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3 years ago

13

Can you solve this for me

1 answer:

jenyasd209 [6]3 years ago

4 0

The number in the blank box should be 44 because it said that "3 times x and 4 times y is 44".

You need to multiply the first equation by 3:

3x + 3y = 39.

Then, subtract the first equation from the second equation:

3x - 3x = 0

4y - 3y = y

44 - 39 = 5

Your new equation should look like this: y = 5

Now, substitute y = 5 into the first original equation:

x + 5 = 13

x = 8

Ans. (x, y) = (8, 5)

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Evaluate. Write your answer as a fraction in simplest form. -1/2 + 7/8 - 5/24

Ymorist [56]

The answer would simplify to 1/6.

3 0

3 years ago

Solve the following differential equation: (1− 5 y +x) dy/dx +y= 5/x −1 .<br><br> C=

Ganezh [65]

Answer:

$y(1+x)+x-5\ln xy=C$

Step-by-step explanation:

Consider the given differential equation is

$(1-\frac{5}{y}+x)\frac{dy}{dx}+y=\frac{5}{x}-1$

$(1-\frac{5}{y}+x)\frac{dy}{dx}=\frac{5}{x}-1-y$

$(1-\frac{5}{y}+x)dy=(\frac{5}{x}-1-y)dx$

Taking all variables on right sides.

$(1-\frac{5}{y}+x)dy-(\frac{5}{x}-1-y)dx=0$

$(-\frac{5}{x}+1+y)dx+(1-\frac{5}{y}+x)dy=0$

Let as assume,

$M=-\frac{5}{x}+1+y$ and $N=1-\frac{5}{y}+x$

Find partial derivatives $\frac{\partial M}{\partial y}$ and $\frac{\partial N}{\partial x}$

$\frac{\partial M}{\partial y}=1$ and $\frac{\partial N}{\partial x}=1$

Since $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ , therefore the given differential equation is exact.

The solution of the exact differential equation is

$\int Mdx+\int N(\text{without x)}dy=C$

$\int (-\frac{5}{x}+1+y)dx+\int (1-\frac{5}{y})dy=C$

$yx-5\ln x+x+y-5\ln y=C$

$y+x+xy-5\ln x-5\ln y=C$

$y(1+x)+x-5(\ln x+\ln y)=C$

$y(1+x)+x-5\ln xy=C$

7 0

3 years ago

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

so

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

so

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

8 1

3 years ago

Read 2 more answers

Which is the longest?<br> A. 2 km<br> B. 25 m<br> C. 2,500 cm<br> D. 3,000 mm

Leona [35]

2km=2000m
25m=25m
2500cm=25m
3000mm=3m

Hence the longest is 2km=2000m

8 0

3 years ago

a conference will take place in a large hotel meeting room. The organizers of the conference have created a drawing to determine

Bogdan [553]

Answer:

313 ft

Step-by-step explanation:

If 12in = 12 ft

313in = x

= 313 ft

4 0

3 years ago