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3 years ago

Please help. here is a screenshot of the question.

Mathematics

1 answer:

Feliz [49]3 years ago

6 0

Hello,

1) the line parallele to ox passing by (1,4) has for equation y=4

f(x)=4 if -1<=x<=1

2) the line pasing through (3,2) and (5,4) has for equation:

y-2=(4-2)/(5-3)(x-3)
==>y=x-3+2
==>y=x-1

f(x)=x-1 if 3<=x<=5.

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Consider m = y2 - y1/ x2 - x1 . Which x1 and x2-values would determine that the line is vertical? Justify your answer

Y_Kistochka [10]

Answer:

$x_2=x_1$

Step-by-step explanation:

We were given the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

This line is vertical if the denominator is zero.

That is when $x_2-x-1=0$

This implies that;

$x_2=x_1$

Justification;

When $x_2=x_1$ , then, the line passes through;

$(x_1,y_1)$ and $(x_1,y_2)$

The slope now become

$m=\frac{y_2-y_1}{x_1-x_1}=\frac{y_2-y_1}{0}$

The equation of the line is

$y-y_1=\frac{y_2-y_1}{0}(x-x_1)$

This implies that;

$0(y-y_1)=(y_2-y_1)(x-x_1)$

$0=(y_2-y_1)(x-x_1)$

$\frac{0}{y_2-y_1}=(x-x_1)$

$0=(x-x_1)$

$x=x_1$ ... This is the equation of a vertical line.

3 0

2 years ago

Evaluate using Definite integrals

swat32

Since $[0,4]=[0,1]\cup(1,4]$ , we can rewrite the integral as

$\displaystyle \int_0^1f(t)\;dt + \int_1^4 f(t)\; dt$

Now there is no ambiguity about the definition of f(t), because in each integral we are integrating a single part of its piecewise definition:

$\displaystyle \int_0^1f(t)\;dt = \int_0^11-3t^2\;dt,\quad \int_1^4 f(t)\; dt = \int_1^4 2t\; dt$

Both integrals are quite immediate: you only need to use the power rule

$\displaystyle \int x^n\;dx=\dfrac{x^{n+1}}{n+1}$

to get

$\displaystyle \int_0^11-3t^2\;dt = \left[t-t^3\right]_0^1,\quad \int_1^4 2t\; dt = \left[t^2\right]_1^4$

Now we only need to evaluate the antiderivatives:

$\left[t-t^3\right]_0^1 = 1-1^3=0,\quad \left[t^2\right]_1^4 = 4^2-1^2=15$

So, the final answer is 15.

4 0

3 years ago

I need answer for this question

just olya [345]

The probability that the aircraft is overloaded is 97.98%, which means the pilot should take the action.

In a Normal distribution with mean ц and standard deviation σ, the z-score of a measure x is given by:

Z = X-ц / σ

· It measures how many standard deviations the measure is from the mean.

· After finding Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

· By the Central Limit Theorem, the sampling distribution of sample means of the size n has standard deviation σ

σ = σ / $\sqrt{n}$

σ is standard deviation

n is the sample size.

Given that the mean and the standard deviation of the population is 176.1 lb and 35.4 respectively.

⇒ ц = 176.1 and σ = 35.4

For a sample of 43 passengers, we have

n = 43

σ = $\frac{35.4}{\sqrt{43}}$

σ = 5.398

Z = X-ц / σ

Z = $\frac{165-176.1}{5.398}$

Z = -2.05 has p- value of 0.9798

The probability that the aircraft is loaded is

1 - p-value of Z

1 - 0.0202 = 0.9798

The probability that the aircraft is overloaded is 97.98%

Know more about Normal probability Distribution: -brainly.com/question/9333901

#SPJ9

6 0

9 months ago

Help me with this fractions work

GREYUIT [131]

Answer: A.) 21/5 but as a mixed number it's 4 1/5 B.) 175/24 but as a mixed number it's 7 7/24

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Evaluate C= 2 xr, for r=8. C= 100 OC= 16 OC= 287 C= 16

____ [38]

C= 2 x r where r = 8
C = 2 x 8
C = 16.
Hope I helped:)

3 0

3 years ago