Which equation represents exponential decay?

Mathematics

1 answer:

MAVERICK [17]3 years ago

6 0

Y=(1/5)^x would be the only equation demonstrating decay of these

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The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lenghts of the bases of

Sati [7]

Answer:

<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>

Step-by-step explanation:

The formula of an area of a triangle:

$A=\dfrac{bh}{2}$

b - base

h - height

We have b = 21cm, h = 6cm.

Substitute:

$A=\dfrac{(21)(6)}{2}=63\ cm^2$

The formula of an area of a trapezoid:

$A=\dfrac{b_1+b_2}{2}\cdot h$

b₁, b₂ - bases

h - height

We have b₁ = 2b₂, therefore b₁ + b₂ = 2b₂ + b₂ = 3b₂.

The area of a triangle and the area of a trapezoid are the same.

Therefore

$\dfrac{3b_2}{2}\cdot h=63$ multiply both sides by 2

$3b_2h=126$ divide both sides by 3

$b_2h=42$ divide both sides by h

$b_2=\dfrac{42}{h}$

$b_1=2b_2\to b_1=2\cdot\dfrac{42}{h}=\dfrac{84}{h}$

8 0

2 years ago

Read 2 more answers

The coordinates of trapezoid ABCD are A(−4, 3), B(2, 3), C(4, −1) and D(−4, −1). A line segment runs through the trapezoid with

madam [21]

The distance from point Y to the y-axis is 4 units and the distance from point Z to the y-axis is 3 units, then the lelgth of the segment YZ is 4+3=7 units.
If a scale factor is 3, then the length of Y'Z' will be 7·3=21 units.

P.S. In the added picture you can see trapezoid ABCD that was dilated by a scale factor 3 about the origin. This may help to understand that all linear values after dilation become multiplied by scale factor.