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3 years ago

What is the measure of angle B in the triangle?

Mathematics

2 answers:

Marat540 [252]3 years ago

8 0

$180 - 120 = 60 \\ 60 - 16 = 44 \\ 44 \div 2 = 22$
x is 22
hope this helps

Sliva [168]3 years ago

5 0

Answer: an inequality in terms of x and 1904 that is true only for values of x that represent years before the start of the Russo-Japanese War is:

x <1904

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Directions: (a) Identify the parent function and (b) describe the transformations.

Zepler [3.9K]

Parent function: y=2^x
Transformations:
Reflection over x-axis
Vertical stretch of 3
Right 1
Up7

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2 years ago

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

3 years ago

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes 5 h

kogti [31]

v=d/t

44=d/5

d=220 mile

v=220/11

v=20 mph

7 0

2 years ago

Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain an

pychu [463]

The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.

The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.

5 0

2 years ago

Use the image below and find the missing angles

Colt1911 [192]

Step-by-step explanation:

w = 34° (alternate interior angles)

x = 34° (vertically opposite angles)

y = 101°

z = 79° (corresponding angles)

7 0

3 years ago