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3 years ago

Which expression is equivalent to 10 102 50 502

Mathematics

1 answer:

pogonyaev3 years ago

3 0

Answer:

$10$

Step-by-step explanation:

$\sqrt{100} \\ \sqrt{10 \times 10} \\ = 10$

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If $120.00 is borrowed for 3 years at 5% how much interest will be generated by the end of the loan? please answer will mark bra

Doss [256]

Answer:

I = prt / 100

120x3x5 / 100

= 18

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3 years ago

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 9-inch perimeter A = sq. in.

Alona [7]

Answer:

$3.9 in^2$

Step-by-step explanation:

The area of a triangle is given by

$A=\frac{1}{2}bh$

where

b is the base

h is the height

Here we have an equilateral triangle, which has the 3 sides of the same length.

Let's call L the length of one side.

We know that the perimeter of the triangle is

p = 9 in

The perimeter is the sum of the three sides, so:

$p=L+L+L=3L$

Therefore, we find the length of the side:

$L=\frac{p}{3}=\frac{9}{3}=3 in$

Therefore the length is the base of the triangle,

$b=L$

The height can be calculated by considering half triangle: the hypothenuse is equal to L, while one side is equal to half the base (b/2), therefore the height is given by Pythagorean's theorem:

$h=\sqrt{L^2-(\frac{b}{2})^2}=\sqrt{3^2-(\frac{3}{2})^2}=2.6 in$

Therefore, the area of the triangle is:

$A=\frac{1}{2}(3)(2.6)=3.9 in^2$

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3 years ago

slader (a) Find parametric equations for the line through (4, 1, 8) that is perpendicular to the plane x − y + 4z = 2. (Use the

Pavel [41]

Answer:

(x(t), y(t), z(t)) = (4 + t, 1 - t, 8 + 4t)

xy - plane (x, y, z) = (2, -1, 0)

yz - plane (x, y, z) = (0, 5, -8)

xz - plane (x, y, z) = (5, 0, 12)

Step-by-step explanation:

The given point (x, y ,z) = (4, 1, 8)

The plane x -y + 4z = 2

Normal vector (n) = < 1, -1, 4 >

The equation of line through point (4, 1, 8) and the plane is:

(x(t), y(t), z(t)) = (4, 1, 8) + t(1, -1, 4)

(x(t), y(t), z(t)) = (4 + t, 1 - t, 8 + 4t)

Any point on the line P(x, y, z) = ( 4 + t, 1 - t, 8 + 4t)

xy-Pane ⇒ z = 0

8 + 4t = 0

4t = - 8

t = -8/4

t = -2

∴

(x, y, z) = (4 - 2, 1 - 2, 8 + 4(-2))

(x, y, z) = (2, -1, 0)

yz-plane ⇒ x = 0

4 + t = 0

t = -4

∴

(x, y, z) = (4 + (-4) , 1-(-4), 8 + 4(-4)

(x, y, z) = (0, 5, -8)

xz-plane ⇒ y = 0

1 - t = 0

-t = -1

t = 1

∴

(x, y, z) = ( 4 + 1, 1 - 1, 8 + 4(1) )

(x, y, z) = (5, 0, 12)

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Answer:

Step-by-step explanation:

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