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Tpy6a [65]
3 years ago
5

What is the value of a + b+c? you may assume that the ray is tangent to the circle?

Mathematics
1 answer:
Vilka [71]3 years ago
4 0

Answer:

Option c

Step-by-step explanation:

Given is a picture of a circle with two arcs angled 54 and 86.

a,b,c are the angles shown as the angle between a chord and tangent, angle between diameter and a chord and also angle between another chord and diameter

Recall the subtended angle theorem for circles

Angle subtended at the centre is double angle subtended at the circumference

Since arc below subtends 86 with centre it will subtend 43 degrees at the circumference.

ie. c= 43 degrees...i

Next is sum of a+b.

Recall tangent theorem that any tangent is perpendicular to the radius at the contact point.  Here a+b is the angle between tangent and radius

Hence a+b=90

Together

a+b+c = 133 degrees

Option c

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Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
Sliva [168]

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  • g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
  • A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.

Step-by-step explanation:

(a) The linear approximation of g(x) at x=b will be ...

  g(x) ≈ g'(b)(x -b) +g(b)

Using the given relations, this is ...

  g'(3) = 3² +7 = 16

  g(x) ≈ 16(x -3) -1

Then the points of interest are ...

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__

(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)

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2 years ago
I’m need this worked out step by step by tonight
Pie

9514 1404 393

Answer:

  -3 ≤ x ≤ 19/3

Step-by-step explanation:

This inequality can be resolved to a compound inequality:

  -7 ≤ (3x -5)/2 ≤ 7

Multiply all parts by 2.

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Add 5 to all parts.

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Divide all parts by 3.

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_____

<em>Additional comment</em>

If you subtract 7 from both sides of the given inequality, it becomes ...

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Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.

__

For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...

  |f(x)| < (some number) . . . . or ≤

If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:

  |f(x)| > g(x)   ⇒   f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0

Any solutions to these inequalities must respect their domains.

8 0
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