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Alex
3 years ago
15

A rectangle and a triangle with the same base and height have the same area. True or false

Mathematics
2 answers:
Tanya [424]3 years ago
8 0

Answer:

False.

Step-by-step explanation:

The triangle has 1/2 the area of the rectangle.

marin [14]3 years ago
5 0

Answer:

<h2>FALSE</h2>

Step-by-step explanation:

The formula of an area of a rectangle:

A_{\boxed{\ }}=lw

l - length

w - width

The fromula of an area of a triangle:

A_\triangle=\dfrac{bh}{2}

b - base

h - height

If l = a and w = h, then

A_\triangle=\dfrac{lw}{2}=\dfrac{1}{2}lw=\dfrac{1}{2}A_\boxed{\ }

<em>The area of the triangle is equal to half the area of the rectangle with the same base and height.</em>

<em>The area of the rectangle is equal to twice the area of the triangle with the same base and height.</em>

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The concentration of dichlorodiphenyltrichloroethane (DDT - an infamous pesticide) in Lake Michigan has been declining exponenti
mojhsa [17]

Answer: A) y=13e^{-0.1359t}

              B) H = 5.10

              C) Yes

Step-by-step explanation: <u>Exponential</u> <u>Decay</u> <u>function</u> is a model that describes the reducing of an amount by a constant rate over time. Generally, it is written in the form: y(t)=Ce^{rt}

A) C is initial quantity, in this case, the initial concentration of DDT. To determine r, using the data given:

y(t)=Ce^{rt}

2.22=13e^{13r}

e^{13r}=0.1708

Using a natural logarithm property called <em>power rule:</em>

13r=ln(0.1708)

r=\frac{ln(0.1708)}{13}

r=-0.1359

The decay function for concentration of DDT through the years is y(t)=13e^{-0.1359t}

B) The value of H is calculated by y=C(0.5)^{\frac{t}{H} }

2.22=13(0.5)^{\frac{13}{H} }

(0.5)^{\frac{13}{H} }=0.1708

Again, using power rule for logarithm:

\frac{13}{H} log(0.5)=log(0.1708)

\frac{13}{H} =\frac{log(0.1708)}{log(0.5)}

\frac{13}{H} =2.55

H = 5.10

Constant H in the half-life formula is H=5.10

C) Using model y(t)=13e^{-0.1359t} to determine concentration of DDT in 1995:

y(24)=13e^{-0.1359.24}

y(24) = 0.5

By 1995, the concentration of DDT is 0.5 ppm, so using this model is possible to reduce such amount and more of DDT.

8 0
2 years ago
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