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4 years ago

Sin75° + sin15º = sin75 – sin15° =

Mathematics

1 answer:

alekssr [168]4 years ago

3 0

Answer: False

Step-by-step explanation:

The left side

1.22474487 does not equal to the right side 0.70710678, which means that the given statement is false.

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If h(x) = x -7 and g(x) =x^2 , which expression is equivalent to (g°h)(5)

Gelneren [198K]

Answer:

Step-by-step explanation:

h(5) = 5 - 7 = -2

g(-2) = (-2)^2 = 4

8 0

3 years ago

A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich

Bess [88]

Answer:

a). k = 2.0794

b). $A_{t}=A_{0}(2^{3t} )$

c). 13107200 cells

d). rate of growth after 6 hours = 27255112

e). 4.76 hours

Step-by-step explanation:

From the formula of bacterial population,

$A_{t}=A_{0}e^{kt}$

Where $A_{t}$ = Bacterial population after time t

$A_{0}$ = Initial population

k = relative growth factor

t = duration or time

a). For $A_{t}=2\times 50=100$ cells

and $A_{0}=50$ cells

Time t = 20 minutes = $\frac{1}{3}$ hours

Now we plug in these values in the formula,

100 = $50(e^{\frac{k}{3}})$

$e^{\frac{k}{3}}=2$

By taking natural log on both the sides of the equation,

$\frac{k}{3}(lne)=ln(2)$

k = 3ln(2) = 2.0794

b). To get the expression we will plug in the value of k in the formula.

$A_{t}=A_{0}e^{kt}$

Since k = 3ln(2)

$A_{t}=A_{0}e^{3t(ln2)}$

Let y = $e^{3t(ln2)}$

By taking natural log on both the sides of the equation,

lny = $ln(e^{3t(ln2)} )$

lny = 3t(ln2)ln(e)

ln(y) = 3t(ln2)

ln(y) = $ln(2)^{3t}$

y = $2^{3t}$

Now our expression will be $A_{t}=A_{0}(2^{3t} )$

c). Number of cells after t = 6 hours

$A_{6}=50(2^{3\times 6} )$

$A_{6}=50(2^{18})$

$A_{6}=50\times (262144)=13107200$

d). We can get the rate of growth by finding derivative of the expression

$\frac{d}{dt}(A_{t})=\frac{d}{dt}[A_{0}(e^{kt}})]$

= $A_{0}[ke^{kt}]$

Now $\frac{d}{dt}(A_{6})=k.A_{6}$

= 2.0794×13107200

= 27255112

e) From the given formula,

$A_{t}=A_{0}(2^{3t} )$

$1000000=50(2^{3t} )$

$2^{3t}=20000$

3t(ln2) = ln(20000)

t = $\frac{ln(20000)}{3(ln2)}$

t = $\frac{9.90349}{2.07944}=4.76$ hours

3 0

3 years ago

What Is the slope of a line perpendicular to y=x-6

postnew [5]

The slope of a line that is perpendicular to y = x - 6 means that the slope has to be a negative reciprocal of the original slope

That means the slope of the line that is perpendicular to y = x - 6 is '-1'

Hope that helps!

7 0

3 years ago

How do i plug in a sin equation for missing side length into a calculator

Anna11 [10]

$\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}$

$\\ \rm\Rrightarrow sin28=\dfrac{x}{20}$

Find value

$\\ \rm\Rrightarrow x=20sin28$

$\\ \rm\Rrightarrow x=9.38=9.4$

3 0

2 years ago

Read 2 more answers

Hi! can someone help with these questions? I’ll mark brainliest :) Have a nice day and thank you!

Delvig [45]

Answer:

7. 32

8. 68

9. 16

10. 29

Step-by-step explanation:

7. =90°-58

=32

8. =68°

9. = (1 + 5x)°

= (1 + 5(16)°

=81

10. = (2x + 3)°

= (2(29) + 3)°

= 61°

6 0

3 years ago