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Xelga [282]
3 years ago
7

Choose and then match the ratio which is equivalent

Mathematics
1 answer:
madreJ [45]3 years ago
4 0

1. 5 to 20 ---> c. 20 to 80

(5/20 and 20/80, both have the same answer(ratio) which is equal to 1/4)

2. 5 to 40 ---> e. 11 to 88

(5/40 and 11/88, both have the same answer(ratio) which is equal to 1/8)

3. 9 to 45 ---> b. 7 to 35

(9/45 and 7/35, both have the same answer(ratio) which is equal to 1/5)

4. 2 to 20 ---> a. 1 to 10

(2/20 and 1/10, both have the same answer(ratio) which is equal to 1/10)

5. 4 to 12 ---> d. 10 to 30

(4/12 and 10/30, both have the same answer(ratio) which is equal to 1/3)

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Find the gradient of the function at given point. f(x,y)=ln(x^2+y^2)
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\nabla f(x,y)=\left\langle\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y}\right\rangle=\left\langle\dfrac{2x}{x^2+y^2},\dfrac{2y}{x^2+y^2}\right\rangle

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Please help, I need this answer
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6.4

Step-by-step explanation:

By the Pythagorean Theorem:

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Hope this helps!

6 0
3 years ago
Read 2 more answers
A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner
algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by  using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

V=x(216-24x-36x+4x^{2})

V=x(4x^{2}-60x+216)

V=4x^{3}-60x^{2}+216x

So now we can find the derivative of the volume:

V'=12x^{2}-120x+216

and set it equal to zero, so we get:

12x^{2}-120x+216=0

and now we can solve. We can start by factoring the left side of the equation, so we get:

12(x^{2}-10x+18)=0

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}

so we substitute the corresponding values:

x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0
3 years ago
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