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3 years ago

A cylinder with a 2 centimeter diameter is drilled through the triangular prism shown on the left find the volume of the prism

Mathematics

1 answer:

saw5 [17]3 years ago

3 0

Answer:

The volume of a prism on its own = 248.5cm^3

The volume of a cylinder = 87.92cm^3

Step-by-step explanation:

The volume does not change for the prism as the hole was drilled.

We can show the drilled space with v(l) and (p) for prism V

v(l) 248.5p - 87.92p + 87.92p

= 248.5p

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fiasKO [112]

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4 years ago

A triangle has two sides measuring 16 and 21. The included angle is 116°. What is the length of the side opposite the 116° angle

Crank

Answer:

Length of the side opposite to angle $116^{\circ}$ is 31.49

Step-by-step explanation:

Included angle can be defined as the angle in between two sides of the triangle.

So angle $116^{\circ}$ is in between sides 16 and 21.

Refer to the attachment for triangle diagram.

To find the length of opposite side, use cosine rule as follows

$a^{2}=b^{2}+c^{2}-2\:b\:c\cos\left(A\right)$

From the diagram, $b = 21,c = 16,\angle A=116^{\circ}$

Substituting the values in the formula,

$a^{2}=\left(21\right)^{2}+\left(16\right)^{2}-2\left(21\right)\left(16\right)\cos\left(116\right)$

Simplifying,

$a^{2}=441+256-225792\left(-0.44\right)$

$a^{2}=991.59$

Taking square root on both sides,

$\sqrt{a^{2}}=\sqrt{991.59}$

$a=31.49$

Therefore length of third side is 31.49

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3 years ago

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Sedbober [7]

Functions can be used to model real world situations.

<em>(60,10) is a possible solution because the input and output are feasible.</em>

From the question, we understand that:

$x = 60$ --- i.e 60 people donated

$f(x) = 10$ ---- i.e. 10 families received the clothes from the 60 people

This means that 10 families received at least 60 clothes from the 60 people that donated.

The above illustration can happen.

<em>Hence, (60,10) is a possible solution.</em>