Mathematics College

Pls help!! Find the area of the lighter shaded region and round to the nearest tenth.

Answers

Answer 1

Answer:

5.1 cm² approximately

Step-by-step explanation:

A lighter= Area inscribed -1/2r² sin80°

A lighter=π r² (80°/360°) -1/2(5 cm)² sin 80°

A lighter=π(5cm)² (80°/360°) -1/2(5 cm)² sin 80°

A lighter=3.14*25cm²(80°/360°) - 12.5cm² sin 80°

A lighter=17.444…cm² - 12.31009... cm²

A lighter=5.13cm² approximately

Answer 2

Answer: =approx 5.13 cm²

Step-by-step explanation:

Lets find the area of the region that is blue ( dark blue+light blue)

S= pi*r^2/360*80=pi*25*2/9=pi*50/9

The lighter region' s area is the S- S(triangle marked with dark blue)

The area of this triangle is r^2*sin(80°)/2= 25*sin(80°)/2=

=12.5*sin(80°)

So the required area Sreg= pi*50/9-12.5*sin(80°)=

= approx 3.14*50/9-12.5*0.985=approx 5.13 cm²

Related Questions

add or subtract as indicated and write the result in standard form 3i+(-6-i)

A:6-4i
B:-6+2i
C:6-2i
D:-6+4i

Answers

Answer:

B: -6+2i

Step-by-step explanation:

3i + (-6 - i) = ⇒ open parenthesis3i - 6 - i = ⇒ simplify-6 + 2i ⇒ answer in standard form of a+bi

What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?

Answers

Answer:

The answer is

4.1 units

Step-by-step explanation:

The distance between two points can be found using the formula

[tex] \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

From the question

The points are (6, -1) and (5, 3)

The distance between the points is

[tex] \sqrt{( {6 - 5})^{2} + ({ - 3 - 1})^{2} } [/tex][tex] = \sqrt{ {1}^{2} + ( { - 4})^{2} } [/tex][tex] = \sqrt{1 + 16} [/tex][tex] = \sqrt{17} [/tex]

= 4.123105

We have the final answer as

4.1 units

Hope this helps you

We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/f t, the cost of the bottom is $2/f t and the cost of the top is $7/f t. If we have 700 determine the dimensions of the field that will maximize the enclosed area.

Answers

Answer:

Dimensions are 350/9 ft and 17.5 ft

Step-by-step explanation:

We are given the cost per ft of all the 4 sides. Let the horizontal be x and the vertical be y.

Now, we will set up the constraint and equation that we are being asked to maximize.

Thus;

700 = 10y + 10y + 7x + 2x

700 = 20y + 9x

Maiking y the subject, we have;

y = (700 - 9x)/20

y = 35 - 9x/20

Now,area of a rectangle is: A = xy

Thus, A = x(35 - 9x/20))

A = 35x - 9x²/20

We can get the critical points by finding the derivatives and Equating to zero

Thus;

dA/dx = 35 - 0.9x

At dA/dx = 0,we have; x = 350/9

At d²A/dx², we have;

d²A/dx² = -0.9

This is negative, thus we will disregard and use the one gotten from the first derivative.

Thus, we will use x = 350/9 ft

Plugging this into the equation y = 35 - 9x/20, we have;

y = 35 - ((9 × 350/9)/20)

y = 17.5 ft

The dimensions of the field that will maximize the enclosed area are 350/9 ft and 17.5 ft and this can be determined by forming the linear equation.

Given :

We are going to fence in a rectangular field. The cost of the vertical sides is $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft.

Let 'x' be vertical, and 'y' be horizontal. So, the linear equation becomes:

700 = 10y + 10y + 7x + 2x

Simplify the above expression.

700 = 20y + 9x

Now, solve the above equation for 'y'.

[tex]\rm y = \dfrac{700-9x}{20}[/tex] --- (1)

Now, the formula of the area of the rectangle is:

A = xy

Now, substitute the value of 'y' in the above formula.

[tex]\rm A = x \times \dfrac{700-9x}{20}[/tex]

[tex]\rm A = 35x -\dfrac{9x^2}{20}[/tex]

Now, differentiate the above equation with respect to 'x' and then equate to 0.

[tex]\rm \dfrac{dA}{dx}=35-0.9x[/tex]

Now, equate the above equation to zero.

35 - 0.9x = 0

x = 350/9

Now, substitute the value of 'x' in equation (1).

[tex]\rm y = \dfrac{700-9\times \dfrac{350}{9}}{20}[/tex]

y = 17.5 ft

For more information, refer to the link given below:

https://brainly.com/question/1631786

part 6: please assist me with these problems

Answers

Answer: 12) 34° 13) 90°

Step-by-step explanation:

[tex]\text{Law of Sines:}\quad \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

12) Given: a = 10.2, b = 6.8, A = 122°

[tex]\dfrac{\sin 122^o}{10.2}=\dfrac{\sin B}{6.8}\\\\\\\dfrac{6.8\sin 122^o}{10.2}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{6.8\sin 122^o}{10.2}\bigg)=B\\\\\\34.4^o=B[/tex]

*****************************************************************************

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped

13) Given: a = 3, b = 4, c = 5, C = ???

3² = 4² + 5² - 2(4)(5) · cos C

9 = 16 + 25 - 40 cos C

9 = 41 - 40 cos C

-32 = -40 cos C

0.8 = cos C

90° = C

Which of the following inequalities matches the graph?

Answers

Answer:

The last option y<4. Y is less than 4 since the shaded region is below 4 on the y Axis.

Answer: D y <4

Step-by-step explanation:

The line is horizontally passing through the 4 which is the y intercept and all the solutions are less than 4.

Find the recursive formula for this general term formula. [tex]t_{n} = n!/9^{-(n-1)}, n\geq 3[/tex]

Answers

Please give me a couple of minutes, I’ll answer in the comment section

what is 1.13 times 0.001

Answers

the answer is 0.001113

The number of customers that visit a local small business is 51,200 and has been continuously declining at a rate of 3.8% each year. What is the approximate number of
customers that visit the business in 14 years?

Answers

Answer:

Final amount of customers =30141.44

Step-by-step explanation:

Amount of customer remaining

A= p(1-r/n)^(nt)

P= initial amount of customers

R= rate but it's a negative rate

N= number of times

T= number of years

A= final amount of customers

A= p(1-r/n)^(nt)

A= 51200(1-0.038/14)^(14*14)

A= 51200(1-0.0027)^196

A= 51200(0.9973)^196

A= 51200(0.5887)

A= 30141.44

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 15% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

Answers

Answer:

0.1198 < p < 0.1802

Step-by-step explanation:

Percentage who had, or intended to cheat (p) = 15% = 0.15.

1 - p = 1 - 0.15 = 0.85

Confidence interval = 95%, z = 1.96 = 2

number of observation= 560

p ± z * √(p * (1 -p)/n)

Lower limit:

0.15 - 2 * √0.15 * 0.85/560

0.15 - 0.0301780 = 0.119822

= 0.1198

Upper limit:

0.15 + 2 * √0.15 * 0.85/560

0.15 + 0.0301780 = 0.180178

= 0.1802

0.1198 < p < 0.1802

find the missing number +(-3)=4

Answers

Answer:

the answer is 7

Step-by-step explanation:

7+(-3)=4

7-3=4

hence shown so missing number is 7

In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x?1 ? x?2 is normal if the
A. populations are normal.
B. population sizes are both greater than 30.
C. populations are nonnormal and the sample sizes are large.
D. sizes are both greater than 30.

Answers

Answer:

C. populations are non normal and the sample sizes are large.

Step-by-step explanation:

To test hypotheses about the difference between two populations means we deal with the following three cases.

1) both the populations are normal with known standard deviations.

2)both the populations are normal with unknown standard deviations.

3) both the populations are non normal in which case both the sample sizes are necessarily large.

So option C is the correct answer.

2x + 5x+3 combine like terms

Answers

Answer:

7x + 3

Step-by-step explanation:

[tex] {e}^{y} + {x}^{3} {y}^{2} + ln(x) = 1[/tex]
and
[tex] \frac{dy}{dt} = 2 [/tex]
when x=1 and y=0.
Find
[tex] \frac{dx}{dt} [/tex]
when x=1 and y=0

Answers

Differentiate both sides implicitly:

[tex]\dfrac{\mathrm d}{\mathrm dt}[e^y+x^3y^2+\ln x]=\dfrac{\mathrm d[1]}{\mathrm dt}[/tex]

[tex]e^y\dfrac{\mathrm dy}{\mathrm dt}+3x^2y^2\dfrac{\mathrm dx}{\mathrm dt}+2x^3y\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm dx}{\mathrm dt}=0[/tex]

Solve for [tex]\frac{\mathrm dx}{\mathrm dt}[/tex]:

[tex]\left(3x^2y^2+\dfrac1x\right)\dfrac{\mathrm dx}{\mathrm dt}=-(e^y+2x^3y)\dfrac{\mathrm dy}{\mathrm dt}[/tex]

[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{e^y+2x^3y}{3x^2y^2+\frac1x}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{xe^y+2x^4y}{3x^3y^2+1}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

Plug in [tex]x=1[/tex], [tex]y=0[/tex], and [tex]\frac{\mathrm dy}{\mathrm dt}=2[/tex]:

[tex]\dfrac{\mathrm dx}{\mathrm dt}=\boxed{-2}[/tex]

Which of these expressions is equivalent to log(16 14)?

Answers

Answer:

log(16) + log(14)

Step-by-step explanation:

a kayak travels in a lake at an average speed of 35m/min. if the perimeter of a lake was 8400 m how many hours does it take for the kayak to travel around the whole lake

Answers

Answer:

I think Its 4hrs

Step-by-step explanation:

8400m÷ 35m = 240mins

240mins= 4hrs

2. What is the sum of the three solutions (find the values for x, y, and z, then add the answers)?
2x + 3y − z = 5 x
− 3y + 2z = −6
3x + y − 4z = −8
please show steps

Answers

Answer:

x = 30/7 , y = 46/7 , z = 48/7

Step-by-step explanation:

Solve the following system:

{2 x + 3 y - z = 5 x | (equation 1)

2 z - 3 y = -6 | (equation 2)

3 x + y - 4 z = -8 | (equation 3)

Express the system in standard form: