a,b,c are all positive integers
a:b=3:8 b:c=6:11
work out the smallest possible value of a+b+c

Answer:

[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]

Step-by-step explanation:

we would like to solve the following trigonometric equation:

[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]

the left hand side can be rewritten using angle sum indentity of sin which is given by:

[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]

therefore Let

Thus substitute:

[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]

simplify addition:

[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]

keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:

[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]

take inverse trig and that yields:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]

add π to both sides of the second equation and that yields:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]

sin function has a period of 2nπ thus add the period:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]

divide I equation by 4 and II by -4 which yields:

[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]

recall that,-½(nπ)=½(nπ) therefore,

[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]

by using a calculator we acquire:

[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]

hence,

the general solution for: for the trig equation are

[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]

Answer:

Option B, $2020.00

Step-by-step explanation:

Volume of the pool,

12×5×14.5+4×5×7

= 1010 ft³

each cubit foot costs $2, so 1010 ft³ will cost,

1010×$2

= $2020

Answer:

Rate of change, is also another word for slope.

Slope --> y2 - y1 / (x2-x1)

Assuming the table is already in xy, the cords are in xy form too.

1) (8,8)

2) (11,10)

Plug points into slope eq

--> 10 - 8 = 2

----> 11 - 8 = 3

2/3 Is the slope/rate of change.

Answer:

u can solve ur self but let me help you

Step-by-step explanation:

simply:subtract 525ml from 512.6 liters

Answer:

1.

= Here,

Narasimha invest = 120,000

Madhu 135,000

pavan =

होय साहेब!!!!!!!!!!

Answer:

On the graphing calculator, use the function normCdf, where

It will result in normCdf(-9999,210,250,46) ≈ 0.192269 or 19.2269%

Answer:

Step-by-step explanation:

Answer:

definition of perpendicular lines

Answer: a = -8

Step-by-step explanation:

Given

-8a - 5 = -7a + 3

Subtract 3 on both sides

-8a - 5 - 3 = -7a + 3 - 3

-8a - 8 = -7a

Add 8a on both sides

-8a - 8 + 8a = -7a + 8a

a = -8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a = -8

Step-by-step explanation:

-8a-5=-7a+3                    Add 5 to both sides.

- 8a = - 7a + 3 + 5           Combine

-8a = - 7a + 8                  Add 7a to both sides

-8a + 7a = 8                    Combine

-a = 8                              Multiply by - 1

a = - 8                          

When you get a weird number like this, you should check it.

LHS = -8(-8) - 5

LHS = 64 - 5

LHS = 59

RHS = -(7*-8) + 3

RHS = -(-56) + 3

RHS = 56 + 3

RHS = 59

So a = - 8 must be right.

Answer:

Step-by-step explanation:

16x^2 = (4x)^2

49 = 7^2

16x^2 - 49 = (4x)^2 - (7)^2

Answer:

f(5) = -2

Step-by-step explanation:

f (x) = -x + 3

Let x = 5

f(5) = -5+3

f(5) = -2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{f(x) = -x + 3}\\\huge\boxed{\rightarrow}\huge\text{ f(x) = -5 + 3}\\\huge\boxed{\rightarrow}\huge\text{ y = -5 + 3}\\\huge\boxed{\rightarrow}\text{ y = -2}\\\\\\\boxed{\boxed{\huge\text{Answer: \bf f(x) = -2}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your \& enjoy your day!}[/tex]

~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

Answer:

98.89

Step-by-step explanation:

Answer: 9/890=0.01011235955

Step-by-step explanation:

Answer:

X= –3, y=26

Step-by-step explanation:

3X+Y=17====> –2(3X+Y)=–34===> –6X–2Y=–34

X+2Y=49

Aight so let's head to the sum

–5X=15===> X=–3

–3+2Y=49===> 2Y=52===> Y=26

0.7% percent is the answer

Answer:

3x -1 =27

3x=28

x=28/3

answer is option 3

[tex]\\ \sf\longmapsto 3x-1=27[/tex]

[tex]\\ \sf\longmapsto 3x=27+1[/tex]

[tex]\\ \sf\longmapsto 3x=28[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{28}{3}[/tex]

Answer:

11

Step-by-step explanation:

Let the number be x

2x + 14 = 4x - 8                  Add 8 to both sides

2x + 14 + 8 = 4x                 Combine

2x + 22  = 4x                     Subtract 2x

22 = 2x                              Divide by 2

11 = x

Answer:

11. 5%

Step-by-step explanation:

1 + percent increase = 1.115

Percent increase = 1.115 - 1 = 0.115 = 11.5 /100 = 11.5 %

Answer:

Step-by-step explanation:

In the exponential form of an equation, the growth or decay rate is found inside the parenthesis. The standard form of an exponential equation is

[tex]y=a(1+r)^x[/tex] if it's growth, or

[tex]y=a(1-r)^x[/tex] if it's decay.

Looking at those equations, logically a growth equation is greater than 1, while a decay equation is less than 1. Obviously, our function is a growth.

To determine the rate of growth, we look closely at (1.115) inside the parenthesis. BECAUSE that is greater than 1, we KNOW it is growth, therefore, it follows the (1 + r) pattern. Let's break up our (1.115) so it models that pattern:

(1.115) --> (1 + .115) and since these are percentages in their decimal form, it follows that 1 is 100% and .115 is 11.5%. Our growth rate is 11.5%

Answer:  43,2

Step-by-step explanation:

[tex]\bf 3\sqrt{216 }=3\cdot 6\sqrt{6}=18\sqrt{6} \approx43.2 \\\\ \sqrt{216} =\sqrt{ 2^{3}\cdot 3^3}=\sqrt{2^2\cdot 3^2\cdot 3\cdot 2}=3\cdot 2\sqrt{3\cdot 2} =6\sqrt{6}[/tex]

the value of 4 tenths x hundreds.

4000

Answer:

40

Step-by-step explanation:

4/10 x 100 = 40

Answer:

x=10, y=24

[tex]\left(34-y\right)^2+y^2=676[/tex]

Step-by-step explanation:

Answer:

x = 10 and y = 24

Step-by-step explanation:

Perimeter of triangle = sum of the 3 sides of the triangle

:. x + y + 26 = 60

x + y = 60 - 26

x + y = 34 ---- (1)

From Pythagoras theorem,

x² + y² = 26²

x² + y² = 676 ---- (2)

From equation (1): y = 34 - x

:. x² + (34 - x)² = 676

x² + 1,156 - 68x + x² = 676

x² + x² - 68x + 1,156 - 676 = 0

2x² - 68x + 480 = 0

x² - 34x + 240 = 0

(x² - 24x) - (10x + 240) = 0

x(x - 24) -10(x - 24) = 0

(x - 24)(x - 10) = 0

x = 24 or 10

y = 34 - x

y = 34 - 10 = 24

:. x = 10 and y = 24

Answer:

The curved surface area of the cone is approximately 329.9 cm²

Step-by-step explanation:

The parameters of the right circular cone are;

The radius of the cone, r = 7 cm

The slant height of the one, l = 15 cm

The curved surface area of a cone, CSA = π·r·l

Therefore;

CSA = π × 7 cm × 15 cm = 105·π cm² ≈ 329.9 cm².

From my knowledge:

²−2−15=0

x=5

x=-3

Answer:

x=5

y=2

w= -5

Step-by-step explanation:

We have that the two matrix are equal, so all corresponding elements are equal.

X-Y=3

From the second row and second column, we have y=2

so x-2=3

x=5

From the third row and the first column, we have w= - 5

Answer:

27

Step-by-step explanation:

Triangle proportionality theorem: when you draw a line parallel to one side of a triangle, it'll intersect the other two sides of the triangle and divide them proportionally

[tex]\frac{26}{39}=\frac{18}{x}[/tex]

Cross multiply and you get 702=26x

x=27

Answer:

x=27

Step-by-step explanation:

-We can use the triangle proportionality theorem: if line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

-we write the proportion and solve for x

[tex]\frac{39}{26} =\frac{x}{18}[/tex]

[tex]x= \frac{39*18}{26}[/tex]

x= 27

Area = Side^2

Area =( 4x + 2 )^2

Area = (4x)^2 + 2(4x)(2) + (2)^2

Area = 16x^2 + 16x + 4

Thus the correct answer is option B .

Answer:

B

Step-by-step explanation:

Area of shaded region + Area of unshaded region = Area of circle

Area of the unshaded sector=256*pi-32*pi=224*pi

Answer:

radius Is 16

total area becomes pi r ^ 2 = 16^2 pi = 256pi

remaining area becomes

256 pi - 32 pi = 224 pi option b

brainliest pls