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3 years ago

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Can someone please respond to me and help me out with these 4 problems I must show my work and include an expression , evaluatio

n and label for my answers or I won’t get full credit 20-22 questions 17-19 I just include an equation, answer and label for each question

1 answer:

AlladinOne [14]3 years ago

4 0

Answer: A train traveled486 miles in 7 hours

They would be going at least 40 - 70

Step-by-step explanation:

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What is the national fruit of India?

ryzh [129]

The National fruit of India is Mango

3 0

2 years ago

Read 2 more answers

What is the solution of the system?

Kryger [21]

Greetings!

Solve the System, using Elimination:
$\left \{ {{4x+2y=18} \atop {2x+3y=15}} \right.$

Multiply Equation #2 by 2:
$\left \{ {{4x+2y=18} \atop {2(2x+3y)=2(15)}} \right.$

$\left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.$

Eliminate variable x:
$-\frac{ \left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.}{0x-4y=-12}$

$4y=-12$

Divide both sides by 4:
$\frac{4y}{4}= \frac{12}{4}$

$y=3$

Input this value into one of the Equations:
$4x+2y=18$

$4x+2(3)=18$

Simplify:
$4x+6=18$

$(4x+6)+(-6)=(18)+(-6)$

$4x=12$

Divide both sides by 4.
$\frac{4x}{4}= \frac{12}{4}$

$x=3$

The Solution to this System (The Point of Intersection):
$\boxed{(3,3)}$

I hope this helped!
-Benjamin

7 0

3 years ago

A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the

Ilya [14]

Answer:

The original selling price would be $ 515.87 ( approx )

Step-by-step explanation:

Let x be the original selling price ( in dollars ),

After marking down 10%,

New selling price = x - 10% of x = x - 0.1x = 0.9x

Again after marking down 30%,

Final selling price = 0.9x - 30% of 0.9x

= 0.9x - 0.3 × 0.9x

= 0.9x - 0.27x

= 0.63x

According to the question,

0.63x = 325

$\implies x =\frac{325}{0.63}\approx 515.87$

Hence, the original selling price would be $ 515.87.

7 0

2 years ago

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:

<u>Fundamental Theorem of Calculus</u>

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

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:

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

<u>Integration by substitution</u>

<u />

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

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

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

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

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

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

<u>Substitute</u> 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})$\end{minipage}}$

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

$\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}$

$\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}$

$\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:$

$\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}$

$\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:$

$\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Learn more about integration by substitution here:

brainly.com/question/28156101

brainly.com/question/28155016

4 0

2 years ago

I can create and use a graph to predict values and justify my results? Help me with this please I would appreciate it

mestny [16]

Answer:

simple even tho im in 6th grade it would be over $100

5 0

2 years ago