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3 years ago

Estimate the answer 102.3 × 4.7

Mathematics

2 answers:

ddd [48]3 years ago

8 0

The estimated answer would be 480.81

Pavel [41]3 years ago

5 0

Answer:

500

Step-by-step explanation:

First of, multiply all of the number by 10 to remove the decimal place ( this will make it less confusing)

So 102.3 x 10= 1023

4.7 x 10 = 47

You will have to round each of the numbers to 1 significant figure (sf) :

1023 round to 1 sf will be 1000

47 rounded to 1 sf will be 50

Then multiply these numbers:

1000 x 50 = 50000

Finally divide by 100 to get back the decimal places

(You divide by 100 because you multiplied by 10 twice, 10 x 10= 100)

You get 500

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Is the function continuous at x = -17

Pavlova-9 [17]

For a function to be continuous at an x-value, say -17, you need to make sure two things line up:

The limit from the left equals the limit from the right.

$\lim_{x \to -17^{-}} f(x) = \lim_{x \to -17^{+}} f(x)$

This limit equals the functions value.

$\lim_{x \to -17} f(x) = f(-17)$

The left hand limit involves the first piece, f(x) = 20x + 1:

$\begin{aligned} \lim_{x \to -17^{-}} f(x) &= \lim_{x \to -17^{-}} (20x+1)\\[0.5em]&= 20(-17)+1\\[0.5em]&= -339\endaligned}$

The right hand limit invovles the second piece, f(x) = -10x^2:

$\begin{aligned} \lim_{x \to -17^{+}} f(x) &= \lim_{x \to -17^{+}} (-10x^2)\\[0.5em]&= -10\cdot (-17)^2\\[0.5em]&= -2890\endaligned}$

Since the two one-sided limits don't match, the function is not continuous at x=-17.

3 0

3 years ago

While taking a ride in a hot-air balloon in Napa Valley, Francisco wonders how high he is. To find out, he chooses a landmark th

mihalych1998 [28]

The solution would be like this for this specific problem:

sin 54 degrees = Height/718.0624

Height = (sin 54 degrees)(718.0624) = 580.9 ft

So the height of the balloon is 580.9 ft. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

8 0

3 years ago

Read 2 more answers

What is the domain (in interval notation) of the following functions?

alexgriva [62]

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$3.\\f(x)=\frac{\sqrt{x}}{x^2-5x}\\\\D:x\geq0\ \wedge\ x^2-5x\neq0\to x\geq0\ \wedge\ x(x-5)\neq0\\\\\to x\geq0\ \wedge\ x\neq0\ \wedge\ x\neq5\to x\in\mathbb{R^+}\ \backslash\ \{5\}\\\\4.\\g(x)=\frac{\sqrt{x}+5}{x^2-x-20}\\\\D:x\geq0\ \wedge\ x^2-x-20\neq0\to x\geq0\ \wedge\ (x+4)(x-5)\neq0\\\\\to x\geq0\ \wedge\ x\neq-4\ \wedge\ x\neq5\to x\in\left$

$5.\\h(x)=\frac{3}{x^2+1}\\\\D:x^2+1\neq0\to x^2\neq-1\to x\in\mathbb{R}\\\\6.\\f(x)=\frac{\sqrt{x-2}}{x+1}\\\\D:x-2\geq0\ \wedge\ x+1\neq0\to x\geq2\ \wedge\ x\neq-1\to x\in\left$

$7.\\g(x)=\frac{x^2}{3x^2-x-2}\\\\D:3x^2-x-2\neq0\to (3x+2)(x-1)\neq0\to x\neq-\frac{2}{3}\ \wedge\ x\neq1\\\\\to x\in\mathbb{R}\ \backslash\ \{-\frac{2}{3};\ 1\}\\\\8.\\h(x)=3(x-4)^2-7\\\\D:x\in\mathbb{R}$

4 0

3 years ago

76.00 km = ft?<br><br><br><br> Please someone help me

kifflom [539]

Answer:

76.00 km = 249344 ft.

4 0

3 years ago

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How to solve this equation 18.5 = -4.5 + 7(k + 6)

yawa3891 [41]

1. Add -4.5 to 18.5
2. Divide 23 by 7
3. Then subtract 6 from -2.7