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Tpy6a [65]
1 year ago
6

Check off the methods of differentiation required, and complete the derivative.

Mathematics
1 answer:
kogti [31]1 year ago
6 0

Given:

f(x)=\sqrt[]{5x^2-2}

f(X) will be differentiated by chain rule.

\begin{gathered} f^{\prime}(x)=\frac{1}{2\sqrt[]{5x^2-2}}\lbrack5(2x)\rbrack \\ f^{\prime}(x)=\frac{5x}{\sqrt[]{5x^2-2}} \end{gathered}

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Pls help me plssss help asap
Anestetic [448]

Answer:

1) 15

2) 18

3) 72

8 0
3 years ago
B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a
skelet666 [1.2K]

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

<h3>How long does it take to fill the dam?</h3>

Given that;

  • Amount of water needed to fill the dam A = 30000 litres
  • Pump rate r = 75 litres per minute
  • Time needed to fill the dam T = ?

To determine how long it take to fill the dam, we say;

Time need = Amount of water needed ÷ Pump rate

T = A ÷ r

T = 30000 litres ÷ 75 litres/minute

T = 400 minutes

Note that; 60min = 1hrs

Hence,

T = 6hours 40minutes

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Learn more word problems here: brainly.com/question/2610134

#SPJ1

8 0
2 years ago
Product of 7.69×5 be greater or less than its estimate of 8×5?
spayn [35]

The product is a bit less than the estimate. In fact, 7.69 is less than 8, and if you start with an equality, i.e.

7.69 < 8

you can multiply both sides by a positive number, and the inequality will still hold:

7.69 \cdot 5 < 8 \cdot 5

8 0
3 years ago
A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen
Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}

The restriction is that the perimeter have to be 12 ft at most:

P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12

We can express b in function of a as:

2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a

Then, the area become:

A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2

To maximize the area, we derive and equal to zero:

\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36

Then, b is:

b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68

3 0
3 years ago
Figure A
Amiraneli [1.4K]
<h2>Answer:</h2>

Figure B

<h2>Step-by-step explanation:</h2>

The Pythagorean Theorem is a^2 + b^2 = c^2, where c is the longest side of the triangle (the hypotenuse).

To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.

In Figure A, if the triangle is right-angled, the equation 3^2 + 6^2 = 8^2 must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.

In Figure B,  if the triangle is right-angled, the equation 5^2 + 12 ^2 = 13^2 must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.

Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.

8 0
3 years ago
Read 2 more answers
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