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3 years ago

What is the angle, in radians, of arcsin(1/2)

1 answer:

6 0

$\frac{\pi}{6}$

When you are asked what is the sin of π/6, or 30 degrees, you would look at the special triangle (30-60-90) to see that sin, or opposite over hypotenuse, of π/6 is 1/2. Arcsin, or csc, will present you with the ratio, 1/2, and ask for the angle. It's essentially working the question backwards.

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There are 4 generations. Daughter, mother, grandma, and great-grandma. The daughter is 44 less than the grandma's age. The great

Snezhnost [94]

Answer:

Age of Grandma = 59 years.

Age of great Grandma = 81 years

Ages of Mother = 38 years

Age of Daughter = 15 years

Step-by-step explanation:

Given:

Total years they all lived = 193

We need to find the ages of all lady.

Solution:

Let the age of grandma be 'x'.

Now Given:

The daughter is 44 less than the grandma's age.

So we can say that;

Age of the Daughter = $x-44$

The great-grandma is 22 more than the grandma's age.

So we can say that;

Age of the great grandma = $x+22$

The mother is 80 less than twice the grandma's age.

So we can say that;

Age of the mother = $2x-80$

Now we can say that;

Total years they all lived is equal to sum of age of grandma, Age of the Daughter, Age of the great grandma, Age of the mother.

framing in equation form we get;

$x+x-44+x+22+2x-80=193\\\\5x-102=193$

Adding both side by 102 we get;

$5x-102+102=193+102\\\\5x= 295$

Dividing both side by 5 we get;

$\frac{5x}{5}=\frac{295}{5}\\\\x= 59\ years$

Hence Age of Grandma = 59 years.

Age of great Grandma = $x+22 =59+22 = 81\ years$

Ages of Mother = $2x-80= 2\times 59-80 = 38\ years$

Age of Daughter = $x-44=59-44=15\ years$

7 0

3 years ago

A construction crew must build 4 miles of road in one week. On Monday, they build 12 mile of road. On Tuesday, they build 13 mil

Julli [10]

$\frac{19}{6}$ many more miles of road are left to build .

<u>Step-by-step explanation:</u>

Here we have , A construction crew must build 4 miles of road in one week. On Monday, they build 1/2 mile of road. On Tuesday, they build 1/3 mile of road. We need to find that How many more miles of road are left to build . Let's find out:

On Monday, they build 1/2 mile of road.
On Tuesday, they build 1/3 mile of road.

Let Miles of road left to build is x So,

⇒ $\frac{1}{2} +\frac{1}{3} +x = 4$

⇒ $x = 4 - (\frac{1}{2} +\frac{1}{3})$

⇒ $x = 4 - (\frac{1(3)+1(2)}{6} )$

⇒ $x = 4 - (\frac{5}{6} )$

⇒ $x = (\frac{4(6)-5}{6} )$

⇒ $x = \frac{24-5}{6}$

⇒ $x = \frac{19}{6}$

Therefore, $\frac{19}{6}$ many more miles of road are left to build .

5 0

3 years ago

Read 2 more answers

Use the grouping method to factor x3 + x2 + 3x + 3

Alex

Answer:

8x +3

Step-by-step explanation:

Just collect the like terms, like terms have the same variable. So in this case, 2x, 3x, 3x all share the variable x, so we can add it together.

So when simplified:

2x +3x + 3x+ 3 = 8x +3

Hope this helped,

Cate

4 0

3 years ago

Read 2 more answers

The image of (6, 9) under a dilation is (4, 6).

Ad libitum [116K]

For this case we have the following ordered pairs:
(6, 9)
(4, 6)
The scale factor can be found in two different ways:
$k = 6/4 = 3/2 = 1.5

k = 9/6 = 3/2 = 1.5$
Therefore, the scale factor is given by:
$k = 1.5
$
Answer:
The scale factor of the dilation is 1.5

8 0

3 years ago

Read 2 more answers

What’s the radius of the circle

topjm [15]

Answer:

radius=2

Step-by-step explanation:

if the circumference=4pi and the formula is 2pir then r must be 2 and would look like this:

C = 2pir

C = 2pi2

C = 2*2pi

C = 4pi

6 0

3 years ago