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2 years ago

Which of the following prime factorizations represents the greatest common factor of 162, 378, and 414?

Mathematics

2 answers:

ExtremeBDS [4]2 years ago

6 0

Answer:

2x3^3

Step-by-step explanation:

Helen [10]2 years ago

5 0

Answer:

The greatest common divisor is:

$2\times 3^2$

Step-by-step explanation:

The greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

162=2×81

= $2\times 3^4$

378= $2\times 3^3\times 7$

and 414= $2\times 3^2\times 23$

Hence,

The greatest common divisor is:

$2\times 3^2$

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Prove that. 1-sin2A=2sin^2(45-A)

Liula [17]

Answer:

Proved

Step-by-step explanation:

2 sin square( 45°-A)

(therefore;

by trigonometry ratios

sin45°=1)

=2sin2(1-A)

=2sin(1-A)

=1+sin2A

hence proved

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Tysm

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2 years ago

Miles has a square garden in his backyard. He decides to decrease the size of the garden by 1 foot on each side in order to make

rusak2 [61]

Answer:

6ft

36ftsquared

Step-by-step explanation:

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2 years ago

Read 2 more answers

• Texas: 2.69 x 10 5 square miles • Rhode Island: 1.21 x 10 3 square miles Determine the difference, in square miles, between th

BabaBlast [244]

Answer:

The difference between the area of Texas and Rhode Island in square miles and scientific notation = (2.68 × 10⁵) square miles.

Step-by-step explanation:

Area of Texas = (2.69 × 10⁵) square miles = 269000 square miles

Area of Rhode Island = (1.21 × 10³) square miles = 1210 square miles

Difference between the Area of the Texas and Rhode Island = 269000 - 1210 = 267,790 square miles = (2.68 × 10⁵) square miles.

The difference between the area of Texas and Rhode Island in square miles and scientific notation = (2.68 × 10⁵) square miles.

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8 0

2 years ago

A scale drawing of a rectangular park is 5 inches wide and 7inches long. The actual park is 280 yards long. What is the area of

choli [55]

280÷7=40. 280-80 = 200. 200×280=5,600 Length divided by scale length to find the amount that each inch scale size equals 40 yards per inch. 5 inches equals 200 yards Then multiply length times width. 200x280=5,600 yds

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2 years ago

Read 2 more answers

a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve a

Neporo4naja [7]

Answer:

Tangent at (1,2) has value $\frac{15}{4}$ . And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

$y^2=x^3+3x^2\hfill (1)$

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

$2y\frac{dy}{dx}=x^3+3x^2$

$\implies \frac{dy}{dx}=\frac{3(x^2+2x)}{2y}$

At (1, 2), tangent line is,

$\frac{dy}{dx}|_{(1,2)}}=\frac{15}{4}$

To find point of intersection of horizontal tangent we have to do,

$\frac{dy}{dx}=0$

$\implies x(x+2)=0\implies x=0 or -2$

Thus,

At x=0, y=0

but snce,

$\lim_{y\to 0}\frac{dy}{dx}\to \infty$

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

6 0

2 years ago