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3 years ago

11

Rob is travelling at a constant speed in a car. He travels 105km in 1 hour and 30 minutes. The speed limit is 80km/h. Is Rob tra

velling within the speed limit? Show how you decide.

1 answer:

abruzzese [7]3 years ago

8 0

Answer:

Yes.

Step-by-step explanation:

Let's first convert his speed to km/h.

$\frac{105km}{1.5h} = 70\frac{km}{h}$ > $80\frac{km}{h}$ . Therefore, Rob is traveling within the speed limit.

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The altitude of a triangle is increasing at a rate of 1.500 centimeters/minute while the area of the triangle is increasing at a

puteri [66]

Answer:

The base of the triangle is shrinking at a rate of $\frac{131}{32}$ centimeters per minute.

Step-by-step explanation:

The formula of the area of a triangle is given by the following expression:

$A = \frac{1}{2}\cdot b \cdot h$

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

The base of the triangle is:

$b = \frac{2\cdot A}{h}$

If $A = 98000\,cm^{2}$ and $h = 8000\,cm$ , the base of the triangle is:

$b = \frac{2\cdot (98000\,cm^{2})}{8000\,cm}$

$b = 24.5\,cm$

The rate of change of the area of the triangle in time, measured in minutes, is obtained after differentiating by rule of chain and using deriving rules:

$\frac{dA}{dt} = \frac{1}{2}\cdot h\cdot \frac{db}{dt} + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$

$\frac{dA}{dt} = \frac{1}{2} \cdot \left(h\cdot \frac{db}{dt}+b \cdot \frac{dh}{dt} \right)$

The rate of change of the base of the triangle is now cleared:

$2\cdot \frac{dA}{dt} = h\cdot \frac{db}{dt} + b\cdot \frac{dh}{dt}$

$h\cdot \frac{db}{dt} = 2\cdot \frac{dA}{dt}-b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2\cdot \frac{dA}{dt} - b \cdot \frac{dh}{dt} }{h}$

Given that $\frac{dA}{dt} = 2000\,\frac{cm^{2}}{min}$ , $b = 24.5\,cm$ , $\frac{dh}{dt} = 1500\,\frac{cm}{min}$ and $h = 8000\,cm$ , the rate of change of the base of the triangle is:

$\frac{db}{dt} = \frac{2\cdot \left(2000\,\frac{cm^{2}}{min} \right)-(24.5\,cm)\cdot \left(1500\,\frac{cm}{min} \right)}{8000\,cm}$

$\frac{db}{dt} = -\frac{131}{32}\,\frac{cm}{min}$

The base of the triangle is shrinking at a rate of $\frac{131}{32}$ centimeters per minute.

5 0

3 years ago

2<br> What is the area of a rectangle with a length of 9 feet and a width<br> of 7 feet?

baherus [9]

Answer:

The area is 63 brainliest pls! :D

Step-by-step explanation:

9*7=63

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3 years ago

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245 is closer to what number in using hundred?

Radda [10]

245 is closer to 200.

So when we do estimation, 245 is round down to 200.

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3 years ago

I ready know the answer i just need to know how to explain it plz help MARK BRAINLIEST TO THE FIRST ONE (32 points)

Alekssandra [29.7K]

Spruce tail because if you round it from the number 8 it will turn the 4 into a 5 turning it into 10.5, which is what you need

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3 years ago

3) Sandy wants to make cookies. To make cookies, she needs 15 cups of flour per

vekshin1

Answer:

She can make 1.6 batches

Step-by-step explanation:

24/15 = 1.6

6 0

3 years ago

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