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3 years ago

Me jackson buys 4 kilograms of peanuts at the sale how many grams of peanuts does he get in all

Mathematics

1 answer:

kolezko [41]3 years ago

5 0

Answer:

4600 grams of peanuts

Step-by-step explanation:

For 2 kg of peanuts the customer will get 300 g free.

So if 4 kg of peanuts the customer will get 600 g free.

1kg = 1000g

If 4kg, thus it is 4000g

All mass of peanut the customer gets is 4000g + 600g = 4600g of peanuts.

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3 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})$\end{minipage}}$

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

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

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

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

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

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

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

Learn more about integration by substitution here:

brainly.com/question/28156101

brainly.com/question/28155016

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2 years ago

Find the value of x. Round to the nearest tenth.

gizmo_the_mogwai [7]

Answer: 76.5

Step-by-step explanation:

Interior angles of a triangle = 180 degrees so then you do 180-27 to get 153. Then 153 divided by 2 = 76.5

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3 years ago

What is the rate of change in decimal form for the points (1,5) (0,-3)

seraphim [82]

Answer:

The rate of change between (1, 5) and (0, -3) would be 8.0.

Step-by-step explanation:

"What is the rate of change between these two points" is the same as asking "what is the slope between these two points".

We are given the two points (1, 5) and (0, -3) and we are asked to find the rate of change (slope) between these two points. To do this, we could use the slope formula to find the rate of change between the two points. The slope formula is:

$\frac{y_2-y_1}{x_2-x_1}$

where (x₂, y₂) and (x₁, y₁) are the two points that we are trying to find the slope between.

Lets make (x₂, y₂) = (1, 5) and (x₁, y₁) = (0, -3). (It does not matter which is (x₂, y₂) and which is (x₁, y₁)). Now plug (x₂, y₂) = (1, 5) and (x₁, y₁) = (0, -3) into the equation:

$\frac{5-(-3)}{1-0} =\frac{8}{1}=8$

8 = 8.0, so the answer would be 8.0.

The rate of change between the two points would be 8.0.

I hope you find my answer helpful. :)

3 0

3 years ago