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2 years ago

Help please i realllyy need help

Mathematics

2 answers:

abruzzese [7]2 years ago

4 0

2 5/8. you can count the tally marks. they are out of 8 and the point stands on the fifth.

vredina [299]2 years ago

3 0

2 and 5/8: You would go from the number the fraction is closest to, and then add the fraction itself.

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Equilateral triangle ABC has an area of \sqrt{3}√ 3 . If the shaded region has an area of \piπK − \sqrt{3}√ 3 , what

Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* At first lets find the length of the side of the Δ ABC

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* Now lets find the radius of the circle

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ $(2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)$

∴ $4=r^{2}+r^{2}-2(r)(r)(-0.5)$

∴ $4=r^{2}+r^{2}-(-r^{2})$

∴ $4=r^{2}+r^{2}+r^{2}$

∴ $4=3r^{2}$

- Divide both sides by 3

∴ $r^{2}=\frac{4}{3}$

- Take square root for both sides

∴ r = 2/√3

* Lets find the value of k

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

7 0

3 years ago

Find the square inches

m_a_m_a [10]

Answer:

The area of the figure is 16

Step-by-step explanation:

If you look closely there are four squares inside the figure so you get the area of one square and times it by four for the area of 16.

5 0

3 years ago

Read 2 more answers

A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

8_murik_8 [283]

To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
where
$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
$e^{r}= \frac{4}{5}$
$ln(e^{r})=ln( \frac{4}{5} )$
$r=ln( \frac{4}{5} )$
$r=-02231$

Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
$A(0)=1250e^{(-0.2231)(0)$
$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
$m= \frac{-1115.72}{10}$
$m=-111.572$
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0

3 years ago

Pampered Pooch charges $5 for one hour of Doggy Daycare $10 for two hours and fifteen dollars for 3 hours what is the rate chang

DochEvi [55]

Answer:

$5 difference in rate at each step or change in hours.

Step-by-step explanation:

4 0

3 years ago

Please help me worth 35 points!!

mixer [17]

Answer:

Solution given:

Volume of rectangular prism=length*breadth*height

for

1st one 4in,3in,6in

Volume=4*3*6=72cu.in

For second one 6in,3in,2in

Volume=6*3*2=36cu.in

For third one 4in ,5in,4in

Volume=4*5*4=80cu.in

For forth one 2in,9in,3in

Volume=2*9*3=54cu.in

7 0

2 years ago

Read 2 more answers