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2 years ago

Rewrite the function by completing the square h(x)=4x^2+4x+1

Mathematics

1 answer:

lisov135 [29]2 years ago

8 0

Answer:

$h(x) = 4(x+\frac{1}{2})^{2}$

Step-by-step explanation:

$h(x)=4x^2+4x+1\\h(x)=4(x^2+x+\frac{1}{4}) \\h(x)=4(x^2+x+\frac{1}{4})\\h(x) = 4(x+\frac{1}{2})^{2}$

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A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas

Fittoniya [83]

Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

$#V=pi r^2 h#$

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

$#V=pi (5m)^2 h#$

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

$#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#$

In the problem, we are given $#3(m^3)/min# which is #(dV)/(dt)#.$

So we need to substitute this in:

$#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#$

Hence, Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>Formula used: </h3>

$#V=pi r^2 h#$

To Learn more visit:

brainly.com/question/4313883

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4 0

2 years ago

Read 2 more answers

Find the volume of the cylinder in terms of π and to the nearest tenth.

Anastaziya [24]

The answer is 18pi
$3 \times 3 \times 2 \times \pi = 18\pi$

good luck

5 0

2 years ago

Yukarıda verilen şekilde,

olga2289 [7]

C, 60 hope this helps it helped me on my test

6 0

2 years ago

WILL MARK BRAINLIEST!! PLZ HELP!!

olasank [31]

Answer:

The answer is D.

Step-by-step explanation:

When x=0, then y=300, so it has to be more than that.

When x=25, y=300, so it has to be less than that.

8 0

2 years ago

If angle pqt is (3x+47)and angle sqr is (6x-25), find the measure of angle sqr

Radda [10]

Answer:

Angle sqr = 119°

Step-by-step explanation:

In the above question, we are given:

angle pqt is (3x+47)°

angle sqr is (6x-25)°

Angle pqt = Angle sat

We solve for x

3x + 47 = 6x - 25

Collect like terms

47 + 25 = 6x - 3x

72 = 3x

x = 72/3

x = 24

We solve for the measure of angle sqr

Angle sqr = (6x - 25)

x = 24

6 × 24 - 25

144 - 25

= 119°

5 0

2 years ago