Ask question

Ask question

All categories

3 years ago

15

Madeleine can type 3 pages in one hour. How many pages will it take her to type a 123- page report?

2 answers:

Maurinko [17]3 years ago

4 0

It would be 41 because 123/3 =41

romanna [79]3 years ago

3 0

The answer is 41 Hope i helped

You might be interested in

Select all equations that are equivalent to 5x + 6/2= 3-(4x +12)

Savatey [412]

Answer:

- 4/3

Step-by-step explanation:

6 0

3 years ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

Please help me I’m crying right now

Semenov [28]

Answer:

24ft²

Step-by-step explanation:

Dude. Go back and relearn the concept man. This is the third time you've been asking the same subject.

Area of triangle = ½BH = ½(6)(8) = 24

5 0

3 years ago

Read 2 more answers

John has 6 boxes of apples each box holds 12 apples. If 4 of the boxes r full and 2 r half full how many apples does John have??

olga55 [171]

Each box holds 12 apples
He has 6 boxes : 4 are full, 2 are half full

4 with 12, 2 with half of 12 (6)

12*4 + (12/2 * 2)
48 + 6*2
48+12
60

3 0

3 years ago

In 9.3 x 10-8 the exponent is a negative number. Which of these describes the value of a number in scientific notation that incl

WARRIOR [948]

Answer:

0.000000093

Step-by-step explanation:

Theres seven zeros after the decimal

6 0

3 years ago