Required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
What is a number?" A number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the greater number
[tex]'y'[/tex] represents the smaller number
As per the given condition equation we have,
[tex]x- y = 44\frac{1}{2} \\\\\implies x-y = \frac{89}{2}[/tex] ______[tex](1)[/tex]
[tex]x-7y =10 \frac{3}{14} \\\\\implies x-7y = \frac{143}{14}[/tex] ______[tex](2)[/tex]
Subtract equation [tex](2)[/tex] from [tex](1)[/tex] to get the required numbers,
[tex]6y = \frac{89}{2} -\frac{143}{14} \\\\\implies 6y = \frac{623-143}{14}\\ \\\implies 6y = \frac{480}{14}\\ \\\implies y = \frac{40}{7}\\ \\\implies y = 5\frac{5}{7}[/tex]
Substitute the value of [tex]'y'[/tex] in [tex](1)[/tex] we get,
[tex]x= \frac{89}{2}+ \frac{40}{7} \\\\\implies x = \frac{623+80}{14} \\\\\implies x= \frac{703}{14}\\ \\\implies x= 50\frac{3}{14}[/tex]
Hence, required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
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if dy/dx= sin x/ cos y and y(0) = 3pi/2, find an equation for y in terms of x
Final answer:
The problem requires finding an equation for y in terms of x given a differential equation and an initial condition. Solving for y, we get:[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Explanation:
To solve this ordinary differential equation (ODE), we can separate variables and then integrate both sides. Given:
[tex]\[\frac{dy}{dx} = \frac{\sin(x)}{\cos(y)}\][/tex]
We separate variables by multiplying both sides by \(dx\) and dividing by Cos(y) to isolate y terms:
[tex]\[\cos(y) \, dy = \sin(x) \, dx\][/tex]
Now, we integrate both sides. For the left side, we integrate with respect to y, and for the right side, we integrate with respect to x:
[tex]\[\int \cos(y) \, dy = \int \sin(x) \, dx\][/tex]
Integrating each side gives us:
[tex]\[ \sin(y) = -\cos(x) + C\][/tex]
Where C is the constant of integration.
Given the initial condition [tex]\(y(0) = \frac{3\pi}{2}\)[/tex], we can plug this into the equation to find [tex]\(C\):[/tex]
[tex]\[ \sin\left(\frac{3\pi}{2}\right) = -\cos(0) + C \][/tex]
[tex]\[ -1 = -1 + C \][/tex]
[tex]\[ C = 0 \][/tex]
So the equation becomes:
[tex]\[ \sin(y) = -\cos(x) \][/tex]
Therefore, solving for y, we get:
[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
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EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.
The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.
Write an equation for the area of the photo in terms of x.
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Use a calculator to find the approximate value of arccos(0.63).
a) 39.05 degrees
b) 50.95 degrees
c) 78.1 degrees
d) 32.21 degrees
Please explain how you achieved this answer. Thanks!
To find the approximate value of arccos(0.63), input 0.63 into the calculator and use the inverse cosine function to find the answer, which is approximately 50.95 degrees. So correct answer is option B.
The approximate value of arccos(0.63) can be found using a calculator.
To find arccos(0.63), you need to input 0.63 into the calculator and then find the inverse cosine or cos^-1 function. On most calculators, this is represented as cos^-1 or arccos.
When you calculate arccos(0.63), you will get approximately 50.95 degrees as the correct answer.
Tom separated the rectangle shown below into 8 equal parts what fraction shows the area of one of the parts
Tom divided the rectangle into 8 equal parts, and each part represents 1/8 of the total area. This fraction is derived from the fact that division of an area into equal parts means each part is one of those parts as a fraction of the whole.
Tom divided the rectangle into 8 equal parts. If we are to find the fraction that represents the area of one of these parts, we simply consider that each part should be an equal division of the whole. Hence, one part out of eight equal parts is represented by the fraction 1/8. This is because division by 8 is equivalent to multiplication by its reciprocal, which is 1/8. This is the same as dividing the rectangle into smaller, more manageable areas, such as rectangles, and determining the area of one such rectangular area.
It's important to understand that in a rectangle divided evenly into parts, any single part represents a fraction of the whole, with the denominator reflecting the total number of parts. In this case, since there are 8 parts, each individual part is 1/8 of the total area. This provides us with a simple way to address problems involving finding fractions of areas, particularly when the total area is partitioned into equally-sized segments.
Which graph is defined by f(x) = |x2 − x − 2|?
what is the inverse of the function f(x) = 4x + 8 a. h(x) 1/4 x - 2
The inverse of the function will be, [tex]\rm y=\frac{1}{4} x-2[/tex]. Option A is correct. The function is obtained by rearranging the equation.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The given function is;
[tex]\rm f(x) = 4x + 8 \\\\ y=4x+8 \\\\[/tex]
After rearranging the equation, we get;
[tex]\rm x=4y+8 \\\\ y= \frac{1}{4} (x-8)\\\\ y=\frac{x}{4} -2\\\\ y=\frac{1}{4} x-2[/tex]
The inverse of the function will be, [tex]\rm y=\frac{1}{4} x-2[/tex].
Hence, option A is correct.
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There are 12 marbles in a bag, and the marbles are either yellow or green. Two marbles will be randomly picked from the bag, without replacing the first one picked. The probability that both marbles will be yellow is 5 33 . How many YELLOW marbles are in the bag?
Answer:
B) 5
Step-by-step explanation:
The probability of picking yellow first is
x
12
. The probability of picking yellow second is
x-1
11
. This will give a solution of
x (x-1)
132
.
5
33
is equivalent to
20
132
. 5 and 4 are the only two consecutive numbers that when multiplied together equal 20. Therefore there are 5 yellow marbles in the bag.
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LET ME KNOW IF ITS CORRECT
Help. I need to explain if she’s right or not
What is the quotient of -3/8 and -1/3
Answer:
its actually a
Step-by-step explanation:
What is the distance between point l (3,5) and point m (9,−7)?
Consider the function f(x)=−23x+5 . What is f(52) ? Enter your answer, as a simplified fraction, in the box.
Step-by-step explanation:
Given function f(x)=−23x+5
We need to find f(52).
In order to find the value of f(52), we need to plug x= 52 in the given above linear function f(x) = -23x+5.
Plugging x= 52, we get
f(52) = -23(52) +5
On multiplying -23 and 52 we get -1196.
Therefore,
f(52) = -1196 +5
And
f(52) = -1191.find the fraction
53*53−32*32/61*61−44*44
Choose all equivalent expression(s).
HELP !!
answer choices in picture
The area of a regular octagon is 35 cm2. What is the area of a regular octagon with sides five times as long?
A. 625 cm2
B. 875 cm2
C. 175 cm2
D. 245 cm2
Answer with Step-by-step explanation:
Area of octagon=2(1+√2)a²
Where a is the length of the side of the octagon
Area=35 cm²
Let a' be the length of side of new octagon
a'=5a
Area=2(1+√2)a'²
=25×2(1+√2)a²
=25×35 cm²
= 875 cm²
Hence, correct option is:
B. 875 cm²
PLZZ HELP AND PLZZ HURRY
What other information is needed to prove that △FGE ~ △IJH by the SAS similarity theorem?
A. ∠F ≅ ∠J
B. ∠I ≅ ∠F
C. ∠E ≅ ∠H
D. ∠G ≅ ∠I
Answer:
I think the answer is B. ∠I ≅ ∠F.
Step-by-step explanation:
(a - b)(a 2 + ab + b 2) HELP
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The Correct answer is Option C) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."
To determine whether the company can build [tex]10[/tex] child bikes (c) and [tex]12[/tex]adult bikes (a) within the given time constraints, we need to check if the total building time and testing time for both types of bikes do not exceed the limits.
Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test, while each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test.
So, the total building time [tex](4c+6a)[/tex] and the total testing time [tex](4c+4a)[/tex]for the given number of bikes should not exceed the maximum limits of [tex]120[/tex] hours and [tex]100[/tex] hours, respectively.
Therefore, the system of inequalities that best represents this scenario is:
[tex]4c+6a\leq 120\\4c+4a\leq 100[/tex]
Option 3) is correct: "Yes, because the bike order meets the restrictions of [tex]4c+6a\leq 120[/tex] and [tex]4c+4a\leq 100[/tex]."
COMPLETE QUESTION:
A bicycle manufacturing company makes a particular type of bike. Each child bike requires [tex]4[/tex] hours to build and [tex]4[/tex] hours to test. Each adult bike requires [tex]6[/tex] hours to build and [tex]4[/tex] hours to test. With the number of workers, the company is able to have up to [tex]120[/tex] hours of building time and [tex]100[/tex] hours of testing time for a week. If [tex]c[/tex] represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build [tex]10[/tex] child bikes and [tex]12[/tex] adult bikes in the week.
A) No, because the bike order does not meet the restrictions of [tex]4c + 6a \leq 120[/tex] and [tex]4c + 4a \leq 100[/tex]
B) No, because the bike order does not meet the restrictions of [tex]4c + 4a \leq 120[/tex] and [tex]6c + 4a \leq 100[/tex]
C) Yes, because the bike order meets the restrictions of [tex]4c + 6a \leq 120[/tex]and [tex]4c + 4a \leq 100[/tex]
D) Yes, because the bike order meets the restrictions of [tex]4c + 4a \leq 120[/tex]and [tex]6c + 4a \leq 100[/tex]
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Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time. The recursive function that gives the number of books Ashley has at any time is = , starting at
Final answer:
To describe Ashley's book giveaway scenario with a recursive function, define the base case as her starting with 100 books and the recursive step reflecting the weekly giveaway of n books, allowing the calculation of remaining books at any week.
Explanation:
Ashley's scenario of giving away books can be described using a recursive function. If she starts with 100 books and plans to give away n books per week, we can denote the total number of books she has after x weeks as f(x). The recursive function that represents this situation can be written as:
f(0) = 100 - This is our base case, where Ashley starts with 100 books before any are given away.
f(x) = f(x-1) - n - This is the recursive step, indicating that the total number of books Ashley has after x weeks is the number she had the week before, minus n, the number of books given away weekly.
This recursive formula allows you to calculate the number of books Ashley will have after any given number of weeks, as long as n is a known constant number of books she gives away each week.
Evaluate the expression 14.3 minus 2 times 5 to the 2nd power divided by 5
Answer:
4.3
Step-by-step explanation:
We are given that an expression
[tex]14.3-2\times 5^2\div 5[/tex]
We have to find the value of given expression.
DMAS rule:
D=Divided first
M=Multiply
A=Addition
S=Subtraction
Using DMAS rule ,
We solve first divide operation
[tex]14.3-2\times 5^{2-1}[/tex]
Using property: [tex]a^x\div a^y=a^{x-y}[/tex]
Then, we get
[tex]14.3-2\times 5[/tex]
Now, we solve multiply operation
[tex]14.3-10[/tex]
Now, we solve subtraction operation
[tex]4.3[/tex]
Hence, [tex]14.3-2\times 5^2\div 5=4.3[/tex]
rank from highest to lowest in order of decresing mass
1 Gg, 100 g, 1 kg, 50 cg, 1 cg, 1 dg, 50 million ng,
Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2.
Raj and Nicole’s polynomial expressions are added to create a sum, written in standard form.
What can you determine about the degree of the sum?
The sum will be degree
.
What can you determine about the number of terms of the sum?
The maximum number of terms of the sum is
, but it could be less.
Answer:
the sum will be degree 5
the maximum number of terms of the sum is 6
Step-by-step explanation:
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Volume of rectangular prism
Area of a parallelogram
Circumference of a circle
Area of a circle
Area of a triangle
Area of a trapezoid
Perimeter of a quadrilateral
-
Item bank:
2L + 2W
πd
πr2
bh
lwh
1/2(b1 + b2)h
1/2 bh
Final answer:
Clear geometry formulas for calculating volume, area, and perimeter include V = lwh for rectangular prisms, A = bh for parallelograms, and C = πd for the circumference of a circle, among others.
Explanation:
Understanding Geometry, Area, and Volume
To help with remembering formulas from geometry, it's essential to understand the relationships between shapes and their dimensions. Here are the correct formulas for each of the items listed:
Volume of a rectangular prism is given by the formula V = lwh (length × width × height).Area of a parallelogram is found using A = bh (base × height).Circumference of a circle requires the formula C = πd or C = 2πr where d is diameter and r is radius.Area of a circle is calculated by A = πr² (pi times radius squared).Area of a triangle can be computed using A = 1/2 bh (half the base times the height).Area of a trapezoid is found with A = 1/2(b1 + b2)h where b1 and b2 are the bases and h is the height.Perimeter of a quadrilateral is the sum of the lengths of all four sides, often expressed as P = 2L + 2W for rectangles, with L being length and W being width.To solve problems in geometry effectively, it's helpful to visualize the shapes and understand how to derive their area and volume using standard formulas. This also applies when dealing with more complex objects, such as spheres and cylinders. In trigonometry, understanding the relationships within a right triangle can be crucial for solving spatial problems.
In what ways do you think presidents today are more powerful than they were in the past?
Modern presidents are more powerful than their predecessors due to access to advanced technologies, executive actions, and media influence.
Explanation:Presidents today are more powerful than they were in the past due to various factors. Firstly, modern presidents have access to advanced technologies such as television, the internet, and social media, which allow them to shape public opinion and build support for their policies. Secondly, they have a greater ability to use executive action, including executive orders and signing statements, to bypass Congress and enact their own policies. Finally, modern presidents can use their popularity and media attention to increase pressure on Congress and influence policy change.
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Complete the following in 4 to 6 sentences: First, list two intellectual property rights. Then, describe why an intellectual property right provides incentives for people to produce creative work.
Final answer:
Intellectual property rights such as patents and copyrights incentivize creative work by providing creators a temporary monopoly, allowing them to recover development costs and potentially make a profit without immediate competition.
Explanation:
Two intellectual property rights are patents and copyrights. A patent gives the inventor the exclusive legal right to make, use, or sell an invention for a limited time, usually for 20 years, and a copyright provides the author exclusive legal rights over their creative works.
Intellectual property rights offer creators monopoly profits during this protected period, acting as significant incentives for the production of creative work.
This exclusive period allows researchers and companies to recover the costs associated with research and development. Without these protections, there would be little to no incentive to invest in creating new works if they could quickly be replicated without any benefit to the creator.
You have been really sick, so you went to the doctor. The culture taken shows you have 400,000 bacteria. Your doctor prescribes a strong antibiotic which makes the bacteria decrease by a half every 4 hours. How many bacteria will be left after a day?
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The simple interest on a principal amount, P, borrowed for T years at R% annual interest is given by the following formula. Which of the following describes the relationship between the variables of the simple interest formula?
1.P depends on R and T
2.R depends on P and T
3.I depends on P, R, and T
4.R depends on I
Answer:
3. I depends on P, R, and T.
Step-by-step explanation:
We have been given the simple interest formula [tex]I=PRT[/tex], where,
I = Amount of simple interest,
P = Principal amount,
T = Time in years,
R= Interest rate.
The bigger principal amount and higher interest rate for a long period of time will result in big amount of interest, while small principal amount at a smaller interest rate and for a small period of time will result in small amount of interest.
Since amount of interest depends on principal amount, rate and time, therefore, 3rd option is the correct choice.
Randy drove 540 miles in three times the time it took Andy to travel 135 miles Andy’s speed was slower than Randy’s by 15 miles per hour what were the rate and time of each?
I really need help please!!!
Let's assume
Randy's speed =x mph
we have
Andy’s speed was slower than Randy’s by 15 miles per hour
so,
Andy's speed =x-15
Randy drove 540 miles
so, we can find time taken by Randy
time = distance / speed
so, we get
[tex]t_R=\frac{540}{x}[/tex]
we can find time taken by Andy
time = distance / speed
so, we get
[tex]t_A=\frac{135}{x-15}[/tex]
Randy drove 540 miles in three times the time it took Andy to travel 135 miles
so,
[tex]t_R=3t_A[/tex]
we can plug it
[tex]\frac{540}{x}=3*\frac{135}{x-15}[/tex]
now, we can solve for x
[tex]540\left(x-15\right)=405x[/tex]
[tex]135x=8100[/tex]
[tex]x=60[/tex]
so,
Calculation of rate:
Randy's speed is 60 mph
Andy's speed =x-15
Andy's speed =60-15=45mph
Calculation of time:
Randy's time is
[tex]t_R=\frac{540}{x}[/tex]
[tex]t_R=\frac{540}{60}[/tex]
[tex]t_R=9 hours[/tex]
Andy's time is
[tex]t_A=\frac{135}{x-15}[/tex]
[tex]t_A=\frac{135}{60-15}[/tex]
[tex]t_A=3 hours [/tex]