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2 years ago

The graph of y =f(x) is shown below. Find all values of x where f (x)=0 (check photo)

Mathematics

1 answer:

Sidana [21]2 years ago

6 0

Answer:

$x = -3$

Step-by-step explanation:

$f(x) = 0\text{ when } x = -3$

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How many ways can 8 students sit in a round table with 8 chairs if...

Marrrta [24]

Answer:

Step-by-step explanation:

there a hundread of times because 8 students 8 chairs they can do what set do want to do.

8 0

2 years ago

A) Findi

Romashka [77]

Answer:

Part A)

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

Part B)

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

Step-by-step explanation:

We have the equation:

$\displaystyle x^2y+y^2x=6$

Part A)

We want to find the derivative of our function, dy/dx.

So, we will take the derivative of both sides with respect to <em>x:</em>

<em /> $\displaystyle \frac{d}{dx}\Big[x^2y+y^2x\Big]=\frac{d}{dx}\big[6\big]$ <em />

The derivative of a constant is 0. We can expand the left:

$\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0$

Differentiate using the product rule:

$\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0$

Implicitly differentiate:

$\displaystyle (2xy+x^2\frac{dy}{dx})+(2y\frac{dy}{dx}x+y^2)=0$

Rearrange:

$\displaystyle \Big(x^2\frac{dy}{dx}+2xy\frac{dy}{dx}\Big)+(2xy+y^2)=0$

Isolate the dy/dx:

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

Hence, our derivative is:

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

Part B)

We want to find the equation of the tangent line at (2, 1).

So, let's find the slope of the tangent line using the derivative. Substitute:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{2(2)(1)+(1)^2}{(2)^2+2(2)(1)}$

Evaluate:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{4+1}{4+4}=-\frac{5}{8}$

Then by the point-slope form:

$y-y_1=m(x-x_1)$

Yields:

$\displaystyle y-1=-\frac{5}{8}(x-2)$

Distribute:

$\displaystyle y-1=-\frac{5}{8}x+\frac{5}{4}$

Hence, our equation is:

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

5 0

2 years ago

Five less than the quotient of a number and 2 equals 8

alexira [117]

Writing this statement symbolically, we get:

--- - 5 = 8

Adding 5 to both sides, we get n/2 = 13. Then n = 26.

8 0

3 years ago

Read 2 more answers

*80 POINTS!!!! PLEASE HELP ME I HAVE BEEN WAITING FOR MORE THAN AN HOUR!!!!!!!!!! MARKING AS BRAINLIEST!! PLEASE SHOW WORK AND E

ruslelena [56]

Answer:

D. tan(-π/6)

Step-by-step explanation:

The tangent function is periodic with a period of π, so ...

tan(5π/6) = tan(5π/6 ± kπ) . . . for any integer k

For k = -1, we have ...

tan(5π/6) = tan(5π/6 -π) = tan(-π/6)

7 0

3 years ago

The altitude of a plane is 1,600 ft. What must be the altitude of a submarine so that the sum of their altitudes is 0?

RSB [31]

You must mean the depth of the submarine.

to make sum = zero the depth of the sub must be -1600 ft..

7 0

3 years ago

Read 2 more answers