All categories

2 years ago

State the size of angle OAB, giving a reason for your answer

Mathematics

1 answer:

Alja [10]2 years ago

5 0

Answer:

Angle OAB = 90°

Reason: tangent theorem of a circle

Step-by-step explanation:

The diagram given shows a tangent line of the given circle with center O. The tangent touches the circle at point A.

The diagram also shows the radius of the circle, OA, drawn from the center to the circle to meet at the point of tangency.

Thus, according to the Tangent Theorem of a circle, the point at which the radius drawn from the center meets the point of tangency = 90°. The tangent is perdendicular to the radius drawn to meet at the point of tangency.

Therefore, angle OAB = 90°

You might be interested in

Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest ra

Oksana_A [137]

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

$A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}$

Substitute values for a and h

$A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}$

Evaluate all squares

$A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}$

$A = 100 + 2 * 10 * \sqrt{25 + 144}$

$A = 100 + 2 * 10 * \sqrt{169}$

Take positive square root of 169

$A = 100 + 2 * 10 * 13$

$A = 100 + 260$

$A = 360$

Hence, the area of the pyramid is 360 unit²

4 0

1 year ago

A garden measuring 16 meters by 8 meters is going to have a walkway constructed all around the perimeter, increasing the total a

Semenov [28]

Answer:

The width of the pathway is:

7 meters.

Step-by-step explanation:

To identify the width of the pathway, you must remember the area formula of a rectangle:

Area of a rectangle = length * width.

From which the width can be cleared:

Width of a rectangle = area / length.

We know that the length of the terrain was not modified since the pathway is in the perimeter of the rectangle (16 m) and that the new area is 240 m^2, so we only have to replace the cleared formula:

Width of a rectangle = 240 m^2 / 16 m = 15 m.

The new width is equal to 15 meters, but since the question is not the total width but the width of the pathway, the width of the previously provided land must be subtracted from the value obtained.

Pathway width = Total width - Garden width.
Pathway width = 15m - 8m = 7 meters.

7 0

1 year ago

Suppose that in a survey of 1,000 U.S. residents, 721 residents believed that the amount of violent television programming had i

Art [367]

Answer: 0.813

Step-by-step explanation:

Let A be the event describes the number of residents believed that the amount of violent television programming had increased over the past 10 years.

& B be the event describes the number of residents believed that the amount of violent television programming had decreased over the past 10 years.

Given : n(A)=721 ; n(B)=454 ; n(A∩B)=362

We know that ,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

i.e. $n(A\cup B)=721+454-362=813$

Also, the total number of U.S. residents surveyed n(S)= 1,000

Then, the proportion of the 1,000 U.S. residents believed that either the amount of violent programming had increased or the overall quality of programming had decreased over the past 10 years will be :-

$P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}=\dfrac{813}{1000}=0.813$