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2 years ago

Which expression represents: twice a number increased by 39

Mathematics

1 answer:

Cerrena [4.2K]2 years ago

8 0

Answer:

2x+39

Step-by-step explanation:

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Find the absolute maximum and absolute minimum values, if any, of the function. (If an answer does not exist, enter DNE.)f(x) =

lyudmila [28]

Answer:

The absolute minimum value is " $-\frac{21}{4}$ " and the absolute maximum value is " $15$ ".

Step-by-step explanation:

Given:

$f(x)=x^2-x-5$

on,

$[0,5]$

By differentiating it, we get

⇒ $f'(x)=2x-1$

Set $f'(x)=0$

then,

⇒ $2x-1=0$

$2x=1$

$x=\frac{1}{2}$ (Critical point)

When x=0,

⇒ $f(x)=-5$

When $x=\frac{1}{2}$ ,

⇒ $f(x)=-\frac{21}{4}$ (Absolute minimum)

When $x=5$

⇒ $f(x)=15$ (Absolute maximum)

7 0

2 years ago

Help please 10 points

xxTIMURxx [149]

Answer:

Step-by-step explanation:

tell me the question ?? did not say the question ok ??

8 0

2 years ago

Using the functions presented in the example, how much can Cam expect to earn if he sells all the corn produced on 1.5 acres?

12345 [234]

Answer:

Cam expect to earn if he sells all the corn produced on 1.5 acres is $8725.

Step-by-step explanation:

Given : $C(a)=7500a-1500$ , $M(C)=0.9C- 50$ and $M(C(a))=6750a-1400$

To find : How much can Cam expect to earn if he sells all the corn produced on 1.5 acres?

Solution :

$C(a)=7500a-1500$

Substitute a=1.5,

$C(1.5)=7500(1.5)-1500$

$C(1.5)=11250-1500$

$C(1.5)=9750$

Now, taking function $M(C)=0.9C- 50$

Substitute C=9750,

$M(9750)=0.9(9750)- 50$

$M(9750)=8775- 50$

$M(9750)=8725$

Now, taking function $M(C(a))=6750a-1400$

Substitute a=1.5,

$M(C(1.5))=6750(1.5)-1400$

$M(C(1.5))=10125-1400$

$M(C(1.5))=8725$

Therefore, Cam expect to earn if he sells all the corn produced on 1.5 acres is $8725.

8 0

2 years ago

What is 4/10, 6/20, and 10/25 in simplest form?

Dennis_Churaev [7]

4/10 in simplest form is 2/5
6/20 in simplest form is 3/10
10/25 in simplest form is 2/5

3 0

2 years ago

Read 2 more answers

Evaluate the integral, show all steps please!

Aloiza [94]

Answer:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x$

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

$\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x$

Integration by substitution

$\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

$\textsf{Let }x=3 \sin \theta$

$\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}$

Find the derivative of x and rewrite it so that dx is on its own:

$\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta$

$\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta$

Substitute everything into the original integral:

$\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta$

$\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$