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1 year ago

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An element with a mass of 320 grams decays by 5.1% per minute. To the nearest tenth of a minute, how long will it be until there

are 200 grams of the element remaining?

1 answer:

HACTEHA [7]1 year ago

7 0

Answer:

X=9

Step-by-step explanation:

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Leo needs 10 red roses and 15 pink daisies for every 5 bouquets he makes for a flower shop. Drag red roses and pink daisies into

Lelechka [254]

For this equation, you need only 2 red roses and 3 pink daisies to make 1 boutique.
So, just multiply 3 * 2 and 3 * 3.
Which is 6 and 9, then add the two together = 15.
Hope this helps!!

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2 years ago

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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

$s$ : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

<u>Ben:</u>

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

<u>Josh:</u>

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ Eqn. (4).

<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em> $h(t)=0$ <em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>

Thus we have for Ben, Eqn. (3) gives:

$h(t)=0-16t^2+60t+40=0$

Using the quadratic expression to find the roots of the quadratic we have:

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$

Since time can only be positive we reject the $t_{2}$ solution and we keep that Ben's book took $t=4.3276$ seconds to reach the ground.

Similarly solving for Josh we obtain

$t_{1}=3.6794sec\\t_{2}=-0.6794sec$

Thus again we reject the negative and keep the positive solution, so Josh's book took $t=3.6794$ seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

$t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482$

So to answer the original question:

<em>Whose textbook reaches the ground first and by how many seconds?</em>

Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of $t=0.6482$

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1 year ago

. A rocket carrying fireworks is launched from a hill above a lake. The rocket will fall into lake after exploding at its maximu

RoseWind [281]

Answer:

Step-by-step explanation:

Since we are not told what to find, we can as well find the time taken by the rocket to reach its maximum height as shown

The rocket reaches its maximum height when the velocity is zero

v = dh/dt

v = -32t+64

Since v = 0 at maximum height

0 = -32t+64

32t = 64

t = 64/32

t = 2secs

Hence the rocket reaches the maximum height after 2secs

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2 years ago

. Donny had a 10-foot board. He used the board to make two shelves. One shelf measured 4 feet 7 inches wide and the other shelf

liberstina [14]

Answer:

The length of the missing piece is 2 ft 3 inches

Step-by-step explanation:

Here in this question, we are interested in calculating the length of the remaining piece of the board given that we have the total length of the board and two other pieces.

Mathematically, the remaining piece length can be calculated by subtracting the lengths of the known pieces

That would be;

10 ft - 4 ft 7 inches - 3 ft 2 inches

In a foot there are 12 inches

Thus

10 ft = 10 * 12 = 120 inches

4 ft 7 inches = 4(12) + 7 = 55 inches

3 ft 2 inches = 3(12) + 2 = 36 + 2 = 38 inches

Thus the length of the remaining piece would now be;

120 -55 -38 = 27 inches

That is same as 24 + 3 inches

24 inches = 2 ft

So 27 inches = 2 ft 3 inches

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2 years ago

Find the volume of the composite space figure to the nearest whole number.

Alika [10]

Figure 1:
3 x 8 x 5 = 120cm³

Figure 2:
2 x 5 x 6 = 60cm³

Total Volume = 120 + 60 = 180cm³

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2 years ago

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