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3 years ago

Find x. I need help please

Mathematics

1 answer:

Misha Larkins [42]3 years ago

3 0

Answer:

$x = 4 \sqrt{3}$

Step-by-step explanation:

By geometric mean theorem and Pythagoras theorem:

${x}^{2} = { (\sqrt{8 \times 4} )}^{2} + {4}^{2} \\ \\ {x}^{2} = { (\sqrt{32} )}^{2} + {4}^{2} \\ \\ {x}^{2} = 32 + 16 \\ \\ {x}^{2} = 48 \\ \\ x = \sqrt{48} \\ \\ x = 4 \sqrt{3}$

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Find the volume of the composite space figure to the nearest whole number.

Romashka [77]

Answer:

d. 944 mm^3

Step-by-step explanation:

The area of a circle is given by ...

A = πr² . . . . . where r is the radius, half the diameter

The area of a circle with diameter 9 mm is ...

A = π(4.5 mm)² = 20.25π mm²

The area of the semi-circular end of the prism is half this value, or ...

semicircle area = (1/2)(20.25π mm²) = 10.125π mm² ≈ 31.809 mm²

The area of the rectangular portion of the end of the prism is the product of its width and height:

A = wh = (9 mm)(6 mm) = 54 mm²

Then the base area of the prism is ...

base area = rectangle area + semicircle area

= (54 mm²) +(31.809 mm²) = 85.809 mm²

This base area multiplied by the 11 mm length of the prism gives its volume:

V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³

The volume of the composite figure is about 944 mm³.

7 0

3 years ago

HELP PLEASE! Thanks :)

Alex Ar [27]

Pi. I don't know what the square root is doing there because it has no number under it.

7 0

3 years ago

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What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

2 years ago

I NEED HELP ON MATH PLS

kicyunya [14]

Answer:

5/2 or 2½ or 2.5

Step-by-step explanation:

20/8 = 2.5

10/4 = 2.5

7 0

3 years ago

Two objects are moving along separate linear paths where each path is described by position, d, and time, t. The variable d is m

Maru [420]

I am not sure about this but here goes nothing: d=2.5t+2.2 is very familiar to y=mx+b y=d m=2.5 x=t b=2.2 to find a new quasion we substitute d and t into place wich equals 1=2.5(0)+b simplification and you get b=1 so your answer is d=2.5t+1

8 0

3 years ago

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