Answer:
50
Step-by-step explanation:
If the first statement its true (At most 0 of the statements are true), there are not true statements in the paper. So, the first statement its false.
Now, if the first statement its false, this mean there must be at least 1 true statement in the paper.
Now, if the second statement its true ( at most 1 of the statements are true) this implies that the third statement its true (if "at most 1" its true, then "as most 2" must be true).
If any statement (besides the first) its true, then all the statement that follows it must be true.
The first non false statement, then, must be the statement made by the person 51: "At most 50 statements are true"
And the 49 statements that follows are true as well.
The numbers are (-8, 3) or (3, -8).
Step-by-step explanation:
- Step 1: Given the product of the numbers are -24 and their sum are -5. Let the numbers be a and b. Form equations out of these details.
⇒ a + b = -5 ⇒ b = -5 - a
⇒ a × b = -24 -------- (1)
- Step 2: Substitute the value of b in eq(1)
⇒ a × (-5 - a) = - 24
⇒ -5a - a² = -24
⇒ a² + 5a - 24 = 0
- Step 3: Solve the quadratic equation for a.
a = (-5 ± √25 - 4 × 1 × -24)/2
= (-5 ± √121)/2
= - 16/2, 6/2 = -8 or 3
- Step 4: For each value of a, find b.
When a = -8, b = -5 +8 = 3
When a = 3, b = -5 - 3 = -8.
Find the area of the cone:
Area of cone: ⅓r^2h
⅓r^2h
= ⅓(3.5)^2(7)
= ⅓(12.25)(7)
= 1/3(85.75)
= 85.75/3
1/3 cup sloshed out:
(85.75/3 )/3
= 29.9 cubic cm
