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3 years ago

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

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

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

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

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mojhsa [17]

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

B) H = 5.10

C) Yes

Step-by-step explanation: Exponential Decay function 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 power rule:

$13r=ln(0.1708)$

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

$r=-0.1359$

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.

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