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2 years ago

Qual a raiz da equação X²+5X-14=0 ?

Mathematics

1 answer:

ElenaW [278]2 years ago

8 0

Answer:

e) Hence 2, -7 are roots of the equation X² + 5X - 14 = 0

Step-by-step explanation:

given equation : X² + 5X - 14 = 0

⇒ X² + 7X - 2X - 14 = 0

⇒ X·(X + 7) - 2·(X + 7) = 0

⇒ (X + 7)·(X - 2) = 0

⇒ X = -7, X = 2

<u>Hence 2, -7 are roots of the equation X² + 5X - 14 = 0</u>

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Find dy/dx by implicit differentiation for ysin(y) = xcos(x)

tatyana61 [14]

Answer:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

Step-by-step explanation:

So we have:

$y\sin(y)=x\cos(x)$

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[y\sin(y)]$

We can use the product rule:

$(uv)'=u'v+uv'$

So, our derivative is:

$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

$=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]$

For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

$=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})$

Simplify:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}$

And we are done for the right.

Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

Differentiate:

$=\cos(x)-x\sin(x)$

So, our entire equation is:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

5 0

2 years ago

A seagull flying in the air over water drops a crab from a height of 45 feet.The distance the crab is from the water as it falls

jonny [76]

For the seagull to catch the crab, h(t)=g(t) so:

-16t^2+45=-13t+23 add 16t^2 to both sides

45=16t^2-13t+23 subtract 45 from both sides

16t^2-13t-22=0 using the quadratic equation:

t=(13±√1577)/32, since t>0

t=(13+√1577)/32 seconds

t≈1.65 seconds (to nearest hundredth of a second)

And the height that this occurs using either original equation is:

h((13+√1577)/32)≈1.59 ft (to nearest hundredth of a foot)

7 0

3 years ago

Gas station X charges $4.00 per gallon of gas. Gas station Y charges $4.12 per gallon of gas. What is the percent increase from

kirill [66]

First, find the increase in charge between the two station. That is:

$4.12-$4.00=$0.12

Then, divide the increase by the price charged by Gas Station X.

$0.12/$4.00=0.03

Lastly, since it is a decimal, transform it to percentage by multiplying 100%

0.03x100%=3%

Hope this is the brainliest answer.

3 0

3 years ago

You drive 140 miles in 2.5 hours and 300 miles in 5.5 hours. What is the rate of change ?

Sveta_85 [38]

The answer is one and five elevenths, or: 1 5/11

this is because 140/2.5 is 56 and 300/5.5 is 54 6/11.

56 - 54 6/11= 1 5/11

7 0

3 years ago

Joyce old 218 cupcakes of lemonade at his lemonade stand. What is 218 rounded to the nearest tens

MAXImum [283]

220

from 218 the 1 is in the tens column. this is the figure that needs to be rounded.

using the following rule

If the digit after the 1 is ≥ 5 then round 1 up to 2

If the digit after the 1 is < 5 then the 1 remains as 1

here the digit after the 1 is 8 so the 1 in the ten's column becomes 2 and the 8 is replaced by 0

218 ≈ 220 ( to the nearest ten )

7 0

3 years ago