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2 years ago

A) 7.7 ft b) 13.4 ft c) 10.3 ft d) 12.3 ft

Mathematics

1 answer:

ELEN [110]2 years ago

3 0

Answer:

D. 12.3 ft

Step-by-step explanation:

This problem requires the use of trigonometric ratios. This one specifically uses the cosine ratio as it provides the hypotenuse and is asking for the side that is adjacent to the angle.

cos(40°)=a/16

cos(40°)×16=a/16×16

cos(40°)×16=a

a=12.256 ft

The length of side a is D. 12.3 ft.

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Plz hurry!!!! thank you!!!!

RoseWind [281]

Answer:

$m\angle KLM=53.13^o$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

$KO=MO=r=5\ units$

$KM=8\ units$

Applying the law of cosines

$8^2=5^2+5^2-2(5)(5)cos(KOM)$

$64=50-50cos(KOM)$

$50cos(KOM)=50-64$

$50cos(KOM)=-14$

$cos(KOM)=-14/50$

$m\angle KOM=cos^{-1}(-14/50)$

$m\angle KOM=106.26^o$

step 2

Find the measure of the arc KM

we know that

$arc\ KM=m\angle KOM$ ----> by central angle

we have

$m\angle KOM=106.26^o$

$arc\ KM=106.26^o$

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising

$m\angle KLM=\frac{1}{2}[arc\ KM]$

we have

$arc\ KM=106.26^o$

substitute

$m\angle KLM=\frac{1}{2}[106.26^o]$

$m\angle KLM=53.13^o$

7 0

2 years ago

For the rational function f(x)=(-13x-27)/(x^(2)-4x-12), F(x)=2

grigory [225]

Should be 3.3125. Hope this helps

8 0

2 years ago

What is 0.15x10^-2 written in scientific notation?

Arada [10]

Step-by-step explanation:

fcgfsykmcsunvdsihjiutt

6 0

2 years ago

Jacob has 6.15 meters of rope. He is going to use 1.2 meters of rope to tie up his boat. How many centimeters of rope does he ha

mojhsa [17]

Answer:

495 cm

Step-by-step explanation:

Remark

When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.

Solution

Remaining rope = starting length - what was used.

Remaining rope = 6.15 - 1.2

Remaining rope = 4.95 meters

Answer

The remaining rope = 4.95 * 100 = 495 cm

5 0

2 years ago

The circumference of Circle K is pi. The circumference of Circle L is 4xpi.

dmitriy555 [2]

Answer:

Ratio of circumferences: $\displaystyle\frac{1}{4}$

Ratio of radii: $\displaystyle\frac{1}{4}$

Ratio of areas: $\displaystyle\frac{1}{16}$

Step-by-step explanation:

Hi there!

We are given:

- The circumference of Circle K is $\pi$

- The circumference of Circle L is $4\pi$

Therefore, the ratio of their circumferences would be:

$\displaystyle\frac{\pi}{4\pi}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for circumference is $C=2\pi r$ , where <em>r</em> is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.

If the circumference of Circle K is $\pi$ , or $1\pi$ , then its radius is $\displaystyle\frac{1}{2}$ .

If the circumference of Circle L is $4\pi$ , then its radius is $\displaystyle\frac{4}{2}$ , which is 2.

Therefore the ratio their radii would be:

$\displaystyle\frac{\frac{1}{2}}{{2}}$ ⇒ $\displaystyle\frac{1}{2}*\frac{1}{2}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for area is:

$A=\pi r^2$

First, let's find the area of Circle K:

$A=\pi (\displaystyle\frac{1}{2})^2\\\\A=\displaystyle\frac{1}{4}\pi$

Now, let's find the area of Circle L:

$A=\pi (2)^2\\A = 4\pi$

Therefore, the ratio of their areas would be:

$\displaystyle\frac{\frac{1}{4}\pi}{4\pi}$ ⇒ $\displaystyle\frac{\frac{1}{4}}{4}$ ⇒ $\displaystyle\frac{1}{4} * \frac{1}{4}$ ⇒ $\displaystyle\frac{1}{16}$ when simplified

I hope this helps!

5 0

1 year ago