Creating and solving inequality

Mathematics

1 answer:

Tom [10]4 years ago

5 0

Answer:

I decided to take a picture since it was easier for me that way. Hope you don't mind. Oh and if my number line isn't clear, the answer is the first number line

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Find the value of c such that the point P(a, b) lies on the graph of the function f.

Alexxandr [17]

$f(x)=x\sqrt{16-x^2}+c;\ P(3;\ 6)\to x=3\ and\ y=6\\\\subtitute\\\\6=3\sqrt{16-3^2}+c\\\\3\sqrt{16-9}+c=6\\\\3\sqrt7+c=6\ \ \ \ |subtract\ 3\sqrt7\ from\ both\ sides\\\\\boxed{c=6-3\sqrt7}$

4 0

4 years ago

4. Automobile policies are separated into two groups: low-risk and high-risk. Actuary Rahul examines low-risk policies, continui

ANTONII [103]

Answer:

Step-by-step explanation:

for n ∈ N

Since Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping.

∴ the probability that Actuary Rahul examines exactly n policies

$(0.9)^{n-1}.(0.1)---(1)$

the probability that Actuary Toby examines more than exactly n policies

$(0.8)^n---(2)$

Given that policies are actually independent

∴ the probability that the event (1) and (2) happens simultaneously is

$(0.9)^{n-1}*(0.1)*(0.8)^n$

∴ the probability that Actuary Rahul examines fewer policies than Actuary Toby

$\sum ^\infty _{n=1} (0.9)^{n-1}*(0.1)*(0.8)^n\\\\=(\frac{0.1}{0.9} \sum ^\infty _{n=1}(0.72)^n\\\\=\frac{1}{9} (\frac{0.72}{0.28} )\\\\=\frac{2}{7} \\\\=0.2857$

<h3>the probability that Actuary Rahul examines fewer policies than Actuary Toby is 0.2857</h3>

5 0

3 years ago

Alicia draws a diagram to represent two forces, F1 and F2, acting on a body. The angle between the directions of the forces is 5

Nastasia [14]

Refer to the diagram shown below.

When the two forces F₁ and F₂ are added vectorially, the resultant force is R.
The angle x = 180° - 50° = 130°.

From the Law of Cosines, obtain
R² = F₁² + F₂² - 2F₁F₂ cos(130°)
Note that 2 cos(130°) = -1.2856.

Answer:
R = √(F₁²+ F₂² + 1.2856 F₁F₂ )