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3 years ago

Please help me answer this with the correct answer :)

Mathematics

1 answer:

BartSMP [9]3 years ago

7 0

Pretty sure is 63 degrees since the one next to it is exactly the same and its 63 degrees

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These cones are similar. find the volume of the smaller cone. round to the nearest tenth.

Kamila [148]

Answer:

Volume of the smaller cone = 8.34 cm³

Step-by-step explanation:

"If two figures are similar, their dimensions will be proportional.

Following this rule,

Ratio of the dimensions of two cones = $\frac{\text{Radius of the large cone}}{\text{Radius of the small cone}}$

= $\frac{r_2}{r_1}$

= $\frac{5}{2}$

= 2.5

Similarly, "ratio of the volumes of two similar figures is cube of the dimensional ratio".

Ratio of the volumes = (ratio of the dimensions)³

$\frac{V_1}{V_2}=(2.5)^3$

$\frac{131}{V_2}=15.625$

$V_2=\frac{131}{15.625}$

= 8.384 cm³

≈ 8.4 cm³

Therefore, volume of the smaller cone is 8.4 cm³.

8 0

3 years ago

Which of the following equations represents a line that is perpendicular to

Andreyy89

Answer:

$\large\boxed{y=\dfrac{1}{2}x}$

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================$

$\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x$

8 0

3 years ago

an ellipse has a center at the origin , a vertex along the major axis at (13,0), and a focus at (12,0). What is the equation of

-BARSIC- [3]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Center = (0, 0)

Vertex = (13, 0)

Focus = (12, 0)

Process

From the data we know that it is a horizontal ellipse.

1.- Calculate "a", the distance from the center to the vertex.

a = 13

2.- Calculate "c", the distance from the center to the focus

c = 12

3.- Calculate b

Use the Pythagorean theorem to find it

a² = b² + c²

-Solve for b

b² = a² - c²

-Substitution

b² = 13² - 12²

-Simplification

b² = 169 - 144

b² = 25

b = 5

4.- Find the equation of the ellipse

$\frac{x^{2} }{13^{2}} + \frac{y^{2}}{5^{2}} = 1$ or $\frac{x^{2} }{169} + \frac{y^{2}}{25} = 1$

7 0

3 years ago

Use logarithms to solve each equation 2x9/8=111

Illusion [34]

<span>We have this equation:
</span>
$2x^{\frac{9}{8}} = 111$

and we need to find the value of x.

First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:

$x^{\frac{9}{8}}=\frac{111}{2}$

Next step we must do is to apply <span>logarithms:
</span>
$logx^{\frac{9}{8}} = log(\frac{111}{2})$

Next, we have to apply identities and then to solve the equation:

$\frac{9}{8}logx = log(\frac{111}{2})$
$logx = \frac{8}{9}log(\frac{111}{2})$
$logx = 1.5504$
$10^{logx} = 10^{1.5504}$

Finally, we have the value of x which was our goal. This is the answer for the question above:

$x= 35.5140$

7 0

3 years ago

A horse has a water barrel in which 3/10 of a gallon is drank out of it every day. How many days will it take the horse to drink

Troyanec [42]

Answer:

140 days

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers