The support vector of the input dsolve('Dy = -3*y') is "dsolve(diff(y,t) == -3*y)".
A symbol is a mathematical object that represents a mathematical entity, such as a number, a variable, or a function. In mathematical software, symbols are used to represent variables, which can be used in mathematical expressions to perform computations.
In the past, character vectors or strings were used to represent symbols in certain mathematical software programs.
In the future release of this software, support for character vectors or strings will be removed. Instead, the program will require users to use the "syms" function to declare variables as symbols.
As an example of how this might be used in practice, consider the differential equation
=> "dy/dt = -3y".
In the past, this equation might have been entered into a mathematical software program using a character vector or string to represent the variable "y".
However, in the future release of this software, the user will need to use the "syms" function to declare "y" as a symbol. The equation would then be entered using the "diff" function, like this:
=> "dsolve(diff(y,t) == -3*y)".
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Construction One linear foot of 12-in. I-beam weighs 25.4 lb. What is the length of a beam that weighs 444.5 lb?
Answer:
17.6 feet.
Step-by-step explanation:
The length of the I-beam can be calculated as follows:
Weight = Length * Weight per Foot
Rearranging this equation:
Length = Weight / Weight per Foot
Substituting the given values:
Length = 444.5 lb / 25.4 lb/ft = 17.6 ft
So, the length of the I-beam is 17.6 feet.
Leila is walking from the park at point P to a restaurant at point R. She wants to stop for a break when the distance she has travelled and the distance she has left to travel has a ratio of 3:5, at which point should Leila stop for her break?
Answer: To determine the point where Leila should stop for her break, we need to find the midpoint of the line segment connecting points P and R, since the midpoint will represent equal distances from both points.
Let the distance between points P and R be d, and let's call the point where Leila stops for her break point B.
Since the ratio of the distance travelled to the distance remaining is 3:5, we know that the distance from B to P is 3/8 of the total distance d, and the distance from B to R is 5/8 of the total distance d.
Therefore, point B is the midpoint of line segment PR, and can be found by dividing the distance between P and R by 2.
Step-by-step explanation:
The base of a triangle is 2inches more than 2 times the height. If the area of the triangle is 12 square inches, find the base and height.
Answer:
Base: 8. Height: 3.
Step-by-step explanation:
Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.
Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
The solution is, the required cost of the used game X= 19.
What is equation?An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
So he bought the $120 game with $82
and 2 equally priced game.
This can be changed to an equation: 120= 82+2X.
The X represents the cost of the used game.
120= 82+2X
-82 -82
——————-
38= 2X
38= 2X
Divide by 2 on both sides
X= 19
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three more than product of 15 and a number n is 153. wright an equation that describes this situation
The equation that describes this situation is, 3 + 15n = 153
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
Given that,
Three more than product of 15,
And a number n is 153.
More than = + (addition)
Product = x (multiplication)
Product of 15 and n = 15 x n = 15n
Therefore, the equation is 3 + 15n = 153.
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x = [ √(a+2) + √(a-2) ]/[ √(a+2) - √(a-2) ], then a =? the correct answer is a = x+(1/x). explain
how.
The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)
How to clear a variable in a radical equation
In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.
First, write the original equation:
x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]
Second, rationalize the expression:
x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]
x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]
x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4
x = [a - √(a² - 4)] / 2
2 · x = a - √(a² - 4)
Third, eliminate the square root operator by algebra properties:
√(a² - 4) = a - 2 · x
a² - 4 = (a - 2 · x)²
Fourth, find the solution to the expression:
a² - 4 = a² - 4 · x · a + 4 · x²
- 4 = - 4 · x · a + 4 · x²
1 = x · a - x²
1 + x² = x · a
a = (1 + x²) / x
a = 1 / x + x
a = x + 1 / x
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6. Application Juanita, who is 1.82 meters tall, wants to
find the height of a tree in her backyard. From the
tree's base, she walks 12.20 meters along the tree's
shadow to a position where the end of her shadow
exactly overlaps the end of the tree's shadow. She is
now 6.10 meters from the end of the shadows. How
tall is the tree?
The height of tree is 9.9372.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
ΔABC ~ ΔDEF only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.
Given;
Juanita is 1.82 meters tall
From the tree's base, she walks 12.20 meters along the tree's shadow to a position where the end of her shadow.
She is now 6.10 meters from the end of the shadows.
Now,
Let, h be the height of the tree;
Here, ΔABC ~ ΔADE,
So, DE/BC = AD/AB
h/1.82 = (6.10 + 12.20)/6.10
h/1.82= 18.30/6.10
h=33.306/6.10
h=5.46
h = 1.82*5.46
= 9.9372
Therefore, by congruency of triangle the answer will be 9.9372.
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How do we rewrite 10^ -1 without using negative exponents?
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
2. The area of a garden plot can be represented by
the expression 85.2z - 58.8. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.
The expression that represents the area of each section is 14z-9
How to find the expression?The expression to denote the area of each section would be: 14z -9
Given that,
The expression for the area of plot area 84z -54
The number of equal sections in which it is divided 6
To find,
The expression for each section = ?
The area of each section = (total area of the garden(/number of equal sections
= (84x-54)/6
= 6(14z-9)/6
=14z - 9
Thus, is the expression that would represent every section's area.
PLEASE PLEASE PLEASE HELP DONT IGNORE
Answer: the first box is does not the 2st box does i hope this helps
Step-by-step explanation:
Answer:
Step-by-step explanation:
(-2, 3) (2, -1)
(-1 - 3)/(2 + 2)= -4/4 = -1
m = -1
does
does not
y - 3 = -1(x + 2)
y - 3 = -x - 2
y = -x + 1
Option 1
Please help!!
In the triangle below, b =______. If necessary, round your answer to two
decimal places.
A
38°
Answer here
8
31.6°
25
SUBMIT
Answer:
Step-by-step explanation:
38.06
Rob loves to run. He set a goal to run more than 390 miles this year.
To date, he has run 127 miles. If he begins to run 18 miles per week,
how long will it take Rob to reach his goal?
Write a two-step inequality, using the values provided in the problem,
that represents this situation. Use x as the variable.
The linear inequality to represent given situation will be 127+18x≥390 where x=no. of weeks and he will take 14.6 weeks to reach his goal.
What is a linear inequality, exactly?
In mathematics, an inequality is a mathematical statement that does not have equal sides. In mathematics, an inequality occurs when a connection results in a non-equal comparison of two expressions or two numbers. In the statement, any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), can be used to replace the equal sign "=". Inequalities are grouped into three forms in mathematics: polynomial inequalities, rational inequalities, and absolute value inequalities.
The symbols " <and >" represent severe disparities, whereas " ≤ and ≥ " represent slack inequalities. A linear inequality resembles a linear equation, but the formula is different.
Now,
Total miles to run=390 mile
He already ran=127 mile
Distance left to run=390-127
=263 mile
Rate of running=18 miles/ week
weeks taken to complete 263 miles=263/18
=14.6 weeks
and given situation can be represented by inequality 127+18x≥390 where x=no. of weeks.
Hence,
The linear inequality to represent given situation will be 127+18x≥390 and he will take 14.6 weeks to reach his goal.
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-ax^(2)+2x+2a if a=7 and x=-5
Answer: -151
Step-by-step explanation:
First Plug everything in
-7(5)^(2)+2(5)+2(7)
Then use order of operations and first deal with the exponent
-7(25)+2(5)+2(7)
then multiply left to right
-175+10+14
combine
so the answer is -151
What is the result when the number 76 is increased by 1.8%? Round your answer to
the nearest tenth.
Answer:
77.4 (nearest tenth)
Step-by-step explanation:
76 is 100% of the original number.
To increase a number by 1.8% it will be 100% + 1.8% = 101.8% of the original number.
[tex]\begin{aligned}\implies \sf 101.8\%\; of\; 76&=\sf \dfrac{101.8}{100} \times 76\\\\&=\sf \dfrac{101.8 \times 76}{100}\\\\&=\sf \dfrac{7736.8}{100}\\\\&=\sf 77.368\\\\&=\sf 77.4\; (nearest\;tenth)\end{aligned}[/tex]
Therefore, the result when the number 76 is increased by 1.8% is 77.4 to the nearest tenth.
Rylon Corporation manufactures Brute and Chanelle perfumes. The raw materials needed to manufacture each type of perfume can be purchased for $3 per pound. Processing 1 lb of raw material requires 1 hour of laboratory time. Each pound of processed raw material yields 3 oz of Regular Brute Perfume and 4 oz of Chanelle perfume. Regular Brute can be sold for $7/oz and Regular Chanelle for $6/oz. Rylon also has the option of further processing Regular Brute and Regular Chanelle to produce Luxury Brute, sold at $18/oz, and Luxury Chanelle, sold at $14/oz. Each ounce of Regular Brute processed further requires an additional 3 hours of laboratory time and $4 processing cost and yields 1 oz of Luxury Brute. Each ounce of Regular Chanelle processed further requires an additional 2 hours of laboratory time and $4 processing cost and yields 1 oz of Luxury Chanelle. Each year, Rylon has 6,000 hours of laboratory time available and can purchase up to 4,000 lb of raw material. Question : what is the simplex algorithm (manual table ) to find a solution to the linear programming problem given above
Convert the problem to standard form and write the initial tableau with slack variables:
Maximize
[tex]Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6[/tex]
Subject to:
[tex]x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000[/tex]
All variables are non-negative.
Tableau
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
s1 1 1 0 0 0 0 1 0 4000
s2 3 3 3 3 3 2 0 1 6000
x5 0 0 1 0 1/3 0 0 0 0
x6 0 0 0 1 0 1/2 0 0 0
The basic variables are s1, s2, x5, and x6.
Step 1: Choose entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.
Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,
corresponding to s1. s1 leaves the basis.
Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
x5 0 0 1 0 1/3 0 0 0 0
s2 3 3 3 3 2 2/3 2/3 0 1/3 24000
x3 1 0 1/3 0 1/3 0 -1/3 0 0
x4 0 1 0 1/3 0 1/2 -1/6 0 0
The basic variables are x5, x3, x4, and s2.
Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.
Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.
As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.
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What is the x-intercept of this equation? 3x + 5y = 9
To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).
What is x-intercept ?
An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.
To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.
So, we have:
3x + 5(0) = 9
3x = 9
x = 3
Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).
To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.
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Fill in the blank to complete the sentence below.
In a standard deck of 52-cards, there are 13 spades and 4 aces, and thus there are
(Type a whole number.)
cards are neither spades nor aces.
Answer: 35
Step-by-step explanation: 52-13-4
A card is drawn from a standard deck of 52 cards and then placed back into the deck. Find the probability that a red card is drawn at least once by the third draw. Round your answer to two decimal places.
Given that there are 26 red cards in the deck of 52 cards, the probability of obtaining a red card on any given draw is 26/52 = 1/2.
What is probability?The probability of the complimentary event—the probability that no red cards are drawn in the first three draws—can be used to determine the likelihood that a red card will be pulled at least once by the third draw.
Particular that there are 26 non-red (black) cards in the 52-card deck, there is a 50% chance that no red cards will be drawn on any given draw.
As a result, the likelihood that none of the three draws will result in a red card is:
(1/2) x (1/2) x (1/2) = 1/8
The likelihood of drawing a red card at least once by the third draw is the counterpart of this probability.
1 - 1/8 = 7/8
Therefore, by the third draw, there is a 7/8 chance of drawing a red card at least once, or 0.88 rounded to two decimal places.
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Consider the graph of the function f(x)=log4(x-2)+2. What are the domain and the range of function f?
Answer:domain is (2, ∞), range is (-∞,∞)
Step-by-step explanation:
domain is (2, ∞) as it aproaches 2 but never reaches and range is (-∞,∞)
Below is a square based pyramid. Calculate the length of side I
The slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.
What is the Pythagoras ruleThe Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we can observe the right triangle with hypotenuse l, height = 15, and base = 8 {half the pyramid base of 16}
the slant height is calculated as follows:
l² = 15² + 8²
l² = 225 + 64
l² = 289
l = √289 {take square root of both sides}
l = 17.
Therefore, the slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.
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Need help quick with this problem!!! [tex]\frac{6x^{-1} y^{-1}}{\sqrt[4]{xy^{4}} }[/tex]
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6}{x^1 y^1 \left( xy^4 \right)^{\frac{1}{4}}}\implies \cfrac{6}{x^1 y^1 \left( x^{\frac{1}{4}}y^1 \right)}\implies \cfrac{6}{x^1x^{\frac{1}{4}} y^1 y^1} \\\\\\ \cfrac{6}{x^{1+\frac{1}{4}} y^{1+1}}\implies \cfrac{6}{x^{\frac{5}{4}} y^2}\implies {\Large \begin{array}{llll} \stackrel{a\quad b \quad ~~ c}{6x^{-\frac{5}{4}}y^{-2}} \end{array}}[/tex]
What is the area of rhombus ABCD?
24.57 cm^2
39.00 cm^2
98.28 cm^2
78.00 cm^2
The area of rhombus ABCD is 98.28 cm². Therefore, option C is the correct answer.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, in rhombus ABCD, AD=10 cm and OC=7.8 cm.
Here, BC²=OC²+OB²
10²=7.8²+OB²
OB²=100-60.84
OB²=39.16
OB=√39.16
OB=6.3 cm
AC=2×7.8
AC=15.6 cm
BD=2×6.3 =12.6 cm
We know that, area of rhombus is 1/2 ×(Product of diagonals)
Now, area= 1/2 ×15.6×12.6
= 98.28 cm²
Therefore, option C is the correct answer.
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Please help me with this question please
a lady sells brouses at 1500 ksh each. she make a profit of sh.150 shillings for each brouse how much does she pay for it
Answer: If the lady sells each brouse for 1500 KSH and makes a profit of 150 KSH for each brouse, then the cost price of the brouse is 1500 KSH - 150 KSH = 1350 KSH.
So, the lady pays 1350 KSH for each brouse.
Step-by-step explanation:
7. The functions f(x)=2* and g(x)=8(2)* are both shown graphed.
The graph of g is certainly a vertical stretch of the function f by a
factor of 8. But, it is also a shift off by three units left. Can you
explain why this is using an exponent law?
The function g(x) = 8(2)^x is also a shift left by 3 units of f(x) = 2^x, as 8 = 2³, hence 8(2)^x = 2^(x + 3).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The functions for this problem are given as follows:
f(x) = 2^x.g(x) = 8(2)^x.8 is the third power of 2, hence:
8 = 2³.
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
8(2)^x = 2³ x 2^x = 2^(3 + x) = 2^(x + 3).
As x -> x + 3, a translation left 3 units happened.
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The radius of a circle is 14 meters. What is the circle's circumference?
Answer: 87.96m
Step-by-step explanation:
Circumference of a circle = 2[tex]\pi[/tex][tex]r^{2}[/tex] --> 2[tex]\pi[/tex]14² = 87.96m
Fill in the blanks so that the solution of the system is (5, 5).
x + y = −5
y = −x +
The requried complete system of equation is given as -2x + y = -5 and y = -x + 10.
What is a system of the simultaneous equations?A system of simultaneous equations, also known as a system of equations, is a set of two or more equations that must be solved at the same time. In a system of two equations, for example, the solution is the set of values of the variables that satisfy both equations simultaneously.
Here,
Given equation are
_x + y = −5 - -- - - -(1)
y = −x + _ - - - - - (2)
Now,
Let the coefficient of x in equation 1 is m and the intercept of equation 2 be y,
In equation 1,
Put the given points (5, 5)
m(5) + 5 = - 5
5m = -10
m = -2
Now,
Put the same point equation 2 with C
5 = -5 + C
C = 10
Thus, the requried complete system of equation is given as -2x + y = -5 and y = -x + 10.
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4. Reginald created a mosaic from 6" square tiles.
If the completed mosaic was 2 feet by 3 feet, how
many square tiles did he use?
Reginald used 2 square tiles to make the mosaic
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The area is the product of the length and width. Hence:
Area = length * width
Reginald created a mosaic from 6" square tiles. Therefore:
Area of tiles = 6 in * 6 in = 36 in²
If the completed mosaic was 2 feet by 3 feet, Hence:
Area of mosaic = 2 feet * 3 feet = 6 feet
1 feet = 12 in
6 feet = 6 feet * 12 in per feet = 72 in²
Number of tiles = Area of mosaic / area of tiles = 72 in² / 36 in² = 2
Reginald used 2 tiles
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need help looking for the anwser
Answer:
need help looking for the anwser here it's the 2.5
How do I do these questions ??
