What is the straight-line distance between (2, -4) and (-3, 8) on a coordinate grid?

A student reads 65 pages per hour proportional relationship

goldfiish [28.3K]

Oh.......kay.... Is that a question? It doesn't look like one.

3 0

3 years ago

Nathan is making a beaded bracelet for every five red beads there are three white beads what is the ratio of red to

Marysya12 [62]

5:3 if there's 5 red beads every 3 white beads, then the ratio of red to white beads is 5:3

3 0

3 years ago

Tickets to a concert went on sale at 10 a.m. by 12 p.m. 208 tickets have already been sold at this rate how many tickets will be

kotegsom [21]

Answer:

We conclude that 520 tickets will be sold in the first 5 hours of the tickets go on sale.

Hence, option A is true.

Step-by-step explanation:

Given that the tickets to a concert went on sale at 10 a.m. by 12 p.m.

10 a.m. by 12 p.m means the total number of hours = 2 hours

Given that the tickets sold in 2 hours = 208

Thus,

Unit rate = 208 tickets / 2 hours

= 104 tickets per hour

Therefore,

Tickets sold in the first 5 hours of the tickets go on sale:

104 × 5 = 520 tickets

Therefore, we conclude that 520 tickets will be sold in the first 5 hours of the tickets go on sale.

Hence, option A is true.

3 0

3 years ago

Find the area that the curve encloses and then sketch it.<br> r = 3 + 8 sin(6)

Rudiy27

Answer:

$A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2$

Step-by-step explanation:

I assume you mean $r=3+8\sin\theta$ :

Use the formula $\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta$ where $a$ and $b$ are the lower and upper bounds and $r(\theta)$ is the equation of the polar curve.

Since the graph is symmetrical about the line $\displaystyle \theta=\frac{\pi}{2}$ , let the bounds of integration be $\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)$ to find half the area of the curve, and then find twice of that area:

$\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta$

$\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\$

$A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053$

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

7 0

3 years ago

Judy and her sister went together to get haircuts. Judy got 9 3/5 inches cut off and her sister got 4 1/10 inches cut off. Compa

disa [49]

Answer:

5 1/2

Step-by-step explanation:

9 3/5 - 4 1/10

First you need to get common denominator, as we see that we need to get the 5 from the 3/5 to ten, so we multiply 3/5 by 2 on both of the numerator and denominator and you will get 6/10. So the new fraction would be 9 6/10 - 4 1/10 = which would be subtractable. Therefore the answer would be 5 5/10 which equals

5 1/2

4 0

2 years ago

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