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3 years ago

Find a and b????????????

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

5 0

Answer:

Below

Step-by-step explanation:

The rule states that:

● | x | < 1 => -1 < x < 1

By anlogy

● | x - 5| < 6 => -6 < x - 5 < 6

● -6 < x - 5< 6

Add 10 both sides to get x + 5 (x-5+10 = x+5)

● -6 + 10 < x - 5 + 10 < 6 + 10

● 4 < x + 5 < 16

So a = 4 and b = 16

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2 years ago

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3 years ago

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2 years ago

What is the measure of arc bc? A. 76 B. 40 C. 96 D. 58

Veseljchak [2.6K]

Answer:

A. 76

Step-by-step explanation:

Angle A is half the difference between the measures of arc DE and BC.

m∠A = (1/2)(DE -BC)

20 = (1/2)(116 -BC) . . . . substitute the given values

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BC = 116 -40 . . . . . . . . add BC -40

BC = 76

_____

Comment on intersecting secants

When the secants intersect inside the circle, the angle where they cross is half the sum of the intercepted arcs. When they intersect outside the circle (as here), the angle where they meet is half the difference of the intercepted acs.

Sometimes it is easier to remember two related relationships than it is to remember just one of them.

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3 years ago

Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2+4x−8y+20=0 has horizontal and vertical t

Komok [63]

Answer:

The parabola has a horizontal tangent line at the point (2,4)

The parabola has a vertical tangent line at the point (1,5)

Step-by-step explanation:

Ir order to perform the implicit differentiation, you have to differentiate with respect to x. Then, you have to use the conditions for horizontal and vertical tangent lines.

-To obtain horizontal tangent lines, the condition is:

$\frac{dy}{dx}=0$ (The slope is zero)

--To obtain vertical tangent lines, the condition is:

$\frac{dy}{dx}=\frac{1}{0}$ (The slope is undefined, therefore the denominator is set to zero)

Derivating respect to x:

$\frac{d(x^{2}-2xy+y^{2}+4x-8y+20)}{dx} = \frac{d(x^{2})}{dx}-2\frac{d(xy)}{dx}+\frac{d(y^{2})}{dx}+4\frac{dx}{dx}-8\frac{dy}{dx}+\frac{d(20)}{dx}$ = $2x -2(y+x\frac{dy}{dx})+2y\frac{dy}{dx}+4-8\frac{dy}{dx}= 0$