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4 years ago

6 decimeters to millimeters?

Mathematics

2 answers:

____ [38]4 years ago

5 0

6 decimeters is equal to 600 millimeters

Likurg_2 [28]4 years ago

4 0

One decimeter is 100 times the size of a millimeter. so 6 decimeter is equal to 600 millimeters. hope that helped

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Work out the volume of this prism. Write your answer<br> a in cm?<br> 120cm<br> 30cm<br> 20 cm

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Step-by-step explanation:

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In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S

Scrat [10]

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a $\triangle RST$ , RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Using the cosine rule:

$cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ$

Now, let us use Sine rule to find other angles:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

$\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ$

$\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ$

Smallest angle is $\angle T$

Correct answer is option A. T

4 0

4 years ago