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3 years ago

A rectangular prism with a volume of 45 cubic centimeters and a height of 3 cm has a base with an area of

Mathematics

1 answer:

olga55 [171]3 years ago

3 0

Answer:

Area: 15cm^2

Base: 5cm

Step-by-step explanation:

The volume of a Rectangular Prism is given as:

V= wlh

Where W = Base

L = Length

H= Height

From the question:

The Volume V = 45cm^3

The Height H = 3

But, Area = Length * Width

Therefore :

Volume V = Area * Height

45 = A * 3

A = 45/3

A= 15cm^2

Solving for Base:

Area = height * Base

15 = 3 * Base

Base = 15/3

Base = 5cm

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Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

No one answer this I’ll mark you as 0

Dennis_Churaev [7]

Answer:

bjdhadvd

Step-by-step explanation:

bhcxg vyogu fbgrdg zfyjvg hbv daihcgdj

5 0

3 years ago

9x−2(4x−3)<5x+12−6x<br> please answer quick thanks :)

Kitty [74]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: x < 3

Interval Notation: (-∞, 3)

6 0

3 years ago

NEED HELP ASAPPPPPPPPP

Nookie1986 [14]

Answer:

A = 57°

B = 19°

C = 104°

Step-by-step explanation:

We have a triangle with 3 angles:

A, B, and C.

We know that:

"Angle A is 3 times larger than angle B"

We can write this as:

A = 3*B

"Angle C was 10° less than 6 times angle B"

This can be written as:

C = 6*B - 10°

And we also know that the sum of all interior angles of a triangle is 180°

Then we also have the equation:

A + B + C = 180°

So we have a system of 3 equations:

A = 3*B

C = 6*B - 10°

A + B + C = 180°

To solve this, the first step is to isolate one of the variables in one of the equations.

We can see that A is already isolated in the first one, so we can skip that step.

Now we need to replace A in the other equations, to get:

C = 6*B - 10°

(3*B) + B + C = 180°

Now we have a system of two equations.

Let's do the same procedure, we can see that C is isolated in the top equation, so we can just replace that in the other equation to get:

3*B + B + (6*B - 10°) = 180°

Now we can solve this for angle B

4*B + 6*B - 10° = 180°

10*B - 10° = 180°

10*B = 180° + 10° = 190°

B = 190°/10 = 19°

Now that we know the measure of angle B, we can input this in the equations:

A = 3*B

C = 6*B - 10°

To find the measures of the other two angles:

A = 3*19° = 57°

C = 6*19° - 10° = 104°

5 0

3 years ago

Question is below....

Kamila [148]

Answer:

Step-by-step explanation:

For window, area 3×2

For wall, area=20×16

=320

Area of wall withot window=320-6

=316

4 0

3 years ago