The ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.
The amount of water, sucrose, and the saline solution used can be expressed as a ratio in its simplest form by finding the greatest common divisor (GCD) of the three quantities and dividing each by it.
1l of water = 1000 ml of water.
Let's find the GCD of the three quantities:
GCD(199,271,1000) = 1
So we can express the amount of water, sucrose, and saline solution needed as a ratio in its simplest form by dividing each of the three quantities by 1
Water : Sucrose : Saline solution = 1000 : 199/1 : 271/1 = 1000:199:271
Hence, the ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.
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write the trigonometric equation for the function with a period of 6. the function has a maximum of 3 at x
The trigonometric equation for the function with a period of 6 is [tex]f(x) = A sin (\frac{\pi}{3}t)[/tex].
What are trigonometric functions?The simplest definition of a trigonometric function is the function of an angle in a triangle, often known as a circular function. It implies that these trig functions can be used to determine the relationship between a triangle's angles and sides.
The general equation of the wave is given by the formula:
f(x) = A sin(wt)
Where, [tex]w = \frac{2\pi}{T}[/tex]
where, T is the time period.
Given that T = 6, substituting the value in the formula we have;
[tex]w = \frac{2\pi}{6}[/tex]
[tex]w = \frac{\pi}{3}[/tex]
Substituting the value of w in the general equation:
[tex]f(x) = A sin (\frac{\pi}{3}t)[/tex]
Hence, the trigonometric equations for the function with a period of 6 is [tex]f(x) = A sin (\frac{\pi}{3}t)[/tex].
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Josh went into a store to buy a $100 item. There was a sale of 35% off all
The sales person gave Josh a 25% discount and then an additional
Is that the same as receiving a 35% discount? Prove your answer.
merchandise.
10% discount.
No, it is not the same as receiving a 35% discount of all the $100 items.
What is a discount?A discount can be defined as the amount of money a seller deducts for their customers from the normal price of the products they are selling.
The percentage discount that is generally on products that are sold for the price of $100 = 35%
The additional discount Josh received were 25% and 10% which is a total of 35% which is different from the general discount.
Therefore, it is not the same as receiving a 35% discount of all the $100 items.
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Complete question:
Josh went into a store to buy a $100 item. There was a sale of 35% off all. The sales person gave Josh a 25% discount and then an additional merchandise.
10% discount. Is that the same as receiving a 35% discount? Prove your answer.
A florist must make 5 identical bridesmaid bouquets for a wedding. She has a budget of $160 and wants 12 flowers for each bouquet. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. She wants twice as many roses as the other two types of flowers combined. Write a system of equations to represent this situation. How many of each type of flower should be in each bouquet?
The flowers was 8 roses, 2 lillies and 2 irises in each of the identical bouquet.
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let x represent the number of roses in each bouquet, y represent the lillies in each bouquet, and z represent the irises.
A florist must make 5 identical bridesmaid bouquets for a wedding. She has a budget of $160, hence:
Cost of flowers in each bouquet = $160/5 = $32
She wants 12 flowers in each bouquet, hence:
x + y + z = 12 (1)
She wants twice as many roses as the other two types of flowers combined, hence:
x = 2(y + z)
x - 2y - 2z = 0 (2)
Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each, hence:
2.5x + 4y + 2z = 32 (3)
From the equations:
x = 8, y = 2, z = 2
There was 8 roses, 2 lillies and 2 irises.
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Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.
What does f(4)=f(30) tell you?
The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.
What is the function?It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.
The function illustrated shows that the weights are the same.
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On a separate sheet of papter solve each system by elimination.
Show your work on how to get the solution given for each system.
1) 6x - 4y = 2
-2x + 4y = 18
(5.7)
3) -4x - 12y=-24
-2x - 4y =-10
(3,1)
2) 5x +4y= -8
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
What is an expression in math?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. No symbols for equality or inequality are present.A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the phrase 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.Given data :
1 ) 6x - 4y = 2
- 2x + 4y = 18
( 5. 7 )
=
= 6x-4y=2
{-2x+4y=18(5.7)}
= [ -2{1+2y}{3}+4y=18. 5.7 ]
= [tex]\frac{-2+8y}{3}[/tex] = 102.6
= y = 38.725
= x = [tex]\frac{1+2\cdot \:38.725}{3}[/tex]
x = 26.15
2) -4x - 12y=-24
-2x - 4y =-10
(3,1)
Solve the equation for x
x = 12 − 4y
− 24 − 2x−4y = −31
Solve using substitution
−24 −2 (12−4y) − 4y = −31
Simplify
− 48 + 4y = −31
Move the constant to the right side
4y= −3 1− (−48)
Subtract the terms
4y = 17
Multiply both sides
4y × [tex]\frac{1}{4}[/tex] = 17 x [tex]\frac{1}{4}[/tex]
Simplify
4y × [tex]\frac{1}{4}[/tex] = [tex]\frac{17}{4}[/tex]
Substitute the given value of y into the equation x = 12 − 4y
x = 12 − 4 × [tex]\frac{17}{4}[/tex]
Simplify the expression
x=−5
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which expression has the same value as 1 2/3 + (-8 1/2)
The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression is 1 2/3+(-8 1/2)
=5/3+(-17/2)
=5/3-17/2
Taking LCM 6
=(10-51)/6
=-41/6
Hence,
The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.
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]Mariam has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $275.67.
She buys 3 bicycle reflectors for $16.32 each and a pair of bike gloves for $24.39.
She plans to spend some or all of the money she has left to buy new biking outfits for $27.40 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Mariam can purchase while staying within her budget.
The number of outfits Mariam can purchase is 7.
The inequality to represent the situation is 560 ≤ 349.02 + 27.40x.
How to represent a situation with an inequality?Mariam has $560 to spend at a bicycle store for some new gear and biking outfits. The price list are as follows:
She buys a new bicycle for $275.67.She buys 3 bicycle reflectors for $16.32 eachA pair of bike gloves for $24.39.She plans to spend some or all of the money she has left to buy new biking outfits for $27.40 each.
The inequality that can be used to determine x, the number of outfits Mariam can purchase within her budget can be calculated as follows:
560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x
where
x = number of biking outfits
560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x
560 ≤ 275.67 + 48.96 + 24.39 + 27.40x
560 ≤ 349.02 + 27.40x
560 - 349.02 ≤ 27.40x
divide both sides by 27.40
210.98 ≤ 27.40x
divide both sides by 27.40
210.98 / 27.40 ≤ x
7.7 ≤ x
Therefore, the number of outfit he can purchase is 7.
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montrer que Si a2 est un multiple de 3 alors a est un multiple de 3
Answer:
Step-by-step explanation:
1
Triangle ABC is an isoceles triangle. find the missing angles and side measures.
Angle C is 70°
Angle A is 30°
Side AC is 12 cm.
answer pls asap quickly
Shaded picture where tree can be planted is attached below as per the scaling given.
What is Scale?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.
Given, Here is a scale drawing of a garden. The scale is 1 cm to 2m
A tree is going to be planted. The tree must be more than 4 m from the patio. The tree must be more than 6m from the pond.
Since Scale is 1: 200
Planted tree distance from Patio = 4 m = 400 cm
in picture = 400 * 1: 200
in picture, Planted tree distance from Patio= 2 cm
Planted tree distance from Ppnd = 6 m = 600 cm
in picture = 600 * 1: 200
in picture, Planted tree distance from Patio= 3 cm
Therefore, Shaded picture where tree can be planted is attached below as per the scaling given.
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In the Tour De France, Alex biked 198 km in 5 hours and Sam biked 298 km in 7 hours. Who biked at a faster rate? Show your work and explain your reasoning. (You may use a calculator).
Answer:
Step-by-step explanation:
21
Answer:
Sam bikes at a faster rate. He can go 42.6 km in one hour while Alex is only able to go 39.6 km in the same amount of time.
Step-by-step explanation:
Alex's unit rate:
198/5 = 39.6 km per hour
Sam's unit rate:
298/7 = 42.6 km per hour rounded to the nearest tenths'
Which equation shows that you can find the power of a power by finding the product of the exponents?
The equation that shows the power of a power property by obtaining the product of the exponents is given as follows:
(y^a)^b = y^(a x b).
Meaning that the lower right option is the correct option.
What is the power of a power rule?The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
A simple example is given as follows:
(2²)³ = 2^(2 x 3) = 2^6.
Hence the general format of the expression is presented as follows:
(y^a)^b = y^(a x b).
Which gives the correct option in the context of this problem, and the correct option is the bottom right option.
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tommy wants to hire a car to drive 850 miles in 8 days how much would it cost him to hire a car from the cheaper side.
Note if Tommy were to hire a car to drive 850 miles in 8 days under the price conditions given, it would cost him £575 to go with the cheaper company which is company B.
To compute the cheaper price, we need to work out how much it comes to if he went with either company.
Company A:
Daily Charge £20
Cost per mile 50p
Given that he goes 850 Miles ;
For 8 days,
His Total cost with Company A is
(20 x 8) + [ (50 *850)/100); recall that 100 pence (p) make 1 British Pound (£)
Thus, 160 + 425
= £585
Thus, to go with Company A, Tommy will spend £585
On the other hand, Tommy's Total cost with Company B is computed as follows;
Daily Charge £40
Cost per mile 30p
Total cost will come to: (40 x 8) + [(30 *850)/100)
= 320 + (25500/100)
= £575
Since Company will charge a total of £585 and Company B will charge a total of £ 575, we can conclude that the cheaper company is company B.
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Full Question:
Tommy wants to hire a car to drive 850 miles in 8 days how much would it cost him to hire a car from the cheaper side. See the attached for the pricing conditions.
the of decision making recognizes that people (a) often use incomplete and imperfect information, (b) are constrained by bounded rationality, and (c) tend to satisfice.
They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.
This type of decision making is known as bounded rationality. Bounded rationality acknowledges that people often make decisions based on incomplete and imperfect information but seek the best possible outcome. People use heuristics and mental shortcuts to make decisions and tend to satisfice, which means they settle on a satisfactory solution rather than searching for the optimal solution. This type of decision making is often used when the complexity of a problem is too great to be solved analytically.
Bounded rationality is a type of decision making which acknowledges that people often make decisions based on incomplete and imperfect information, and seek the best possible outcome using heuristics and mental shortcuts. They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.
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Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is $\frac{K \sqrt{6}}{\sqrt{\pi}}$, then what is $K$
When the volume of this sphere is [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex], then the value of K is 8
As per the data given:
The length of the cube is 2 units.
First, we have to determine the surface area of the cube.
The formula for the surface area of the cube:
A = 6 (side × side)
A = 6 (2 × 2)
A = 6 (4)
A = 24 square units
The surface area of a cube is 24 square units.
Also given that the surface area of a cube and the surface area of a sphere is equal.
The formula for the surface area of the sphere.
A = 4π [tex]r^{2}[/tex]
Where r is the radius of the sphere.
4π [tex]r^{2}[/tex] = 24
π [tex]r^{2}[/tex] = 6
[tex]r^{2}[/tex] = [tex]\frac{6}{\pi }[/tex]
r = [tex]\sqrt{\frac{6}{\pi } }[/tex]
The radius of the sphere is [tex]\sqrt{\frac{6}{\pi } }[/tex]
Also given the volume of the sphere as [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex]
Here we have to determine the value of K.
The volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
Where r is the radius of the sphere.
[tex]\frac{4}{3} \pi r^{3}[/tex] = [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex]
[tex]\frac{4}{3} \pi (\sqrt{\frac{6}{\pi } }) ^{3} = \frac{K \sqrt{6} }{\sqrt{\pi } }[/tex]
[tex]\frac{4}{3} \pi {\frac{6}{\pi } }= K[/tex]
K = 4 × 2
K = 8.
Therefore the value of K = 8.
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(5n+ 5.82) + (2.29n+7.67) = (5n+______) + (5.82 +____
Answer:
(5n + 2.29n) + (5.82 + 7.67)
Step-by-step explanation:
Arrange the steps in the correct order to solve the equation,
3(22-5) - 4 = 10
add 4 to each side of the
equation:
3/22 - 5) = 14
use the exponential property and
write in decimal form:
(2 - 5)log2 = log4.67
log4.67
find the value of toga
and substitute
2-5 = 2.23
simplify
23.625
take the log of each side:
log(22+ - 5) = log('9).
2 - 5 - 1034.87
divide each side by log 2
tog?
add 5 to each side of the
equation
2+ = 2.23 +5
divide both sides of the equation
The steps in the correct order to solve the equation: [tex]3\times 2^{(2t-5)} - 4 = 10[/tex] is given below and the solution to given equation is t = 3.625
Consider given equation: [tex]3\times 2^{(2t-5)} - 4 = 10[/tex]
We arrange the given steps in correct order to solve given equation.
Step 1:
Add 4 to each side of the equation.
⇒ [tex]3\times 2^{(2t - 5)} = 14[/tex]
Step 2:
Divide each side of equation by 3
⇒ [tex]2^{(2t - 5)} =\frac{14}{3}[/tex]
Step 3:
Take the log of each side of equation.
[tex]log 2^{(2t-5)} = log(\frac{14}{3})[/tex]
Step 4:
use the exponential property and write (14/3) in decimal form:
⇒ (2t - 5) log(2) = log(4.67)
Step 5:
Divide each side by log 2
⇒ 2t - 5 = log(4.67) / log(2)
Step 6:
Find the value of log(4.67) / log(2) and substitute
⇒ 2t - 5 = 2.23
Step 7:
Add 5 to each side of the equation
⇒ 2t = 2.23 + 5
Step 8:
Simplify
t = 3.625
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Why is 1 called a universal factor?
1 is a universal factor. It is a factor of all numbers. The number itself is a factor of the number as it divides itself entirely.
A factor is a number that divides another number and leaves no remainder. In other words, if multiplying two whole numbers gives us a product, the numbers we are multiplying are factors of the product because they are divisible by the product. There are two processes for finding factors: multiplication and division.
For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 absolutely and 12 ÷ 6 = 2 absolutely. The other factors of 12 are - 1, 2, 4, and 12.
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Which coordinate plane shows the equation. It's due today
ten students wrote a test, and the distribution of scores is shown on the frequency table. if the average (arithmetic mean) score is 62, what is the value of x ?
From the given information, the value of x in the given table is 42.5.
To find the value of x, we can use the formula for the arithmetic mean (average) of a set of numbers:
Arithmetic mean = (sum of all numbers) / (number of numbers)
Given that the average score on the test is 62, we can use this information to find the sum of all the scores.
Given that number of students is 1,2,3 and 4 with scores of 40,55,70 respectively, we can use this information to find the sum of all the scores.
Sum of all scores = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x)
Now we can substitute the given average score and the number of students into the equation and solve for x.
62 = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x) / 10
620 = 40 + 110 + 210 + 4x
4x = 170
x = 42.5
So, the value of x is 42.5
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The complete question is -
ten students wrote a test, and the distribution of scores is shown in the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?
Score - 40, 55, 70, x
Number of students - 1, 2, 3, 4
Select the correct answer from the drop-down menu. A study revealed that, compared with children who do not have autism, most autistic children have underdeveloped motor skills. However, siblings of autistic children do not have any motor impairment. Based on this excerpt, we can conclude that autism
Is associated with motor impairment but does not cause it
Autism is defined as the development of disability caused by differences in the brain.
People with autism often have problems with social communication and interaction, restricted or repetitive behaviors or interests, and also have different ways of learning, moving, or paying attention.
The study didn't explain the timeline of their findings, so we can conclude this research takes data at one time.
Research that doesn't take before and after exposure data cannot be used to derive causation since we can't prove that the condition happens after exposure.
But this study still can predict association by risk ratio or odds ratio depending on the study design.
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Solve the triangle. Round each angle to the nearest degree and round each Side to the nearest hundredth. Do not use rounded answers in your calculations to find missing measures.
Answer:
The length of the third side (Hypotenuse) is 7.1556411313
Step-by-step explanation:
In order to find the third side(Hypotenuse) we use a formula called the phytogorean theorem which was invented by a philosopher named Pythagoras.
[tex]a^{2} +b^{2} =c^{2}[/tex]
We now apply the given values to the equation
[tex]5.96^{2} + 3.96^{2} = c^{2}[/tex]
Squaring the numbers we get,
[tex]35.5216+15.6816 = c^{2}[/tex]
[tex]51.2032[/tex] [tex]= c^{2}[/tex]
We now find the root of the number to find the hypotenuse which is,
[tex]\sqrt{51.2032} = c[/tex]
[tex]7.1556411313 = c[/tex]
Hence , the length of the third side (Hypotenuse) is 7.1556411313
Lesley is baking cookies. She makes one batch using 1 1/4 cups sugar and 1 1/2 cups flour.
Lesley needs to bake an additional smaller batch of cookies.
To make this new batch of cookies, she uses 1 cup of sugar.
Using this ratio, how many cups of flour should Lesley use in the new batch of cookies?
The 1 1/4 cups of sugar and 1 1/2 cups of flour used in making one batch, indicates that the number of cups of flour Lesley should use in the new batch of cookies, expressed as a mixed fractions is 1 1/5 cups
What is a mixed fraction?A mixed fraction consists of the sum of the quotient and the fraction of the remainder divided by the divisor, of a fraction which has a larger numerator than the denominator.
The amount of sugar and flour required to make one batch of cookies specified in mixed fractions are;
Amount of sugar = 1 1/4 cups
Amount of flour = 1 1/2 cups
The amount of sugar in the additional batch = 1 cup of sugar
The ratio of the quantities of the sugar and flour between original batch and the new batch is therefore;
Sugar in original batch/(Sugar in new batch) = (Flour in original batch)/(Flour in the new batch)
[tex]\frac{1\frac{1}{4} }{1} =\frac{1\frac{1}{2} }{y}[/tex]
Where;
y = The number of cups of flour required in the new batch
Cross multiplying, we get;
[tex]y \times 1\frac{1}{4} = 1\frac{1}{2}[/tex]
[tex]y = \frac{1\frac{1}{2} }{1\frac{1}{4} } = \frac{6}{5} =1\frac{1}{5}[/tex]
The number of cups of flour needed in the new batch is, y = 1 1/5 cups
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A semicircle is constructed along each side of a right triangle with legs 6 inches and 8 inches. The semicircle placed along the hypotenuse is shaded, as shown. What is the total area of the two non-shaded crescent-shaped regions
The total area of the two non-shaded crescent-shaped regions =25π ^2
The length of hypotenuse = 10
(6^2 + 8^2 = 10^2 )
Therefore, the radius of the large semicircle equals 5.
area of large semi-circle = 25π
As a result, the total area of the two non-shaded regions is 25π^ 2
A semicircle is formed when a circle is divided in half along its diameter
The circumference of a semicircle is curved, and the diameter is straight.
A semicircle has a right angle of 90.
For example PR is a diameter and (angle PRQ=25. The size of (angle QPR) is (angle PQR=90circ) because it is the angle in a semicircle. The sum of triangle's three angles is 180.
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from an ordinary deck of 52 cards, five cards are drawn randomly. what is the probability of drawing
The probability of drawing exactly three face cards is given as follows:
0.0660 = 6.60%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Considering that a standard deck is composed of 52 cards, of which 12 are face cards, and 5 cards are taken, the values of the parameters are given as follows:
N = 52, k = 12, n = 5.
The probability of drawing exactly three face cards is P(X = 3), obtained as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,52,5,12) = \frac{C_{12,3}C_{40,2}}{C_{52,5}} = 0.0660[/tex]
Missing InformationThe problem asks for the probability of drawing exactly three face cards.
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In this problem we present another way of discovering the second linearly independent solution of (1) when the roots of the auxiliary equation are real an equal. (a) If m_1 notequalto m_2, verify that the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0 hasy = e^m_1x - e^m_2 x/m_1 - m_2 as a solution. (b) Think of m_2 as fixed and use I'Hospital's rule to find the limit of the solution in part (a) as m_1 rightarrow m_2. (c) Verify that the limit in part (b) satisfies the differential equation obtained from the equation in part (a) by replacing mi by m_2.
All the Individuals solutions are solved below:
a) To verify that y = e^m_1x - e^m_2 x/m_1 - m_2 is a solution of the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0, we can substitute y into the equation and simplify:
y" = m_1^2e^m_1x - m_2^2e^m_2x
y' = m_1e^m_1x - m_2e^m_2x
so:
y" - (m_1 + m_2)y' + m_1 m_2y = m_1^2e^m_1x - m_2^2e^m_2x - (m_1 + m_2)(m_1e^m_1x - m_2e^m_2x) + m_1 m_2(e^m_1x - e^m_2x/m_1 - m_2) = 0
b) To find the limit of the solution in part (a) as m_1 right arrow m_2, we can use I'Hospital's rule. The limit is:
lim (m_1 -> m_2) e^m_1x - e^m_2 x/m_1 - m_2 = e^m_2x - e^m_2 x/m_2 - m_2 = e^m_2x - e^m_2x - m_2 = -m_2
c) To verify that the limit in part (b) satisfies the differential equation obtained from the equation in part (a) by replacing mi by m_2, we can substitute -m_2 into the equation:
y" - (m_2 + m_2)y' + m_2 m_2y = 0
y" - 2m_2y' + m_2^2y = 0
which is the differential equation of a constant function, and -m_2 is a constant function. Therefore, the limit in part (b) satisfies the differential equation.
It should be noted that the solution y = e^m_1x - e^m_2 x/m_1 - m_2 is a linearly independent solution of the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0, and it can be used in combination with the general solution y = c_1e^m_1x + c_2e^m_2x to find the general solution of the differential equation.
Therefore, All the Individuals' solutions are solved.
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b. Darla plans to drive to the market 14 miles from her house, then to the post office 3 miles
and then return home, which is 15 miles from the post office. Assuming she drives
entire time, how much time will she spend driving as she runs her errand Round pr
hundredths place.
At a constant speed of 45 miles per hour it will take 0.71 hours for Darla to run her errands and get back home.
What is constant speed?
An object is considered to be moving at a constant speed when it covers the same distance in the same amount of time. When moving at a constant pace, an object covers a certain distance in a fixed amount of time.
Darla drives at a constant speed of 45 miles per hour.
She drives for y miles and it takes her x hours.
The number of miles Darla can drive in x hours is y = 45x.
Darla drives to the market, 14 miles from her house.
Then she drives to the post office, 3 miles from the market.
Then she drives back to her house, 15 miles from the post office.
Calculate Darla's total distance travelled -
14 + 3 + 15 = 32 miles
Now, substituting the value of y with 32 -
32 = 45x
x = 32/45
x = 0.71
Therefore, the time taken by Darla is 0.71 hours.
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A tank hold 49 literof oil. If 7 liter leak what the percentage of oil ha leaed?
The percentage of oil that has leaked from the tank is 14.29%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
Given that,
The capacity of the tank = 49 litres.
Total litres of oil leaked = 7 litres.
Mathematically, the percentage for the amount of oil leakage in this tank is given by this formula:
Percentage = oil leakage/tank capacity *100
Substituting the given parameters into the formula, we have:
Percentage = 7/49 *100 = 14.29%
Thus, The percentage of oil that has leaked from the tank is 14.29%.
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6 ft tall man walks at the rate of 5 ft/sec toward a street light that is 16 ft above the ground. a. at what rate is the length of his shadow changing when he is 10 ft from the base of the light?
According to the concept of differentiation the length of his shadow changing when he is 10 feet from the base of the light is 10 feet.
Here we have given that the height of man = 6 feet
And the Height of light is 15 feet
Then the Rate of walk by man is written as
=>dx/dt = 5 feet per second.
Here we have to find the rate at which the tip of his shadow is moving when he is 10 feet from the base of the light.
Here by using ratio of similar triangles we have write it as,
=> 15/y = 6/(y - x)
When we do the cross multiplication on it, then we get
=> 15(y - x) = 6y
=> 15y - 6y = 15x
=> 9y = 15x
When we dividing by 3 on both sides then we get
=> 3y = 5x
While we differentiating both sides with respect to t then we get
=> 3(dy/dt) = 5(dx/dt)
=> dy/dt = (5/3)(6)
When we simplify this one, then we get
=> dy/dt = 10 ft/s
Hence the rate at which the tip of his shadow is changing is 10 ft/s.
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A sequence is defined by the term-to-term rule
Un+1 = U²₁ + 5
Given that u, = 1,
a) find u₁
b) find u₂
c) find u
Answer:
Step-by-step explanation:
a) To find u1, we can use the term-to-term rule given in the problem:
Un+1 = U²₁ + 5
We know that u1 = 1, so we can substitute that into the equation:
u2 = 1² + 5 = 1 + 5 = 6
b) To find u2, we can use the same term-to-term rule and substitute the value of u1 (which is 6) into the equation:
u3 = 6² + 5 = 36 + 5 = 41
c) To find un, we can use the term-to-term rule and substitute the value of un-1 into the equation.
un = un-1² + 5
It's important to note that the value of n is not given so we can't calculate the value of un.
Therefore, u1 = 6, u2 = 41, and we can't calculate un without knowing the value of n.
