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Mathematics

1 answer:

Elena L [17]2 years ago

3 0

Evaluate the derivative of f(x) at x = 1. I'll use the limit definition:

$\displaystyle \lim_{x\to1} \frac{f(x)-f(1)}{x-1} = \lim_{x\to1} \frac{6x^2-x^3-5}{x-1} = \lim_{x\to1}(-x^2+5x+5) = 9$

Then using the point-slope formula, the equation of the tangent line to f(x) at the point (1, 5) is

y - 5 = 9 (x - 1)

y = 9x - 4

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Which of the following statements is the converse of the statement, "If each of two angles has a measure of 28 degrees, then the

kogti [31]

Answer:

1.) If two angles have equal measures, then the measure of each is 28 degrees.

Step-by-step explanation:

The converse of a statement simply swaps the positions of the "if" and "then" clauses. Without any modification for clarity or readability, the converse would be ...

if <em>two angles are equal in measure</em>, then <em>each of the two angles has a measure of 28 degrees</em>.

3 0

3 years ago

The shortest side of an isosceles triangle is 2x - 3 inches long. the longer sides are 6 inches longer than the shortest side. t

Zolol [24]

Side 1 = short side = 2x-3
side 2 = longer side = (short side) + 6 = (2x-3)+6 = 2x+3
side 3 = side 2 = 2x+3

Side 2 and side 3 are the longer two congruent sides

Add up the three sides and set them equal to the given perimeter of 33. Solve for x

(side1)+(side2)+(side3) = perimeter
(2x-3)+(2x+3)+(2x+3) = 33
(2x+2x+2x) + (-3+3+3) = 33
6x+3 = 33
6x+3-3 = 33-3
6x = 30
6x/6 = 30/6
x = 5

If x = 5, then the longer sides are 2*x+3 = 2*5+3 = 10+3 = 13 inches each
(note: the short side is 2*x-3=2*5-3=10-3 = 7 inches)

Answer: 13 inches

8 0

3 years ago

Please answer the question below

alexandr402 [8]

The value of x in the given sector is determined as 7.1.

<h3>Area of the sector</h3>

Total area of the sector = area of the shaded + area of the unshaded

Since shaded and unshaded areas are equal, the value of x is calculated as follows;

πr²θ/360 = πx²60/360 + πx²60/360

πr²θ/360 = 2(πx²θ/360)

πr² = 2(πx²)

r² = 2x²