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3 years ago

13

1 Aling Sol wanted to redesign her old wooden box with a dimension of 20 cm

1 answer:

jekas [21]3 years ago

8 0

Answer:

400 cm² of stickers

Step-by-step explanation:

A wooden box has the shape of a rectangular prism.

To solve for the above question, we would be using the formula for the Surface Area of a rectangular prism to calculate how much stickers are required .

The formula for the surface area of a rectangular prism =

A=2(wl + hl + hw)

l = Length = 20cm

w = Width = 4cm

h = Height = 5m

Hence,

= 2 × (4 × 20 + 5 × 20 + 5 × 4)

=400 cm²

Therefore, 400cm² of stickers would be needed to cover the wooden box.

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Cam has 32 dollars. How many roses can he afford to buy?

Vlad [161]

Answer:

8 roses

Step-by-step explanation:

roses cost about 4 dollars, and 8 times 4=32

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

How do you convert 2.25 • 10^6 into standard form?

IRINA_888 [86]

Answer:

2,250,000

Step-by-step explanation:

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3 years ago

The total bill for drinks and a pizza for three people is $14.90 before tax. The group wants to leave a 15% tip on the cost of t

andreyandreev [35.5K]

Answer:

$2.24

Step-by-step explanation:

Since we are trying to find a percentage of something, we can multiply whatever we're trying to find a percentage from by 0.X where X is equal to the number of the percentage. So in this case it's 15%. We can multiply $14.90 by 0.15 and we get 2.23500. Since we cannot have 2.235 dollars, we must round up decimal places.

The tip would be 2 dollars and 24 cents. ($2.24).

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3 years ago

What is the volume of a rectangular solid that is 40 centimeters long, 10 centimeters wide, and 5 centimeters high?

Arturiano [62]

The formula for the volume of a rectangular solid is V = L*W*H

Multiply out the length, width and height given: 40*10*5 = 400*5 = 2000

The volume is 2,000 cubic centimeters

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4 years ago