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3 years ago

Skye needs 50 g of sugar to make 30 biscuits.

Mathematics

1 answer:

olga_2 [115]3 years ago

5 0

Answer:600g

Step-by-step explanation: 50x3=150 150x4=600 since 30x4=120

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What is 6/10 rounded to the nearest half

belka [17]

6/10 rounding to the nearest half would be 1, not 0.

Reason for this: Here is a number line to help you!

|----|----|

Left line = 0

Middle line = 1/2

Right line = 1

Here is another rule!

0/10, 1/10, 2/10, 3/10, 4/10 = rounded to the nearest half would be 0

5/10, 6/10, 7/10, 8/10, 9/10, 10/10 = rounded to the nearest half would be 1.

So 6/10 rounded to the nearest half is 1.

Hope this helped!

Plz mark brainliest!

5 0

3 years ago

What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?

scoray [572]

Answer:

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to c} x = c$

Special Limit Rule [L’Hopital’s Rule]:
$\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]:
$\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify given limit.

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}$

Step 2: Find Limit

Let's start out by directly evaluating the limit:

[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}$

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

[Limit] Apply Limit Rule [L' Hopital's Rule]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}$
[Limit] Differentiate [Derivative Rules and Properties]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}$
[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}$

∴ we have evaluated the given limit.

___

Learn more about limits: brainly.com/question/27807253

Learn more about Calculus: brainly.com/question/27805589

___

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

3 0

2 years ago

Find the area of a square with a diagonal of 8cm.

klio [65]

You have to use the Pythagorean theorem but there is a little twist here since a square has has equal sides. So:
x^2+x^2=8
2x^2=8
2/2x^2=8/2
x^2=4
√x^2=√4
x=2
The side of the square is 2.
So now the area of a square is:
Side×Side
2×2=4
The area of the square is 4 centimetres

7 0

3 years ago

The numbers 2-12 are written on cards and placed in the bag.what is the probability of picking an even number then replacing it

weeeeeb [17]

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

There are 11 numbers on cards.

6 cards contain even numbers.

Answer: p(even) = 6/11

There is only one card with a 7. After the first card is picked and returned, there are 11 cards in the bag again.

p(even then 7) = p(even) * p(7) = 6/11 * 1/11 = 6/121

Answer: p(even then 7) = 6/121

4 0

3 years ago

I am having trouble with this ellipse problem. Please help right away

Vitek1552 [10]

Answer:

a. The distance from the center to either vertex

Step-by-step explanation:

The distance from the center to a vertex is the fixed value a. The values of a and c will vary from one ellipse to another, but they are fixed for any given ellipse.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

3 0

3 years ago