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Svetllana [295]
2 years ago
9

The base of a triangle is shrinking at a rate of 5 cm/s and the height of the triangle is increasing at a rate of 9 cm/s. Find t

he rate at which the area of the triangle changes when the height is 12 cm and the base is 4 cm.
Provide your answer below:
The rate of change of the area of the triangle is ___ cm²/s.
Mathematics
1 answer:
creativ13 [48]2 years ago
3 0

Answer:

Step-by-step explanation

Area of a triangle

      A = ½bh

dA/dt = ½(b(dh/dt) + h(db/dt)

dA/dt = ½(4(9) + 12(-5))

dA/dt = ½(36 - 60)

dA/dt = ½(-24)

dA/dt = -12 cm²/s

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3 0
3 years ago
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What is the equation of a line that has a slope of -1/2 and goes through the point (-2,4) ?
yarga [219]

Answer:

y-2=-1/2(x+2)

Step-by-step explanation:

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4 0
3 years ago
Please help me now ! Thank you
jarptica [38.1K]
First we'll do two basic steps. Step 1 is to subtract 18 from both sides. After that, divide both sides by 2 to get x^2 all by itself. Let's do those two steps now

2x^2+18 = 10
2x^2+18-18 = 10-18 <<--- step 1
2x^2 = -8
(2x^2)/2 = -8/2 <<--- step 2
x^2 = -4

At this point, it should be fairly clear there are no solutions. How can we tell? By remembering that x^2 is never negative as long as x is real. 

Using the rule that negative times negative is a positive value, it is impossible to square a real numbered value and get a negative result. 

For example
2^2 = 2*2 = 4
8^2 = 8*8 = 64
(-10)^2 = (-10)*(-10) = 100
(-14)^2 = (-14)*(-14) = 196

No matter what value we pick, the result is positive. The only exception is that 0^2 = 0 is neither positive nor negative.

So x^2 = -4 has no real solutions. Taking the square root of both sides leads to

x^2 = -4
sqrt(x^2) = sqrt(-4)
|x| = sqrt(4)*sqrt(-1)
|x| = 2*i
x = 2i or x = -2i
which are complex non-real values


5 0
3 years ago
In ΔHIJ, the measure of ∠J=90°, HI = 88 feet, and IJ = 62 feet. Find the measure of ∠I to the nearest tenth of a degree.
devlian [24]

Answer:

Step-by-step explanation:

8 0
2 years ago
2. It costs Edgar $2.65 one way to ride the bus to work. He uses the bus to go to and from work four days per week. He buys a bo
Maurinko [17]
$27

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Add the daily cost of the water bottle (1.45) to make his total cost for one day, which is 6.75
Multiply this number by 4 (because he goes 4 days a week) to get $27 for one week.
6 0
2 years ago
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