Solve for x. 4(2x + 1) = 3(x + 8)

The population of a certain species of fish has a relative growth rate of 1.1% per year. It is estimated that the population in

Juliette [100K]

Answer:

(a) n(t) = P(0)*e^(0.010939940t)

(b) 12,674,681 (nearest unit)

(c) 14 years (nearest year)

Step-by-step explanation:

rate = 1.1% / year = 1.011

(a)

P(0) = 12,000,000 = population in 2010

In compound interest format, after t years

P(t) = P(0)* (1.011)^t

Given format = P(0)* e^(rt)

therefore

e^(rt) = 1.011^t use law of exponents

(e^r)^t = 1.011^t

e^r = 1.011

r = log_e(1.011) = 0.010939940 (to 9 decimal places)

required formula is

n(t) = P(0)*e^(0.010939940t)

(b)

in 2015,

P(0)=12000000, n = 5 (years after 2010)

n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)

(c)

to reach 14 million, we equate

n(t) = 14,000,000

12,000,000 *e^(0.010939940*t) = 14,000,000

e^(0.010939940*t) = 14000000/12000000 = 7/6

take log on both sides

0.010939940*t = log(7/6)

t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.

See graph attached. Y-axis is in millions, x-axis is in years.

4 0

3 years ago

Given that Cos0=5/13,find a)Tan0,b)Sin0,c)Sec0,d)Co sec0,e)Cot0,

aliina [53]

Step-by-step explanation:

cos 0=5/13. B/H

p=√h2 - b2

= √13 square -5 square

=√169 -25

=√144

=12 Ans

Tan0=p/b =12/5. , sin0=p/h =12/13,. sec0= h/b =13/5 ,. Co sec0 =h/p =13/12 , cot0 =b/p=5/12

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4 0

2 years ago

Find the length of diagonal HJ. Round to the nearest hundredth.

Alisiya [41]

Answer:

The length of the diagonal HJ is 10.82 units

Step-by-step explanation:

* Lets revise the rule of the distance between two points

- $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ , where

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ are the two points

* Lets use this rule to find the length of the diagonal HJ

∵ The coordinates of point H are (-4 , 3)

∵ The coordinates of point J are (5 , -3)

∴ $x_{1}=-4$ and $x_{2}=5$

∴ $y_{1}=3$ and $y_{2}=-3$

- Lets find the length of the diagonal HJ by using the rule above

∴ HJ = $\sqrt{(5-(-4))^{2}+(-3-3)^{2}}=\sqrt{(5+4)^{2}+(-6)^{2}}$

∴ HJ = $\sqrt{(9)^{2}+36}=\sqrt{81+36}=\sqrt{117}=10.81665$

∴ HJ = 10.82

* The length of the diagonal HJ is 10.82 units

7 0

3 years ago

1. Use the formula S(d)=√9.8d to calculate the estimated speed, in meters per second, of a tsunami if the disturbance occurred a

postnew [5]

Answer: 1. 210 meters per second .

2. 756 kilometers per hour.

Step-by-step explanation:

Given : The formula $S(d)=\sqrt{9.8d}$ to calculate the estimated speed, in meters per second of a tsunami.

1. If the disturbance occurred at an ocean depth of 4,500 meters.

Then put d= 4500 in the above formula , we get

$S(d)=\sqrt{9.8\times4500}$

$S(d)=\sqrt{44100}=\sqrt{21\times21\times10\times10}\\\\=\sqrt{210^2}=210$

Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .

Also, A meter per second is equal to 3.6 kilometers per hour.

i.e. 1 meter per second = 3.6 kilometers per hour

Then by unitary method ,

210 meters per second = $3.6\times210$ kilometers per hour

=756 kilometers per hour.

3 0

3 years ago

The parent cosine function is transformed to create the function . which graphed function has the same amplitude as function m?

Shkiper50 [21]

Based on the graph given, the option that will show the same amplitude as function m is graph D.

<h3>Which graphed function is this about?</h3>

The cosine function is seen as:

f(x) = A*cos(kx) + M

And the functions are:

A stands for amplitude,
k is angular frequency,
M is the midline.

When the function is m(x) = -2*cos(x+π).

The absolute value of the amplitude will be 2*|-2| = 4

Therefore, the option that can have the requirement above is graph D.

Learn more about cosine from

brainly.com/question/23563998

#SPJ4

8 0

1 year ago