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2 years ago

What is the volume, in cubic meters, if the prism below?

Mathematics

1 answer:

Fiesta28 [93]2 years ago

6 0

<h3>Answer: 1848 cubic meters</h3>

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Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

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A pound of oranges cost $3 less than a pound of pears. Together, 8 pounds of oranges and 4 pounds of pears cost $30. How much wo

jek_recluse [69]

A pound of oranges cost x dollar => A pound of pears cost x+3 dollar

We have: 8x+4(x+3)=30 => 12x=30-12=18 =>x=1.5

5 pounds of pears cost: 5(x+3)=5(1.5+3)=5*4.5= 22.5 (dollar)

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3 years ago

Is the sqrt of 1 - sin^2 theta = cos theta true? If so, in which quadrants does angle theta terminate?

Genrish500 [490]

Answer:

Answer: The answer is option B.

Step-by-step explanation:

Here,

We have,

${ \sin }^{2} theta \: + {cos}^{2}theta = 1$

${cos}^{2} \: theta = 1 - {sin}^{2} \: theta$

$cos \: theta = \sqrt{1 - { \sin }^{2}theta }$

So, it's true; and it lies in quadrant 1 and 4.

The reason according to the "CAST" rule cos theta is in 1st and 3rd quadrant cos theta is positive.

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3 years ago

I need help with number 17. I have no idea what I’m doing!

kakasveta [241]

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3 years ago

A line has gradient 5.

MAVERICK [17]

Answer:

x = k - 3

Step-by-step explanation:

Given parameters:

Gradient of the line = 5;

Coordinates; M(x, 8)

N(k, 23)

Solution:

If we use the expression for finding the slope of the line, we can solve this problem;

Slope = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

where

x₁ = x y₁ = 8

x₂ = k y₂ = 23

Input the parameters:

5 = $\frac{23 - 8}{k -x }$

15 = 5(k - x)

3= k- x

k - x = 3

Express x in terms of k;

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Multiply through by -1;

x = -3 + k

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3 years ago

Find the multiplicative inverse of 3 − 2i. Verify that your solution is corect by confirming that the product of

leonid [27]

Answer:

$\frac{3}{13} + \frac{2i}{13}$

Step-by-step explanation:

The multiplicative inverse of a complex number y is the complex number z such that (y)(z) = 1

So for this problem we need to find a number z such that

(3 - 2i) ( z ) = 1

If we take z = $\frac{1}{3-2i}$

We have that

$(3- 2i)\frac{1}{3-2i} = 1$ would be the multiplicative inverse of 3 - 2i

But remember that 2i = √-2 so we can rationalize the denominator of this complex number

$\frac{1}{3-2i } (\frac{3+2i}{3+2i } )=\frac{3+2i}{9-(4i^{2} )} =\frac{3+2i}{9-4(-1)} =\frac{3+2i}{13}$

Thus, the multiplicative inverse would be $\frac{3}{13} + \frac{2i}{13}$

The problem asks us to verify this by multiplying both numbers to see that the answer is 1:

Let's multiplicate this number by 3 - 2i to confirm:

$(3-2i)(\frac{3+2i}{13}) = \frac{9-4i^{2} }{13} =\frac{9-4(-1)}{13}= \frac{9+4}{13} = \frac{13}{13}= 1$

Thus, the number we found is indeed the multiplicative inverse of 3 - 2i

4 0

3 years ago