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Lynna [10]
3 years ago
13

Please answer the question!

Mathematics
1 answer:
Airida [17]3 years ago
7 0

ANSWER

Area = 2\sqrt{3}  \:  {cm}^{2}

EXPLANATION

We need to use the Pythagoras Theorem to find the height of the triangle.

{a}^{2}  +  {b}^{2}  =  {c}^{2}

({2 \sqrt{3}) }^{2}  +  {b}^{2}  =  {4}^{2}

12 +  {b}^{2}  = 16

{b}^{2}  = 16 - 12

{b}^{2}  = 4

Take positive square root to get;

b =  \sqrt{4}  = 2

Area =½bh

Area =  \frac{1}{2}  \times  2\sqrt{3}  \times 2

Area = 2\sqrt{3}  \:  {cm}^{2}

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Subtract - 8 from 18.<br> The answer is
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In rectangle MNOP, MO = 4x - 10 and NP = 2x + 4.<br> What is the length of a diagonal?
slega [8]

Answer:

18

Step-by-step explanation:

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4x - 10 = 2x+4

4x-2x = 4 + 10

2x = 14

x = 14/2

x = 7

SInce MO and NP are the diagonal

Length of diagonal = 4x- 10

Length of diagonal = 4(7) - 10

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hence the required length is 18

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Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant
Viktor [21]

Answer:

Therefore k= \frac{ln2 }{18}, A=184

Step-by-step explanation:

Given function is

T(t)=230 -e^{-kt}

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

138=230 -Ae^{-k\times 18}

\Rightarrow  -Ae^{-18k}=138-230

\Rightarrow  Ae^{-18k}=92 .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

184=230-Ae^{-k\times 36}

\Rightarrow Ae^{-36k}=230-184

\Rightarrow Ae^{-36k}=46.......(2)

Dividing (2) by (1)

\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}

\Rightarrow e^{-18k}=\frac{46}{92}

Taking ln both sides

ln e^{-18k}=ln\frac{46}{92}

\Rightarrow -18k =ln (\frac12)

\Rightarrow -18k= ln1-ln2

\Rightarrow k= \frac{ln2 }{18}

Putting the value k in equation (1)

Ae^{-18\frac{ln2}{18}}=92

\Rightarrow A e^{ln2^{-1}}=92

\Rightarrow A.2^{-1}=92

\Rightarrow \frac{A}{2}=92

\Rightarrow A= 92 \times 2

⇒A= 184.

Therefore k= \frac{ln2 }{18}, A=184

7 0
3 years ago
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