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mario62 [17]
3 years ago
9

Can someone please help me with these two?? (With a clear answer please)

Mathematics
1 answer:
suter [353]3 years ago
4 0
Try this solution:
rule: the volume of any cylinder can be calculated with formula: V=πr²h, where r - the radius of the base, h - height  of the cylinder.
Using the formula written above:
5. V=π*25*6=150*3.1415≈471.2389≈471.2 cm³;
6. V=π*64*4=256*3.1415≈804.2477≈804.3 cm³
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Given: △ABC, m∠A=60°,<br> m∠C=45°, AB=9<br> Find: Perimeter of △ABC,<br> Area of △ABC
stellarik [79]

Answer:

Perimeter of ΔABC: \frac{27}{2} + \frac{9}{2} * \sqrt6 units

Area of ΔABC: \frac{81}{8}*\sqrt3 + \frac{243}{8} units

<u>Skills required: HS Geo, Special Triangles</u>

Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

  • This states that if the side opposite the 30 degree angle is x, the side opposite the 60 degree angle is x*\sqrt3, and the side opposite the 90 degree angle is 2x.

AB is 9 units, and it is opposite the 90 degree angle. This means that 2x=9, x = \frac{9}{2} ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is \frac{9}{2} units. Segment BD (the height) is \frac{9}{2} * \sqrt3.

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

  • This states that if the side opposite the 45 degree angle is x, the other side opposite a 45 degree angle is also x, but the hypotenuse (side opposite the right (90 degree) angle) is \sqrt{2}*x.

BD is \frac{9}{2} * \sqrt3, which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is \frac{9}{2} * \sqrt6.

4) Area is \frac{1}{2}*b*h, the base (b) is AC (which is \frac{9}{2}+\frac{9}{2}*\sqrt3), the height is BD (\frac{9}{2}*\sqrt3). When multiple you will get \frac{81}{4}*\sqrt3 + \frac{243}{4}, then this multiplied by 1/2 is

\frac{81}{8}*\sqrt3 + \frac{243}{8} <--> this is the area!

5) Perimeter is just the sum of all side: 9 + \frac{9}{2} + \frac{9}{2} * \sqrt6 = \frac{27}{2} + \frac{9}{2} * \sqrt6 unit

6 0
3 years ago
George and Lea each toss a tetrahedral die with faces numbered 1 through 4, and then multiply the two resulting numbers. If the
Anna007 [38]

Answer:

I think the total number of combinations of 3 from 6 = 6C3 = 20

All possible combinations of 3 which have a product divisible by 3 must contain either a 3 or a 6.

So the number not divisible must be 3 combinations from the number 1, 2, 4, and 5.= which is 4

So the required probability is 20-4 ? 20 = 16/20 = 0.8 Answer

Hope this help you! :)

6 0
2 years ago
44) The difference of two numbers is 76. The second number is 20% of the first number. What are the numbers?
Nina [5.8K]

Answer:

C

Step-by-step explanation:

Not A b/c the difference b/w 85 and 17 is not 76

Not D b/c the difference b/w 97 and 17 is not 76

Not B b/c 16 is not 20% of 92

By the process of elimination the answer is C

3 0
3 years ago
The radius of a circle is 19 cm. Find its area in terms of pi​
yan [13]

Answer:

38π cm

Step-by-step explanation:

The area of a circle of radius r is A = 2πr.

If the radius is 19 cm, then the area is A = 2π(19 cm), or 38π cm.

3 0
3 years ago
Find the total surface area of this cylinder . Give your answer to 1 decimal place 7cm 15 cm
Leto [7]

Answer:

Step-by-step explanation:

r = 7 cm

h = 15cm

pi = 3.14

Top and bottom (These questions drive you crazy when you don't know if there is both a top and bottom).

Area = 2* pi *r^2 = 2 * 3.14 * 7^2

Area = 2 * 3.14 * 49

Area =                                                        307.72  Don't round this.

Cylinder body

Cylinder body = Circumference * h = 2*pi * r * h

Cylinder body = 2* 3.14 * 7 * 15

Cylinder body =                                      <u> 659.4</u>

<u />

Total =                                                      967.12

Rounded        967.1     Answer

3 0
2 years ago
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