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3 years ago

Can someone please help me? Thanks

Mathematics

1 answer:

Daniel [21]3 years ago

6 0

Answer:

693 sq. m.

Step-by-step explanation:

The figure consists of a triangular prism (Bottom Part) and a Triangular Pyramid (Top Part). We will find the volume of each and add it up to get volume of total figure.

1. Volume of Triangular Prism = Area of Triangular Base * Height

Area of Triangular Base = (1/2)*base*height

Given that the triangle is a right triangle, we find the unknown side by using Pythagorean Theorem, which tells us:

Leg^2 + Another Leg^2 = Hypotenuse^2

8.8^2 + Another Leg^2 = 13.7^2

77.44+ Another Leg^2 = 187.69

Another Leg (unknown side, or the base of the triangle) = Sqrt(187.69-77.44) = 10.5 (this is base of triangle)

So, we have:

Area of Triangular Base = $\frac{1}{2}*10.5*8.8=46.2$

Thus,

Volume of Triangular Prism = 46.2 * 10(given) = 462 sq.m.

2. Volume of Triangular Pyramid = (1/3) * area of triangular base * height

Here, area of triangular pyramid is 46.2 (already found)

the height of the pyramid is 25 - 10 = 15

SO, we have:

Volume of Triangular Pyramid = $\frac{1}{3}*46.2*15=231$ sq. m.

Now we sum them up and get total volume of the figure:

Total Volume of Figure = 462+ 231 = 693 sq. m.

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a carpenter is cutting dowels from a piece of wood that is 10 inches long. how many 1/2 dowels can the carpenter cut?

Tasya [4]

The wood is 10 inches and you're cutting it into 1/2 pieces, so divide 10 by 1/2, which is 20, The carpenter can cut 20 dowels.

3 0

3 years ago

Read 2 more answers

And 1. if a person bought 1 share of google stock within the last year, what is the probability that the stock on that day close

ElenaW [278]

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The graph would be bell shaped. So the odds are 50/50

6 0

3 years ago

Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate,

Dmitry [639]

Answer:

Correct answer: at 2 p.m. the population was 10,000

at 3 p.m. the population was 50,000

Step-by-step explanation:

At 1 p.m. population was 2,000

At 2 p.m. or after first hour, the population of bacteria increases

in this way 2,000 · k

At 3 p.m. or after second hour, the population of bacteria increases

2,000 · k²

At 4 p.m. or after third hour, the population of bacteria increases 2,000 · k³

2,000 · k³ = 250,000 => k³ = 250,000 / 2,000 = 125

k = ∛125 = 5 => k = 5

At 2 p.m. or after first hour, the population of bacteria was 2,000 · 5 = 10,000

At 3 p.m. or after second hour, the population of bacteria was 2,000 · 5² =

= 2,000 · 25 = 50,000

God is with you!!!

6 0

3 years ago

30 points! please help!

stiks02 [169]

Answer:

Therefore

15.

$25c^{2}-9$

16.

$(y+8)(y+1)$

17.

$(x-3y)(x-7y)$

Step-by-step explanation:

15.

$(5c^{2} +3)(5c^{2}-3)$

Using the Identity (a + b)(a - b) = (a² - b²) we get

Consider here a = 5c and b = 3 then we will have

$((5c)^{2} -(3)^{2})=25c^{2}-9$ .....as required

16.

$y^{2}+9y+8$

Here Factorize 8 such that sum up to be 9

∴ 8 × 1 = 8 and 8 + 1 =9

$y^{2}+9y+8\\y^{2}+8y+y+8\\y(y+8)+1(y+8)\\(y+8)(y+1)$ ... as required

17.

$x^{2}-10xy+21y^{2}$

Here Factorize 21 such that sum up to be -10

∴ -3 × -7 = + 21 and -3 - 7 = - 10

$x^{2}-10xy+21y^{2}\\x^{2}-3xy-7xy+21y^{2}\\x(x-3y)-7y(x-3y)\\(x-3y)(x-7y)$ ........as required

Therefore

15.

$25c^{2}-9$

16.

$(y+8)(y+1)$

17.

$(x-3y)(x-7y)$

4 0

3 years ago

Read 2 more answers

natima [27]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.

The store keeps an inventory of 80 shovels, then

x+y+z=80

The store always buy twice as many spade shovels as square, so

x=2z

The total cost of all shovels is

16x+9.60y+12.80z=1,072

a) The system of three equations is

$\left\{\begin{array}{l}x+y+z=80\\ \\x=2z\\ \\16x+9.60y+12.80z=1,072\end{array}\right.$

b) In matrix form this is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}80\\0\\1,072\end{array}\right)$

c) The determinant is

$\left\|\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right\|=0-32+9.60-0+19.20-12.80=-16$

d) Find three determinants:

$\left\|\begin{array}{ccc}80&1&1\\ 0&0&-2\\ 1,072&9.60&12.80\end{array}\right\|=0-2,144+0-0+1,536-0=-608$

$\left\|\begin{array}{ccc}1&80&1\\ 1&0&-2\\ 16&1,072&12.80\end{array}\right\|=0-2,560+1,072-0+2,144-1,024=-368$

$\left\|\begin{array}{ccc}1&1&80\\ 1&0&0\\ 16&9.60&1,072\end{array}\right\|=0+0+768-0-0-1,072=-304$

So,

$x=\dfrac{-608}{-16}=38\\ \\y=\dfrac{-368}{-16}=23\\ \\z=\dfrac{-304}{-16}=19$

e) If the store doubled all prices and inventory, then the new matrix is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 32&19.20&25.60\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}160\\0\\2,144\end{array}\right)$

7 0

3 years ago