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1 year ago

10

How many triangles are formed by the angles and sides (45°, 108°, 7 cm)--unique triangle, more than one triangle, or no triangle

?

1 answer:

Kruka [31]1 year ago

5 0

Answer:

no triangle triangle is formed

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7,014 + 2,415 + 774 + 30 = _____

Cloud [144]

9,459

8,444

23,963

9,304

3,719

7 0

2 years ago

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$

3.1.1.

$f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3$

Differentiate one term at a time:

• power rule

$\left(4x^5\right)' = 4\left(x^5\right)' = 4\cdot5x^4 = 20x^4$

$\left(\dfrac1{4x^2}\right)' = \dfrac14\left(x^{-2}\right)' = \dfrac14\cdot-2x^{-3} = -\dfrac1{2x^3}$

$\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}$

The last two terms are constant, so their derivatives are both zero.

So you end up with

$f'(x) = \boxed{20x^4 + \dfrac1{2x^3} + \dfrac1{3x^{2/3}}}$

8 0

1 year ago

Imagine that you are the chief information officer for a medium-sized company that sells pre-packaged ingredients for healthy me

lina2011 [118]

Answer:

Employers will look to see which workers are applying themselves. They want workers who are flexible, have good attitudes, are loyal to their company, practice good judgement, and are unselfish. Workers who go out and do work that is not formally assigned to them and expand the scope of their responsibilities are rewarded with promotions. Workers who maintain extensive professional networks and learn new skills are also prime candidates for promotion.

This was the example answer. Hope this helps!! HAVE AN AMAZING DAY!

8 0

2 years ago

Kendra was asked to find the number of students who planned to attend the evening symphony performance. She was told that 40 per

navik [9.2K]

Picture related to the question is attached below

Answer:

Kendra should have divided by 2 instead of multiplying by 2

Step-by-step explanation:

40 percent = percentage who plan to attend

100% = total percentage of student

From the question ;

When reducing percentages, division is employed and this the equation should be :

40/2 ÷ 100/2

40/2 * 2/100

20 * 1/50

20/50

= 0.4

0.4 * 50

= 20 students

6 0

2 years ago

Read 2 more answers

You have been saving $12 each week for many weeks. One day, you decide to count your savings and find that you have $384. Choose

Alex_Xolod [135]

Answer:

D or the last one.

Step-by-step explanation:

Honestly, you got me kinda confused. Is it saying that there is multiple equations to answer this? Well anyways, D would be the answer. When the variable (w) is beside the coefficient, it means you multiple them together. (W) standing for weeks multiplied by 12 which is how much you earn each week would get you the total amount. The rest just don't make sense.

4 0

2 years ago