Factor k 2 + 8k + 15. answers. (k + 1)(k + 15) (k + 8)(k + 7) (k + 3)(k + 5)

y2(y2−4)=x2(x2−5)y2(y2−4)=x2(x2−5) Multiplying the polynomials gets us to y4−4y2=x4−5x2y4−4y2=x4−5x2. Taking the derivative with respect to xx gets us: 4y3y′−>!8yy′=4x3−10x4y3y′−>!8yy′=4x3−10x. Factoring to get y′y′ by itself: y′(4y3−8y)=4x3−10)y′(4y3−8y)=4x3−10). Divide through to get y′y′ by itself: y′=4x3−10x4y3−8yy′=4x3−10x4y3−8y. You could make your life a bit easier by factoring this into y′=2x(2x2−5)4y(y2−2)y′=2x(2x2−5)4y(y2−2). You could cancel out a factor of 22 to get y′=x(2x2−5)2y(y2−2)y′=x(2x2−5)2y(y2−2). To find the slope, plug in your points x=0,y=−2x=0,y=−2 into our equation for y′y′ to find the slope of the line. Note that the slope is 00. To find the equation of the tangent line, use that value for mm you just found (m=0m=0) and your given points into the point-slope formula and you find that the tangent line is y=−2y=−2.

Thats what my Aunt said... Idk

4 0

3 years ago

Teh slope between two points is calculated by finding the change in y-values and dividing by the change in x-values. for example

Nimfa-mama [501]

Hi there!

The change of y-values is
- 15 - 22 = - 37
The change of x-values is
7 - - 8 = 7 + 8 = 15

Therefore, the slope of this line is
$\frac{ - 37}{15} = - 2 \frac{7}{15}$

4 0

3 years ago

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square f

mojhsa [17]

Okay
we have the rate of change of AC = d(AC)/dt = -2
the rate of change od BC = d(BC)/dt
area = (1/2) *AC) (BC)
taking differential on both sides we ge
d(A)/dt = 1/2){ (BC) d(AC)/dt + (AC) d(BC)/dt)}....(1)
again
when AC= 3
applying pythagorous thm
we get
(5)^2 =(3)^2 +(BC)^2
hence we get BC = 4
now we need to find d(BC)/dt
we have
(5)^2 = (AC)^2 +(BC)^2
taking differenial
0=2(AC) d(AC/dt) +2BC d(BC)/dt
that is
d(BC)/dt = -(3) *(-2)/4 ..(at AC =3)
hence
d(BC)/dt = 3/2
substituting these values in equation (1)
d(A)/dt = (1/2) {4 * -2 + 3 *3/2}

which gives
d(A)/dt = -7/4

The rate, in square feet per second, at which the area is changing when AC = 3 is -7/4 ft/sec.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

4 0

3 years ago

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