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3 years ago

Find the surface area of the regular pyramid

Mathematics

1 answer:

ANEK [815]3 years ago

3 0

Answer:

The general formula for the total surface area of a regular pyramid is T. S. A. =12pl+B where p represents the perimeter of the base, l the slant height and B the area of the base.

Step-by-step explanation:

To find the surface area of a pyramid, start by multiplying the perimeter of the pyramid by its slant height. Then, divide that number by 2. Finally, add the number you get to the area of the pyramid's base to find the surface area.

For example, If you are finding the surface area of a hexagonal pyramid, and you know that the length of one edge of the base is 4 cm, you would calculate {\displaystyle 4\times 6=24}4\times 6=24 to find the perimeter of the base, since a hexagon has six edges, or sides. Thus, the perimeter of the base is 24 cm, so your surface area formula will look like this: {\displaystyle SA={\frac {24\times h}{2}}+B}SA={\frac {24\times h}{2}}+B

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joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces.How many fluid ounces of water does he

olga nikolaevna [1]

1 cup = 8 fluid oz

8 × 8 = 64

So Joshua drinks 64 fluid ounces a day

Hope this helped. Have a great day!

5 0

3 years ago

Read 2 more answers

Determine the explicit formula in the sequence 11, 14, 19, 26, 35

slamgirl [31]

Answer:

Pattern is you add odd numbers, as in 1, 3, 5, 7, 9, etc.

Step-by-step explanation:

11 + 3 = 14

14 + 5 = 19

19 + 7 = 26

26 + 9 = 35

hope this helps

3 0

3 years ago

the base of the founten is rectangular . its dimention 1 2/3 feet by 2 2/3 feet . what is the area of the base of the founten

Montano1993 [528]

The area of a rectangle is calculated by multiplying the length of the rectangle and the width of the rectangle. In this case, the length (the longer side) is 2 2/3 feet while the width (shorter side) is 1 2/3 feet. To multiply fraction, first convert mixed numbers into improper fractions:

2 2/3 = 8/3
1 2/3 = 5/3
Multiplying the two fractions yield:
8/3 x 5/3 = 40/9 ft2

The final answer is 40/9 ft2 or 4 4/9 ft2.

3 0

3 years ago

Please help!! Write a matrix representing the system of equations

frozen [14]

Answer:

$(4, -1, 3)$

Step-by-step explanation:

We have the system of equations:

$\left\{ \begin{array}{ll} x+2y+z =5 \\ 2x-y+2z=15\\3x+y-z=8 \end{array} \right.$

We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:

$\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}$

Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.

In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:

$\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}$

Where the (x, y, z) is our solution set.

Reducing:

With our system, we will have the following matrix:

$\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}$

What we should begin by doing is too see how we can change each row to the reduced-form.

Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:

$\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}$

Now, we can multiply R₂ by -1/5. This yields:

$\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}$

From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:

$\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}$

We can eliminate the -5 in R₃ by adding 5(R₂). This yields:

$\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}$

We can now reduce R₃ by multiply it by -1/4:

$\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}$

Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:

$\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}$

And finally, we can eliminate the second 1 by adding -(R₃):

$\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}$

Therefore, our solution set is $(4, -1, 3)$

And we're done!

3 0

3 years ago

Ben sells homemade cards at a craft fair. He wants to earn more than $50 at the fair. He sells his cards for $2 and he has alrea

Kryger [21]

Answer:

He must sell 8 cards to reach the minimum goal.

Step-by-step explanation:

Giving the following information:

He wants to earn more than $50 at the fair.

He sells his cards for $2 and he has already earned $36.

First, we need to calculate the money required to reach the minimum goal:

51 - 36= $15

Now, we write the inequality:

2*x >15

x= number of cards sold.

x>15/2

x> 7.5

He must sell 8 cards to reach the minimum goal.

7 0

3 years ago