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2 years ago

Compare the number of friends at the beginning of a month and at the end of that month if it decreased by 60 and increased by 80

Mathematics

1 answer:

inn [45]2 years ago

3 0

Answer:

plus 20 or positive

Step-by-step explanation:

-60+80= 20

positive

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Suppose the total weight of the fish caught stayed the same but instead of 100 fish caught during the weeklong fishing trip only

Paha777 [63]

The weight of each fish would be multiplied by 10.

Assume the first time, the weight was 800 lb. Since there were 100 fish caught, the weight of each fish would be 800/100 = 8 lb.

This time, however, only 10 fish were caught. The weight would be 800/10 = 80 lb.

80 = 8(10), so the weight is 10 times more.

4 0

3 years ago

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vert

xz_007 [3.2K]

After every drop,the ball bounces to half it's previous height. With that understood.

1st drop -The ball drops 10m

1st bounce - 5m up
2nd drop - 5m down

2nd bounce - 2.5m up
3rd drop - 2.5m down

3rd bounce - 1.25m up
4th drop - 1.25m down

4th bounce - 0.625m up
5th/last drop - 0.625m down

To find the total vertical distance, you add them all.

10+5+5+2.5+2.5+1.25+1.25+0.625+0.625
=29.25m travelled in all.

6 0

3 years ago

Carol is going to make a wooden pyramid and then paint it. She drew the net of a square pyramid as shown below to help her plan

rodikova [14]

The given pyramid's total surface area is 3. 24.0 square feet.

Step-by-step explanation:

Step 1:

To calculate the surface area of the given figure, we need to find the surface areas of the different shapes in the figure.

There are 3 triangles and 1 square in the figure.

Step 2:

All the triangles are similar.

The surface area of a triangle = $\frac{1}{2} (baselength)(height).$

The similar triangles have a base length of 3 feet and a height of 2.5 feet.

The surface area of 1 similar triangle = $\frac{1}{2} (3)(2.5)= 3.75$ square feet.

The surface area for all the similar triangles = $3.75 (4) = 15$ square feet.

Step 3:

The surface area of a square is the square of its side length. The square has a side length of 3 feet.

The surface area of the square = $a^{2} = 3^{2} =9$ square feet.

Step 4:

To calculate the total surface area we sum up all the individual surface area.

The total surface area = $15 + 9 = 24$ square feet which is the third option.

3 0

2 years ago

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$