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3 years ago

Cora is creating a rectangular prism. The base of her prism is shown below. She plans to have a height of 8

Mathematics

1 answer:

Brut [27]3 years ago

6 0

Answer:

See the explanation.

Step-by-step explanation:

Cora is making a rectangular prism. She plans to have 8 inches if height. What will be the volume of the rectangular figure?

As the figure formed is a rectangular prism. we need to find the volume of rectangular prism. Volume of prism will be:

Volume = Length · Width · Height

As she wants to have 8 inches of height, substitute it in the given equation:

Volume = 8(Length · Heights) inch³

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Will give brainliest. Find the length and measure of each arc. Show your work.

o-na [289]

Problem 1

The circumference is the full perimeter around the circle. You can think of it as the combination of "circle" and "fence" to get "circumference", but there might be other tricks to remember the term.

Anyways, the formula to get the circumference of a circle is

C = 2*pi*r

In this case, r = 14 is our radius so,

C = 2*pi*r

C = 2*pi*14

C = 28pi .... exact circumference in terms of pi

We only want a portion of this circumference as shown by the piece of the circle darkened. The fractional portion we want is 135/360 of a circle. Divide the angle by 360 to get the fractional portion you want. If the angle was say 180 degrees, then 180/360 = 1/2 is the fractional portion.

So we take 135/360 and multiply it by the value of C found earlier

arc length = (fractional portion)*(circumference)

arc length = (135/360)*28pi

arc length = 10.5pi

That's the exact arc length in terms of pi. Use a calculator to find that

10.5pi = 32.9867228626929

Or you could use pi = 3.14 to say

10.5*pi = 10.5*3.14 = 32.97

Which is fairly close to what the calculator is saying

-----------------

<h3>Summary:</h3>

Exact arc length = 28pi

Approximate arc length (using calculator) = 32.9867228626929

Approximate arc length (using 3.14 for pi) = 32.97

Units are in feet

When I write "using calculator", I mean using the calculator's stored version of pi, instead of pi = 3.14

======================================================

Problem 2

We could use the same idea as problem 1, or we could use the formula below. The formula is just a quick way of encapsulating what I discussed earlier.

L = arc length

x = central angle

L = (x/360)*2*pi*r

L = (150/360)*2pi*13

L = (65/6)pi .... exact arc length

L = 34.0339204138894 .... approx arc length (using calculator)

L = 34.0166666666667 .... approx arc length (using 3.14 for pi)

-----------------

<h3>Summary:</h3>

Exact arc length = (65/6)pi

Approximate arc length (using calculator) = 34.0339204138894

Approximate arc length (using 3.14 for pi) = 34.0166666666667

Units are in meters

8 0

4 years ago

Mr.Ronaldo earns 46,650 in annual gross income. He will pay 7% in income tax this year. What is the amount of income tax that Mr

insens350 [35]

Hey there!

To find the amount of tax, we simply multiply 0.07 (the percentage) by his income.

0.07*46650=3265.5

Therefore, he will pay $3,265.50 in income tax.

I hope this helps!

8 0

3 years ago

Is this a right triangle why or why not?

Marysya12 [62]

Answer:

No, it does satisfy the Pythagorean Theorem

Step-by-step explanation:

In right triangle a² + b² = c²

Where a and b = legs and c = hypotenuse

The given measures of the legs are 3 and 7 and the given measure of the hypotenuse is √57

Which means that if this is a right triangle then 3² + 7² = √57²

3² = 9

7² = 49

√57² = 57

9 + 49 = 58

we're left with 57 ≠ 58 which is not true, meaning that , that is not a right triangle

3 0

3 years ago

A total of 4 buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 3

Mandarinka [93]

Answer:

76.2838

Step-by-step explanation:

E[X+Y] = E[X] + E[Y]

E[X] is the average of X or expectancy of X

E[Y] is the average or expectancy f Y

E[X] = 40P(student is in bus 1)+33P(student is in bus 2)+25P(student is in bus 3)+50P(student is in bus 4)=

40(40/148) + 33(33/148) + 25(25/148) + 50(50/148) = 39.2838

E[Y] = (number of students)/(number of drivers) = 148/4 = 37

So E[X+Y] = 39.2838 + 37 = 76.2838

6 0

4 years ago

Una piscina rectangular de 15 m de largo por 9m de ancho está rodeada por un camino de cemento de ancho uniforme. ¿Si el área de

malfutka [58]

Answer:

El ancho del camino es 1.5 m.

Step-by-step explanation:

Una piscina rectangular posee 15 m de largo por 9 m de ancho.

El área de un rectángulo es igual a la base por la altura. Es decir, lado mayor por lado menor. Entonces el área de la piscina es 15 m* 9 m= 135 m²

La piscina está rodeada por un camino de cemento de ancho uniforme, al cual se denomina x y estará en unidades de metros (m). Entonces el largo de la piscina sumado al ancho a ambos lados de la piscina será 15 m + 2*x, mientras que el ancho de la piscina sumado al largo a ambos lados de la piscina es 9 m + 2*x. Entonces este área se puede expresar como

(15 m+2*x)*(9 m+ 2*x)

Entonces al área de la piscina sumado al camino se le resta el área de la piscina y da como resultado el área del camino, cuyo valor es 81 m²:

El área total - área de la piscina = área del camino

(15 m +2*x)*(9 m+ 2*x) - 135 m²= 81 m²

Resolviendo:

15*9 m²+15*2*x + 9*2*x + 2*x*2*x - 135 m²= 81 m²

135 m² + 30*x + 18*x + 4*x² - 135 m²= 81 m²

48*x + 4*x² = 81 m²

48*x + 4*x² - 81 m²= 0

Siendo una ecuación cuadrática donde a= 4, b= 48 y c= -81, entonces:

$\frac{-48+-\sqrt{48^{2}-4*4*(-81) } }{2*4}$

Resolviendo:

$\frac{-48+\sqrt{48^{2}-4*4*(-81) } }{2*4}= 1.5$

$\frac{-48-\sqrt{48^{2}-4*4*(-81) } }{2*4}= -13.5$

Como las distancias solo pueden ser positivas, entonces <u><em>el ancho del camino es 1.5 m.</em></u>

En la imagen adjunta se puede observar un gráfico de la piscina más el camino

5 0

3 years ago