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3 years ago

Explain how the digit 7 can have different values

Mathematics

1 answer:

kakasveta [241]3 years ago

7 0

It could be 7 groups of 1 3 groups of 2 with one left over or 2 groups of 3 with 1 left over

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You are designing a rectangular poster to contain 7575 in2 of printing with a 33-in margin at the top and bottom and a 11-in m

erma4kov [3.2K]

Answer:

The dimensions of the rectangular poster is 15 in by 5 in.

Step-by-step explanation:

Given that, the area of the rectangular poster is 75 in².

Let the length of the rectangular poster be x and the width of the rectangular poster be y.

The area of the poster = xy in².

$\therefore xy=75$

$\Rightarrow y=\frac{75}{x}$ ....(1)

1 in margin at each sides and 3 in margin at top and bottom.

Then the length of printing space is= (x-2.3) in

=(x-6) in

The width of printing space is = (y-2.1) in

=(y-2) in

The area of the printing space is A =(x-6)(y-2) in²

∴ A =(x-6)(y-2)

Putting the value of y

$\Rightarrow A =(x-6)(\frac{75}{x}-2)$

$\Rightarrow A = 87-\frac{450}{x}-2x$

Differentiating with respect to x

$A '= \frac{450}{x^2}-2$

Again differentiating with respect to x

$A''=-\frac{900}{x^3}$

To find the minimum area of printing space, we set A' = 0

$\therefore \frac{450}{x^2}-2=0$

$\Rightarrow 450 =2x^2$

$\Rightarrow x^2=225$

$\Rightarrow x=\pm 15$

Now putting x=±15 in A''

$A''|_{x=15}=-\frac{900}{15^3}$

$A''|_{x=-15}=-\frac{900}{(-15)^3}=\frac{900}{(15)^3}>0$

Since at x=15 , A"<0 Therefore at x=15 , the area will be minimize.

From (1) we get

$y=\frac{75}{x}$

Putting the value of x

$y=\frac{75}{15}$

=5 in

The dimensions of the rectangular poster is 15 in by 5 in.

4 0

3 years ago

May I please get the answers to the first 4 of these problems?

Ugo [173]

Given:
A(3,0)
B(1,-2)
C(3,-5)
D(7,-1)

1) reflect across x=-4
essentially calculate the difference between the x=-4 line and Px and "add" it in the other direction to x=-4
A(-4-(3-(-4)),0)=A(-11,0)
B(-4-(1-(-4)),-2)=B(-9,-2)
C(-4-(3-(-4),-5))=C(11,-5)
D(-4-(7-(-4)),-1)=D(-15,-1)

2) translate (x,y)->(x-6,y+8)
A(-3,8)
B(-5,6)
C(-3,3)
D(1,7)

3) clockwise 90° rotation around (0,0), flip the x&y coordinates and then decide the signs they should have based on the quadrant they should be in
A(0,-3)
B(-2,-1)
C(-5,-3)
D(-1,-7)

D) Dilation at (0,0) with scale 2/3, essentially multiply all coordinates with the scale, the simple case of dilation, because the center point is at the origin (0,0)
A((2/3)*3,(2/3)*0)=A(2,0)
B((2/3)*1,(2/3)*-2)=B(2/3,-4/3)
C((2/3)*3,(2/3)*-5)=C(2,-10/3)
D((2/3)*7,(2/3)*-1)=D(14/3,-2/3)

7 0

3 years ago

Is a linear model or a quadratic model a better fit?

ValentinkaMS [17]

Answer:

linear model

Step-by-step explanation:

linear graph will produce a straight line

7 0

3 years ago

If you want 2 cookies and you only have.50 cents and the cookies cost 10 dollars how much money will you have to get if you only

scoray [572]