All categories

3 years ago

Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

1 answer:

4 0

5:2 is a 5 to 2 ratio
a midpoint P between tow points is
((x1+x2)/2, (y1+y2)/2)
I would start there, adjust it to get a ratio of 5:2 from 1:2
for one thing the point should be on the line between the other two points

You might be interested in

Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $200 a month and an additional $12 for

Roman55 [17]

Answer:

200 + 12n = 644 Answer: 37

Step-by-step explanation:

200 + 12n = 644

12n = 444

n = 37

Floyd sold 37 albums last month

7 0

3 years ago

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

Pls help with this one I will give brainliest thank you! Number 5

melamori03 [73]

Answer:

The volume of the fish tank is 48000 cubic centi meter.

Step-by-step explanation:

The volume of a Cuboid is l*b*h (length*breadth*height)

Here,

length(l) =60 cm

breadth(b)= 20 cm

height(h)=40 cm

Volume=l*b*h

Volume= 60cm*20cm*40cm

Volume= 48000 cubic centimeter

5 0

3 years ago

Read 2 more answers

How do you simplify the radical expression, 24- sqrt(720 over 4

baherus [9]

24- sqrt(720/4) divide 720 by 4

24 - sqrt (180) now break down 180 to 9*4*5

24- sqrt(9) *sqrt(4) *sqrt (5) so 9becomes 3, 4 becomes 2

24- 3*2*sqrt(5) multiply 3 and 2

24-6sqrt(5)

7 0

3 years ago

What are the clear steps for solving for x question (5x + 2)

Alenkinab [10]

Answer:

x= -2/5

Step-by-step explanation:

(5x+2)=0

-2 -2

5x=-2

------------

x= -2/5

6 0

3 years ago