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3 years ago

Derivative of 2ln(secx)

1 answer:

5 0

2tan(x)

i. take the 2 out
ii. derivative of acos is -sin
iii. derivative of In is -ve inverse

so we have 2 times sin(x)/cos(x) hence 2tan(x)

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In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

2 years ago

Mrs. Henderson wants to put wallpaper border around her living room the room is 18 ft by 22 ft. How many feet of border are need

irga5000 [103]

If I am understanding the question, and assuming the living room is a rectangle, then the border should be 80 ft

8 0

3 years ago

what is the circumference of the circle with an arc length of 11 and an interior angle of 27° Round to nearest tenth plz

igor_vitrenko [27]

Answer:

146⅔ units

Step-by-step explanation:

27° : 11

360° : X

X = (11/27) × 360

X = 146 ⅔

6 0

2 years ago

Read 2 more answers

3. given that m < APC is 104° in circle P, find the degree measure of Arc ABC

lilavasa [31]

Answer:

Answer is 256 degrees

Step-by-step explanation:

You basically take the degree that they gave you, which is 104, now take 360 (that's the measurement of the whole circle) and subtract it by 104 to get your answer.

5 0

2 years ago

Can I get help please with all 20 questions I have 156points

motikmotik

Answer:

It’s the third ans

Step-by-step explanation:

7 0

2 years ago