All categories

3 years ago

Laura walked 612 laps of a circular path in 2 hours. At that rate, how many laps of the path did she walk in one hour?

Mathematics

1 answer:

kari74 [83]3 years ago

8 0

Answer:

306 laps

Step-by-step explanation:

If Laura walked 612 laps in 2 hours then if you divide 2 by 2 then it will give you 1, which is 1 hour. This means that if you divide 612 by 2, it should give you the answer of 306, the amount of laps in 1 hour. I hope this helps!

You might be interested in

Consider the curve y=x2+3x+5. (a) Find the slope of the secant line to the curve through the points P=(4,33) and Q=(4+h,(4+h)2+3

lawyer [7]

Answer:

a) The slope of the secant line is 11 + h

b) The slope of the curve at P is 11

c) The equation of the tangent line at P is y = 11x - 11

Step-by-step explanation:

y=x²+3x+5

(a) Find the slope of the secant line to the curve through the points P=(4,33) and Q=(4+h,(4+h)²+3(4+h)+5)

(4+h)²+3(4+h)+5 = 16 + 8h + h² + 12 + 3h + 5 = 33 + 11h + h²

slope (m) = yq - yp/xq - xp → m = 33 + 11h + h² - 33/4 + h - 4

m = 11h + h²/h = h(11+h)/h = 11 + h

The slope of the secant line is 11 + h

(b) Use your answer from part (a) to find the slope of the curve at the point P.

As P (4,33) = (4+0, 33+0) at P h is 0, so the slope at P is 11 + 0 = 11

The slope of the curve at P is 11

y - yp = m(x - xp) → y - 33 = 11(x - 4) → y - 33 = 11x - 44 → y = 11x - 11

The equation of the tangent line at P is y = 11x - 11

3 0

3 years ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

The mean number of touchdowns per football game is 3.7 with a population standard deviation of 0.9. A random sample of 31 footba

frez [133]

Answer:

Right Tail

P(x>3.9)= 0.108

Step-by-step explanation:

In excel, type =NORM.DIST(3.9, 3.7, 0.162, TRUE).

4 0

3 years ago

A train travels at a constant rate of 45 miles per hour

chubhunter [2.5K]

There’s no question to answer but if the train is going 45 mph it is going 1.333 miles per minute

3 0

3 years ago

Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the

sammy [17]

Answer:

1. The volume of the pile is 4,399.7719 m^3

2. The number of sanders to be filled from a pile is 638

Step-by-step explanation:

Here, we firstly would calculate the volume of the pile

Mathematically, that will be;

V = 1/3 * pi * r^2 * h

from the question, h = 14.2

Mathematically, r = d/2

r = 34.4/2 = 17.2 m

So the volume will be:

V = 1/3 * 3.142 * 17.2^2 * 14.2

V = 4,399.7719 m^3

To find the number of sanders to be filled,

we simply divide the volume obtained by the volume a sander can take

That will be;

4,399.7719/6.9

= 637.6 which is 638

4 0

3 years ago