Answer:
(a) Law connecting the variables:
[tex]M = \frac{5}{8}Ir^{2}[/tex]
(b) r = 8 and r = -8
Step-by-step explanation:
(a) Equation for a joint variation is:
[tex]M = KIr^{2}[/tex] where K is the constant
Substituting the provided values of M, I and r:
= [tex]20 = K(8)(2^{2} )[/tex]
= [tex]20 = K(8)(4)[/tex]
= 20 = 32K
= [tex]K = \frac{20}{32}[/tex]
[Divide the numerator and the denominator by the highest common factor (i.e. 4)]
= [tex]K = \frac{5}{8}[/tex]
Therefore:
[tex]M = \frac{5}{8}Ir^{2}[/tex]
(b) [tex]M = \frac{5}{8} I r^{2}[/tex]
Substituting the values of M and I:
[tex]400 = \frac{5}{8} (10)r^{2}[/tex]
[tex]400 = \frac{5}{8} (10)r^{2}[/tex]
[tex]400 = \frac{50}{8} r^{2}[/tex]
[tex]\frac{(400)(8)}{500} =r^{2}[/tex]
[tex]\frac{3200}{50} = r^{2}[/tex]
[tex]64 =r^{2}[/tex]
Taking the square root on both sides of the equation:
[tex]r = \sqrt{64}[/tex]
[tex]r = 8[/tex] and [tex]r = -8[/tex]
Find the values of k and m in the parallelogram?
Answer:
In order to find the values of k and m in a parallelogram, you would need to have additional information such as the coordinates of the points that make up the parallelogram and the formulas or equations that relate k and m to these points.
Here is one way to find the values of k and m in a parallelogram:
Label the four vertices of the parallelogram as A, B, C, and D with the opposite sides parallel to each other.
Find the slope of the line segment AB by using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let the slope of AB be represented by k.
Find the slope of the line segment AD by using the same formula and let it be represented by m.
The values of k and m are now found.
Please note that, this method is only applicable if the Parallelogram is not degenerate i.e, it is not a rectangle or a line.
It is also important to keep in mind that different formulas or equations may be used depending on the specific context of the problem. It is also important to check that the slopes of opposite sides are equal.
Step-by-step explanation:
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answer:
They will meet after 4 hours from the departure------------------------
The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.
The remainder of the distance is reducing by:
110000 + 90000 = 200000 km an hourTime to travel before they meet:
(710000 - 110000)/200000 = 600000/200000 = 3 hoursAdd the first hour to this to get total travel time of 4 hours.
solve the inequality:
||x-3|-2|≤1
Answer:
-1 ≤ x ≤ 5
Step-by-step explanation:
-1 ≤ x ≤ 5 is the answer
I will give brainliest, if you get this correct
Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
Step-by-step explanation:
To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.
The equation for a linear regression line is:
y = a + bx
where a is the y-intercept and b is the slope of the line.
To find the slope of the line (b), we can use the formula:
b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)
To find the y-intercept (a), we can use the formula:
a = (∑y - b(∑x)) / n
Given the data provided, we can calculate the following values:
∑x = 142
∑y = 150
∑xy = 2430
∑x^2 = 10304
n = 8
By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:
b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5
a = (150 - 0.5(142)) / 8 = 13.5
Therefore, the regression equation for the costs related to age of cars is:
y = 13.5 + 0.5x
To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:
y = 13.5 + 0.5(12) = 16.5
So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
The actual sum is
0
A i need help for this math please
Answer:
the answer is 0
Step-by-step explanation:
because the question you asked has no digits other than 0
The function is defined below. (Will give brainliest.)
H(x)= x+2/x^2+4x+4
Find all values of that are NOT in the domain of H.
If there is more than one value, separate them with commas.
The value of x that is not in the domain of the function is given as follows:
x = -2.
What is the domain of a function?The domain of a function is the set that contains all the possible input values for the function.
The function in this problem is defined as follows:
H(x) = (x + 2)/(x² + 4x + 4).
The function is a fractional function, meaning that the denominator cannot assume a value of zero.
Hence the values of x that are not in the domain of the function are obtained as follows:
x² + 4x + 4 = 0
(x + 2)² = 0
x + 2 = 0
x = -2.
Hence the value of x = -2 does not belong to the domain of the function H(x), as it would make the denominator assume a value of zero.
More can be learned about the domain of a function at https://brainly.com/question/10687170
#SPJ1
6, 12, 15, 60, 65, ?
Answer:
390
Step-by-step explanation:
The pattern here is inversing between multiplying and adding
6 to 12 = ×2
12 to 15 = +3
15 to 60 = ×4
60 to 65 = +5
This means that to get the next number you must do ×6 since the next pattern has to be × and the number must be 6!
65 × 6 = 390
Have a lovely day :)
PLEASE HELP ME ASAP IREADY
4 hundreds is 10 times as much as 4 thousandths
No, 4 hundreds is not 10 times as much as 4 thousandths.
How to compare 4 hundreds and 4 thousandths?Numbers in the tens are numbers that are multiples of 10, such as 10, 20, 30, 40, etc.
4 hundreds is equal to 4 × 100 = 400.
4 thousandths is equal 4/1000 = 0.004
To compare their magnitudes, we can divide 0.4 by 0.004:
400 ÷ 0.004 = 100000
So 4 hundreds (400) is significantly larger than 4 thousandths (0.004).
Therefore, 4 hundreds is 100000 times as much as 4 thousandths.
Learn more about Numbers in tens on:
brainly.com/question/23846183
#SPJ1
identify the vertex of the parabola
I WILL MARK BRAINLIEST
Answer:(1,0) which is the second one in the picture
Step-by-step explanation:The vertex is in (1,0).
Need help for 50 points.
Answer:
Step-by-step explanation:
Answer:
The Graph is Below
Step-by-step explanation:
what is the solution to this equation?
[tex](\frac{1}{4})x^+{1}=32[/tex]
[tex]\cfrac{1}{4}x+1=32\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{4}x+1 \right)=4(32)}\implies x+4=128\implies x=124[/tex]
Multiply the previous term by 3 and subtract 4 The second term of the sequence is 5. Find the difference between the first and fourth terms of the sequence.
Answer:
72
Step-by-step explanation:
Given that the second term of the sequence is 5, and that we are to multiply the previous term by 3 and subtract 4, we can use that as a recursive formula to find the other terms of the sequence.
The first term of the sequence is:
5*3-4 = 11
The third term of the sequence is:
53-4=11
113-4=29
The fourth term of the sequence is:
53-4=11
113-4=29
29*3-4=83
The difference between the first and fourth terms of the sequence is:
83-11 = 72
So the difference between the first and fourth terms of the sequence is 72.
what is the solution to -82-3(2x+4)=2(7x+1)-3(2x+4)
Answer:
according to BODMAS RULE
first step is to open the bracket , and solve
-82 - 6x - 12= 14x + 2 -6x -12
-82=14x + 2
-84 = 14x
x= -6
3) You inherit $2,500 and decide to invest it in an account that earns 1.5% interest
compounded monthly.
a) Write an equation to model this scenario.
b) How much money is in the account 15 years after you first invested?
Therefore , the solution of the given problem of interest comes out to be
A = $3,130.37 is the amount after 15 years.
What exactly is meant by interest?Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.
Here,
Given :
a ) the equation that can be formed is
2500x - 1.5y = 30
b)
Using compound formula :
=> Then solve the equation for A
A = P(1 + r/n)nt
A = 2,500.00(1 + 0.015/12)(12)(15)
A = 2,500.00(1 + 0.00125)(180)
A = $3,130.37
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
In ΔXYZ, x = 89 cm, z = 84 cm and ∠Z=70°. Find all possible values of ∠X, to the nearest degree.
The value of angle X Is 85° ( nearest degree)
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.
therefore x/sin X = z/sinZ
89/sinX = 84/sin 70
89sin70 = 84sin X
= 89× 0.94 = 84sinX
=83.66 = 84sin X
sin X = 83.66/84
sinX = 0.996
X = sin^-1 0.996
X = 85° ( nearest degree)
learn more about sine rule from
https://brainly.com/question/20839703
#SPJ1
factorise 6xy - 5x squared
Answer:
see full calculations in below
Step-by-step explanation:
Answer:
don't know my dear friend
Ill give brainiest for the answer
Answer:
m∠10 = 41°
Step-by-step explanation:
If ∠9 and ∠10 are complementary. Then ∠7 and ∠8 are complementary as well. Complementary angles meameansns they sum up to 90 degrees.
m∠7 + m∠8 = 90
m∠7 + 41 = 90
m∠7 = 90 - 41 = 49°
Given that m∠7 ≅ m∠9. So m∠9 = 49° and m∠10 = 41°.
How do you do this math problem involving csc? Can you do it on a ti-84 calculator?
Explanation:
The TI-84 calculator is fairly powerful and can handle things like this, but it's not needed to be honest. Any calculator will do.
"csc" is shorthand for "cosecant". It's the reciprocal of sine.
csc = 1/sin
Recall that
sin = opposite/hypotenuse
which means
csc = 1/sin = hypotenuse/opposite
What we'll need are the hypotenuse and opposite sides. Plot the points (0,0) and (-20,21). Draw a segment between them. This forms the hypotenuse of the right triangle shown below. This triangle is in the quadrant Q2 in the upper left corner. The hypotenuse 29 is found using the pythagorean theorem a^2+b^2 = c^2.
Use a = 20 and b = 21 to find c = 29.
According to that diagram, we can then say:
csc = hypotenuse/opposite = 29/21
Cyprian was allowed a discount of 11% for goods at sh 800 and a discount of 8.6% for worth 17000.What percentage discount was he allowed altogether
The percentage discount that Cyprian was allowed altogether was 8.21%.
What is the percentage discount?The percentage discount is a portion of the sales price that reduces the amount the purchaser or customer pays for their purchase.
Percentages are ratios of a value or variable compared to another or the whole matter.
We express Percentages as the quotients of the division operations multiplied by 100.
In this situation, the overall percentage discount is worked out step by step as follows:
Discount on goods worth Sh. 800 = 11%
= Sh. 88 (Sh. 800 x 11%)
Discount on goods worth Sh. 17,000 = 8.6%
= Sh. 1,462
The total value of goods = Sh. 17,800 (Sh. 800 + Sh. 17,000)
Percentage discount = 8.21% (Sh. 1,462/Sh. 17,800 x 100)
Thus, overall, the total discount based on the full value of goods Cyprian bought was 8.21%.
Learn more about percentage discounts at https://brainly.com/question/843074
#SPJ1
Please help to solve this
Hope it helps.
If you have any query, feel free to ask.
Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the function of Maureen's car is 26,525 (0.92)
a = 26,525 and b = 0.92
What is an exponential function?Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting value
b = the base function
x = the exponents
Considering the problem,
the starting = $26,525
the base = depreciation
the exponents = x
A year ago hence x = 1
$24,403 = $26,525(b)¹
b = 24,403 / 26,525
b = 0.92
hence we can say that a = 26,525 and b = 0.92
Learn more about exponential function here:
https://brainly.com/question/29716012
#SPJ1
To which set does the number
11 belong. Choose the most descriptive answer.
O rational
O irrational
O whole
O natural
Answer:
Step-by-step explanation:
The number 11 belongs to the set of natural numbers. Natural numbers are the set of all positive whole numbers, including 0, and the number 11 is a positive whole number.
The diagram shows a prism. 1m 2m front 2m 1m 2m side front elevation Draw the front elevation and the side elevation of the prism on the grids. Use a scale of 2 squares to 1 m. side elevation
The required Front view and a Side view of the given prism have been shown.
What is 3d geometry?3D geometry is the study of shapes in 3D space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in 3D space, three criteria are required.
Here,
"Front view" and "side view" refer to two different perspectives of an object or a scene. "Front view" is a perspective of the object or scene as seen from the front, and "side view" is a perspective of the object or scene as seen from the side.
Thus, the required Front view and Side view of the given prism has been shown.
Learn more about 3d -geometry here:
https://brainly.com/question/15451289
#SPJ1
7Mr's sharma spends 17/25 parts of her earning of her children education. how many childrene percent does she spends on her daughter education How many percent does she save.
If Mrs. Sharma spends 17/25 parts of her earnings on her children's education, then she is spending (17/25) x 100 = 68% of her earnings on her children's education.
If the number of children is the same, she spends 68%/number of children on her daughter education.
If she spends 68% of her earnings on her children's education, then she is saving 100 - 68 = 32% of her earnings.
So, she spends 68% on her daughter education and she saves 32% of her earning.
9 cm Find the area of the square. Remember A = s² Area of the square cm 2
What is the slope for the graph?
A: -5
B: -1/2
C:2
D: -1/5
Answer:
Step-by-step explanation:
Since we are given two points in the graph, we can use the slope equation shown below:
(y2-y1)/(x2-x1)
reading the graph left from right (1,11) will be the first point and (3,1) the second. plug in and solve!
(1-11)/(3-1) = -10/2 = -5
The slope is -5
a negative slope makes sense since the graph is leaving the first quadrant.
hope this helps!
Answer: A) -5. Graph slope.
Step-by-step explanation:
The formula to calculate the slope of the line is:
[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{x_2-x_1}{y_2-y_1} }}[/tex]
We have that the points are:
A (x₁, y₁) = 1, 11B (x₂, y₂) = 3,1We substitute these points in the previous formula and solve:
[tex]\boldsymbol{\sf{m=\dfrac{x_2-x_1}{y_2-y_1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{1-11 }{3-1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{-10}{5} }}\\ \\ \\ \boxed{\boldsymbol{\sf{m=-5}}}[/tex]
To learn at https://brainly.com/question/14295592Does anyonw know how to solve:
cos2a=4/5?
The value of a is 18.43°
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, cos2a=4/5
cos 2a = 4/5
2a = cos⁻¹(4/5)
2a = 36.86°
a = 18.43°
Hence, the value of a is 18.43°
Learn more about trigonometric ratios, click;
https://brainly.com/question/25122825
#SPJ1
what’s the numerator for the rational expression?
The numerator of the rational expression will be 6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 1 / b + 5 / b = x / b.
The expression will be solved as below,
E = (1/b) + (5/b)
E = ( 1 + 5 ) / b
E = 6 / b
Hence, the numerator will be equal to 6.
To know more about an expression follow
https://brainly.com/question/28134715
#SPJ1
$2750 is invested at an interest rate of 3.5% APR compounded quarterly. Determine the amount after 7 years. Round your answer to the nearest hundredth.
Answer:
The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = 2750, r = 0.035, n = 4 (because interest is compounded quarterly) and t = 7 (because we are trying to find the balance after 7 years).
So the formula becomes:
A = 2750(1 + 0.035/4)^(4*7)
By plugging the number into the formula we can find the final amount after 7 years
A = $3,974.23
So the amount of money in the account at the end of 7 years is $3,974.23, rounded to the nearest hundredth.
