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3 years ago

This question is worth 50 points, make sure to provide ALL calculations without using a calculator, though.

Mathematics

1 answer:

Fed [463]3 years ago

7 0

Answer:

Step-by-step explanation:

Use the formula for the volume of a cone:

V = (1/3)(area of base / round opening)(height of cone)

In this case we're interested in the following:

(1/3)(area of base / round opening)(height of cone) ≤ 535 cm³

First, mult. both sides by 3 to elim. the fraction 1/3:

(area of base)(height) ≤ 1605 cm³

Since the height is 8 cm, we now have:

(area of base) / (8 cm) = 1605 cm³, or

(area of base) = (1605 cm³) · (8 cm) = 200.625 cm²

The formula for the area of a circle is A = 3.14·r², where r is the radius.

If the area of the base is 200.625 cm², as found above, this equals 3.14r², and so

r² = (200.625 cm²) / (3.14) = 63.89 cm²

Then the radius must be +√63.89 cm, or 8 cm

and the diameter must be 2r = 2(8 cm) = 16 cm. This would be the largest width of the container.

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The length of a sticky note measures 77 millimeters.express this length in meters explain your thinking include an equation with

Eva8 [605]

The length of the sticky notes is $\bf77\times{10^{-3}}{\text{meter}}$ .

Further explanation:

Given:

The length of sticky notes is measured as 77 millimeters.

Calculation:

Since 1 meter contains 1000 mm, it can be written as follows:

$\begin{aligned}1000{\text{mm}}&\to{\text{1meter}}\\{\text{1mm}}&\to\frac{{\text{1}}}{{1000}}{\text{meter}}\\{\text{1mm}}&\to{10^{-3}}{\text{meter}}\\x\,{\text{mm}}&\to x \times {10^{-3}}{\text{meter}} \\ \end{aligned}$

Now, substitute 77 for x in above expression to obtain the length of sticky notes in meter as follows:

$77\,{\text{mm}}\to77\times{10^{-3}}{\text{meter}}$

Thus, the length of the sticky notes is $\bf77\times{10^{-3}}{\text{meter}}$ .

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Answer Details :

Grade: Middle School

Subject: Mathematics

Chapter: linear equation

Keywords:

Millimeters, meter, equation, sticky notes, measurements, length, function, substitution, Mexico, site, direct substitution, elimination, graph, middle term factorization, scientific notation.

3 0

3 years ago

Read 2 more answers

If the length of AO is double the length of CO, the length of BO is?

andreev551 [17]

BO is double that of DO. In other words, BO is two times longer than DO. The answer is choice B

For example, if DO were 3 units long, then BO would be 6 units long (2*3 = 6). This works because the triangles DCO and BAO are similar triangles. The corresponding sides are in the same ratio or proportion to one another. The larger triangle (BAO) has sides that are twice as long as the smaller triangle's (DCO) corresponding sides.

Side note: we can prove the triangles to be similar using the AA (angle angle) similarity theorem. The first pair of angles are the vertical angles DOC and BOA which are congruent to each other.The second pair is CDB and ABD which are congruent by the alternate interior angle theorem. Check out the attached image for a visual.