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3 years ago

Find two consecutive positive integers such the sum of their squares is 145

Mathematics

1 answer:

White raven [17]3 years ago

8 0

Answer:

8 and 9

Step-by-step explanation:

Let these two consecutive positive numbers be x and x + 1

so... x^2 + (x + 1)^2 = 145

x^2 + x^2 + 2x + 1 = 145

2x^2 + 2x + 1 = 145

2x^2 + 2x = 144

2*(x^2 + x) = 144

(x^2 + x) = 72

x^2 + x - 72 = 0

Use the Diamond method for factoring.

-72 = 9 * -8 and 9 + (-8) = 1

x^2 + x - 72 = (x - 8)*(x + 9) = 0

so x = 8 or x = -9, but x > 0 so only x = 8

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Suppose you are given a cube made of magnesium (mg) metal of edge length 2.15 cm. (a) calculate the number of mg atoms in the cu

SVETLANKA909090 [29]

solution:

a) To calculate the volume of cube of edge 1.0cm

Volume= (edge)³

=(100cm) ³

= 1cm³

To find the mass of MG atoms

Density = mass/volume

Mass of mg = 1.74g/cm³ x 1cm³

= 1.74g

To find the number of mg atoms,

Molar mass of mg = 24.31g

24.31g mg contain 6.022 x 10²³ atoms of mg

1.74g mg contain = 6.022 x 10²³mg atoms/24.31g mg x 1.74g mg

= 0.4310 x 10²³mg atoms

= 4.31 x 10²² mg atoms

B) to find the volume occupied by mg atoms

Total volume of cube = 1 cm³

Volume occupied by mg atoms

= 74% of 1cm³

=74/100 x 1cm³= 0.74cm³

To find the volume of 1 mg atom

4.31 x 10²² mg atoms occupy 0.74 cm³

1 atom will occupy 0.74cm³

1 atom will occupy = 0.74cm³/4.31 x 10²²mg atoms x 1mg atom

volume of 1 mg atom = 0.1716 x 10⁻²²cm²

Volume of 1 mg atom = 4/3 π³ in the form of sphere.

4/3πr³ = 0.1716 x 10⁻²²cm³

R³ = 0.1716 x 10⁻²²cm³x 4/3 x 7/22

R³ = 0.04095 x 10⁻²²cm³

R = 0.1599 x 10⁻⁷cm

1 = 10⁻¹⁰cm

= 0.1599 x 10⁻⁷cm

= 1pm/1 x 10⁻¹⁰cm x 0.1599 x 10-7cm

= 1.599 x 10² pm

R= 1.6 x 10²pm

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3 years ago

Randy spins the arrow on a spinner with 5 equal sections labeled A,B,C,D, and EVEN. Then ,he rolls a 6-sided number cube with si

aivan3 [116]

You have 1 out of 5 chances to get a A in the spinner
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8 0

3 years ago

Read 2 more answers

Identify the k-value that makes the relationship shown in the table below proportional.

uysha [10]

Answer:

The value of k that makes the relationship shown in the table below proportional is $\mathbf{\frac{1}{2}}$

Step-by-step explanation:

The relation is proportional if $y=kx \:or\:k=\frac{y}{x}$

Putting values of x and y to find k.

For x =2 and y =1 k is: $k=\frac{y}{x}=\frac{1}{2}$

For x =4 and y =2 k is: $k=\frac{y}{x}=\frac{2}{4} =\frac{1}{2}$

For x =6 and y = 3 k is: $k=\frac{y}{x}=\frac{3}{6} =\frac{1}{2}$

For x = 8 and y = 4 k is: $k=\frac{y}{x}=\frac{4}{8} =\frac{1}{2}$

For x =10 and y = 5 k is: $k=\frac{y}{x}=\frac{5}{10} =\frac{1}{2}$

So, The value of k that makes the relationship shown in the table below proportional is $\mathbf{\frac{1}{2}}$

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3 years ago

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Yakvenalex [24]

First, replace all variables with the given values.
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