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3 years ago

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Consider a prism ABCA'B'C' whose base is an equilateral triangle of side a. The projection of A' onto ABC is the centroid of ABC

. The side AA' makes an angle of 60° with the base. Calculate the volume of prismatic block.

2 answers:

luda_lava [24]3 years ago

4 0

Answer: The base of the prism ABCA1B1C1 is an equilateral triangle ABC with side a. Point A1 is projected onto the center (middle) of edge BC and the angle between. ... BC and the angle between the edge AA1 and the plane ABC is 60 degrees. ... I tried several ways to calculate the area but the answer is not the ...

Step-by-step explanation:

Serggg [28]3 years ago

3 0

Answer:

lsu is there to help you with this question

Step-by-step explanation:

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Prove that sin3a-cos3a/sina+cosa=2sin2a-1

Sloan [31]

Answer:

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

Step-by-step explanation:

we are given

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

we can simplify left side and make it equal to right side

we can use trig identity

$sin(3a)=3sin(a)-4sin^3(a)$

$cos(3a)=4cos^3(a)-3cos(a)$

now, we can plug values

$\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}$

now, we can simplify

$\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}$

$\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}$

$\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}$

now, we can factor it

$\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}$

$\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can use trig identity

$sin^2(a)+cos^2(a)=1$

$\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}$

we can cancel terms

$=3-4(1-sin(a)cos(a))$

now, we can simplify it further

$=3-4+4sin(a)cos(a))$

$=-1+4sin(a)cos(a))$

$=4sin(a)cos(a)-1$

$=2\times 2sin(a)cos(a)-1$

now, we can use trig identity

$2sin(a)cos(a)=sin(2a)$

we can replace it

$=2sin(2a)-1$

so,

$\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1$

7 0

3 years ago

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Need help :)<br><br><br><br> pleaseeeeeee :(

gayaneshka [121]

Answer: $x\geq 88$

This means that he has to save at least $88 or more to have enough money.

Step-by-step explanation:

He has $37 and he needs to save more (+) but we don't know how much more that is, so that's why that is our unknown value. (x). The sum of them has to be at least 125 or greater.

$37+x\geq 125$

Subtract 37

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8 0

3 years ago

A weekly report for new agents at a vacation sales company is shown in the histogram.

bearhunter [10]

Answer:

6

Step-by-step explanation:

More than 10 means 11, 12, 13, 14, 15, 16.

From the histogram, number of salespersons who sold

11 -12 packages is 1;
13-14 packages is 2;
15-16 packages is 3.

In total, number of the new agents which sold more than 10 vacation packages is

$1+2+3=6$

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2 years ago

Triangle ABC is an isosceles triangle in which side

Shkiper50 [21]

Answer:

Option B.

Step-by-step explanation:

Consider the below figure attached with this question.

It is given that triangle ABC is an isosceles triangle.

From the below figure it is clear that the vertices of triangle are A(-2,-4), B(2,-1) and C(3,-4).

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using this formula, we get

$AB=\sqrt{(2-(-2))^2+(-1-(-4))^2}=\sqrt{16+9}=5$

$BC=\sqrt{(3-2)^2+(-4-(-1))^2}=\sqrt{1+9}=\sqrt{10}$

$AC=\sqrt{(3-(-2))^2+(-4-(-4))^2}=\sqrt{25}=5$

Now,

Perimeter of triangle ABC = AB + BC + AC

$=5+\sqrt{10}+5$

$=10+\sqrt{10}$

So, perimeter of triangle ABC is $10+\sqrt{10}$ units.

Therefore, the correct option is B.

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3 years ago

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satela [25.4K]

Answer:

Step-by-step explanation:

The 3 angles must add up to 180. So

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3 years ago

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