Which best describes the angles of some rhombuses?

You roll a number cube numbered from 1 to 6. What is the probability that the number is a 3? (Answers are rounded to the nearest

labwork [276]

Answer:

1/6

Step-by-step explanation:

6 0

3 years ago

A peqch pie is made with 13 peaches, which are evenly distributed throughout the pie. If Joe ate one slice that contained exactl

bekas [8.4K]

Answer:

138.5°

Step-by-step explanation:

Since the peach pie is a circle, we have a total angle of 360°.

We need to determine what fraction of the total pie of 13 peaches is the 5 peaches contained in Joe's slice.

This is number of peaches in Joe's slice/total number of peaches in pie = 5/13. To find the angle Joe's slice measures, we multiply 5/13 by 360°.

So, 5/13 × 360°

= 0.3846 × 360°

= 138.46°

≅ 138.5° to the nearest tenth of a degree

3 0

3 years ago

You can earn 5 coins What is the slope of the function below? y = 4x +4

artcher [175]

Answer:

The slope is 4

Step-by-step explanation:

The answer is 4

5 0

3 years ago

Find the quotient. 1. (a a 8. 2

kirill [66]

Answer:

what was it what aa or 2 8 kesa question

4 0

3 years ago

NO LINKS OR FILES!

Archy [21]

(a) If the particle's position (measured with some unit) at time t is given by s(t), where

$s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}$

then the velocity at time t, v(t), is given by the derivative of s(t),

$v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}$

(b) The velocity after 3 seconds is

$v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}$

(c) The particle is at rest when its velocity is zero:

$\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}$

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

$\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|$

In interval notation, this happens for t in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt$

By definition of absolute value, we have

$|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)$

In part (d), we've shown that v(t) > 0 when -√11 < t < √11, so we split up the integral at t = √11 as

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt$

and by the fundamental theorem of calculus, since we know v(t) is the derivative of s(t), this reduces to

$s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}$

7 0

3 years ago