Model for the Combined variation is [tex]F = \frac{km}{d^{2} }[/tex]
Equation to find the mass of the rocket in terms of F and d is :
[tex]m=\frac{F d^{2} }{k}[/tex]
What is Force ?A force is the quantity that change the motion of the object. Force is that influence which can cause any object having some mass, to change it's position or to accelerate from it's original position.
Force (F) and mass (m) of any object are directly proportional to each other. More the mass of the object , more the force will require to accelerate it.
Mathematically, we can write the equation of force as :
F = m . a
where , m = mass of the object
a = constant value
In the statement given,
As, force of gravity varies directly with its mass
Therefore, F= k m , where k is a constant
Also force is inversely varies with square of distance d
Thus, F = k / d²
Combining both equations :
[tex]F = \frac{km}{d^{2} }[/tex]
and the equation of mass in terms of F and d can be written as :
[tex]m=\frac{F d^{2} }{k}[/tex]
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Please help with question
Answer:
320
Step-by-step explanation:
Use PEMDAS - order of operations
5(2)^2 + 3(10)^2
5 x 4 + 3 x 100
20 + 300
320
Identify each function or situation as an example of exponential growth or decay. What is the y -intercept?
c. You put $ 2000 into a college savings account for four years. The account pays 6% interest annually.
The function is exponential growth function and the y- intercept is (0,$2000).
Given that the we put $ 2000 into a college savings account for four years and the account pays 6% interest annually.
Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.
If a is positive and b is greater than 1 then it is exponential growth.
If a is positive and b is less than 1 but greater than 0 then it exponential decay.
When we put $2000 in our college savings account and we receive 6% annual interest then this situation can be modeled by using equation f(x)=a(1+r)ˣ in which we put a=$2000, r=6%, x=4
Thus we will receive the amount after 4 years:
f(4)=2000(1+(6/100))⁴
Since equation is an exponential growth function so it is also an exponential growth function.
Now, to find the y-intercept we will put x=0.
So, y-intercept is (0,$2000).
Hence, By putting $2000 into a college savings account for four years and the account pays 6% interest annually the function is exponential growth function and the y-intercept is (0,2000).
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24. Find K between M(1, -3) and N(4, 6) such that the
ratio of MK to KN is 1:2.
Answer:
Find K between M(1, -3) and N(4, 6) such that the
ratio of MK to KN is 1:2.
Step-by-step explanation:
Find K between M(1, -3) and N(4, 6) such that the
ratio of MK to KN is 1:2.
The coordinates of point K are (2, 0).
Given that there are three points M, K and N, such that M = (1, -3) and N = (4, 6) and the ratio of MK to KN is 1:2.
We need to find the coordinates of point K.
To find point K between M(1, -3) and N(4, 6) such that the ratio of MK to KN is 1:2, we can use the concept of section formula.
Let's assume the coordinates of point K are (x, y).
The section formula states that if a point K divides a line segment MN in the ratio m:n, then the coordinates of K are given by:
x = (n·x₁ + m·x₂) / (m + n)
y = (n·y₁ + m·y₂) / (m + n)
where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.
In this case, the ratio of MK to KN is 1:2, so m = 1 and n = 2.
Substituting the coordinates of M(1, -3) and N(4, 6) into the formula:
x = (2·1 + 1·4) / (1 + 2)
= (2 + 4) / 3
= 6 / 3 = 2
y = (2·(-3) + 1·6) / (1 + 2)
= (-6 + 6) / 3
= 0 / 3
= 0
So, the coordinates of point K are (2, 0).
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simplify 25p^6q^9 / 45p^8q^4. write answer using a positive exponent
/ is division
^ elevated to
The simplification of 25p^6q^9 / 45p^8q^4 using a positive exponent;
Division is 5p^6 q^9 / 9p^8 q^4Elevated form is 5/9 p^-2 q^5What are algebraic expressions?Algebraic expressions are expressions made up of factors, variables, terms, coefficients and constants.
They are also comprised of arithmetic operations such as addition, subtraction, multiplication, division, etc
We also know that index forms are also know as standard forms.
They are mathematical expressions showing the power of exponent of a variable in terms of another variable.
Given the index algebraic forms;
25p^6q^9 / 45p^8q^4
Using the rule of indices, we take the negative exponent of the divisor and multiply through.
We have;
5p^6 q^9 × 9p^-8 q^-4
Add exponential values
5/9 p^6-8 q^9 -4
5/9 p^-2 q^5
Thus, the expression is simplified to 5/9 p^-2 q^5
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Create two ratios that are equivalent to 1/3 using multiplication
the three equivalent ratios to the ratio 1 : 3 will be 2 : 6 , 3 : 9 and 4 : 12.
We are given a fraction 1 / 3
This can also be written as a ratio as 1 : 3
Now, the equivalent ratios to it will be:
First one:
1 × 2 : 3 × 3
= 2 : 6
Second one:
1 × 3 : 3 × 3
= 3 : 9
Third one:
1 × 4 : 3 × 4
= 4 : 12
Therefore, the three equivalent ratios to the ratio 1 : 3 will be 2 : 6 , 3 : 9 and 4 : 12.
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12+15 in distributive property
Answer:
3(4 + 5)
Step-by-step explanation:
An earthquake of magnitude 9.1 occurred in 2004 in the Indian Ocean near Indonesia. It was about 74,900 times as strong as the greatest earthquake ever to hit Texas. Find the magnitude of the Texas earthquake. (Remember that an increase of 1.0 on the Richter scale means an earthquake is 30 times stronger.)
a. Can you write an exponential or logarithmic equation?
The Magnitude of earthquake that hit Texas is 5.8; The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex].
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
Magnitude of earthquake that hit Indian Ocean = 9.1 [tex]I_1[/tex] = Intensity of weaker earthquake[tex]I_2[/tex] = Intensity of greater earthquake.To find: Magnitude of earthquake that hit Texas.
Finding:
From the given, [tex]\frac{I_2}{I_1}[/tex] gives the ratio of the greater earthquake's intensity to the weaker earthquake's intensity.This ratio, when written as an exponential equation, equals [tex]30^M[/tex] where M is the increase in magnitude difference:=> [tex]\frac{I_2}{I_1}[/tex] = [tex]30^M[/tex]
For [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:
=> 74900 = [tex]30^M[/tex]
Taking logarithm on both sides, with base 10 gives:
=> log (74900) = log ([tex]30^M[/tex])
As [tex]log_b(a)^m = m(log_b(a))[/tex],
=> log (74900) = M ( log (30))
=> [tex]\frac{log(74900)}{log (30)}[/tex] = M
=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.
Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.
The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]
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Alissa has two pieces of carpet runner one is 2 1/3 yards long and the other is 3 1/3 yard long she needs 10 yards of carpet runner altogether how much more does she need to buy
Shop A sells a dress for $79.50 with a 20% discount while Shop B sells the same dress for $69.50 with a 10% discount. Write down a calculation you could do mentally to help you decide which shop to buy the dress from.
Shop A sells a dress for $79.50 with a 20% discount while Shop B sells the same dress for $69.50 with a 10% discount is $ 318 and $ 625.5.
The proportion of value in relation to the original value is measured using the percentage discount concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage.
Let x be the actual cost of the dress in the store. A
20/100 ×x = 79.50 x = 79.50 ×100/20 xx = 7950/20
x = $ 397.5
The actual cost of clothing A is $397.5.
Discount of outfit A therefore equals 20%
$397.5-79.5$= $ 318
Let x represent the true cost of dress B.
(10/100)× x = 69.50$
x = $695
The actual cost of dress B is $695.
So, the dress B's discount is 10%.
$ 695 - 69.50 = $ 625.5
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Question 11 and 12 need help
Answer:
This is for #12
-2 > x
set notation: {x│x < -2}
interval notation: x∈(-∞, -2)
Step-by-step explanation:
-3(x+2) > 10+5x
-3x-6 > 10+5x
+3x +3x
-6 > 10+8x
-10 -10
-16 > 8x
÷8 ÷8
-2 > x
set notation: {x│x < -2}
interval notation: x∈(-∞, -2)
what is the probability that at least one of the top three cards in a well shuffled deck of cards is a jack, queen, or king?
The probability that at least one of the top three cards is a jack, queen, or king is 0.289%.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
A deck has a total of 52 cards.
A deck of cards has four jacks.
A deck of cards has four queens.
A deck of cards has four kings.
The total number of jacks, queens, and kings is 4 + 4 + 4 = 12.
Then the probability that at least one of the top three cards is a jack, queen, or king will be:
P = ( 12 / 52 ) × ( 8 / 51 ) × ( 4 / 50 )
P = ( 6 / 26 ) × ( 8 / 51 ) × ( 2 / 25)
P = 96 / 33150
P = 0.289%
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Solve each equation. Check your answers. ln x-ln 3=4
The value of ln x-ln 3=4 is 163.7
What is logarithm function?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the logarithm of that number.
given, our equation is -
ln x-ln 3=4
It can be expressed in the form of
⇒ loge (x/3) = 4
⇒ e⁴ = x/3
⇒ x = 3e⁴
⇒ 163.7
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SINE / COSINE RULE , bro help me
Using the law of sines, the length of side x, to 1 decimal place, is: 10.8 cm.
How to Apply the Law of Sines?The law of sines states that:
Sin A/a = sin B/b = sin C/c.
Let:
Measure of angle A = 81°
a = x = ?
Measure of angle B = 40°
b = 7 cm
Plug in the values into Sin A/a = sin B/b to find the value of x
Sin 81/x = sin 40/7
Cross multiply
(x)(sin 40) = (sin 81)(7)
Divide both sides by sin 40
(x)(sin 40)/sin 40 = (sin 81 × 7)/sin 40
x = (sin 81 × 7)/sin 40
x = 10.8 cm (to 1 decimal place)
Therefore, using the law of sines, the length of side x, to 1 decimal place, is: 10.8 cm.
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Simplify each number. 32 . 256¹/₂
32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 32 = 2 x 2 x 2 x 2 x 2 = [tex]2^{5}[/tex]
Prime factorization of 256= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = [tex]2^{8}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} . a^{n } =a^{m+n}[/tex]
According to the given condition,
∴[tex]32 = 2^{5}[/tex]
[tex]256^{\frac{1}{2}} = (2^{8})^{\frac{1}{2} }[/tex]
∴ 32. [tex]256^{\frac{1}{2} }[/tex] = [tex]2^{5}[/tex] × [tex](2^{8})^{\frac{1}{2} }[/tex]
Applying the laws of indices mentioned above,
32. [tex]256^{\frac{1}{2} }[/tex] = [tex]2^{5}[/tex] × [tex](2^{8 X }^{\frac{1}{2} })[/tex]
= [tex]2^{5}[/tex] × [tex]2^{4}[/tex]
= [tex]2^{5 + 4}[/tex] = [tex]2^{9}[/tex]
= 512.
Thus, 32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.
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Inverse of [2,48] and [56,2130] ?
Answer: inverse of 2,48 there is none and the inverse of 56,2130 there is none
Step-by-step explanation: hope this helps
HELP ASAP ONLY IF YOU KNOW THE ANSWER
Decide if the following biconditional statement is true or false:
Two angles are congruent if and only if they are vertical angles
True or false?
Answer: TRUE
Step-by-step explanation:
i got it right.
An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is $5,000. After introducing several plans to prevent loss, it randomly samples 200 policyholders and finds the mean amount per claim was $4,800 with a standard deviation of $1,300. Does it appear the prevention plans were effective in reducing the mean amount of a claim? use the 0. 05 significance level. A. What is the decision rule? (negative amount should be indicated by a minus sign. Round your answer to 3 decimal places. )
In this case, the population consists of an insurance company's policyholders. The sample consists of his 200 policyholders under study. The sample size is 200.
H0: µ ≥ $5,000
Ha: µ < $5,000 (claimed)
As we can see that the sample size is 200, which is way greater than 30, so a z-test is appropriate here.
z(test) = (4800 - 5000) / (1300 / √200) = -2.1757
p (z = -2.1757) = 0.0148
The critical z-value for the left-sided test at α = 0.05 is -1.645
The tested value of z is less than the critical value, so we reject the null hypothesis. The hypothesis drawn here ( null hypothesis) will be rejected as an alternate decision because the p-value is less than the significance level (0.05).
At the 0.05 significance level, the prevention plan effectively reduced the average amount of harm. Insurers should continue these plans and try to improve them where possible.
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A light bulb consumes 16200 watt-hours in 4 days and 12 hours. How many watt-hours does it consume per day?
watt-hours per day
Answer:
3600
Step-by-step explanation:
16500/4.5 to find watt-hours per day.
PLEASE I NEED THE ANSWER TO THIS solve for x
The sides of a triangle
it's longest attitude:
are 35cm, 54cm and 61cm, respectively. The lenght of
The length of the longest altitude of the triangle is 24 √5 cm.
The sides of the triangle that are given are:
35 cm, 54 cm and 61 cm
We need to find the longest altitude of the triangle.
We know that:
s = ( a + b + c ) / 2
s = ( 35 + 54 + 61 ) / 2
s = 150 / 2
s = 75
s - a = 75 - 35
s - a = 40
s - b = 75 - 54
s - b = 21
s - c = 75 - 61
s - c = 14
Area, A = √ s (s − a)(s − b)(s − c)
A = √ 75 (40) (21) (14)
A = 420 √ 5 cm²
Now, area is also equal to:
Area = 1 / 2 × b × h
420 √5 = 1 / 2 × 35 × h
h = 420 √ 5 × 2 ÷ 35
h = 24 √5 cm
Therefore, the length of the longest altitude of the triangle is 24 √5 cm.
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Expand each logarithm.
log₇49 x y z
If the expression is log₇49 x y z, then the expansion of the expression is 2+log x/ log 7+log y/log 7 +log z/ log 7.
Given that expression is log₇49 x y z.
We are required to find the expanded value of the expression.
The change of base formula is basically used to re-write a logarithm operation as a fraction of logarithms with a new base.
The expression is log₇49 x y z.
log₇49xyz= (log 49+log x+log y+log z)/log 7
We know that log mn=log m+ log n.
=log [tex]7^{2}[/tex]/ log 7+log x/log 7+log y/ log 7+ log z/log 7
=2 log 7/log 7+log x/log 7+log y/ log 7+ log z/log 7
=2+log x/log 7+log y/ log 7+ log z/log 7
Hence if the expression is log₇49xyz, then the expanded form is
2+log x/log 7+log y/ log 7+ log z/log 7.
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Which function represents this sequence -10,-2,6,14
Answer:
8n-18
Step-by-step explanation:
You can use this formula: 1st term+(n-1)(difference)
First term of sequence: 10
Difference between each term: 8
-10+(n-1)(8)
= -10+8n-8
= 8n-18
What’s the algebraic expression of:
Six times the sum of a and b squared minus four times the product of a and b squared
The algebraic expression is 6(a+ b)² + 4(ab)².
What is algebraic expression?The concept of representing numerical values with letters or alphabets without providing their precise values The fundamentals of algebra taught us how to represent an unknown value using letters like x, y, and z. Here, these letters are referred to as variables. A mathematical expression may have both variables and constants. A coefficient is any value that is introduced before and increased by a variable.
Given that,
So, six times the sum of (a+ b)
Then, four times the product of (ab)
Therefore, the algebraic expression is 6 (a+ b)² + 4(ab)².
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Jordin worked 23 hours and 44 minutes. He's paid $13.00 an hour. How much will he get paid?
Change minutes to hours then multiply.
This is pay, so round all answers to the nearest cent if necessary. Two decimal places
Answer:
hola
Si por qué le tenías que restar ala fracción equivalente
add 8 in the hundreds place 724,062.58
Answer:
724,862.58
Step-by-step explanation:
7 (hundred thousands)
2 (ten thousands)
4 (one thousands)
,
0 (hundreds)
6 (tens)
2 (ones)
.
5 (tenths)
8 (hundreths)
Answer:
I think that your answer would be 724,862.58
Step-by-step explanation:
Create a real life context that can be represented by the linear equation y=-2.65x+ 25.
Answer:
If you have 2 dollars and 65 cents per day, and you get 25 dollar commission.
Step-by-step explanation:
Two years ago a father was four times as old as his son. Three years from now the father will be only
three times as old as the son. How old is each now?
If x represents the son's age two years ago, which expression represents his father's age three years
hom now?
3x+15
3x+3
x+3
An expression which represent his father's age three (3) years from now is: A. 3x + 15.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to write and solve this word problem, we would assign variables to the son's and father's age and then evaluate the resulting algebraic expression.
Let x represent the son's age two years ago.Let y represent the father's age three years ago.Translating the word problem into an equation, we have;
y = 4x
y + 2 + 3 = 3(x + 2 + 3)
y + 5 = 3(x + 5)
y + 5 = 3x + 15
Therefore, an expression which represent his father's age three years from now is 3x + 15.
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Example: if XYZ - RST, find the value of x.
Answer:
x = 12
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{XY}{RS}[/tex] = [tex]\frac{XZ}{RT}[/tex] ( substitute values )
[tex]\frac{5x-3}{3x+2}[/tex] = [tex]\frac{60}{40}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
2(5x - 3) = 3(3x + 2) ← distribute parenthesis on both sides )
10x - 6 = 9x + 6 ( subtract 9x from both sides )
x - 6 = 6 ( add 6 to both sides )
x = 12
answer with work and for brainliest
The solutions of the expressions are as below:
10. -9x - 2; x = -4 3411. 24 - 8x; x = -2.25 4212. 15x + 9; x = -1/10 7.513. (a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis
(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis
(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis
(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis
How to solve the given expressions10. -9x - 2; x = -4
-9x - 2 for x = -4
= -9 * -4 - 2
= 36 - 2
= 34
11. 24 - 8x; x = -2.25
= 24 - 8 * - 2.25
= 24 + 18
= 42
12. 15x + 9; x = -1/10
= 15 * -1/10 + 9
= -1.5 + 9
= 7.5
13.
a are points in the x axis and b are points in the y axis
(a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis
(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis
(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis
(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis
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please help, I put down the drop down menu this time
Answer:
0.2 billion visits per year
Step-by-step explanation:
-
Hope that helps.