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2 years ago

7

A large field measures 70 feet by 525 feet. If you divide it up into equal square garden plots, what size would the largest poss

ible plot be with sides of whole number length?

1 answer:

fenix001 [56]2 years ago

7 0

9514 1404 393

Answer:

35 feet square

Step-by-step explanation:

The greatest common factor of 70 and 525 is 35. The largest square plot can be 35 feet on a side.

70 = 2·35

525 = 15·35

__

I like to find the GCD (greatest common divisor) using Euclid's algorithm. We find the remainder when dividing the larger by the smaller. When that remainder is not zero, we replace the larger number with the remainder, and repeat. When the remainder is zero, the divisor is the GCD.

525/70 = 7 r 35

70/35 = 2 r 0 . . . . . 35 is the GCD

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i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

2 years ago

2. solve 4w − 7k = 28 for k. show your work

NISA [10]

4w-7k=28
-7k+4w+-4w=28+-4w
-7k=-4w+28
-7k/-7=-4w+28/-7
k=4/7w-4

:)

5 0

3 years ago

Anyone got me with them quick maths?

Natali5045456 [20]

Answer:

Its B

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Compare 9.36 and 9.359

Sati [7]

Try this option (this is not the only way!):

1. the rule: if 'number_1' - 'number_2' > 0, then number_1>number_2. If 'number_1'-'number_2'<0, then number_2>number_1.

2. according to the rule above: 9.36-9.359=0.001. 0.001>0, it means, 9.36>9.359.

6 0

3 years ago

3 3/4 times 2 1/3 times 7/2<br><br><br><br><br><br> I really need some help on this

MrRa [10]

<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>:</em><em>)</em>

3 0

2 years ago

Read 2 more answers