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creativ13 [48]
2 years ago
5

A triangle's base is increasing at the rate of 3 inches/sec, its height at 2 inches/sec. At what rate is the area of the rectang

le increasing when base is 10 inches and height is 14 inches
Mathematics
1 answer:
Triss [41]2 years ago
3 0

Answer:

dA/dt = 31  in²/ sec

Step-by-step explanation:

The area of the triangle is:

A(t)  = (1/2)*b*h     where  b is the base and h the height

Differentiation on both sides of the equation we obtain

dA/dt  =  (1/2)* db/dt * h + (1/2)* dh/dt * b   (1)

db/dt  = 3 in/sec

dh/dt =  2 n/sec

b =  10 in

h = 14 in

By substitution in (1)

dA/dt =  0,5* 3*14 +  0,5* 2*10

dA/dt =  21 in² /sec + 10 in²/sc

dA/dt = 31  in²/ sec

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The events are independent. By definition, it means that knowledge about one event does not help you predict the second, and this is the case: even if you knew that you rolled an even number on the first cube, would you be more or less confident about rolling a six on the second? No.

An example in which two events about rolling cubes are dependent could be something like:

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Event B: The second cube returns a higher number than the first one.

In this case, knowledge on event A does change you view on event B (and vice versa): if you know that you rolled a 6 on the first cube you don't want to bet on event B, while if you know that you rolled a 1 on the first cube, you're certain that event B will happen.

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Write the phrase as a rate in simplest form.<br> 320 miles on 34 gallons
Dmitriy789 [7]

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Find the slope of the line containing the points (1, 2) and (6, 12).
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Step-by-step explanation:

5 0
2 years ago
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Help ASAP:Solve : 0.84+91.279
jeka94

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Step-by-step explanation:

0.84+91.279=92.119

Hope this helps!

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3 years ago
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Find the area and the circumference of the circle with the radius 6yd.
fgiga [73]

Answer:

<h2>A = 36π yd² ≈ 113.04 yd²</h2><h2>C = 12π yd ≈ 37.68 yd</h2>

Step-by-step explanation:

The formula of an area of a circle:

A=\pi r^2

The formula of a circumference of a circle:

C=2\pi r

<em>r</em><em> - radius</em>

<em />

We have <em>r = 6yd</em>.

Substitute:

A=\pi(6^2)=36\pi\ yd^2

C=2\pi(6)=12\pi\ yd

If you want round the answers, then use <em>π ≈ 3.14</em>

A\approx(36)(3.14)=113.04\ yd^2

C\approx(12)(3.14)=37.68\ yd

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3 years ago
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