Please help. Given formula, just plug it in to find answer.

The amount of polonium-210 remaining, p(t), after t days in a sample can be modeled by the exponential function p(t) = 100e−0.00

Archy [21]

Answer:

% Po lost = 100[1 - e^(-0.005t)] %; 73.0 g

Step-by-step explanation:

p(t) = 100e^(-0.005t)

Initial amount: p(0) = 100

Amount remaining: p(t) = 100e^(-0.005t)

Amount lost: p(0) – p(t) = 100 - 100e^(-0.005t) = 100[1 - e^(-0.005t)]

% of Po lost = amount lost/initial amount × 100 %

= [1 - e^(-0.005t)] × 100 % = 100[1 - e^(-0.005t)] %

p(63) = 100e^(-0.005 × 63) = 100e^(-0.315) = 100 × 0.730 = 73 g

The mass of polonium remaining after 63 days is 73 g.

4 0

2 years ago

Divide $200 in the ratio 3:2. What is the result?

s2008m [1.1K]

Answer:

b) $120 , $ 80

Step-by-step explanation:

Ratio = 3 :2

Total = 3 + 2 = 5

3/5 of 200 = $\frac{3}{5}*200$

= 3 * 40

= $ 120

2/5 of 200 = $\frac{2}{5}*200$

= 2 * 40

= $ 80

5 0

2 years ago

joe worked 8 hours on Monday. If he worked 40 hours in the week what is the fraction of the total time worked on monday

maria [59]

Joe worked 8/40 or 1/5 of that time on Monday.

6 0

2 years ago

Classify the following triangle

maks197457 [2]

Answer:

Isosceles and obtuse

Step-by-step explanation:

It is not a scalene triangle because it has two same lengths 41 degrees and 41 degrees.

<u>It is a </u>Isosceles triangle because two of the sides have the same lengths 41 degrees and 41 degrees

<u>It is an</u> obtuse triangle because it has on obtuse angle which is 98 and two acute angles that are 41 degrees

It is not an equilateral because not all of the sides are the same lengths

It is not a right triangle because there are 90 degree angles

It is not an acute triangle because not all the angles are acute angles

4 0

2 years ago

Read 2 more answers

Help with this question.

pychu [463]

Answer:

$angleS=83^o$

$angleR=23^o$

Step-by-step explanation:

<h3><u>The Law of Sines</u></h3>

The Law of Sines states that for a given triangle (in a plane), the ratio formed by the Sine of any one of the three interior angles and the side across from it is equal to a common number.

If a triangle is drawn in standard form, with the three vertices identified as A, B, and C, and the interior angles at each vertex simply identified as angleA, angleB, angleC, the sides across from those angles are identified as a, b, and c, respectively. Given such a labeling for a triangle, the Law of Sines gives the following equation:

$\frac{sin(angleA)}{a} =\frac{sin(angleB)}{b} =\frac{sin(angleC)}{c}$

From the picture you presented, with triangle RST, side r is on the right and unlabeled, side s is shown in red, and side T is shown in green. The interior angles for R and S are unlabeled, and angle T is defined as 74 degrees. The Law of Sines would give the following relationship for your triangle:

$\frac{sin(angleR)}{r} =\frac{sin(angleS)}{s} =\frac{sin(angleT)}{t}$

Substituting known values...

$\frac{sin(angleR)}{r} =\frac{sin(angleS)}{12.7ft} =\frac{sin(74^{o} )}{12.3ft}$

It should be noted that without information about the length of side r, angle R cannot be found directly with the Law of Sines because that portion of the equation holds two unknowns. However, if the other two angles of the triangle are known, angle R can be solved for by using the Triangle Sum Theorem.

<h3><u>Finding Angle S</u></h3>

Focusing in on the ratio with known values on the far right, and the ratio containing angleS first:

$\frac{sin(angleS)}{12.7ft} =\frac{sin(74^{o} )}{12.3ft}$

... multiplying both sides of the equation by 12.7 ft...

$sin(angleS) =\frac{sin(74^{o} ) * 12.7ft}{12.3ft}$

Note that the right side of the equation has units of feet in both the numerator and denominator (with no addition or subtraction), so the units will cancel. Simplifying the right side of the equation by evaluating the expression in a calculator (make sure you're in "degree" mode), will yield a unit-less number:

$sin(angleS) = .9925222389...$

Undoing the sine function, and solving for the measure of angle S will require taking the "arcsin" of both sides of the equation...

$arcsin(sin(angleS))=arcsin(0.9925222389...)\\angleS=arcsin(0.9925222389...)\\angleS=82.98876661...^o\\angleS=83^o$ <u />

<u />

<h3><u>Finding Angle R</u></h3>

Knowing both angleS and angleT, we can apply the Triangle Sum Theorem to solve for angle R.

Triangle Sum Theorem: The sum of all 3 interior angles in a triangle (in a plane) is 180 degrees.

$angleR+angleS+angleT=180^o\\angleR+83^o+74^o=180^o$

Using the subtraction property of equality to isolate angleR and combining like terms...

$angleR=180^o-83^o-74^o\\angleR=23^o$

8 0

1 year ago