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3 years ago

Can someone please help me with this? This is very hard!! :(

Mathematics

2 answers:

adell [148]3 years ago

6 0

The answer to your question is .40 mr SmokeyRN !

ArbitrLikvidat [17]3 years ago

6 0

The answer is simple. To convert a fraction into a decimal take the numerator(the top number) and divide it by the denominator(the bottom number) so the fraction shown above is 4/10. There are two ways. Number 1: u know that 1/10 equals 0.1 so 4/10 equals 0.4 because the 4 needs to be in the tenths place. Number 2: take 4 (numerator) divide it by 10 (denominator) so 4 divided by 10 equals 0.4 so your answer is C=0.40. (PS: 0.4=0.40)

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What is the equation to find area of a parallelogram

olchik [2.2K]

A=BH

Area = Base x the Hight

6 0

3 years ago

Find the constant of variation for the relationship f(x)= 40x

statuscvo [17]

The constant variation of k is 40. Hope that helps.

7 0

3 years ago

As of 2016, New York City has a population of 8.55 million and a land area of 300 square miles. Manhattan is a section of New Yo

sineoko [7]

Answer: 42804 people per square mile

Step-by-step explanation:

As we know Population density = $\dfrac{Number\ of\ people}{Area}$

Given, population of New York City = 8.55 million

Area of New York City = 300 square miles

Then, population density of New York City = $\dfrac{8.55\text{ million}}{300\text{ square miles}}$

$=\dfrac{8550000}{300\text{ square miles}}=28500\text{ people per square mile}$ [1 million = 1,000,000]

Population of Manhattan = 1.64 million = 1640000

Area of Manhattan = 23 square miles

population density of Manhattan = $\dfrac{1640000}{23}\approx71304\text{ people per square mile}$

Difference = 71304 - 28500 =42804

Hence, population density of Manhattan is 42804 people per square mile greater than that of New York City.

3 0

3 years ago

Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients.

Anika [276]

Answer:

$\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }$

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

$x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})$

Now we can substitute in the equation

$x^2y''(x)+9xy'(x)-20y(x)=0\\ e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\ \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\ \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\$

so the new equation is

$y''(t)+ 8y'(t)-20y(t)=0$

the auxiliary equation is

$x^2+8x-20=0\\ x^2-2x+10x-20=0\\x(x-2)+10(x-2)=0\\(x+10)(x-2)=0\\ x=-10\text{ or }x=2$

so the solutions of the new equation are

$y(t)=ae^{2t}+be^{-10t}$

with a and b real

$x(t)=e^t\\ t(x)=ln(x)$

$y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}$

hope this helps

do not hesitate if you have any questions

8 0

3 years ago

A company manufactures two types of fishing rods, standard and folding. The cost of manufacturing 2 folding rods and 1 standard

Mrac [35]

Answer:

Step-by-step explanation:

A company manufactures two types of fishing rods, standard and folding. The cost of manufacturing 2 folding rods and 1 standard is $35. If 5 standard and 7 folding rods were manufactured, the cost would be $145. How much does it cost to manufacture each type of rod.

let S = standar rod

F= folding rod

2F + S =35

2F + S -2F =35 - 2F

or S = 35-2F

7F + 5S =145

7F + 5S -7F =145 -7F

or 5S =145-7F

Since S=35-2F

5S = 5X (35-2F)

5S = 175 -10F

which equals 145-7F

175-10F = 145-7F

175-10F +10F = 145 -7F + 10F

175 = 145 +3F

175 -145 =145 -145 + 3F

30 = 3F

F = 10

but S =35 - 2F

so S = 35 -2X10

S = 35-20 =15

check:

if F = 10 and S = 15

then 5S +7F should equal 145

5X15 + 7X10 = 75 + 10 =145

so F=10, S=15

7 0

2 years ago