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1 year ago

Use a composite figure to estimate the area of the figure. The grid has squares with side lengths of 1.5 cm.

Mathematics

1 answer:

ipn [44]1 year ago

4 0

The area of the composite figure in which the length of squares is 1.5 cm is 49.1 $cm^{2}$

Given that the grid has squares with side lengths of 1.5 cm.

We are required to find the area of the composite figure.

The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.

Finding the area of the rectangle.

A=(3*1.5)(4*1.5)=27 $cm^{2}$

Finding the area of the semicircle at the top of the rectangle.

A=1/2 π $(2*1.5)^{2}$ =4.5 π $cm^{2}$

Finding the area of the semicircle at the right of the rectangle.

A=1/2 π $(1.5*1.5)^{2}$

=2.53π $cm^{2}$

Total area =27+4.5π+2.53π

=27+7.03π

Use π=3.14

=27+7.03*3.14

=49.1 $cm^{2}$

Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 $cm^{2}$ .

Learn more about area at brainly.com/question/25965491

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iren2701 [21]

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2 years ago

The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec

igomit [66]

Answer:

The length is 7 m

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Step-by-step explanation:

length = x

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length * width = area

It is given that the area is 70 $m^{2}$

From there

x * (2x - 4) = 70

$2x^{2}$ - 4x = 70

$2x^{2}$ - 4x - 70 = 0

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Now we have a quadratic equation, which is a $x^{2}$ + bx + c = 0, where a $\neq$ 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = $-2^{2}$ - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are $\frac{- b - \sqrt{D} }{2a}$ and $\frac{- b + \sqrt{D} }{2a}$

$x_{1}$ = $\frac{- (-2) - \sqrt{144} }{2}$ = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

$x_{2}$ = $\frac{- (-2) + \sqrt{144} }{2}$ = 7 > 0 (this one is right)

Calculating the dimensions

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2 years ago

A radioactive substance has a continuous decay rate of 0.056 per minute. How many grams of a 120 gram sample will remain radioac

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Answer:

The mass of the radioactive sample after 40 minutes is 12.8 g.

Step-by-step explanation:

The mass of the sample can be found by using the exponential decay equation:

$N_{t} = N_{0}e^{-\lambda t}$

Where:

N(t): is the amount of the sample at time t =?

N₀: is the initial quantity of the sample = 120 g

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Hence, the mass of the sample after 40 min is:

$N_{t} = N_{0}e^{-\lambda t} = 120g*e^{-0.056min^{-1}*40 min} = 12.8 g$

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2 years ago

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Oksi-84 [34.3K]

Answer:

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2 years ago

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Answer:

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Step-by-step explanation:

Using the rules of exponents

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Simplifying the product of the first 2 terms

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Simplifying the third term

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Performing the division, that is

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