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3 years ago

In the diagram below AQRS is an equilateral triangle and RT

Mathematics

1 answer:

Minchanka [31]3 years ago

5 0

Answer:

The answer is D.

Step-by-step explanation:

AQRT is a 30-60-90 triangle.

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Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

If the area of a baseball diamond (shape of a square) is 8100 ft squared, how would you find the distance from 1st base to 3rd b

Readme [11.4K]

Answer:

Exact distance = $90\sqrt{2}$ feet
Approximate distance = 127.2792 feet.

===========================================================

Explanation:

The area of the square is 8100 square feet, abbreviated ft^2.

Apply the square root to find the distance from any base to its adjacent counterpart (eg: from 1st to 2nd base). So we get sqrt(8100) = 90 ft as that side distance. Notice that 90*90 = 8100.

If you were to draw a line from 1st base to 3rd base, then you would split the square into two congruent right triangles. Each right triangle is isosceles (the two legs being 90 ft each).

Use the pythagorean theorem to find the hypotenuse.

$a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{90^2+90^2}\\\\c = \sqrt{2*90^2}\\\\c = \sqrt{2}*\sqrt{90^2}\\\\c = \sqrt{2}*90\\\\c = 90\sqrt{2} \ \text{ ... exact distance}\\\\c \approx 127.2792 \ \text{ ... approximate distance}\\\\$

The distance from 1st to 3rd base is roughly 127.2792 feet.

5 0

2 years ago

Work out (3.6 x 10^-5) ÷ (1.8 x 10^2) give your answer in standard form

tatuchka [14]

.000036/180=.0000002

3 0

3 years ago

Find the value of x in the triangle shown below.

almond37 [142]

Answer:

x=69.41860973

Step-by-step explanation:

We can use the law of sines

sin x sin 55

------------- = -----------

4 3.5

Using cross products

3.5 sin x = 4 sin 55

Divide each side by 3.5

sin x = 4/3.5 sin 55

Take the inverse sin of each side

x = sin ^-1 ( 4/3.5 sin 55)

x=69.41860973

7 0

3 years ago

Simple Interest:<br><br>54000 x 0.038 x (3/12) = <br> I don't know what I'm doing wrong

kirill115 [55]

The simple interest rate equation is I = Prt
I = interest
P = principle ($54,000)
r = rate (3.875%)
t = time (3 months, so .25 years)

I = Prt
I = (54,000)*(.03875)*(.25)
I = $523.125

8 0

3 years ago

Read 2 more answers