What is 1/3 of 3/7 and Explain Why

What is the length of the line to the nearest sixteenth of an inch

Inga [223]

the length of the line is 2 1/16

8 0

3 years ago

Please help me with this question and thank you for your help

Volgvan

The question is asking for the pattern of change within the given numbers. As you can see, the number decreases by 0.02 from left to right. Therefore, D is the correct answer. The whole number and tenths place remains constant as the hundredths place lowers by 2.

4 0

3 years ago

Read 2 more answers

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

81^3/4 how do i simply/?

Slav-nsk [51]

When you have something to an exponent and the exponent is a fraction it basically means the numerator is the power of the number and denominator is the root of the number.
81^3= 531441
4 root (531441)=27
if you have a graphing or scientific calculator you should be able to enter straight in 81^(3/4).

7 0

3 years ago

If a jar contains 3 blueberry, 4 ginger, 1 green, and 6 regular tea bags, what is the probability that a blueberry or ginger tea

Nonamiya [84]

Answer:

3/14

Step-by-step explanation:

Well first, add up all the numbers, and you get: 14.

Then, the blueberry has 3 tea bags. So, if there are 14 total bags, with 3 blueberry bags, the answer would be: 3/14.

6 0

3 years ago

Read 2 more answers