The correct formula for [tex]\( r \)[/tex] rearranged from [tex]\( v = \frac{GM}{r} \) is \( r = \frac{GM}{v} \)[/tex].
To rearrange the formula [tex]\( v = \frac{GM}{r} \)[/tex] to solve for [tex]\( r \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[ v = \frac{GM}{r} \][/tex]
2. Multiply both sides of the equation by [tex]\( r \)[/tex] to get rid of the denominator:
[tex]\[ vr = GM \][/tex]
3. Divide both sides of the equation by [tex]\( v \)[/tex] to isolate [tex]\( r \)[/tex]:
[tex]\[ r = \frac{GM}{v} \][/tex]
This gives us the rearranged formula for [tex]\( r \)[/tex] in terms of [tex]\( G \), \( M \), and \( v \)[/tex]
Mille pays 4 percent state income tax on his earnings if he earns 1867 how much income tax can he expect to pay?
What is the probability that a point chosen at random on the grid will lie in the unshaded region?
a. 5/8
b. 2/5
c. 3/8
d. 3/5?
Determine the total number of roots of each polynomial function
g(x) = 5x - 12x2 + 3
Answer:- The total number of roots in the given polynomial function is 2.
Explanation:-
We know that corollary of Fundamental Theorem of Algebra tells that polynomial will have exactly as many roots(m) as its degree(m>0).
The given polynomial function [tex]g(x)=5x-12x^2+3[/tex] is a quadratic polynomial with degree 2.
Thus by corollary of Fundamental theorem of algebra
The total number of roots in the given polynomial function must be 2.
David is 6 years old. his sister lauren is half his age. so when david is 100 how old will lauren be?
The age of sister will be 97 years.
What is mathematical operations?Using operands and a math operator to calculate a value is referred to as an "operation" in mathematics. The rules that apply to the given operands or numbers are predetermined by the math operator's symbol.
A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation.
Given David age = 6 years
his sister age = half of David age = 6/2 = 3
David is 3 years older than his sister
equation for ages of both David and his sister is
David age = Sister age + 3
when David is 100 years
sister age = David age - 3 = 100 - 3 = 97
Hence when David is 100 years old his sister will be 97 years.
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Given the measure of angle a is 33°. find the sum of the measures of the complementary angle, supplementary angle and vertical angle for angle a
The sum of the measures of the complementary, supplementary, and vertical angles for angle a of 33° is 237°.
The question asks for the sum of the measures of the complementary angle, supplementary angle, and vertical angle for angle a, given that angle a is 33°.
The complementary angle to angle a would be one that adds up to 90° with angle a. Since angle a is 33°, the complementary angle would be 90° - 33° = 57°.
The supplementary angle to angle a is one that adds up to 180° with angle a. The supplementary angle would thus be 180° - 33° = 147°.
The vertical angle to angle a shares the same measure as angle a, because vertical angles are equal. So, the vertical angle measure is 33°.
To find the total sum of these angles, you would add 57° + 147° + 33° = 237°.
ABC is a right triangle with right angle C. Ab = 18 cm m
What is BC
Round answer to nearest tenth
One inlet pipe can fill an empty pool in 12 hours, and a drain can empty the pool in 20 hours. How long will it take the pipe to fill the pool if the drain is left open?
If one inlet pipe can fill the pool in 12 hours and the drain can empty it in 20 hours, the combined rate of the two is 1/30 pools per hour. Therefore, it will take 30 hours to fill the pool with the drain open.
Explanation:The question addresses a common concept in mathematics, which is rates and work problems. To determine the time it takes for the inlet pipe to fill the pool with the drain open, we first have to figure out the rates at which the pipe fills and the drain empties the pool.
If an inlet pipe can fill the pool in 12 hours, its rate of work is 1/12 pool per hour. Similarly, if the drain can empty the pool in 20 hours, then its rate is 1/20 pool per hour.
When both the inlet and drain are open, their combined rate will be the fill rate minus the drain rate, which is (1/12) - (1/20) = 1/30 pool per hour.
Therefore, at the combined rate, it will take 1 divided by 1/30 = 30 hours to fill the pool with the drain open.
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When both the inlet pipe and drain are open, it will take 30 hours to fill the pool, computed by dividing the total work done (1 pool) by the net rate (1/30 pool/hour).
Explanation:In mathematics, problems such as these are usually solved by working with the concept of rates. In this scenario, we have two rates: the inlet pipe, and the drain. The rate of the inlet pipe is 1 pool per 12 hours, or 1/12 pool/hour. The rate of the drain is 1 pool per 20 hours, or 1/20 pool/hour. The net rate when both are open is thus (1/12 - 1/20) pool/hour, which simplifies to 1/30 pool/hour. To find out how long (t) it will take to fill the pool with both the inlet and drain open, we would use the fact that Rate x Time = Work Done. The Work Done in this case is 1 (equivalent to one pool), and the rate we’ve calculated as 1/30 pool/hour.
So, solving for time, we get:
t = Work Done / Rate = 1 pool / (1/30 pool/hour) = 30 hours.
So, it would take 30 hours to fill the pool with the inlet pipe and the drain open.
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Which of the following congruence statements does not prove that two triangles are congruent?
ASA
SAS
SSA
SSS
The congruence statement that does not prove that two triangles are congruent is SSA (Side-Side-Angle).
The SSA congruence is not a valid congruence criterion for triangles because it may not necessarily guarantee congruence.
Having two sides and a non-included angle equal in two triangles does not ensure that all corresponding angles and sides are equal.
In some cases, two triangles with SSA congruence may not be congruent.
The other three congruence criteria (ASA, SAS, SSS) are valid and sufficient to prove congruence between two triangles.
ASA (Angle-Side-Angle):
This criterion states that if two triangles have two corresponding angles and the included side between those angles equal, then the triangles are congruent.
ASA is a valid criterion because it guarantees that all corresponding angles and sides are equal, leading to congruence.
SAS (Side-Angle-Side):
This criterion states that if two triangles have two pairs of corresponding sides and the included angle equal,
then the triangles are congruent. SAS is also a valid criterion because it ensures that the corresponding sides and angles are equal, thus establishing congruence.
SSA (Side-Side-Angle): This criterion states that if two triangles have two pairs of corresponding sides equal and a non-included angle equal,
then the triangles are congruent. SSA is NOT a valid criterion for proving triangle congruence. It is also known as the "ambiguous case" or "the one and only case."
This is because, in some situations, two triangles with SSA congruence may not actually be congruent.
There can be more than one possible triangle that satisfies the given conditions, leading to ambiguity.
SSS (Side-Side-Side): This criterion states that if two triangles have all three pairs of corresponding sides equal,
then the triangles are congruent. SSS is a valid criterion for proving congruence as it guarantees that all corresponding sides are equal, resulting in congruent triangles.
Therefore, ASA, SAS, and SSS are valid congruence criteria that ensure congruence between triangles. However, SSA is not a reliable criterion for proving triangle congruence, as it may lead to multiple possible triangles.
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[tex] \sqrt{ \frac{3}{16} } [/tex]
Rational or irrational?
A particular investment account offers an interest rate of 8% each year. An investor puts $3,500 into the account. For tax purposes, he wants to determine the number of years, t, for which the account will have less than $6,000. Write an inequality to represent this situation, and use it to determine the number of years for which the account will have less than $6,000.
Final answer:
The compound interest inequality for the investment account is 3500(1 + 0.08)^t < 6000. Solving this, we find that the account will have less than $6,000 for approximately 6 years.
Explanation:
To solve this problem, we will use the formula for compound interest which is [tex]A = P(1 + r)^t,[/tex] where:
A is the future value of the investment/loan, including interestP is the principal investment amount ($3,500 in this case)r is the annual interest rate (decimal)t is the number of years the money is invested or borrowed forWe are trying to find the number of years, t, when the account will have less than $6,000, at an annual interest rate of 8%, i.e., r = 0.08.
The inequality will be:
[tex]3500(1 + 0.08)^t < 6000[/tex]
To solve for t, we first divide both sides by 3,500:
[tex](1 + 0.08)^t[/tex]< ≈ 1.7143
Now, take the natural logarithm of both sides:
[tex]ln((1 + 0.08)^t) < ln( 1.7143)[/tex]
t · ln(1.08) < ln(≈ 1.7143)
Divide both sides by ln(1.08) to isolate t and calculate:
t < ≈ ln(≈ 1.7143) / ln(1.08) < ≈ 6.6
Therefore, the investment account will have less than $6,000 for approximately 6 years.
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use?
Answer: equation of a linear function in point-slope form
Step-by-step explanation:
Given : The equation of a linear function in point-slope form passing through point [tex](x_1,y_1)[/tex] is
[tex]y -y_1 = m(x -x_1)[/tex]
The equation written by Harold correctly
[tex]y = 3(x - 7)[/tex]
It can be written as:[tex]y-0 = 3(x - 7)[/tex]
When we compare to the equation of a linear function in point-slope form, we get [tex]y_1=0,\ x_1=7[/tex]
Hence, the point used by Harold = [tex](x_1,y_1)=(7,0)[/tex]
A car traveled at 60 miles per hour for 2½ hours. if one inch equals 20 miles on a map, how far has the car traveled on the map?
On average, a shooter can hit his target one time in four. if he fires 4 shots in a row, what is the probability that he will hit his target?
ASAP HELP FOR NUMBER 6!! ANSWER CORRECTLY FOR 6a and B!!
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Jean earns a graduated commission of 4% on her first 2,000 of sales and 8% on all sales over 2,000.Jean's sales for the past week totaled to 3,925.What was her commission for the week?
One mile is 5280 feet. there are 3600 seconds in one hour. how many feet per second, rounded to the nearest hundredth, does a car travel when it is traveling at 60 miles per hours
you learn from your science teacher that the water expands when you freeze it. the next time you freeze your water bottle,you will leave room for the water to expand so that the bottle dose not crack.
what kinda reasoning did you use
Lesson 1: identify pairs of lines and angles draw two lines intersected by a transversal. label corresponding angles ∠1 and ∠2. label alternate interior angles ∠3 and ∠4. label alternate exterior angles ∠5 and ∠6. label consecutive interior angles ∠7 and ∠8. label vertical angles ∠9 and ∠10. answers
Which lines or segments are parallel? Justify your answer.
How to write 3,000,000+600,000+80,000+10 in standard form
Mrs. Gordon had $40 to spend on cookies and pies. She bought 4 cookies, each of which cost $3. She spent twice as much on pies as she spent on cookies. Mrs. Gordon bought 3 pies that each cost the same amount. How much did each pie cost? $ How much money did Mrs. Gordon have left after buying the cookies and pies? $
Mrs. Gordon had $40 to spend on cookies and pies. She bought 4 cookies, each of which cost $3. She spent twice as much on pies as she spent on cookies. Mrs. Gordon bought 3 pies that each cost the same amount. How much did each pie cost? $ How much money did Mrs. Gordon have left after buying the cookies and pies? $
Lithium has 3 protons. how many neutrons are in the isotope lithium-8?
Answer:
Number of neutrons=5
Step-by-step explanation:
We are given that
Number of protons in lithium=Z=3
Mass number of lithium=A=8
We have to find the neutrons in the isotope lithium-8.
We know that
Number of neutrons=A-Z
Where A= Mass number
Z= Number of protons=Atomic number
Substitute the values then we get
Number of neutrons=8-3=5
Answer : 5
The number of the neutrons that we have in the isotope lithium-8 is 5 neutrons.
What is the proton?The quantity of protons in an element's nucleus is indicated by the element's atomic number. Lithium has three protons on average because it has an atomic number of three.
You deduct the atomic number from the mass number (the sum of the protons and neutrons in the nucleus) to get the number of neutrons in an isotope. In this instance, the isotope lithium-8, which has a mass number of 8, is present.
Mass number - Atomic number = Number of neutrons
8 - 3 = 5
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There are 45 questions on your math exam. You answered 810810 of them correctly. How many questions did you answer correctly?
Name three decimals between 0.55 and 0.56
The required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.
We have to determine the three decimals between 0.55 and 0.56
As per the attached number line,
Three decimals between 0.55 and 0.56 are :
⇒ 0.552, 0.553, and 0.554
Hence, the required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.
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The width of a rectangle is 12ft the perimeter of the rectangle is 42 what is the length of the rectangle
Answer:
9
Step-by-step explanation:
2w+2L=42
2(12)+2L=42
24+2L=42
-24 on both sides
2L=18
divide by two
L=9
Study the Proof: Give the reasons for the missing reason. List the number and then state the reason
The equation y=20646 x 0.86^x estimates the value of a brand of car x years after it was purchased new. milo purchased this brand of car when it was new. to the nearest dollar, what will be the approximate value of milos car 11 years after he purchased it?
Answer:
The approximate value of milos car 11 years after he purchased it is 3929.
Step-by-step explanation:
The given equation is
[tex]y=20646(0.86)^x[/tex]
Here, y is the estimates the value of a brand of car x years after it was purchased new.
We have to find the approximate value of milos car 11 years after he purchased it.
Substitute x=11 in the given equation.
[tex]y=20646(0.86)^{11}[/tex]
[tex]y=3929.33346204[/tex]
[tex]y\approx 3929[/tex]
Therefore the approximate value of milos car 11 years after he purchased it is 3929.
What are the new coordinates of the point (-3, 7) after it has been rotated 90° counterclockwise about the origin?
Is 267 the largest number in the sum of 3 integers evaluated from 269?