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3 years ago

a line passes through the point (-9,7) and has a slope of -4/3 write an equation in point slope form for this line

Mathematics

1 answer:

DENIUS [597]3 years ago

5 0

The answer would be: Y= -4/3x - 5

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A train leaves at 14.54 and arrives at its destination at 15.47. If the train travelled 66 km, what was it's average speed in km

JulijaS [17]

Answer: average speed of the train = 4,483.0 km/h

Step-by-step explanation:

Speed = Distance / Time

Distance = 66 km

Time = 15.47 cancelling 15, we have 60 sec added to 47 sec

- 14.54

= 14. 107 60 + 47

- 14. 54

53secs

53secs to hours becomes =

60 secs = 1 min

60 min= i hour

therefore 53seconds =53/3600=0.0147222hours

Speed= 66/ 0.0147222= 4,483.025

Rounding to 1 dp becomes= 4,483.0 km/h

3 0

3 years ago

What is the slope of the line which passes through (4, 7) and (2, 3)? (5 points)

Basile [38]

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 7)

m = $\frac{7-3}{4-2}$ = $\frac{4}{2}$ = 2

3 0

3 years ago

george rented a bike for 4 hours. There was a $10 deposit to pay in addition to the hourly rate. What was the hourly rate if the

steposvetlana [31]

Answer:

13.75

Step-by-step explanation:

65 - 10 =55

55 ÷ 4 = 13.75

4 0

2 years ago

f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

Kruka [31]

Answer:

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

Step-by-step explanation:

We want to find the Riemann sum for $\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx$ with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$

where $\Delta{x}=\frac{b-a}{n}$ .

Step 1: Find $\Delta{x}$

We have that $a=0, b=\frac{3\pi }{4}, n=6$

Therefore, $\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}$

Step 2: Divide the interval $\left[0,\frac{3 \pi}{4}\right]$ into n = 6 sub-intervals of length $\Delta{x}=\frac{\pi}{8}$

$a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b$

Step 3: Evaluate the function at the left endpoints

$f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3$

$f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386$

$f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964$

$f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527$

$f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0$

$f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527$

Step 4: Apply the Left Riemann Sum formula

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

5 0

3 years ago

Find the distance between the two points rounding to the nearest tenth (if necessary).

stiks02 [169]

It’s 10

Explanation: you use the distance equations
Which in this case is the one in the picture.

6 0

3 years ago