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2 years ago

HELP IN NEED!

Mathematics

1 answer:

laiz [17]2 years ago

6 0

Answer:

$AB=12\sqrt{3}\ cm$

Step-by-step explanation:

If AB is tangent to the circle, then angle ABO is right angle and triangle AOB is special $30^{\circ}-60^{\circ}-90^{\circ}$ triangle. In this triangle, the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,

$AO=2BO=2\cdot 12=24\ cm.$

By the Pythagorean theorem,

$AB^2=AO^2-BO^2,\\ \\AB^2=24^2-12^2,\\ \\AB^2=576-144=432,\\ \\AB=12\sqrt{3}\ cm.$

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The base of the triangle decreases by 30% and the height increases by 20%.

sergeinik [125]

Answer:

Area decreases by 16%

Step-by-step explanation:

Use formula for the area of the triangle

$A=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}$

Initial triangle:

The base is 18 cm

The height is 5 cm

The area is

$A_{initial}=\dfrac{1}{2}\cdot 18\cdot 5=45\ cm^2$

New triangle:

The base is $(1-0.3)\cdot 18=0.7\cdot 18=12.6\ cm$

The height is $(1+0.2)\cdot 5=1.2\cdot 5=6\ cm$

The area is

$A_{new}=\dfrac{1}{2}\cdot 12.6\cdot 6=37.8\ cm^2$

Area decreases by

$100\%-\dfrac{37.8}{45}\cdot 100\%=100\%-84\%=16\%$

5 0

3 years ago

He lays the shorter edfe and finds the frame

il63 [147K]

By laying on the short edge the frame of it is 6

5 0

3 years ago

Research results showed that experimental Drug R had a minimal to modest effect in reducing the symptoms of generalized anxiety

Angelina_Jolie [31]

Answer:

The variable that may change in response to the increase of the drug is the GAD symptoms by a 37,5%.

Step-by-step explanation:

According to the results of the first experiment with a mass of 200 mg of Drug R, they obtain a reduced of the GAD symptoms by a 25 percent evidenced by the Hamilton Anxiety Scale.

If they decided to increase the mass of Drug R to 300 mg the results expected are a increase of the porcentange of the reduced symptoms of generalized anxiety disorder, according to the tendence of the first hypothesis and the Hamilton Anxiety Scale.

We can express this increase by using the three simple rule. Where if 200 mg of Drug R reduced the 25% of the GAD symptoms, if we increase to 300 mg of Drug R how much porcentage this amount will be reduced.

Doing the maths 300mg × 25%=7500mg%,

⇒ 7500mg% ÷ 200mg = 37,5%.

In conclusion if they increased the mas of Drug R to 300 mg they will be reduced the generalized anxiety disorder (GAD) to a 37,5%.

3 0

3 years ago

What is the volume of a cone with a radius of 2 and a height of 19?

kykrilka [37]

Remember that the cone volume formula is $V=\pi r^2\frac{h}{3}$ , with r = radius and h = height. Using our information, we can form our equation as such: $V=\pi 2^2\frac{19}{3}$ (I'll be keeping the answer in pi form.)