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3 years ago

Complete the following state lament and round to the nearest hundredth

Mathematics

1 answer:

nekit [7.7K]3 years ago

3 0

Answer:

7.07

Step-by-step explanation:

If you substitute in 0 for x:

2(0)^2 + 5sqrt(2)

You'd end up with 5 root 2, which is 7.07

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I have a 6 grader thst needs help with percentages; what assistance do you have here.

mr Goodwill [35]

Answer:

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Step-by-step explanation:

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3 years ago

the equation shows the radius of the algae,f(d), in mm,after d days: f(d)=7(1.06)^d the radius of the algae was approximately 13

Andrei [34K]

Answer:

$\begin{gathered} A)\text{ }Domain:\text{ \lparen0,11\rparen} \\ B)\text{ the y-intercept represents that in 0 days the diameter of the algae will be 7 mm.} \\ C)\text{ rate of change= 0.64. This means that on average the algae grows 0.64mm per day.} \end{gathered}$

Step-by-step explanation:

If the radius of the algae was approximately 13.29 mm, substitute f(d)=13.29 and solve for d to determine the domain:

$\begin{gathered} 13.29=7\left(1.06\right)^d \\ \frac{13.29}{7}=1.06^d \\ d=\frac{\text{ log\lparen13.29/7\rparen}}{\text{ log\lparen1.06\rparen}} \\ d=11 \\ \text{ Then, the domain:} \\ (0,11) \end{gathered}$

B. The y-intercept is obtained when d=0, hence;

$\begin{gathered} d=0 \\ f(0)=7(1.06)^0 \\ f(0)=7 \end{gathered}$

Therefore, the y-intercept represents that in 0 days the diameter of the algae will be 7 mm.

C. Now, to determine the rate of change of a function, use the following equation:

$\text{ rate of change=}\frac{change\text{ over y}}{change\text{ over x}}$

Then, determine the value of f(4):

$\begin{gathered} f(4)=7(1.06)^4 \\ f(4)=8.83 \end{gathered}$

Hence, the rate of change on that interval of the function:

$\begin{gathered} \text{ rate of change=}\frac{13.29-8.83}{11-4} \\ \text{ rate of change=0.64 } \end{gathered}$

This means that on average the algae grows 0.64mm per day.

8 0

1 year ago

John lives in Vermont and Julie lives in Florida. One January day, it was 52°F in Florida and 9°F in Vermont. What was the diffe

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

52-9=43

8 0

2 years ago

Find the solution to the differential equation dz/dt = 7te^4z that passes through the origin.

andreev551 [17]

Answer:

$z=(\frac{-1}{4} )ln|1-14t^{2}|\\$

Step-by-step explanation:

from the equation, $\frac{dz}{dt}=7te^{4z}\\$ .

we can give different approach to the equation, but to make it simple and direct, let separate the equation by bringing all like terms to the same side i.e

$\frac{dz}{e^{4z}}=7tdt\\e^{-4z} dz=7tdt$ .

if we integrate both side,

$\int\limits^a_b{e^{-4z} } \,dz =\int\limits^a_b {7t} \,dt$

$-1/4e^{-4z} +c_{1}=7/2t^{2} +c_{2}\\-1/4e^{-4z}= 7/2t^{2} +c_{2}-c_{1}\\let c_{2}-c_{1}=c \\-1/4e^{-4z}= 7/2t^{2} +c$

since the equation passes through the origin, and at the origin z=0 and t=0

we substitute this values and solve for the constant c

$e^{-4*0}= 7/2*0 +c\\c=1$ .

If we substitute the value of c into the equation we arrive at

$(-1/4)e^{-4z}= (7/2)t^{2}+1\\ e^{-4z}=1-14t^{2} \\$

if we the the natural logarithm of both sides, we arrive at

$-4z=ln|1-14t^{2}|\\z=(\frac{-1}{4} )ln|1-14t^{2}|\\$

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3 years ago

Please help answer <br>A ans C please <br>on the image.

photoshop1234 [79]

In January and June the inflation rate was the highest. From June to December the inflation rate continued to go lower and lower. In December the inflation rate was the lowest it has ever been.

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3 years ago