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3 years ago

Juan construyó una rampa que tiene 5 m de largo y 1 m de altura. ?Cuánto mide la distancia (d) que recorre al subir la rampa

Mathematics

1 answer:

satela [25.4K]3 years ago

7 0

Answer:

$d=\sqrt{26}\ m$ or $d=5.1\ m$

Step-by-step explanation:

<em>The question in English is</em>

Juan built a ramp that is 5 m long and 1 m high. How much is the distance (d) he travels when he climbs the ramp?

let

x -----> the length of the ramp

y ----> the height of the ramp

d ----> the distance Juan travels when he climbs the ramp

we know that

Applying the Pythagoras Theorem

$d^{2}=x^{2}+y^{2}$

we have

$x=5\ m$

$y=1\ m$

substitute the given values

$d^{2}=5^{2}+1^{2}$

$d^{2}=26$

$d=\sqrt{26}\ m$ -----> exact value

$d=5.1\ m$ ----> approximate value

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if alpha and beta are the roots of the equation 3x^2-9x+2=0 find the values of: (I) alpha ×beta + alpha^2 × beta. (ii) alpha^2-a

Kryger [21]

Answer:

in steps

Step-by-step explanation:

The question did not state if alpha>beta or alpha<beta, so the answer will have 2 answers for each questions

3x²-9x+2=0

x = (-(-9) ± √(-9)²-4*(3)*(2)) / (2*3)

x = (9 + √57) / 6 or x = (9 - √57) / 6 (alpha and beta) or (beta and alpha)

(I) alpha (a) ×beta (b) + alpha² × beta = ab (1+a)

= ((9 + √57) / 6) ((9 - √57) / 6) (1 + (9 ± √57))

= ((9² - (√57)²)/36) (10 ± √57)

= (24/36) (10 ± √57)

= 2/3 (10 ± √57) or (11.7 or 1.63)

(ii) alpha²-alpha×beta+beta² = a² -2ab + b² +ab = (a - b)² + ab

if a is alpha

= ((9 + √57) / 6) - ((9 - √57) / 6)) + ((9 + √57) / 6) ((9 - √57) / 6))

= √57/3 + 2/3

= (√57 + 2) / 3

if a is beta

((9 - √57) / 6) - ((9 + √57) / 6)) + ((9 - √57) / 6) ((9 + √57) / 6))

= - √57/3 + 2/3

= - (√57 + 2) / 3

3 0

3 years ago

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollar

uranmaximum [27]

Complete question :

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? A. h = (h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b)÷ r b. h = h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b ÷ r c. h = h equals left-parenthesis StartFraction p Over 0.7 EndFraction right-parenthesis divided by r minus b.÷ r – b d. h = h equals StartFraction p minus b Over 0.7 EndFraction divided by r. ÷ r

Answer:

[(p/0.7) - b] / r

A. h = (h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b)÷ r b. h = h equals StartFraction p Over 0.7 EndFraction minus b divided by r.

Step-by-step explanation:

Given the equation :

p = 0.7(rh + b)

Make h the subject

Divide both sides by 0.7

p / 0.7 = 0.7(rh + b) / 0.7

p/ 0.7 = rh + b

Subtract b from both sides :

(p/0.7) - b = rh + b - b

(p/0.7) - b = rh

Divide both sides by r

[(p/0.7) - b] / r = rh/ r

[(p/0.7) - b] / r = h

7 0

3 years ago

10x0+10x1<br> what is the answer ?

sesenic [268]

Answer:

Step-by-step explanation:

10x0 is 0

10x1 is 10

6 0

2 years ago

Read 2 more answers

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

During a blizzard, Daniel lost power for 40 hours. His neighbor lost power for 2 days. Whose power was out longer?

andriy [413]

Answer:

his neighbors

Step-by-step explanation:

there are 48 hours in 2 days, which means that his neighbors power was out longer.

8 0

2 years ago