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1 year ago

Factor the expression given below. Write each factor as a polynomial in

Mathematics

1 answer:

kherson [118]1 year ago

6 0

The factorization of the expression of 43x³ + 216y³ is

(7x + 6y)(49x² - 42xy + 36y²)

Step-by-step explanation:

The sum of two cubes has two factors:

1. The first factor is $\sqrt[3]{1st}$ + $\sqrt[3]{2nd}$

2. The second factor is ( $\sqrt[3]{1st}$ )² - ( $\sqrt[3]{1st}$ ) ( $\sqrt[3]{2nd}$ ) + ( $\sqrt[3]{2nd}$ )²

Ex: The expression a³ + b³ is the sum of 2 cubes

The factorization of a³ + b³ is (a + b)(a² - ab + b²)

∵ The expression is 343x³ + 216y³

∵ $\sqrt[3]{343x^{3}}$ = 7x

∵ $\sqrt[3]{216y^{3}}$ = 6y

∴ The first factor is (7x + 6y)

∵ (7x)² = 49x²

∵ (7x)(6y) = 42xy

∵ (6y)² = 36y²

∴ The second factor is (49x² - 42xy + 36y²)

∴ The factorization of 43x³ + 216y³ is (7x + 6y)(49x² - 42xy + 36y²)

The factorization of the expression of 43x³ + 216y³ is

(7x + 6y)(49x² - 42xy + 36y²)

Learn more:

You can learn more about factors in brainly.com/question/10771256

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The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are

castortr0y [4]

Answer:

i think c 21600pi

Step-by-step explanation:

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2 years ago

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A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

maksim [4K]

Answer:

Boat traveled 553.24 feet towards the lighthouse.

Step-by-step explanation:

In the figure attached AB is the light house of height 200 feet.

Angle of depression of the boat from the top of a lighthouse = angle of elevation of the lighthouse from the boat = 14°52'

so 1' = $\frac{1}{60}$ degree

so angle of elevation at point C = 14 + $\frac{52}{60}$

So angle of elevation from C = (14 + 0.87) = 14.87°

Similarly, when boat arrives at point D angle of elevation = 45°10' = 45 + $\frac{10}{60}$ = 45.17°

Now we have to calculate the distance CD, traveled by the boat.

In ΔABC

tan14.87 = $\frac{200}{BC}$

0.2655 = $\frac{200}{BC}$

BC = $\frac{200}{0.26552}$

BC = 753.239 feet

Similarly in ΔABD

tan45.17 = $\frac{200}{BD}$

1 = $\frac{200}{BD}$

BD = 200 feet

So distance CD = BC - BD

CD = 753.239 - 200

= 553.24 feet

Therefore, Boat traveled 553.24 feet towards the lighthouse.

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1 year ago

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In ΔMNO, the measure of ∠O=90°, ON = 65, MO = 72, and NM = 97. What is the value of the tangent of ∠M to the nearest hundredth?

PilotLPTM [1.2K]

Answer:

Therefore the value of tangent of ∠ $M$ is $42$ °.

Step-by-step explanation:

Given that,

In Δ $MNO$ , ∠ $O=90$ °, $ON=65,$ $MO=72,$ and $NM=97.$

and we have to find the value of tangent of ∠ $M.$

Diagram of the given triangle is shown below:

Now,

Δ $MNO$ is a right angle triangle, so we can use all the trigonometric ratio.

$sin\alpha =\frac{Perpendicular}{Hypotenuse}$

$cos\alpha =\frac{Base}{Hypotenuse}$

$tan\alpha =\frac{sin\alpha }{cos\alpha }$ = $\frac{Perpendicular}{Base}$

tangent of ∠ $M$ = $\frac{Perpendicular}{Base}$

= $\frac{ON}{MO}$

= $\frac{65}{72}$

= $0.90278$

∴∠ $M$ = $tan^{-1} (0.90278)$

= $42.0750$ ° ≅ $42$ °

Therefore the value of tangent of ∠ $M$ is $42$ °.

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1 year ago

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

masha68 [24]

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

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1 year ago

A 20-inch diameter bicycle tire rotates 200 times.

fenix001 [56]

Answer: B)1,047 feet

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate the circumference of the tire:

Circumference(C): π x diameter

C = π (20) = 62.83 inches.

Since 1 foot is equal to 12 inches.

62.83 ÷ 12 = 5.23 feet

Finally we have to multiply the result by 200:

5.23 x 200 = 1,047 feet

Feel free to ask for more if needed or if you did not understand something.

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2 years ago