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3 years ago

Solve for each indicated angle measure or variable in the figure. m x

Mathematics

1 answer:

Elis [28]3 years ago

3 0

If vertical angles are congruent you know

84=4x
21=x

You also know that angle M is supplementary to the angle
, measuring 84. Supplementary means it adds to 180 so if you take the difference you get

180-84=M
96=M

Also M is vertical to the last unknown angle so since vertical angles are congruent the last angle is also 96

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Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve the following. The half-life of a certai

Akimi4 [234]

Answer:

It will take 7 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

$A=A_0 e^{kt}$

Where,

$A_0$ = Initial amount of the substance,

If the half life of the substance is 19 years,

Then if t = 19, amount of the substance = $\frac{A_0}{2}$ ,

i.e.

$\frac{A_0}{2}=A_0 e^{19k}$

$\frac{1}{2} = e^{19k}$

$0.5 = e^{19k}$

Taking ln both sides,

$\ln(0.5) = \ln(e^{19k})$

$\ln(0.5) = 19k$

$\implies k = \frac{\ln(0.5)}{19}\approx -0.03648$

Now, if the substance to decay to 78% of its original amount,

Then $A=78\% \text{ of }A_0 =\frac{78A_0}{100}=0.78 A_0$

$0.78 A_0=A_0 e^{-0.03648t}$

$0.78 = e^{-0.03648t}$

Again taking ln both sides,

$\ln(0.78) = -0.03648t$

$-0.24846=-0.03648t$

$\implies t = \frac{0.24846}{0.03648}=6.81085\approx 7$

Hence, approximately the substance would be 78% of its initial value after 7 years.

5 0

3 years ago

The rectangular bar is connected to the support bracket with a 10-mm-diameter pin. The bar width is w = 70 mm and the bar thickn

german

Answer:

P_max = 9.032 KN

Step-by-step explanation:

Given:

- Bar width and each side of bracket w = 70 mm

- Bar thickness and each side of bracket t = 20 mm

- Pin diameter d = 10 mm

- Average allowable bearing stress of (Bar and Bracket) T = 120 MPa

- Average allowable shear stress of pin S = 115 MPa

Find:

The maximum force P that the structure can support.

Solution:

- Bearing Stress in bar:

T = P / A

P = T*A

P = (120) * (0.07*0.02)

P = 168 KN

- Shear stress in pin:

S = P / A

P = S*A

P = (115)*pi*(0.01)^2 / 4

P = 9.032 KN

- Bearing Stress in each bracket:

T = P / 2*A

P = T*A*2

P = 2*(120) * (0.07*0.02)

P = 336 KN

- The maximum force P that this structure can support:

P_max = min (168 , 9.032 , 336)

P_max = 9.032 KN

3 0

3 years ago

15% of what number is 900?

Ugo [173]

Answer:

135

Step-by-step explanation:

15/100 × 900 = 15 × 9 = 135

3 0

3 years ago

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La cantidad de horas h que debe dormir una persona joven de n años está dada por la siguiente expresión:

natulia [17]

Answer:

Option D doesn't make any sense.

Step-by-step explanation:

D) 7 hours of sleep correspond to an age of 19 years.

That is wrong.

If we use the expression provided

hours = 8 + 0.5*(18 -age)

hours = 8 + 0.5*(18 -19)

hours = 8 + 0.5*(-1)

hours = 7.5

8 0

3 years ago

N÷102=0.123<br> What is the value of n

Sonbull [250]

Answer:

n = 12.546

Step-by-step explanation:

to find the value of n we need to transpose

n ÷ 102 = 0.123

n = 0.123 × 102

n = 12.546

6 0

3 years ago

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