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3 years ago

When finding the 9th term in a geometric sequence with a common ratio of 2 and a first

Mathematics

1 answer:

Zarrin [17]3 years ago

5 0

Answer:

Step-by-step explanation:

Nth term of a geometric sequence is given as:

$t_n = a r^{(n-1)}$ ...(1)

Plugging n = 9, a = 3 and r = 2 in the above equation, we find:

$t_9 = (3) (2)^{9-1}$

$t_9 = (3) (2)^{8}$ ... (2)

Comparing equations (1) & (2), we obtan:

(n - 1) = 8

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3 years ago

In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.

Sveta_85 [38]

Answer:

0.51 cm

Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

$\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm$

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

$\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M$

In the right triangle, two acute angles are always complementary, so

$m\angle M=90^{\circ}-m\angle P=90^{\circ}-21^{\circ}=69^{\circ}$

Thus,

$MH=1.43\cos 69^{\circ}\approx 0.51\ cm$

7 0

3 years ago

The area of a rectangle is pool is (15x-9) square units. Factor 15x-9 to find possible dimensions of the pool

Darya [45]

This is the concept of algebra, given that the area of a rectangular pool is (15x-9), the possible dimensions of the pool by factoring will be:
Area=length×width
Area=(15x-9)
factoring the above we get:
Area=3(5x-3)
therefore the possible dimension will be:
length=5x units
width=3 units

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3 years ago

Read 2 more answers

When you divide a whole number by a whole number( other then one), the quotient is a smaller number?

Ostrovityanka [42]

Yes because division always makes numbers smaller. For example: 12 divided by 4 equals 3.

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3 years ago

How to find angle of x in angles

rodikova [14]

Answer:

By using the one the straight line degrees if your doing it for a circle or 180 degrees for a triangle.