Answer:
(a) 4
(b) 2√3
(c) 60°
(d) 120°
Step-by-step explanation:
(a) The relationship between tangents and secants is ...
CB^2 = CD·CA
Filling in the given values, we find ...
CB^2 = 2·(2+6) = 16
CB = √16 = 4
The length of BC is 4 units.
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(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.
CA^2 = CB^2 +AB^2
8^2 = 16 +AB^2
AB = √48 = 4√3
The radius is half the length of AB, so the radius is 2√3.
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(c) The measure of angle C can be determined from the cosine relation:
cos(C) = CB/CA = 4/8 = 1/2
C = arccos(1/2) = 60°
The measure of angle C is 60°.
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(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.
The measure of arc AD is 120°.
Answer:
b ≈ 7.54 cm
Step-by-step explanation:
Pythagorean Theorem
a² + b² = c²
a and b are the sides and c is the hypotenuse
hypotenuse is 11 cm
a side is 8 cm
so
8² + b² = 11²
64 + b² = 121
-64 -64
b² = 57
√b² = √57
b ≈ 7.54 cm ( use ≈ because its rounded so its not exact)
If you add a zero at the end it is easier to understand. 0.20 > 0.18 because 20 is greater than 18
Answer: The oldest one is Vredfort Crater.
Step-by-step explanation:
The data is:
Chicxulub was formed 6.5x10^7 years ago.
Vredfort was formed 2x10^9 years ago.
Sudbury basin was formed 1.8x10^9 years ago.
Acraman crater was formed 5.8x10^8 years ago.
We want to find the oldest, so we need to find the larger number of the 4 we have.
For this, we need to see at the exponents, the larger the exponent the larger the number.
We have two with a 9 in the exponent:
Vredfort and Sudbury.
Now we look at the number, Vredfort has 2x10^9 and Sudbury has 1.8x10^9.
Both have the same exponent, but the scalar of Vredfort is larger (2 is greater than 1.8) so we have that Vredfort is older.
