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2 years ago

Please help me with this #9

Mathematics

1 answer:

mel-nik [20]2 years ago

7 0

$\text{First term,} ~ a = 5\\\\\text{Common ratio,}~ r = \dfrac{10}5 = 2\\\\\text{Nth term} = ar^{n-1} = 5\cdot2^{n-1}\\\\\text{4th term } = 5\cdot 2^{4-1} = 5 \cdot 2^3 = 40\\\\\text{5th term} = 5 \cdot 2^{5-1} = 5 \cdot 2^4 = 80\\\\\text{Hence the next two terms are 40 and 80.}$

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Find the volume of the garden shed

Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

$\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}$

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

$\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}$

Therefore:

$\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}$

<h3><u>Volume of the garden shed</u></h3>

$\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}$

6 0

1 year ago

Read 2 more answers

Concider the graph of the polynomial function p(x)=(x-1)(x+2)(x+5)

yulyashka [42]

I need to see the horse??

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3 years ago

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Sophie [7]

N = 9

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more help:

Q = G

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P = F

H = R

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3 years ago

A kite is flying 20 ft off the ground. Its line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If neces

Kryger [21]

Answer:

The answer to your question is 25 ft

Step-by-step explanation:

Data

height = 20 ft

leg = 15 ft

length of the line = ?

To solve this problem use the Pythagorean theorem.

Height = short leg = b

leg = long leg = a

length of the line = hypotenuse = c

- Substitution

c² = (20)² + (15)²

-Simplification

c² = 400 + 225

c² = 625

-Result

c = $\sqrt{625}$

c = 25 ft

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3 years ago

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Answer:

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Step-by-step explanation:

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<em>Ex.</em> 9641 vs. 1946 9641 is larger.

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3 years ago