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Westkost [7]
3 years ago
6

2

Mathematics
1 answer:
insens350 [35]3 years ago
8 0

Answer:

Part 1) x-intercept is -4;y-intercept is 8

Part 2) x-intercept is 16; y-intercept is 20

Part 3) x+6y=24

Part 4)

Part a) 4.75k+2.25p=22

Part b) The graph in the attached figure

Step-by-step explanation:

Part 1) Find the x- and y-intercept of the line

we have

-10x+5y = 40

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

-10x+5(0) = 40

-10x=40

x=-4

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

-10(0)+5y = 40

5y = 40

y=8

therefore

x-intercept is -4;y-intercept is 8

Part 2) Find the x- and y-intercept of the line

we have

5x+4y=80

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

5x+4(0)=80

5x=80

x=16

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

5(0)+4y=80            

4y=80

y=20              

therefore

x-intercept is 16; y-intercept is 20

Part 3) Write y=-(1/6)x+4 in standard form using integers.

we know that

The equation of a line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

we have

y=-\frac{1}{6}x+4

Multiply both sides by 6 to remove the fraction

6y=-x+24

Adds x both sides

x+6y=24

Part 4) The grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound.

Part a) Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $22

Part b) Graph the equation

Part a)

Let

k -----> the number of pounds of kumquats bought

p ----> the number of pounds of Asian pears bough

we know that

The number of pounds of kumquats bought (k) multiplied by it cost of $4.75 a pound plus the number of pounds of Asian pears bough (p) multiplied by it cost of $2.25 a pound must be equal to $22

so

4.75k+2.25p=22

Part b) Graph the equation

To graph the line find out the intercepts

Let

k the first coordinate of the point

p the second coordinate of the point

The k-intercept is the value of k when the value of p is equal to zero

so

For p=0

4.75k+2.25(0)=22

4.75k=22

k=4.63

so

The k-intercept is the point (4.63,0)

The p-intercept is the value of p when the value of k is equal to zero

so

For k=0

4.75(0)+2.25p=22

2.25p=22

p=9.78

so

The k-intercept is the point (0,9.78)

using a graphing tool

Plot the intercepts and join the points to graph the line

see the attached figure

Remember that the weight cannot be a negative number

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Step-by-step explanation:

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So

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we also have

\bf F(G(x,y))=F(x, y, 3-x^2-y^2)=(xy,y(3-x^2-y^2),x(3-x^2-y^2))=\\\\=(xy,3y-x^2y-y^3,3x-x^3-xy^2)

and so

\bf F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})=(xy,3y-x^2y-y^3,3x-x^3-xy^2)\cdot(2x,2y,1)=\\\\=2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2

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5 0
3 years ago
What is the antiderivative of 3x/((x-1)^2)
Maslowich

Answer:

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Step-by-step explanation:

Given

\int \:\:3\cdot \frac{x}{\left(x-1\right)^2}dx

\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx

=3\cdot \int \frac{x}{\left(x-1\right)^2}dx

\mathrm{Apply\:u-substitution:}\:u=x-1

=3\cdot \int \frac{u+1}{u^2}du

\mathrm{Expand}\:\frac{u+1}{u^2}:\quad \frac{1}{u}+\frac{1}{u^2}

=3\cdot \int \frac{1}{u}+\frac{1}{u^2}du

\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx

=3\left(\int \frac{1}{u}du+\int \frac{1}{u^2}du\right)

as

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\int \frac{1}{u^2}du=-\frac{1}{u}        ∵     \mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1

so

=3\left(\ln \left|u\right|-\frac{1}{u}\right)

\mathrm{Substitute\:back}\:u=x-1

=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)

\mathrm{Add\:a\:constant\:to\:the\:solution}

=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C

Therefore,

\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C

4 0
3 years ago
3.29<___
Drupady [299]

Answer:

3.29 is less than 3.4

D. 3.4

3 0
2 years ago
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