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2 years ago

What is the common ratio for the geometric sequence below, written as a fraction?

Mathematics

2 answers:

loris [4]2 years ago

7 0

Answer:

5/8

Step-by-step explanation:

Hope this helps :)

MaRussiya [10]2 years ago

3 0

5/8 hope this helps!!

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NEED HELP ASAP!<br> find the volume of the cylinder

denpristay [2]

Answer:

V = 314.2 ft^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h r is the radius (5) and h is the height (4)

Using the pi button for pi

V = pi (5^2) (4)

V =314.1592654

Rounding to the nearest tenth

V = 314.2 ft^3

3 0

3 years ago

You put 5000 and a bank account that will give you 2% interest on the money in the account every year how much money will be in

ANEK [815]

Answer:

$7,429 I think (it has to be 20 characters ignore this part)

8 0

2 years ago

Tienes un triángulo equilátero con lados de 10cm, lo divides en dos partes de manera horizontal tal que el área de ambos figuras

Tanya [424]

Answer:

x = 10/√2 ≈ 7.07

Step-by-step explanation:

Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.

Aplicando el teorema de Tales, sabemos que:

$\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}$

También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:

$\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2$

Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:

$(l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}$

Podemos entonces despejar x de la siguiente manera:

$h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07$

6 0

3 years ago

7.<br> Write three other fractions that are equivalent to 10 Explain or show your reasoning.

Tpy6a [65]

Answer:

500/50, 600/60, 700/70

Step-by-step explanation:

500/50 equals 10 and so do the others. This is because the fraction line means division.

Have a nice day!!!!!! :-)

3 0

3 years ago

What is the exact value of sin(theta + beta)?

NISA [10]

Answer: $\frac{-3\sqrt{13}+4\sqrt{3}}{20}$

This is the single fraction of -3*sqrt(13)+4*sqrt(3) up top all over 20.

sqrt = square root

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

Explanation:

Angle theta is between pi and 3pi/2. This places the angle in quadrant Q3 where both cosine and sine are negative

Use the pythagorean trig identity to get the following:

$\sin^2 \theta + \cos^2 \theta = 1\\\\\sin^2 \theta + \left(-\frac{\sqrt{3}}{4}\right)^2 = 1\\\\\sin^2 \theta + \frac{3}{16} = 1\\\\\sin^2 \theta = 1 - \frac{3}{16}\\\\\sin^2 \theta = \frac{16}{16} - \frac{3}{16}\\\\\sin^2 \theta = \frac{16-3}{16}\\\\\sin^2 \theta = \frac{13}{16}\\\\\sin \theta = -\sqrt{\frac{13}{16}} \ \text{ ... sine is negative in Q3}\\\\\sin \theta = -\frac{\sqrt{13}}{\sqrt{16}}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\$

Angle beta is in Q1 where sine and cosine are positive.

Draw a right triangle with legs 3 and 4. The hypotenuse is 5 through the pythagorean theorem. In other words, we have a 3-4-5 right triangle.

Since $\tan \beta = \frac{3}{4}$ , this means $\sin \beta = \frac{3}{5} \ \text{ and } \ \cos \beta = \frac{4}{5}$

Use these ideas:

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

In this case we have: opposite = 3, adjacent = 4, hypotenuse = 5.

-------------------------------------

To recap:

$\cos \theta = -\frac{\sqrt{3}}{4}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\\cos \beta = \frac{3}{5}\\\\\sin \beta = \frac{4}{5}\\\\$

They lead to this

$\sin\left(\theta + \beta\right) = \sin \theta * \cos \beta - \cos \theta * \sin \beta\\\\\sin\left(\theta + \beta\right) = -\frac{\sqrt{13}}{4} * \frac{3}{5} - \left(-\frac{\sqrt{3}}{4}\right) * \frac{4}{5}\\\\\sin\left(\theta + \beta\right) = -\frac{3\sqrt{13}}{20}+\frac{4\sqrt{3}}{20}\\\\\sin\left(\theta + \beta\right) = \frac{-3\sqrt{13}+4\sqrt{3}}{20}\\\\$

6 0

2 years ago