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3 years ago

The three sides of a triangle are 4cm, 6cm and 8cm.

Mathematics

1 answer:

yarga [219]3 years ago

6 0

Answer:

In bold below.

Step-by-step explanation:

(a) The largest angle is opposite the largest side.

So by the Cosine Rule:

8^2 = 4^2 + 6^2 - 2*4*6 cos x

cos x = (8^2 - 4^2 - 6^2) / (-2*4* 6)

= -0.25.

x = 104.48 degrees.

(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48

= 11.62

= 3 √15.

Area = 1/2 * altitude * base

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.

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Find the diameter(s) of circle O.

schepotkina [342]

Answer:

The diameter of the circle O is <em>12 units</em>

Step-by-step explanation:

There is no data in the image provided. To better help you, I'm assuming we have an arbitrary value of

$BC=6\sqrt{2}$

and the triangle B0C is right

<u>Relations in the Circle</u>

The diameter (D) is twice the radius (r) and the radius is the distance measured from the center of the circle to any point of the circumference.

Since the triangle B0C has a right angle, BD is the hypotenuse and 0B=0C=r

Applying Pythagoras's theorem:

$BC^2=r^2+r^2=2r^2$

Thus we have

$2r^2=(6\sqrt{2})^2$

$2r^2=72$

$r^2=36$

$r=6$

The diameter of the circle O is D=2(6) = 12 units

5 0

3 years ago

Sum of -6x^2-1 and x+9

Bumek [7]

Answer:

-6x^2+x+8

Step-by-step explanation:

9+-1=8

3 0

2 years ago

Read 2 more answers

Easy Cooking is a cooking supply company. Last year, the company sold a total of 5,340 ovens. This year, they sold 7,743 ovens.

jenyasd209 [6]

Answer:

45%

Step-by-step explanation:

Given data

Last year, the company sold a total of 5,340 ovens

This year, they sold 7,743 ovens

Percent increase= final-initial/initial*100

substitute

Percent increase= 7,743-5,340/5,340*100

Percent increase= 2403/5,340*100

Percent increase=0.45*100

Percent increase=45%

Hence the increase is 45%

7 0

2 years ago

The price of a gallon of milk was $2.65. The price rose y dollars after the last hurricane. Then the price dropped $0.15 and lat

My name is Ann [436]

The expression that represents the current price of milk is y +2.55. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

5 0

2 years ago

When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and foun

Anestetic [448]

Answer:

The tree was 175 centimeters tall when Vlad moved into the house.

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

Step-by-step explanation:

The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:

$H(t) = H(0) + at$

In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.

He measured it once a year and found that it grew by 26 centimeters each year.

This means that $a = 26$

$H(t) = H(0) + 26t$

4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?

This means that when t = 4.5, H(t) = 292. We use this to find H(0).

$H(t) = H(0) + 26t$

$292 = H(0) + 26*4.5$

$H(0) = 292 - 26*4.5$

$H(0) = 175$

The tree was 175 centimeters tall when Vlad moved into the house.

How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

This is t for which H(t) = 357. So

$H(t) = H(0) + 26t$

$H(t) = 175 + 26t$

$357 = 175 + 26t$

$26t = 182$

$t = \frac{182}{26}$

$t = 7$

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

7 0

2 years ago