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3 years ago

What is the measure of <DCF

Mathematics

2 answers:

Pavlova-9 [17]3 years ago

8 0

Answer:

The measure of angle DCF is 129 degrees.

Step-by-step explanation:

Angle DCF is the sum of angle DCE plus angle ECF.

This is because, DCF is the main angle and DCE and ECF are its two parts.

Hence, the measure of angle DCF will be = $75+54=129$ degrees.

The answer is :

The measure of angle DCF is 129 degrees.

Shtirlitz [24]3 years ago

5 0

129 degrees you just add DCE and ECF together

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A lake polluted by bacteria is treated with an antibacterial chemical. Aftertdays, thenumber N of bacteria per milliliter of wat

jeyben [28]

Answer:

N(1)=50 is a minimum

N(15)=4391.7 is a maximum

Step-by-step explanation:

<u>Extrema values of functions </u>

If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.

We are given a function (corrected)

$N(t) = 20(t^2-lnt^2)+ 30$

$N(t) = 20(t^2-2lnt)+ 30$

(a)

First, we take its derivative

$N'(t) = 20(2t-\frac{2}{t})$

Solve N'(t)=0

$20(2t-\frac{2}{t})=0$

Simplifying

$2t^2-2=0$

Solving for t

$t=1\ ,t=-1$

Only t=1 belongs to the valid interval $1\leqslant t\leqslant 15$

Taking the second derivative

$N''(t) = 20(2+\frac{2}{t^2})$

Which is always positive, so t=1 is a minimum

(b)

$N(1)=20(1^2-2ln1)+ 30$

N(1)=50 is a minimum

(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15

(d)

$N(15)=20(15^2-2ln15)+ 30$

N(15)=4391.7 is a maximum

7 0

3 years ago

Simplify.<br> <img src="https://tex.z-dn.net/?f=%5Csqrt32%20%2B%20%5Csqrt16%2B%20%5Csqrt8" id="TexFormula1" title="\sqrt32 + \sq

svetoff [14.1K]

Answer:

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Step-by-step explanation:

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$\sqrt{16} = \sqrt{4 \times 4} = 4$

$\sqrt{8} = \sqrt{2 \times 2 \times 2} = 2 \sqrt{2}$

$4 + 4\sqrt{2} + 2 \sqrt{2} = 4 + 6 \sqrt{2}$

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ratelena [41]

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