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3 years ago

Which graph is the line (y-4)=1/4(x-2)

1 answer:

8 0

(y-4) = 1/4 (x-2)
really a question of algebra
step 1: get rid of fractions, multiply both sides by 4
4( y-4) = 4(1/4 [x - 2])
4y - 16 = x- 2
4y = x - 2 + 16
4y = x + 14

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A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four re

ddd [48]

Answer:

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which $\theta$ is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = $2\pi$ radians

So, the change in angle with respect to t ( time ),

$\frac{d\theta}{dt}=8\pi\text{ radians per min}$

Let x be the distance of beam from P,

$\implies \tan \theta = \frac{x}{2}$

Differentiating with respect to x,

$\sec^2 \theta \frac{d\theta}{dt}=\frac{1}{2}\frac{dx}{dt}$

$(1+\tan^2 \theta) (8\pi) = \frac{1}{2}\frac{dx}{dt}$

$(1+\frac{x^2}{2^2})(8\pi) = \frac{1}{2}\frac{dx}{dt}$

If x = 1 km,

$(1+\frac{1}{4})8\pi =\frac{1}{2}\frac{dx}{dt}$

$\frac{5}{4}8\pi = \frac{1}{2}\frac{dx}{dt}$

$\implies \frac{dx}{dt}=\frac{80\pi}{4}= 20\pi\approx 62.8\text{ km per min}$

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

7 0

4 years ago

PLEASE HELP ASAP 40 PTS !!!!

snow_tiger [21]

Answer:

a If we make the parent function 2sqrt(x) then we translate to the left 4 units and up 5 units

Step-by-step explanation:

y = sqrt(4x+16) +5

y = sqrt(4 (x+4)) +5

y = sqrt(4) sqrt(x+4) +5

y =2sqrt(x+4) +5

f(x) = sqrt(x) this is the parent function

g(x) = sqrt(x+4) This moves it to the left 4 units

h(x) = 2 sqrt (x+4) This stretches it by 2 in the y direction

j(x) = 2 sqrt(x+4) +5 This moves it up by 5 units

y = 2sqrt(x+4) +5

This is to the left 4 units, stretched 2 units in the y direction and up 5 units

If we make the parent function 2sqrt(x) then we translate to the left 4 units and up 5 units

8 0

3 years ago

Order the following from greatest to least -12, 12, -19, 1 1/2(BTW this is a mixed number ;-; ) , 5

Firlakuza [10]

Answer:

12, 5, 1 1/2, -12, -19

Step-by-step explanation:

hope this helped!

5 0

4 years ago

Results of a survey conducted in 15 large cities within the U.S. finds that the average commute time one way to/from work is 25.

irina1246 [14]

Answer:

We conclude that commute time in her city is less than the amount reported by the survey which is 25.4 minutes.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 25.4 minutes

Sample mean, $\bar{x}$ = 22.1 minutes

Sample size, n = 15

Alpha, α = 0.10

Sample standard deviation, s = 5.3 minutes

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 25.4\text{ minutes}\\H_A: \mu < 25.4\text{ minutes}$

We use one-tailed t(left) test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{22.1 - 25.4}{\frac{5.3}{\sqrt{15}} } = -2.411$

Now, $t_{critical} \text{ at 0.10 level of significance, 14 degree of freedom } = -1.345$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, there is enough evidence to conclude that commute time in her city is less than the amount reported by the survey which is 25.4 minutes.

7 0

4 years ago

HELP.. What angle pair relationship is shown?

Greeley [361]

Answer: Corresponding

7 0

3 years ago

Read 2 more answers