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3 years ago

5

Jade and Kate were running around Lincoln Park. Jade started running at 12:00pm at a rate of 3 kilometers per hour. However, Kat

e was too busy watching TV that she started running at 12:30pm at a rate of 3 kilometers per hour. Mathematically, at what time will they meet?

1 answer:

xxTIMURxx [149]3 years ago

8 0

Answer: Kate ran about 4.82803 kilometers.

Step-by-step explanation:

So 1 mile ≈ 1.60934 kilometers.

To find out how far Kate ran in kilometers, you can multiply how far she ran in miles by 1.60934.

3 × 1.60934 ≈ 4.82803

Kate ran about 4.82803 kilometers.

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Find the value of x in the triangle shown below. one angle is 102 and the other angle is 48 and the third one is x

lora16 [44]

Answer:

30

Step-by-step explanation:

Since you know all the angles have to add up to 180 degrees, you add 102 and 48. That is 150. 180 degrees-150 degrees equals 30 degrees.

5 0

3 years ago

Read 2 more answers

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

Ahh help plss!! thank u

AnnZ [28]

Basically you’re multiplying them both
(x^3 + 2x - 1)(x^4 - x^3 + 3)

so you need to make sure you multiply each one, if you do it right, you should end up with
x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x -x^4 +x^3 -3

simplify by adding like terms
x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3

your answer would be the third option

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3 years ago

How many 2/4’s are in 2

swat32

Im pretty sure that answer is four!

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2 years ago

How to find the value of a+b+c given that a=4,b=3 and c= -2

Alexus [3.1K]

Answer: 5

Step-by-step explanation: 4 + 3 + -2 = 5

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3 years ago