Using trig to solve for missing angles

Answer:

Solution: To determine mass of the block we can use second Newton' law \vec F=m\vec a

F

=m

a

. The force and acceleration according the problem is directed along a horizontal surface, and we can omit the vector sign in Newton's law. The force we know F=45NF=45N, thus we should deduce the acceleration. The problem does not specify the initial speed at which time began to count, so for the first time interval, we may write the kinematics equation in the form

(1) S_1=v_1\cdot t_1+a\frac {t_1^2}{2}S

1

=v

1

⋅t

1

+a

2

t

1

2

, where S_1=8m, t_1=2s S

1

=8m,t

1

=2s , other quantities we don't know. The similar equation we can write for next time interval

(2) S_2=v_2\cdot t_2+ a\frac{t_2^2}{2}S

2

=v

2

⋅t

2

+a

2

t

2

2

. where S_2=8.5m, t_2=1s S

2

=8.5m,t

2

=1s

Note that during the first time interval, the speed of the block increased in accordance with the law of equidistant motion and it became the initial speed of the second interval, i.e.

(3) v_2=v_1+a\cdot t_1v

2

=v

1

+a⋅t

1

Substitute (3) to (2) we get

(4) S_2=(v_1+a\cdot t_1)\cdot t_2+ a\frac{t_2^2}{2}=v_1\cdot t_2+a\cdot t_1\cdot t_2+a\frac{t_2^2}{2}S

2

=(v

1

+a⋅t

1

)⋅t

2

+a

2

t

2

2

=v

1

⋅t

2

+a⋅t

1

⋅t

2

+a

2

t

2

2

From equation (1) and (4) we can exclude unknown quantity v_1v

1

, then remain only one unknown aa. For determine aa we dived (1) by t_1t

1

, (4) by t_2t

2

to find the average speed at time intervals and subtract (1) from (4).

(5) \frac {S_2}{t_2}-\frac {S_1}{t_1}=v_1+a\cdot t_1 +a\frac {t_2}{2}-(v_1+a\frac{t_1}{2})=a\frac{t_1+t_2}{2}-

t

2

S

2

−

t

1

S

1

=v

1

+a⋅t

1

+a

2

t

2

−(v

1

+a

2

t

1

)=a

2

t

1

+t

2

− For acceleration we get

(6) a=2\cdot ( {\frac{S_2}{t_2}-\frac{S_1}{t_1})/(t_1+t_2)}=2\cdot \frac{(8.5m/s-4m/s)}{3s}=3ms^{-2}a=2⋅(

t

2

S

2

−

t

1

S

1

)/(t

1

+t

2

)=2⋅

3s

(8.5m/s−4m/s)

=3ms

−2

For mass from second Newton's law we get

(7) m=\frac{F}{a}=\frac{45N}{3ms^{-2}}=15kgm=

a

F

=

3ms

−2

45N

=15kg

Answer: The mass of the block is 15 kg

Answer:

[tex]f(x + 3) = {(x + 3)}^{3} [/tex]

Shifted left with x-intercept at (-3,0) and the y-intercept at (0,27)

Step-by-step explanation:

here's the answer to your question

9514 1404 393

Answer:

Step-by-step explanation:

1) The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (4 -(-3))/(3 -0) = 7/3

__

2) The y-intercept is the point where x=0:

  (x, y) = (0, -3) . . . . . y = -3

__

3) Then the slope-intercept equation is ...

  y = mx + b . . . . . . . line with slope m and y-intercept b

  y = 7/3x -3

Answer:

30-5ab-14+6ab

16-ab ans

Answer:

[tex] \boxed{ab + 16} [/tex]

Step-by-step explanation:

5 (6 – ab) + 2 (-7 + 3ab)

[distribution property]

(6)(5) – (ab)(5) + (-7)(2) + (3ab)(2)

30 – 5ab – 14 + 6ab

[group like terms]

(6ab – 5ab) + (30 – 14)

ab + 16

9514 1404 393

Answer:

  A.  $674.43

Step-by-step explanation:

The account balance is given by ...

  A = P(1 +r/12)^(12t) . . . . . principal P invested at annual rate r for t years

  A = $500(1 +0.06/12)^(12·5) = $500(1.005^60)

  A ≈ $674.43

Answer:

66.6666666667

Step-by-step explanation:

answer is 66.6666666667

The solution of the division of 5⁻² by 8^(1/3) will be 50.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given numbers will be solved as:-

Division = ( 8 ^ (1/3) / 5⁻²

Division = 2 x5²

Division = 50

Therefore, the solution of the division of 5⁻² by 8^(1/3) will be 50.

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Answer:

Value of given expression is 3⁻¹⁴

Step-by-step explanation:

Given expression:

3⁻⁸ x 3⁻⁴ x 3⁻²

Find:

Value of given expression

Computation:

⇒ 3⁻⁸ x 3⁻⁴ x 3⁻²

⇒ 3[⁻⁸⁻⁴⁻²]

⇒ 3⁻¹⁴

Value of given expression is 3⁻¹⁴

Answer:

Below

Step-by-step explanation:

From the graph the first local minimum is -16.18

The local maximum is 3.75

The second local minimum is -3.

Answer:

----------------------

Hope it helps..

Have a great day!!

Given:

The given equation is:

[tex]16-3p=\dfrac{2}{3}p+5[/tex]

To find:

The value of p.

Solution:

We have,

[tex]16-3p=\dfrac{2}{3}p+5[/tex]

Multiply both sides by 3.

[tex]3(16-3p)=3\left(\dfrac{2}{3}p+5\right)[/tex]

[tex]48-9p=2p+15[/tex]

Isolating the variable terms, we get

[tex]48-15=2p+9p[/tex]

[tex]33=11p[/tex]

Divide both sides by 11, we get

[tex]\dfrac{33}{11}=p[/tex]

[tex]3=p[/tex]

Therefore, the required solution is [tex]p=3[/tex].

Answer:

p=3

Step-by-step explanation:

i got it right on khan

Answer:

[tex]{ \tt{ {x}^{2} + {y}^{2} - 6x - 2y + 4 = 0 }} [/tex]

Center:

[tex]{ \tt{(3, \: 1)}}[/tex]

Radius:

[tex]{ \tt{radius = \sqrt{ {g}^{2} + {f}^{2} - c } }} \\ = \sqrt{36 + 4 - 4} \\ = 6 \: units[/tex]

Answer:

A) 5

Step-by-step explanation:

Step-by-step explanation:

Solution

First equation x ² - 4

= (x+2) (x-2)

Second equation = x ³ +8 + = x³+2^3

= (x-2) (x² + x₁2 +2²) = (x-2) (x² + 2x+4)

3 Third equation = x ² + 5x + 6

= x² + 6x= x +6 = x(x+6)-1(x+6)

(x-1) (x+6)

H.C. F= x-2

Answer:

A. Function

B. Not a function

C. function

Answer:

0.017741

Step-by-step explanation:

Answer:

Odd symetry I think

Step-by-step explanation:

Sorry I'm new can you be my friend too please?

Hope this helps!:)

Have a nice day.

Keep scrolling for more....

Have a great day

You can do anything you put your mind to

^_^

:)

This is it

Answer:

65°

Step-by-step explanation:

The sum of angles in a triangle =180

53°+62°+?°=180°

115°+?°=180°

?°=180°-115°

Rate the answer If you love everything I did n explanation

Answer:

65 degrees

Step-by-step explanation:

Angles in a triangle add up to 180, so 180 - 53 - 62 = 65.

Answer:

26.124

Step-by-step explanation:

SOH CAH TOA

tan 43 = about 0.933

than times it by 28 and get

26.124

Answer:

I think 5q+3(8-q) =36 is the answer for this question

Based on the amount the restaurant manager spends on the juice mixture, the amount of cherry juice can be found as 5q + 3(8 – q) = 8.

Assuming the cherry juice is q and the lime juice is r, the following formulas would be true:

q + r = 8

5q + 3r = 36

The first equation can be rewritten as:

q + r = 8

r = 8 - q

Using substitution into the second formula we get:

5q + 3r = 36

5q + 3(8 - q) = 36

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Answer:

6x-5 if x<5

Step-by-step explanation:

If x<5, then x-5<0.

If x-5 is negative, then |x-5)=-(x-5) or -x+5.

5x - |x - 5|

5x-(-x+5) provided x<5

5x+x-5 by distributive property

6x-5 combined liked terms

Answer:

LP = 15

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{LM}{LN}[/tex] = [tex]\frac{LQ}{LP}[/tex] , substitute values

[tex]\frac{4}{10}[/tex] = [tex]\frac{LQ}{LQ+QP}[/tex]

[tex]\frac{2}{5}[/tex] = [tex]\frac{LQ}{LQ+9 }[/tex] ( cross- multiply )

5LQ = 2(LQ + 9) = 2LQ + 18 ( subtract 2LQ from both sides )

3LQ = 18 ( divide both sides by 3 )

LQ = 6

Then

LP = LQ + QP = 6 + 9 = 15

Answer:

dddjshsbs zhzusushwbsgzyzhsbssbs s hsbd d dhd ssbshebebs shyshs s sbshss s s

Step-by-step explanation:

shshshsnsnsjzj shsjs s sjsn s s snsnsbzbznnz ssjs s snsnsmkzkxnz

Answer: See explanation

Step-by-step explanation:

Your question isn't well written, the store contains $227 and not $277.

let c be the number of $1 bills

let f be the number of $5 bills

let t be the number of $10 bills.

Therefore, the equation will be:

1c + 5f + 10t = 227

Since there are six more $5 bills than $10 bills, therefore,

f = t+6

Also, the number of $1 bills is two more than 24 times the number of $10 bills and this will be:

c = 24t + 2

Now, we substitute the equation for f and c into the main equation and this will be:

1c + 5f + 10t = 277

1(24t + 2) + 5(t + 6) + 10t = 227

24t + 2 + 5t + 30 + 10t = 227

39t + 32 = 227

39t = 227 - 32

39t = 195

t = 195/39

t = 5

Therefore, there are 5 $10 bills

Since c = 24t + 2

c = 24(5) + 2

c = 120 + 2

c = 122

Therefore, there are 122 $1 bills

Since f = t+6

f = 5+6

f = 11

Therefore, there are 11 $5 bills.

Step-by-step explanation:

L.H.S

tanA * cosecA

=sinA/cosA * 1/sinA

now cancel sinA and sinA

then,

1/cosA

= secA

= RHS

hence proved

Answer:

D; 2 * 3; -4

Step-by-step explanation:

The dimension of the matrix refers to the number of elements in a row multiplied by the number of elements is a column

In a row, we have 2 elements, in a column , we have 3 elements

So the matrix is of 2 * 3 dimension

a21, refers to the element in the matrix that is in the row 2 column 1 and that is -4

Answer:

y = 3x+4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 3x+4