 10 true
5×3 - (-2) = 13
15 + 2 = 13
17 = 13 false
so, it was NOT a solution.
Solve the following inequality.
3x> -3
Answer:
x>-1
Step-by-step explanation:
divide 3 on both sides
Select ALL the true statements about the scatter plot below.
A. The graph shows a linear association
B. The graph has no outliers
C. The graph shows a nonlinear association
D. The graph shows a positive association
E. The graph could be used to show an association between the hours worked and the amount earned
The true statements about the scatter plots are
(a) the graph shows a linear association(d) the graph shows a positive association(e) The graph could be used to show an association between the hours worked and the amount earnedHow to determine the true statement about the scatter plot?From the graph of the scatter plot, we have the following highlights:
The points appear to be on a straight line; this represents a linear associationOne point is relatively far from other points on the plot; this means the graph has an outlierAs the points on the x-axis increases, the points on the y-axis increases; this means a positive associationThe above highlights mean that (a), and (d) are true
Since the graph is a linear association, then it can be used to model hourly rates
This means that (e) is true
Hence, the true statements about the scatter plots are (a), (d) and (e)
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A farm house shelters 10 animals some are pigs and some are ducks. Altogether there are 36 legs. How many pigs are there?
Answer:
8 pigs are there according to the questions because in question there is told that there are pigs as well as ducks
PLEASE HELP ASAP!
Solve the inequality below. Enter your answer as an inequality, such as x < 2/3 or x > -3.
x/16 < -3
solve for x ~
[tex]\bold\pink{x {}^{2} + 5x - 6 = 0}[/tex]
ty! ._.
[tex] \qquad \qquad \rm \large \dag \: Answer \: \dag[/tex]
We have been given a Quadratic equation, where we have to find the real values of x ~
So, let's proceed with middle term splitting method :
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 5x - 6 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: x {}^{2} + 6x - x - 6 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x(}^{} x + 6) - 1(x + 6) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (x + 6)(x - 1) = 0[/tex]
Now, we have two conditions here~
Either (x + 6) = 0
[tex]\qquad \sf \dashrightarrow \: x = - 6[/tex]
or (x - 1) = 0
[tex]\qquad \sf \dashrightarrow \: x = 1[/tex]
Simplify the expression: 9( – 10+ – 5y)+7y
Can anyone help with math models?? Please…?
Answer:
12*1/4= 3
30 is C
16*3/4 = 12
31 is B
Answer:
30: C
31: B
Step-by-step explanation:
30: If the width of the vegetable garden is 1/4 of it's length, we have to divide the length of the garden (12 feet) by 4 and we get 3 feet.
31: We just need to multiply 16 by 3/4 and we get 12.
Question 1
Algebra
I will mark as brainlest!!!
Answer:
(x-6)^2 =40
Step-by-step explanation:
The correct answer is (x-6)^2 =40
why??
Expand (x-6)^2
x^2 -12x+36 =40
Transpos 40 to the left side
So,
x^2 -12x+36 -40
Which is
x^2 -12x -4=0
What should NOT be included in your summary of the non-fiction text you are analyzing?
A. Every small detail listed.
B. Who the audience is
C. What the tone of the text is.
D. Main ideas.
Answer:
A. Every small detail listed.
Step-by-step explanation:
This is incorrect because a summary is short. Listing every small detail would make your summary too long.
hope this helps
have a good day
Please help me :)
Thank you :)
Answer:
90 degrees :)
Step-by-step explanation:
x and 90 are supplementary.
x + 90 = 180
x = 90
[tex]\sqrt({3\sqrt{3} )^{2} +5^{2}[/tex]
Answer:
2√13
Step-by-step explanation:
⇒ √(3√3)² + 5²
⇒ √27 + 25
⇒ √52
⇒ 2√13
Solve 2(x – 11)2 = 128.
evaluate tan (cos^-1x3/5)
Answer:
tan cox³ / 5s
Replace ^-1 with ^(-1)
Replace x3 with x³
Step 1Simplify
x³ / 5
Use equation to solve
tan • ((co • (s-1)) • x³ / 5)
Step 2Take the previous equation and format it in a simpler form
tan • ((co • (s-1)) • x³ / 5) ⇒ tan • cox³ / 5s
Result
tan cox³ / 5s
Find the next number in the sequence: 1, 1, 2, -1, 1, -2, -1
answer:-1
reason :
Once the numbers add up, once they decrease
what does it mean?
it mean that:
The first and second numbers we add are one, they become two
The second and third numbers are one and two. We subtract the second number from the third number, it becomes negative one and ...
1+1=2
1-2=-1
2+(-1)=1
-1-(+1)=-2
1+(-2)=-1
so we should - them
-2-(-1)=-1
The next number in the given sequence will be negative 1.
What is a sequence?
A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
The first and second numbers we add are one, they become two.
The second and third numbers are one and two. We subtract the second number from the third number, it becomes a negative one, and ...
1 + 1 = 2
1 - 2 = - 1
2 + (-1) = 1
-1 - (+1) = -2
1 + (-2) = -1
Then the next number in the sequence will be given as,
-2 - (-1) = -1
The next number in the given sequence will be negative 1.
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A furniture shop produces two types of custom made chairs. If the price of one type of chair is three times the price of the other, and the total price for both is $15365, what is the price of other chair?
Answer:
The price of other chair is $3841.25
Step-by-step explanation:
Step 1: Write equations.
First equation: The price of one type of chair is three times the price of the other.
Let x be the price of one type of chair and y the price of the other type of chair.
[tex]x = 3y[/tex]
Second equation: The total price for both is $15365
[tex]x + y = 15365[/tex]
Step 2: Solve the system of equations.
1) [tex]x = 3y[/tex]
2) [tex]x + y = 15365[/tex]
Substitute x in the second equation with x from first.
[tex]x + y = 15365\\(3y) + y = 15365[/tex]
Now solve for y (y is the price of the other chair).
[tex]4y = 15365\\y = \frac{15365}{4}\\y = \$3841.25[/tex]
The coordinates of point A on a grid are (−2, −4). Point A is reflected across the y-axis to obtain point B. The coordinates of point B are (, −4).
The coordinates of the point B are given as (2, - 4)
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Under a reflection in the y- axis
A point (x, y) → (- x, y), hence
A(- 2, - 4) → B(2, - 4)
Therefore the coordinates of the point B are given as (2, - 4)
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Does anyone know the answer? Please help me Thank you in advance! Algebra (Exploring Slope)
Answer:
Step-by-step explanation:
slope is rise over run 2/5, and it's positive b/c the line goes up hill.
when X =0 then the line is at -6
y = (2/5)X - 6
slope = 2/5
y intercept is -6
Fill in the table using this function rule.
y=5x-1
Answer:
Step-by-step explanation:
Answer:
(-2, -11)
(0, -1)
(2, 9)
(4, 19)
Step-by-step explanation:
when x = -2:
⇒ y = 5(-2) - 1
⇒ y = -10 - 1
⇒ y = -11
when x = 0:
⇒ y = 5(0) - 1
⇒ y = 0 - 1
⇒ y = -1
when x = 2:
⇒ y = 5(2) - 1
⇒ y = 10 - 1
⇒ y = 9
when x = 4:
⇒ y = 5(4) - 1
⇒ y = 20 - 1
⇒ y = 19
Help please:
Rewrite the problem in terms of some using the double-angle formula.
Answer:
sin2x = √3/2.
Step-by-step explanation:
sin2x = 2 sinx cosx
So sinx cosx = 1/2 sin2x
So 1/2 sin2x = √3/4
sin2x = √3/4 * 2
sin2x = √3/2.
You have a wire that is 20 cm long. You wish to cut it into two pieces. One-piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?
The circumference of the circle is [tex]C =\dfrac{20\pi}{4+\pi}[/tex] when A is a minimum.
What is circumference?The circumference of the circle is the length of the curve traced out from the fixed point which is equidistant from the locus of the curve.
Let the side of the square be s
and the radius of the circle be r
The perimeter of the square is = 4s
The circumference of the circle is =2πr
Given that the length of the wire is 20 cm.
According to the problem,
4s + 2πr =20
⇒2s+πr =10
[tex]s=\dfrac{10-\pi r}{2}[/tex]
The area of the circle is = πr²
The area of the square is = s²
A represents the total area of the square and circle.
A=πr²+s²
Putting the value of s
[tex]A =\pi r^2 +(\dfrac{10-\pi r}{2})^2[/tex]
[tex]A =\pi r^2 +(\dfrac{10}{2})^2-2\times \dfrac{10}{2}\times \dfrac{\pi r}{2}+(\dfrac{\pi r}{2})^2[/tex]
[tex]A = { \pi r^2}(\dfrac{4+\pi}{4})-5\pi r+25[/tex]
For maximum or minimum [tex]\dfrac{dA}{dr}=0[/tex]
Differentiating with respect to r
[tex]\dfrac{dA}{dr}=\dfrac{2\pi r(4+\pi )}{4}-5 \pi[/tex]
Again differentiating with respect to r
[tex]\dfrac{d^2A}{dr^2}=\dfrac{2\pi (4+\pi )}{4}[/tex] > 0
For maximum or minimum
[tex]\dfrac{dA}{dr}=0[/tex]
[tex]\dfrac{2\pi r(4+\pi )}{4}-5 \pi=0[/tex]
[tex]r = \dfrac{10\pi}{\pi (4+\pi)}[/tex]
[tex]r=\dfrac{10}{4+\pi}[/tex]
Therefore the circumference of the circle is
C = 2 π r
[tex]C = \dfrac{20 \pi }{4+\pi }[/tex]
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Out of 500 people sampled, 395 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Give your answers as decimals, to four places
< p
Answer:
Sample proportion (phat) = 180/400 = 0.45z-critical value for 95% confidence interval is z-score for probability = 0.975 = 1.96CI = phat +/- z-critical value * sqrt((phat)(1-phat)/sample size) = 0.45 +/- 1.96 * sqrt(0.45 * 0.55/400) = 0.45 +/- 0.049 = 0.401, 0.499
Given OQ below, is YOR a minor arc, a major arc, or a semicircle?
A. Minor arc
B. Semicircle
C. Major arc
The arc YOR of the circle is the major arc
What is the Area of the Sector?In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
θ/360 * πr²
where;
θ is the central angle of the sector
r is radius
Now, looking at the given options we can say that the only one that represents the area of the sector is;
A = n/360 * πr²
where n is the central angle of the sector
Given data ,
Let the arc of the sector be represented as YOR
Now , the center of the circle is Q
The angle subtended by the minor arc of the circle = 150°
So , the remaining angle = 360° - 150° = 210°
And , the angle subtended by the major arc = 210°
So , the arc YOR is the major arc of the circle
Hence , the major arc is YOR
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Help
What is the greatest common factor of the terms of the polynomial - 16/4 + 12y2 – 4y?
GCF=?
Answer:
i would like to. the answer is 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer would be 4, because 4 factors into every number.
look at the attachment and see if you can solve please
The first step in finding the incenter of the triangle, JKL using paper folding is to Fold the paper so that the legs of ∠K overlap.
How can we use the paper folding method?The first step in using the paper folding method is to fold the paper so that the legs of the triangle overlap.
Then unfold the paper and draw a line at the crease you find. This will allow you to label the point of intersection after you do the same for all the sides of the triangle. This point is the incenter.
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FIND THE EXACT AREA OF THE SHADED PLEASE HELP ILL GIVE BRAINLIESTTTT
Check the picture below.
so we have a rectangle with two circles, the rectangle is a 21x10.5 and the circle's have a radius of 5.25, so let's get the area of the two circles and subtract it from the whole area of the containing rectangle.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(21)(10.5)}~~ - ~~\stackrel{two~circles}{2[\pi (5.25)^2]}}\implies 220.5~~ - ~~55.125\pi ~~\approx~~47.32[/tex]
PLEASE HELP !!
martian wants to save $20,000 to use as a down payment when he purchases a house. the function t represents the total amount he saves after m months, as shown.
T(m)= 5000+250m
how many months will it take martian to save $20,000
Answer:
60 months
Step-by-step explanation:
20 000 = 5000 + 250 m
20 000 - 5000 = 250 m
(15 000) / 250 = m = 60 months
Answer:
It would take roughly four months
Step-by-step explanation:
month one: 5,250
month two: 10,500
month three: 15,750
month four: 21,000
(2x2 + 10x + 12) ÷ (x + 3)
Answer:
(2)(2)+10x+12/x+3
=
10x+16/x+3
Step-by-step explanation:
Use natural logarithms to solve the equation. Round to the nearest thousandth.
7e2x + 10 = 29
Answer:
[tex]x=\frac{ln(\frac{19}{7}) }{2}[/tex]
Step-by-step explanation:
7*e^2x + 10 = 29
Subtract 10 to both side.
7*e^2x = 19
Divide 7 to both side.
e^2x = 19/7
Inverse e with ln.
ln(19/7) = 2x
Divide 2 to both side.
[tex]x=\frac{ln(\frac{19}{7}) }{2}[/tex]
(2 + 8) : 5 + 3 x 4 – (1 + 5) : 2 =
The simplified form of the expression (2 + 8) : 5 + 3 x 4 – (1 + 5) in the ratio is 10 : 11.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
(2 + 8) : 5 + 3 x 4 – (1 + 5) : 2 =
10 : 5 + 12 - 6
10 : 11
The simplified form of the expression in the ratio is 10 : 11.
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