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3 years ago

Find the length of side x in simplest radical form with a rational denominator.

Mathematics

1 answer:

kogti [31]3 years ago

6 0

Answer:

since it is Right angled isosceles triangle it's base side are equal

by using Pythagoras law

x²+x²=1²

2x²=1

x=√{1/2}or 0.707 or 0.71

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The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol

Elina [12.6K]

Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is $\frac{7}{10}$

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is $\frac{343}{1,000}$

Part c) The volume of the smaller pyramid is $4,116\ m^{3}$

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid

$z=\frac{x}{y}$

substitute the values

$z=\frac{21}{30}$

Simplify

$z=\frac{7}{10}$ -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

substitute

$\frac{7}{10}^{3}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{343}{1,000}$ -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

$(\frac{7}{10})^{3}=\frac{x}{12,000}$

$x=\frac{343}{1,000}(12,000)=4,116\ m^{3}$

8 0

3 years ago

Help me plz :((((((

Softa [21]

Answer:

160 degrees

Step-by-step explanation:

8 0

2 years ago

The La Jolla tide pools are 67.5 miles from the SLMS. A map shows that 2 inches = 15 miles. What distance is SLMS from the tide

Gwar [14]

Answer:

Step-by-step explanation:

because you have to divide by 15's

5 0

3 years ago

Read 2 more answers

(20 points)

chubhunter [2.5K]

V = (1/4)(π* d² * h)
V = (1/4)(π * 10² * 12) 
V = (1/4)(1200π) 
V = 300π 
[ V ≈ 942 cubic units . . . . . to 3 s.f. ] 
V ≈ 942 cubic units

8 0

3 years ago

Read 2 more answers

Use logarithmic differentiation to find dy/dx

liq [111]

Answer:

dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

Step-by-step explanation:

y = (x^2 - 3)^sinx

ln y = ln (x^2 - 3)^sinx

ln y = sin x * ln (x^2 - 3)

1/y * dy/dx = sin x * {1 / (x^2 - 3)} * 2x + ln(x^2 - 3) * cos x

1/y dy/dx = 2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)

dy/dx = [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)] * y

dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

7 0

3 years ago