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3 years ago

(03.01 LC)

Mathematics

1 answer:

lutik1710 [3]3 years ago

8 0

Answer:

The length of the other leg is 4.58 units.

Step-by-step explanation:

A² + B² = C² Use Pythagorean Theorem

2² + B² = 5² Simplify

4 + B² = 25

-4 -4 Subtract 4 from both sides

B² = 21 Take the square root of both sides

B = 4.58 units

If this answer is correct, please make me Brainliest!

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I'm studying a new bacteria that doubles in numbers every 25 minutes. If i start with 50 bacteria, how long until i have 5 milli

dimaraw [331]

Answer:

415.63 minutes

Step-by-step explanation:

Growth can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it grows by using t=25 minutes and $\frac{A_{0}}{A} =2$ or double the amount at that time. The first step we always take is to divide $A_0$ by A.

$[tex]\frac{A_{0}}{A}=e^{rt}\\2=e^{r(25)}$

$2=e^{(25)r}$

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 2=ln e^{(25)r}\\ln 2=25r (ln e)\\\frac{ln2}{25} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 25.

We solve with a calculator $\frac{ln2}{25} =r\\0.0277=r$

We change 0.0277 into a percent by multiplying by 100 to get 2.77% as the rate.

The equation is $A=A_0e^{0.0277t}$ .

We repeat the step above substituting A=5,000,000, $A_0$ =50, and r=0.02777. Then solve for t.

$5000000=50e^{0.0277t}\\\frac{5000000}{50} =e^{0.0277t}\\100000=e^{0.0277t}\\ln100000=lne^{0.0277t}\\ln100000=0.02777t(lne)\\\frac{ln100000}{0.0277} =t$

t=415.63 minutes

6 0

3 years ago

Evaluate the line integral c y3 ds, c.x = t3, y = t, 0 â‰¤ t â‰¤ 3

Temka [501]

$\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\int_{t=0}^{t=3}t^3\sqrt{1^2+(3t^2)^2}\,\mathrm dt=\int_0^3t^3\sqrt{1+9t^4}\,\mathrm dt$

Take $u=1+9t^4$ so that $\mathrm du=36t^3\,\mathrm dt$ . Then

$\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\frac1{36}\int_{u=1}^{u=730}\sqrt u\,\mathrm du=\frac{730^{3/2}-1}{54}$

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3 years ago

What times what equals 234

inessss [21]

2 x 117
3 x 78
6 x 39
9 x 26
13 x 18

5 0

3 years ago

Plsss answerrrr I give brainliest thank uuu

arsen [322]

Answer:

The answer is 48m, I hope this answer is correct!

Step-by-step explanation:

For each cube there are 6 sides so, 1 cube has the value of 6m so, since there are 8 cubes, the volume is 48m.

Please give me Brainliest!

Have a good day,

-johannelbekian (You can call me "Despacito Spider" Btw)

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2 years ago

PLEASE HELP FAST!!!!!!!!!!!!!!!!!!!!!! Which two numbers on the number line have an absolute value of 1?

Alisiya [41]

Answer:

Step-by-step explanation:

-1 and 1.

They are both 1 away from 0, meaning that the absolute value of both are 1.

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2 years ago