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3 years ago

A student performed the following steps to find the solution to the equation x^2+14x+40=0 where did the student go wrong

2 answers:

7 0

I don't fully know exactly what your asking and I'm new at this, but I think you're asking about what is the center and radius of a circle right? In that case, this is what I came up with (Don't know if this is what you want, sorry) :(
First step: You do -40 to the current +40, and transfer it to the other side of the equal symbol, making the 0 turn into a -40.
Second step: It should now look like this - (x^2+14x) = -40
Third step: Divide the 14 by 2, which gives you a positive 7, then square that 7, which gives you 49. It shall look like this now - (x^2+14x+49) = 9. The nine is now there at the end because you add the 49 to the negative 40.
Fourth step: Remember the 7? Well, we use it now. It should currently look like this - (x+7) = 9.
Fifth step: The Center can now be found, and remember for the center you do the opposite of what the number is, in this case, the positive 7, will be a negative 7 in the center. Since there is no y found, it will remain as 0. (I think) This is how It looks - Center: (-7, 0)
Sixth step (Final step): Now the radius must be found, we will now look at the nine at the other side of the equal symbol. We square root that now! So the radius = 3.
Answers: Center: (-7, 0) Radius: 3. (Or if asked to find diameter, then it would be double the 3. Meaning Diameter=6.
Comment: I'm only a 9th grader, so sorry If I got this wrong. Trying to help :p lol.

Yanka [14]3 years ago

7 0

Answer:

It was in step 3

Step-by-step explanation: APEX

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The sum of two numbers is 90. Their difference is 18. Find the numbers.

Naddik [55]

Answer:

36 & 54

Step-by-step explanation:

By Question :-

Sum of numbers = 90 .
Difference of numbers = 18 .

Let :-

First Number be x .
Second number be y .

According to 1st condition :-

$: \implies$ x + y = 90

According to 2nd condition :-

$: \implies$ x - y = 18

Adding the equations :-

$: \implies$ 2x = 18 + 90

$: \implies$ 2x = 108

$: \implies$ x = 54

Therefore :-

$: \implies$ First number = 54

$: \implies$ Second number = 36

5 0

3 years ago

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Please help me answer this question

stealth61 [152]

The value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

<h3>Differentiation</h3>

From the question, we are to determine dy/dx for the given functions

(i) $x^{2} sin^{2}2x$

Let $u = x^{2}$

and

$v = sin^{2} 2x$

Also,

Let $w= sin2x$

∴ $v = w^{2}$

First, we will determine $\frac{dv}{dx}$

Using the Chain rule
$\frac{dv}{dx} = \frac{dv}{dw}.\frac{dw}{dx}$

$v = w^{2}$

∴ $\frac{dv}{dw} =2w$

Also,

$w= sin2x$

∴ $\frac{dw}{dx} =2cos2x$

Thus,

$\frac{dv}{dx} = 2w \times 2cos2x$

$\frac{dv}{dx} = 2sin2x \times 2cos2x$

$\frac{dv}{dx} = 4sin2x . cos2x$

Now, using the product rule

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

From above

$u = x^{2}$

∴ $\frac{du}{dx}=2x$

Now,

$\frac{dy}{dx} = x^{2} (4sin2x.cos2x)+ sin^{2}2x (2x)$

$\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $xy^{2}+y^{2}x^{3} +2=0$

Then,

$x.2y\frac{dy}{dx}+ y^{2}(1)+y^{2}.3x^{2} + x^{3}.2y\frac{dy}{dx} +0=0$

$2xy\frac{dy}{dx}+ y^{2}+3x^{2}y^{2} + 2x^{3}y\frac{dy}{dx} =0$

$2xy\frac{dy}{dx}+2x^{3}y\frac{dy}{dx} =- y^{2}-3x^{2}y^{2}$

$\frac{dy}{dx} (2xy+2x^{3}y)=- y^{2}(1+3x^{2})$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy+2x^{3}y}$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy(1+x^{2}) }$

$\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Hence, the value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Learn more on Differentiation here: brainly.com/question/24024883

#SPJ1

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2 years ago

Ms. Anastasopoulos has 30 students. 4/5 of the students have pets. OF the students who have pets, 2/3 of them have a dog as a pe

Lena [83]

Answer:

Step-by-step explanation:

since 4/5 have a pet, you would divide by 5.

30÷5=6

but since only 4 have a pet, you would multiply that by 4 to get 4/5

6×4=24

24 students have pets

now you would divide by 3, as 2/3 have a dog

24÷3=8

but only 2/3 have dog, so you would multiply by 2

8×2=16

I'm sure there is a simpler way but this is how I would do it.

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3 years ago

4 gallons equals liters

IRISSAK [1]

Answer:

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Step-by-step explanation:

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4 0

3 years ago

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