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3 years ago

Planes X and Y and points C, D, E, and F are shown.

Mathematics

1 answer:

viva [34]3 years ago

5 0

Answer:

The answer is below

Step-by-step explanation:

The planes are shown in the image below.

From the image, points D and E are on plane Y, while point F is on plane X.

A) The line that can be drawn through points C and D is contained in plane Y.

This statement is wrong because point C is not in plane Y

B) The line that can be drawn through points D and E is contained in plane Y.

Correct. Since both points D and E are on plane Y, hence The line that can be drawn through points D and E is contained in plane Y.

C) The only point that can lie in plane X is point F.

This statement is correct because from the image only point F is on plane X.

D) The only points that can lie in plane Y are points D and E.

This statement is correct because from the image only point D and E is on plane Y.

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A substance with a half life is decaying exponentially. If there are initially 12 grams of the substance and after 70 minutes th

77julia77 [94]

Answer: 233 min

Step-by-step explanation:

This problem can be solved by the following equation:

$A=A_{o} e^{-kt}$ (1)

Where:

$A=7 g$ is the quantity left after time $t$

$A_{o}=12 g$ is the initial quantity

$t=70 min$ is the time elapsed

$k$ is the constant of decay for the material

So, firstly we need to find the value of $k$ from (1) in order to move to the next part of the problem:

$\frac{A}{A_{o}}=e^{-kt}$ (2)

Applying natural logarithm on both sides of the equation:

$ln(\frac{A}{A_{o}})=ln(e^{-kt})$ (3)

$ln(\frac{A}{A_{o}})=-kt$ (4)

$k=-\frac{ln(\frac{A}{A_{o}})}{t}$ (5)

$k=-\frac{ln(\frac{7 g}{12 g})}{70 min}$ (6)

$k=0.00769995 min^{-1}$ (7) Now that we have the value of $k$ we can solve the other part of this problem: Find the time $t$ for $A=2 g$ .

In this case we need to isolate $t$ from (1):

$t=-\frac{ln(\frac{A}{A_{o}})}{k}$ (8)

$t=-\frac{ln(\frac{2 g}{12 g})}{0.00769995 min^{-1}}$ (9)

Finally:

$t=232.697 min \approx 233 min$

5 0

3 years ago

By first calculating the size of angle LMN, calculate the area of triangle MNL. You must show all your working.

RSB [31]

Answer:

m(∠LMN) = 67.44°

Area of ΔMNL = 16.66 square units

Step-by-step explanation:

By applying Sine rule in the ΔLMN,

$\frac{\text{Sin}M}{\text{NL}}=\frac{\text{Sin}N}{\text{ML}}$

$\frac{\text{Sin}M}{7.2}}=\frac{\text{Sin}38}{\text{4.8}}$

SinM = $\frac{\text{Sin}38\times 7.2}{4.8}$

SinM = 0.9235

M = $\text{Sin^{-1}}(0.9235)$ $\text{Sin}^{-1} (0.9235)$

M = 67.44°

m(∠M) + m(∠N) + m(∠L) = 180°

67.44 + 38 + m(∠L) = 180°

m(∠L) = 180 - 105.44

m(∠L) = 74.56°

Area of ΔMNL = $\frac{1}{2}(\text{ML})(\text{NL})\text{Sin}(74.56)$

= $\frac{1}{2}(4.8)(7.2)(0.96391)$

= 16.66 square units

3 0

4 years ago

What number is 42% of 150

professor190 [17]

Answer:

42% of 150 is 63.

Explanation:

63/150 = 42/100

42/100 is equal to 21/50.

21/50 x 150 = 63.

63/150 = 21/50

6 0

3 years ago

Factor the expression. 3p + 21

bagirrra123 [75]

I believe that the answer is p+7

7 0

3 years ago

Hey besties i need sum help with this pls

statuscvo [17]

The correct answer is A

6 0

3 years ago