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4 years ago

Geometry; Inscribed Angles.Find the value of y. Please explain!

Mathematics

2 answers:

r-ruslan [8.4K]4 years ago

7 0

Answer:

y = 48° is the answer.

Step-by-step explanation:

In the figure attached, length of small arc = 66°

This small arc makes an angle at the center of the circle = 66°

By definition, angle formed by the arc at the center is double of the measure of the angle inscribed by the small arc at the point on a circle.

Therefore, m (arc) = 66° = 2.(x)

x = $\frac{66}{2}=33$

Similarly, y = $\frac{96}{2}=48$

y = 48° will be the answer.

Butoxors [25]4 years ago

3 0

check the picture below.

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Can Someone please answer and explain. It's just one problem and there a picture. Thank you

Mice21 [21]

Vertices (3,0),(-3,0) co-vertices (0,-5),(0,5)

transverse axis (line passing vertices) is on(or parallel to) x-axis then formula is
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
..notice.. x^2 is on positive / y^2 is on negative

center (h,k) is midway between vertices = (0,0)
we have h = k = 0 and now formula is
x^2/a^2 - y^2/b^2 = 1

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x^2/3^2 - y^2/5^2 = 1 ... answer is the 1st

6 0

3 years ago

Plssss help!!!! A garden table and a bench cost $778 combined. The garden table costs $72 less than the bench. What is the cost

Fiesta28 [93]

Answer:

The bench costs $425

Step-by-step explanation:

$425 + 353 = 778$

How I did it::

$778 \div 2$

$389 - 36 = 353$

$389 + 36 = 425$

3) Check

$425 + 353 = 778$

7 0

3 years ago

A circle has a radius of 9 inches. The Radius is multiplied by 2/3 to form a second circle. How is the ratio of the areas relate

liraira [26]

Answer:

$\frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)} = \frac{81}{36} = (\frac{r_{1} }{r_{2}}) ^{2}$

The above expression shows that ratios of the areas of the circles are equal to the square of the ratio of their radii.

Step-by-step explanation:

Radius of first circle $(r_{1})$ = 9 inches

Area of first circle = $\pi r_{1} ^{2}$

Area of first circle = 9 × 9 × π = 81 π

Now, since the radius is multiplied by 2/3 for from a new circle.

∴ Radius of the second circle = $9 \times \frac{2}{3} = 6\ inches$

Area of second circle = $\pi r_{2} ^{2}$

Area of second circle = 6 × 6 × π = 36 π

Now,

$\frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)} = \frac{81\pi }{36\pi }$

$\frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)} = \frac{81}{36} = (\frac{9}{6}) ^{2} = (\frac{r_{1} }{r_{2}}) ^{2}$

∵ $(r_{1})$ = 9 inches and $(r_{2})$ = 6 inches

The above expression shows that ratios of the areas of the circles are equal to the square of the ratio of their radii. i.e., $\frac {radius\ of\ first\ circle)^{2} }{(radius\ of\ second\ circle)^{2} } = \frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)}$

8 0

3 years ago

If 5-y^2=x^2 then find d^2y/dx^2 at the point (2, 1) in simplest form.

ratelena [41]

Answer:

y"(2, 1) = -5

Step-by-step explanation:

Step 1: Define implicit differentiation

5 - y² = x²

Step 2: Find dy/dx

Take implicit differentiation: -2yy' = 2x
Isolate y': y' = 2x/-2y
Isolate y': y' = -x/y

Step 3: Find d²y/dx²

Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
Substitute y': y" = [-y - (-x/y)(-x)] / y²
Simplify: y" = [-y - x²/y] / y²
Multiply top/bottom by y: y" = (-y² - x²) / y³
Factor negative: y" = -(y² + x²) / y³

Step 4: Substitute and Evaluate

y"(2, 1) = -(1² + 2²) / 1³

y"(2, 1) = -(1 + 4) / 1

y"(2, 1) = -5/1

y"(2, 1) = -5

3 0

3 years ago

DochEvi [55]

Answer:

Step-by-step explanation:

The midpoint of two coordinates (x1, y1) and (x2, y2) is expressed as;

M(X,Y) = {(x1+x2)/2, (y1+y2)/2}

Given the points A(h, k) and B(h,j)

x1 = h, y1 = k, x2 = h, y2 = j

Substitute into the formula;

M(X,Y) = {(x1+x2)/2, (y1+y2)/2}

M(X,Y) = {(h+h/2, (k+j)/2}

M(X,Y) = {(2h)/2, (k+j)/2}

M(X,Y) = {h, k+j/2}

hence the coordinates of point M is {h, k+j/2}

7 0

4 years ago