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3 years ago

What is the measure of AC

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

6 0

Angle ABC is an inscribed angle so would be half of the arc.
So, 4x-5.5=1/2(5x+25)
4x-5.5=5/2x+25/2
4x-5.5=2.5x+12.5
4x-2.5x=12.5+5.5
1.5x=18
x=12

So angle ABC=4(12)-5.5=48-5.5=42.5
Arc AC=5(12)+25=60+25=85

Check: 42.5(2)=85

Answer: Arc AC is 85

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Find the volume of the composite figure.First, find the volume of the cylinder.Use 3.14 for it.CylinderVolume = [?] cm9 cm9 cmCu

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Solution

- The question gives us a composite figure made up of a cylinder and a cube.

- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.

- The formulas needed for this calculation are:

$\begin{gathered} Volume\text{ of Cylinder}=\pi\times r^2\times h \\ where, \\ r=radius\text{ of the cylinder} \\ h=height\text{ of the cylinder} \\ \\ Volume\text{ of Cube}=l^3 \\ where, \\ l=dimension\text{ of the cube} \\ \\ Volume\text{ of Composite figure}=Volume\text{ of Cylinder }+Volume\text{ of Cube} \\ \end{gathered}$

- With the information above, we can proceed to solve the question

Volume of the Cylinder:

$\begin{gathered} V=\pi\times r^2\times h \\ r=\frac{6}{2}=3\text{ \lparen Since 6cm is the diameter of the cylinder\rparen} \\ h=4 \\ \\ \therefore V=\pi\times3^2\times4 \\ \\ V=36\pi cm^3 \end{gathered}$

Volume of Cube:

$\begin{gathered} V=l^3 \\ l=9 \\ \therefore V=9^3=729cm^3 \end{gathered}$

Volume of Composite Figure:

$\begin{gathered} V=36\pi+729 \\ use\text{ }\pi=3.14 \\ \\ V=36\left(3.14\right)+729 \\ \\ V=842.04cm^3 \end{gathered}$

Final Answer

The volume of the composite shape is 842.04 cm³

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1 year ago

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3 years ago

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4 years ago

Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make it a 12% detergent solution. which equation c

Sliva [168]

The problem is about adding water to detergent solution to make a detergent solution.

In the problem g is taken for the number of gallons of water.

So, we can rephrase the given problem in simple words as

g gallons of water is added to 11 gallons of 18% detergent solution to get 12% detergent solution.

Let us write it in form of an equation,

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