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3 years ago

If each dimension of the rectangular prism is doubled, how will its total surface area change?

Mathematics

2 answers:

kow [346]3 years ago

7 0

Answer:

It increases by 4

Step-by-step explanation:

Troyanec [42]3 years ago

3 0

Answer:

In a rectangular prism, all six surfaces are rectangles as shown ... to length X width, ( l⋅w , the surface area of the sides can be calculated by ... Total surface Area = A=2(l+w)h+2lw=2(lh+wh+lw). If we double all three dimensions we get: ... Doubling the dimensions makes the surface area 4 times the original ...

1 answer

Step-by-step explanation:

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How do you solve this problem? what are the steps? what to do?

adell [148]

Micho tito sancho peludo negro y cabezon

3 0

3 years ago

Triangle A has side lengths of 10 units, 24, units, and 26 units. Ryan cut out 2 copies of triangle A and joined them together t

sergejj [24]

Answer:

Perimeter of Rectangle will be 68 units.

Step-by-step explanation:

Given:

Length of side 1 = 10 units

Length of side 2 = 24 units

Length of side 3 = 26 units

Now we will check whether the triangle A is right angle triangle or not;

$(Length of side 3)^{2} = 26^2 = 676$

$(Length of side 2)^{2} = 24^2 = 576$

$(Length of side 1)^{2} = 10^2 = 100$

Now From above we can see that;

676 = 576 + 100

Hence we can say ;

$(Length of side 3)^{2} = ](Length of side 2)^{2} + (Length of side 1)^{2}$

By Converse of Pythagoras theorem.

"Hence When the square of the length of the hypotenuse is equal to sum of the square of other two sides we can say that triangle is a right angled triangle."

Now Given:

Ryan cut out 2 copies of triangle A and joined them together to form a rectangle.

So we can say that the hypotenuse side of the triangle will become diagonal of the rectangle and other two side will become length and width.

Now;

Length of rectangle = 24 units

Width of rectangle = 10 units.

We need to find the perimeter of rectangle.

Now Perimeter of rectangle is 2 times sum of Length and width.

framing in equation form we get;

Perimeter of rectangle = $2(l+w) = 2\times (24+10) = 2\times 34 =68 units.$

Hence Perimeter of Rectangle will 68 units.

4 0

3 years ago

From the top of a vertical tower, 331 feet above the surface of the earth, the angle of depression to a doghouse is 28 degrees 8

Elena L [17]

Answer:

619.13 feet

Step-by-step explanation:

Please find the attachment.

Let x represent the distance between doghouse to the foot of the tower.

We have been given that from the top of a vertical tower, 331 feet above the surface of the earth, the angle of depression to a doghouse is 28 degrees 8'. We are asked to find the distance between doghouse to the foot of the tower.

First of all, we will convert our given angle into degrees as it is given in degrees and minutes.

We will divide 8 by 60 to convert 8 minutes into degrees as:

$\frac{8}{60}=0.13333$

The doghouse, tower and angle of depression forms a right triangle with respect to ground, where, 331 feet is opposite side and x is adjacent side to angle 28.13 degrees.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(28.13^{\circ})=\frac{331}{x}$

$x=\frac{331}{\text{tan}(28.13^{\circ})}$

$x=\frac{331}{0.534623339864}$

$x=619.12747783$

Upon rounding to nearest hundredth, we will get:

$x\approx 619.13$

Therefore, the doghouse is 619.13 feet far from the foot of the tower.

6 0

3 years ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$