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2 years ago

In a particular triathlon the athletes cover 1/24 of the total distance by

Mathematics

1 answer:

pav-90 [236]2 years ago

5 0

Answer:

15/8

Step-by-step explanation:

Let "d" be the total distance, that is, the distance for swimming (s), running (r) and going by bike (b).

d = s + r + b [1]

1/24 of the total distance is covered by swimming.

s = 1/24 d [2]

1/3 of the distance is covered by running.

r = 1/3 d [3]

If we replace [2] and [3] in [1], we get

d = 1/24 d + 1/3 d + b

b = d - 1/24 d - 1/3 d

b = 24/24 d - 1/24 d - 8/24 d

b = 15/24 d = 5/8 d

The ratio of the distance covered by bike to the distance covered by running is:

b/r = (5/8 d)/(1/3 d) = 15/8

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3 years ago

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2 years ago

Select all values of x that make the inequality -x + 8 ≥11 true.

mash [69]

-x + 8 ≥ 11

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3 years ago

Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

<u>Zero Product Property</u>: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

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Leona [35]

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2 years ago