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Debora [2.8K]
3 years ago
15

How to find the surface area and the volume of this prism

Mathematics
1 answer:
kotegsom [21]3 years ago
7 0
 hope this helps!
..........

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Car is moving on a circle on a plane. At time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y
Aleks [24]

Answer:

we have centre of circle as (30,40) and radius = 1

Step-by-step explanation:

Given that a car is moving on a circle on a plane.

At time t (seconds),

x(t) = 10 sin(200t + 3) + 30

and

y(t) = 10 cos(200t + 3) + 40

x-30 = 10 sin(200t + 3) \\y-40 = 10 cos(200t + 3) + 40

when we square and add both the equations we get

(x-30)^2 + (y-40)^2 = 1

(since sin square + cos square = 1 always)

i.e. we have centre of circle as (30,40) and radius = 1

3 0
3 years ago
The formula I = PRT where I = Interest, P = principal, R = rate, and T = time is used to calculate the amount of simple interest
Marta_Voda [28]

Answer:

T= I divided by the quantity P times R

6 0
3 years ago
What is the numerator of the simplified sum?
sashaice [31]

Answer:

4x + 6

Step-by-step explanation:

\frac{x}{x² + 3x + 2} + \frac{3}{x + 1}

To determine what the numerator would be, after simplifying both fractions, take the following steps:

Step 1: Factorise the denominator of the first fraction, x² + 3x + 2.

Thus,

x² + 2x + x + 2

(x² + 2x) + (x + 2)

x(x + 2) +1(x + 2)

(x + 1)(x + 2)

We would now have the following as our new fractions to add together and simplify:

\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}

Step 2: find the highest common factor of the denominator of both fractions.

Highest common factor of (x + 1)(x + 2) and (x + 1) = (x + 1)(x + 2)

Step 3: To add both fractions, divide the highest common factor gotten in step 2 by each denominator, and then multiply the result by the numerator of each fraction.

Thus,

\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}

\frac{x + 3(x + 2)}{(x + 1)(x + 2)}

\frac{x + 3x + 6)}{(x + 1)(x + 2)}

\frac{4x + 6)}{(x + 1)(x + 2)}

Therefore, the numerator of the simplified form sum of both fractions = 4x + 6

8 0
3 years ago
Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,
omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

<u>Pyramid A</u>

s = 4 -- base sides

V = 36 -- Volume

<u>Pyramid B</u>

s = 6 --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

V = \frac{1}{3} * B * h

Where B represents the area of the base equilateral triangle, and it is calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

B = \frac{1}{2} * s^2 * sin(60)

B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}

B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}

B = 4\sqrt 3

The height is calculated from:

V = \frac{1}{3} * B * h

This gives:

36 = \frac{1}{3} * 4\sqrt 3 * h

Make h the subject

h = \frac{3 * 36}{4\sqrt 3}

h = \frac{3 * 9}{\sqrt 3}

h = \frac{27}{\sqrt 3}

To calculate the volume of pyramid B, we make use of:

V = \frac{1}{3} * B * h

Since the heights of both pyramids are the same, we can make use of:

h = \frac{27}{\sqrt 3}

The base area B, is then calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where

s = 6

So:

B = \frac{1}{2} * 6^2 * sin(60)

B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}

B = 9\sqrt 3

So:

V = \frac{1}{3} * B * h

Where

B = 9\sqrt 3 and h = \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9 * 27

V = 81

6 0
3 years ago
Read 2 more answers
La ecuación de la recta que pasa por los puntos (2,-1) y (1,-5) es:
77julia77 [94]

Given:

A line passes through the points (2,-1) and (1,-5).

To find:

The equation of the line.

Solution:

If a line passes through the two points, then the equation of the line is

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

The line passes through the points (2,-1) and (1,-5). So, the equation of the line is

y-(-1)=\dfrac{-5-(-1)}{1-2}(x-2)

y+1=\dfrac{-5+1}{-1}(x-2)

y+1=\dfrac{-4}{-1}(x-2)

y+1=4(x-2)

Using distributive property, we get

y+1=4(x)+4(-2)

y+1=4x-8

Subtract 1 from both sides.

y+1-1=4x-8-1

y=4x-9

Therefore, the correct option is B.

5 0
3 years ago
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