At a sale this week, a desk is being sold for $285.60. This is 34% of the original price.
What is the original price?
well, let's say the original price is "x", which namely 100% of the price of the product, we also know that 285.60 is 34% of that.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 285.60&34 \end{array}\implies \cfrac{x}{285.60}=\cfrac{100}{34}\implies \cfrac{x}{285.60}=\cfrac{50}{17} \\\\\\ 17x=14280\implies x = \cfrac{14280}{17}\implies x = 840[/tex]
find the point (x,y) on the curve where dy/dx = 0
a. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]
Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives
[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]
[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]
and so
[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]
Set this equal to zero and solve for t :
[tex]1-e^{2t} = 0[/tex]
[tex]1 = e^{2t}[/tex]
[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]
[tex]0 = 2t \ln(e)[/tex]
[tex]0 = 2t[/tex]
[tex]t=0[/tex]
This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).
b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,
[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]
We have
[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]
and we've already committed dx/dt. So
[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]
Substitute the first and second derivative into the differential equation:
[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]
[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]
[tex]4e^{6t} -e^{2t}= 0[/tex]
[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]
[tex]4e^{4t} - 1 = 0[/tex]
[tex]4e^{4t} = 1[/tex]
[tex]e^{4t} = \dfrac14[/tex]
[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]
[tex]4t \ln(e) = -\ln(4)[/tex]
[tex]4t = -\ln(4)[/tex]
[tex]t = -\dfrac{\ln(4)}4[/tex]
The variables x and y are related proportionally. When x = 8, y = 14. Find y when x = 48. When x = 48, y = what.
Y might be 84. Considering 6*8=48, it would probably be the same with Y, so 14*6=84.
Hopefully this is correct but sorry if it isn't.
Which statement is true?
A person needs to fill 10 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes. How long to finish filling the remaining jugs?
Answer:
15
Step-by-step explanation:
The work of a student to solve the equation 3(2x - 4) = 8 + 2x + 6
Answer:
false
Step-by-step explanation:
3(2×−4)=8+2×+6
Multiply 3 and 2 to get 6.
6(−4)=8+2×6
Multiply 6 and −4 to get −24.
−24=8+2×6
Multiply 2 and 6 to get 12.
−24=8+12
Add 8 and 12 to get 20.
−24=20
Compare −24 and 20.
A refreshment stand makes 5 large servings of frozen yogurt from 8 pints. Graph the line and then write
its equation. Let the x-axis represent the number of pints and the y-axis represent the number of
servings. Use only fractional form, if necessary.
Answer:
x= (8/5)
Step-by-step explanation:
x= 8÷5
evaluate the equation/expression
x=1.6
then convert to a fraction x= BasePoly 1.6 → 16/10 →8/5
Answer:
Pls help me I think its 5/8
Step-by-step explanation:
For each value of v, determine whether it is a solution to 59 = 3 - 7v.
Answer:
[tex]59=3-7v[/tex]
Subtract 3 from both sides:
[tex]59-3=3-7v-3[/tex]
[tex]56=-7v[/tex]
[tex]-7v=56[/tex]
[tex]v=-8[/tex]
-8 is the only solution.
Answer:
well I think it's -6
Step-by-step explanation:
7×-6=-42+3=39
¿Qué fuerza media se requiere para que un objeto de 2 Kg aumente su velocidad de 5 m/s a 12 m/s en una distancia de 8 m?
Answer:
14.87
Step-by-step explanation:
Para conocer cual es la fuerza que necesita el cuerpo para aumentar su velocidad de 5 m/s a 12 m/s en 8 m
Necesitamos conocer la aceleración y para conocer la aceleración debemos saber cuanto tiempo tarda en recorrer los 8m
Vf = Vo +a(t)
12 = 5 +a(t) -------> Vamos a despejar el tiempo.
t = 7/a
X= Vo(t) +1/2a(t²)
X= 5(7/a)+1/2a( 7/a )²
8 = 35/a+49/2a
a = 7.43 m/s²
Ahora que conocemos la aceleración podemos calcular la fuerza como:
F = m*a
F = 7.43 * 2 kg.
F = 14.87
Five kittens are sharing 6 cups of milk equally. How much milk does each kitten get?
Answer:
1 1/5
Step-by-step explanation:
We know that there is 5 kittens that have to eat six bowls of milk
Each cat would get 1 whole bowl of milk. All the kittens have to share 1/5 of the sixth bowl of milk.
Five kittens are sharing 6 cups of milk equally so 1 1/5 cup of milk is given to each kitten.
What is meant by Mathematical expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Expressions in writing are made using mathematical operators such addition, subtraction, multiplication, and division.. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Arithmetic operations are the most fundamental type of mathematical expression. Any combination of numbers and a mathematical operation, such as multiplication, addition, subtraction, or division, are considered arithmetic operations. For instance, the arithmetic operation 9 + 14/2 - 6*(5 + 3) results in -32.
Given,
6 cup of milk so there are 5 kitten
To give 6 cup of milk to 5 kitten is=6/5
= 6/5
=1 1/5
Therefore Five kittens are sharing 6 cups of milk equally so 1 1/5 cup of milk is given to each kitten.
To learn more about Mathematical expression refer to:
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what is 2x-3 when x=1
Solve for x given that
4x + 2
7
Answer:
x = - 1/2 or -0.5
Step-by-step explanation:
Steps on the pic above
What is the y intercept of y= 3x + n
Answer:
Step-by-step explanation:
1
1/2(-4+6x)=1/3x+2/3(x+9)
Answer:
X=4
Step-by-step explanation:
1. Simplify the expression
2. Multiply the fractions:
3. Break up the fraction:
4. Find the greatest common factor of the numerator and denominator:
5. Factor out and cancel the greatest common factor:
6. Simplify the fraction:
7. Multiply the fractions:
8.Solve by distributing:
9. Simplify the arithmetic:
10.Break up the fraction:
11. Find the greatest common factor of the numerator and denominator:
12. Factor out and cancel the greatest common factor:
13.Combine the fractions:
14. Combine the numerators
15. Find the greatest common factor of the numerator and denominator:
16. Factor out and cancel the greatest common factor:
17. Simplify the right side:
A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2333 class attendees. The data is summarized in the table below. Class Type and Member Status of Class Attendees Class Type Member Non-Member Barre 157 232 Boot Camp 259 258 Boxing 282 215 Spinning 161 235 Yoga 271 263
The likelihood that a class attendee is a non-member of the gym taking a barre class or a member of the gym taking a boot camp class is 0.009.
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The marketing team has gathered data from a random month, in which there were 2039 class attendees.
The probability that a class attendee is a non-member of the gym and is attending a barre class
= 185/2039
= 0.09
The probability that a class attendee is a member of the gym and is attending a boot camp class
= 204/2039
= 0.10004
The probability for both the event would be
= 0.09 x 0.10004
= 0.009
The complete question is attached with the answer below.
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What is the rectangular form of theta = 3pi/4?
Please answer this question if you 100% know this answer.
a. x - y = 0
b. x - y = 1
c. x + y = 0
d. x + y = 1
The answer was not a.
Answer:
c. x + y = 0
Step-by-step explanation:
The terminal ray of the angle θ = 3π/4 extends to the upper left through the 2nd quadrant with a slope of -1. It lies on the line ...
y = -x
x + y = 0 . . . . . . add x to get this standard form equation
HELP!!!! What are the domain and range of the exponential growth function
a . Domain x>-3; Range: All real numbers.
b . Domain: All real numbers; Range: All real numbers.
c . Domain: x>-3; Range: y> -3
d . Domain: All real numbers; Range: y>-3
Step-by-step explanation:
D is the right answer.
remember, the domain is the interval or set of all valid values of x (the input variable). that means the values from left to right. there is no limitation visible. especially not around x = -3.
the range is the interval or set of valid values of y (the result variable). that means the values from bottom to top. and here we see, that the function never goes below y=-3.
these 2 facts make D the right answer.
HELP PLSSSSSSSSSSSSSS
Answer:
120
Step-by-step explanation:
Answer:
x=17.7
Step-by-step explanation:
Pythagorean theory
a²+b²=c²
16²+7.5²=c²
256+56.25=c²
√312.25=√c²
c=17.7
which could be the function graphed below ??
Answer:
D [tex]\sqrt{x+4}[/tex]
Step-by-step explanation:
Write the expression 4^4(4^-7)(4) using a single exponent
[tex]4^4(4^7)4\implies 4^4\cdot 4^7\cdot 4^1\implies 4^{4+7+1}\implies 4^{12}[/tex]
Answer:
real answer 4^-2
Step-by-step explanation:
just did on edge
What is the numerical answer?
length = inches
Answer:
31.5 inches
Step-by-step explanation:
If 2 centimeters is 9 inches, then 1 centimeter is 4.5 inches. Then, just multiply by 7.
help quick due in 10 minutes you will be reported if you spam Ivan is 75 inches tall if his brother Logan was 5 inches shorter, he would be exactly half Evan's height How tall is Logan? Enter your answer as a decimal in the box,
Answer:
35
Step-by-step explanation:
if not correct I'm very very sorry I tried my best for this</3
How many hours in a day?
Answer:24 hours are in a day
y + y + y + y + ytytyty
Collect like terms
Graph the linear equation. X = - 4y
A rectangular field is six times as long as it is wide. If the perimeter of the field is 1190 feet, what are the dimensions of the field?
A) Write an equation you can use to answer the given question. Let w be the width of the field. Do not solve the equation yet. The equation is _______
(Make sure you use the correct variable.)
B) Use your equation to find the dimensions of the field.
The width of the field is ____________ feet.
The length of the field is ____________ feet.
ATQ
[tex]\\ \tt\longmapsto 2(x+6x)=1190[/tex]
[tex]\\ \tt\longmapsto 2(7x)=1190[/tex]
[tex]\\ \tt\longmapsto 7x=595[/tex]
[tex]\\ \tt\longmapsto x=595/7[/tex]
[tex]\\ \tt\longmapsto x=85[/tex]
Length=6(85)=510ftWidth=85ftFor a particular event, 808 tickets were sold for a total of $3110. If students paid $3 per ticket and no student paid $5 per ticket. How many students tickets were sold?
if there is a 1 4 chance that it will rain for your fourth of july brbeque what is the probability it wont rain
Answer:
86% chance
Step-by-step explanation:
there is an 86% chance it won't rain because 100%-14%=86%
x + 6 - 6x + 10
integers
Answer:
-5x + 16
Step-by-step explanation:
I didn't see a equal sign so I assume that x cannot be x = -5/16
So I combined like terms of x and -6x to get -5x as well as +6 and +10 to get 16.
To get my final answer as -5x + 16.
whats the answer can someone answer please
Answer:
both are c
Step-by-step explanation: