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2 years ago

Evaluate this function at x = 2: f(x)= 3x + 20 *

Mathematics

2 answers:

trasher [3.6K]2 years ago

5 0

Answer:

Step-by-step explanation:

Fitst, you substitute

f(2) = 3(2) + 20

f(2) = 6 + 20

f(2) = 26

your answer is 26

r-ruslan [8.4K]2 years ago

4 0

Answer:

c.) 26

Step-by-step explanation:

f(2) = 3(2) + 20

f(2) = 6 + 20

f(2) = 26

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How would I find the integral of <img src="https://tex.z-dn.net/?f=%5Cint%5Cfrac%7Btdt%7D%7Bt%5E4%2B2%7D" id="TexFormula1" title

kotegsom [21]

Let $t=\sqrt y$ , so that $t^2=y$ , $t^4=y^2$ , and $\mathrm dt=\dfrac{\mathrm dy}{2\sqrt y}$ . Then

$\displaystyle\int\frac t{t^4+2}\,\mathrm dt=\int\frac{\sqrt y}{2\sqrt y(y^2+2)}\,\mathrm dy=\frac12\int\frac{\mathrm dy}{y^2+2}$

Now let $y=\sqrt2\tan z$ , so that $\mathrm dy=\sqrt2\sec^2z\,\mathrm dz$ . Then

$\displaystyle\frac12\int\frac{\mathrm dy}{y^2+2}=\frac12\int\frac{\sqrt2\sec^2z}{(\sqrt2\tan z)+2}\,\mathrm dz=\frac{\sqrt2}4\int\frac{\sec^2z}{\tan^2z+1}\,\mathrm dz=\frac1{2\sqrt2}\int\mathrm dz=\dfrac1{2\sqrt2}z+C$

Transform back to $y$ to get

$\dfrac1{2\sqrt2}\arctan\left(\dfrac y{\sqrt2}\right)+C$

and again to get back a result in terms of $t$ .

$\dfrac1{2\sqrt2}\arctan\left(\dfrac{t^2}{\sqrt2}\right)+C$

3 0

3 years ago

A genetic experiment with peas resulted in one sample of offspring that consisted of 414 green peas and 154 yellow peas. a. Cons

alekssr [168]

Answer: a. The interval in percentage is (23.46% , 30.76%)

b. No

Step-by-step explanation: To determine the confidence interval of a proportion, first find the percentage of yellow in that population:

phat = $\frac{154}{414+154}$

phat = 0.2711

The level α is 95%

1 - α = 0.05

α/2 = 0.025

As the population is bigger than 30, use z-test.

According to the table, z-score for α/2 = 0.025 is z = 1.96

The error for the interval is:

E = z. $\sqrt{\frac{phat(1-phat)}{n} }$

E = 1.96. $\sqrt{\frac{0.2711(1-0.2711)}{568} }$

E = 1.96*0.01865

E = 0.0365

The lower and higher limits of the interval are:

phat - E = 0.2711 - 0.0365 = 23.46%

phat + E = 0.2711 + 0.0365 = 30.76%

In conclusion, the 95% confidence interval to estimate the percentage of yellow is (23.46%,30.76%)

b. No, because 25% is inside the interval meaning that it doesn't contradict the expectations.

5 0

2 years ago

How can you express 1/4 as a percent?

olganol [36]

Answer:

if 4/4 is 100% then you can divide it by 2 to get 50% and it becomes 2/4 then divide by 2 again to get 1/4 or 25%

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

How many times does 0.15 go into 500?

Alexxx [7]

One way is to divide 500 by 0.15
500/0.15=3333.3333333
the answer is about 3333 times

4 0

3 years ago

Read 2 more answers

Integrate <img src="https://tex.z-dn.net/?f=e%5E%7B4x%7D%5Csqrt%7B1%2Be%5E%7B2x%7D%20%7D%20dx" id="TexFormula1" title="e^{4x}\sq

AnnyKZ [126]

Answer:

$(\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C$

Step-by-step explanation:

Step(i):-

Given that the function

f(x) = $e^{4x} \sqrt{1+e^{2x} }$

Now integrating on both sides, we get

$\int\limits{f(x)} \, dx = \int\limits{e^{4x} \sqrt{1+e^{2x} } dx$

= $\int\limits{e^{2x} e^{2x} \sqrt{1+e^{2x} } dx$

Step(ii):-

Let $1 + e^{2x} = t$

$e^{2x} = t -1$

$2e^{2x}dx = d t$

$e^{2x}dx = \frac{1}{2} d t$

= $\int\limits{( \sqrt{1+e^{2x} }) e^{2x} e^{2x} dx$

= $\int\limits {\sqrt{t}(t-1)\frac{1}{2} dt }$

= $\frac{1}{2} \int\limits {\sqrt{t} (t) -\sqrt{t} ) dt }$

= $\frac{1}{2} \int\limits {(t^{\frac{1}{2} } t^{1} +t^{\frac{1}{2} } ) } \, dx$

$= \frac{1}{2} \int\limits {(t^{\frac{3}{2} } +t^{\frac{1}{2} } ) } \, dx$

= $\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{3}{2}+1 } + \frac{t^{\frac{1}{2} +1} }{\frac{1}{2}+1 } )+C$

= $\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{5}{2} } + \frac{t^{\frac{1}{2} +1} }{\frac{3}{2} } )+C$

= $\frac{1}{2} (\frac{t^{\frac{5}{2} } }{\frac{5}{2} } + \frac{t^{\frac{3}{2} } }{\frac{3}{2} } )+C$

= $(\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C$

Final answer:-

= $(\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C$

3 0

2 years ago