How do I fully simplify this?

Answer:

This a vector addition problem and you need to know the law of cosines and law of sines to solve this problem.

Two vector forces of 80lbs and 70 lbs act on an object at 40 degree angle between them.

The magnitude of the resultant force can be found by applying the law of cosines:

c2 = a2 + b2 - 2abcos140°

where a = 80, b = 70 and c is the resultant force vector you are asked to find

Once you find the magnitude of the resultant force, then you can find the angle it makes wrt the 70lb force using the law of sines:

sinα/a = sin140°/c

where α is the angle opposite side a, or the angle between the resultant and the 70lb vector that you are asked to find. so it would be 140lbs

Step-by-step explanation

The probability that she will obtain a scholarship given that she is accepted by the college is 0.54.

Given that the probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35, to determine, if the probability that she is accepted by the college is 0.65, the probability that she will obtain a scholarship given that she is accepted by the college, the following calculation must be performed:

Therefore, the probability that she will obtain a scholarship given that she is accepted by the college is 0.54.

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Answer:

D şıkkı iyi dersler hadi

Answer:

C: [tex](2x+5)(4x^2-10x+25)[/tex]

Step-by-step explanation:

First of all, you need to be able to recognize the two terms as cubes, and what they are cubes of. In this case, [tex]8x^3 = (2x)^3[/tex] and [tex]125=5^3[/tex].

Then you have to find a way you like to remember the formula for how to factorize. The way I do it is by saying "the binomial has the same zero as the original, so [tex]x^3+a^3=(x+a)(...)[/tex] and [tex]x^3-a^3 = (x-a)(...)[/tex] and the whole expression has one minus sign attached to the second term of either factor. In the sum of cubes first parenthesis has a plus, so the second term of the other parentesis has to take that minus: [tex]x^3+a^3=(x+a)(x^2-ax+a^2)[/tex] while in the difference of cubes you already used a minus, so everything else goes plus: [tex]x^3-a^3=(x-a)(x^2+ax+a^2)[/tex]

Or you commit the two formulas to memory.

Formula:

We know that

nth term of the AP is Tn = a+(n-1)d

Where, a = First term

d = Common difference

n = number of terms

Now,

Given that

pth term of the A.P. = Tp = q

⇛a + (p-1)d = q

⇛(p-1)d = q - a

⇛d = (q-a)/(p-1) →→→→(i)

and

qth term of the A.P. = Tq = p

⇛a + (q-1) d = p

⇛ (q-1)d = p-a

⇛ d = (p-a)/(q-1) →→→→(ii)

From Eqn(i) and Eqn(ii)

⇛(q-a)/(p-1) = (p-a)/(q-1)

On applying cross multiplication then

⇛(q-a)×(q-1) = (p-a)×(p-1)

⇛q²-q-aq+a = p²-p-ap+a

⇛q²-q-aq = p²-p-ap

⇛ap-aq = p²-p+q-q²

⇛a(p-q) = (p²-q²)-(p-q)

⇛a(p-q) = (p+q)(p-q)-(p-q)

⇛ a(p-q) = (p-q){(p+q)-1}

On cancelling (p-q) both sides then

⇛a = (p+q-1) →→→→Eqn(iii)

On Substituting the value of a in Eqn(ii) then

⇛ d = [p-(p+q-1)]/(q-1)

⇛d = (p-p-q+1)/(q-1)

⇛d = (-q+1)/(q-1)

⇛d = -(q-1)/(q-1)

⇛d = -1

We have,

a = p+q-1 and d = -1

Now, rth term of the AP

⇛ Tr = a + (r-1)d

⇛Tr = (p+q-1)+(r-1)(-1)

⇛ Tr = p+q-1+(-r+1)

⇛ Tr = p+q-1-r+1

⇛ Tr = p+q-r

Therefore, Tr = p+q-r

Answer: rth term of the given A.P. is p+q-r

Answer:

rth=q+p+qxp

Step-by-step explanation:

rth= 3 of the T and Tq added together and joined.

Answer:

E

Step-by-step explanation:

[tex]\sqrt{\dfrac{64}{49}} = \dfrac{\sqrt{64}}{\sqrt{49}} = \dfrac 87[/tex]

Answer:

E

Step-by-step explanation:

The two numbers whose sum is 7500 and whose product  is a maximum value are 3750 and 3750.

Let the two numbers be x and y.

Since their sum equals 7500,

x + y = 7500  (1)

Their product f(x,y) = xy  (2)

We desire to maximize the product.

From (1), x = 7500 - y

Substituting x into (2), we have

f(x,y) = xy

f(x,y) = (7500 - y)y

f(y) = 7500y - y²

To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.

So, df(y)/dy = d(7500y - y²)/dy

f'(y)/dy = d(7500y)/dy - dy²/dy

f'(y)/dy = 7500 - 2y

Equating it to zero, we have

7500 - 2y = 0

7500 = 2y

y = 7500/2

y = 3750

To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.

So, f"(y) = d(7500 - 2y)dy

f"(y) = 0 - 2

f"(y) = -2 < 0.

So, y = 3750 gives a maximum for f(y) = f(x, y)

Since x = 7500 - y

Substituing y = 3750 into the equation, we have

x = 7500 - 3750

x = 3750

So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.

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Answer:

(1/2)x + 4 - 4 = 10 - 4

2(1/2)x = 6 * 2

x = 12

Answer:

Step-by-step explanation:

Answer:

A  yes     B No    C  Yes

Step-by-step explanation:

The length of the third side is greater than the difference and less than the sum of the two smallest sides.

8, 5, 7    Using the 5 and 7  the third side is > (7 - 5) and < (5 + 7)

                                              the third side is  > 2  and < 12 so 8 is OK

10, 3, 7   Use the two smallest number: 3 and 7

                                               the third side is  > (7 - 3) and < (3 + 7)    

                                               the third side is > 4 and < 10   No it is 10

9, 5, 15    Use the two smallest number 9, 5

                                               the third side is > (9 - 5) and < (9 + 5)  

                                               the third side is > 4 and < 14       Yes  

Answer:

A. 8, 5 , 7

Step-by-step explanation:
the other guy who answered  gave two yes's so I chose one and A. was correct.

Answer:

x+y=12.96, or 12.96=y=x then you can solve for x and then the other half of the total is the other amount

Answer:

W = 10

Step-by-step explanation:

W / 5 + 20 = 22

W / 5 - 20 = 22 - 20

W / 5 = 2

W * 5 = 2 * 5

W = 10

Step-by-step explanation:

[tex] \frac{w}{5} + 20 = 22 \\ \\ \frac{w}{5 } = 22 - 20 \\ \\ \frac{w}{5} = 2 \\ \\ w = 5 \times 2 \\ \\ w = 10[/tex]

Answer:

Look at images below ^^

Step-by-step explanation:

I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.

Therefore, the solved inequality is z > -4.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

63

Step-by-step explanation:

you divide and add then subtract

Answer:

Which of the following graphs is described by the function given below?

y = 2x2 + 6x + 3

-A. Graph A

The function y = 2x^2 + 6x + 3 is a quadratic function that has a vertex of (-1.5,-1.5)

The equation of the function is given as:

y = 2x^2 + 6x + 3

Differentiate

y' = 4x + 6

Set to 0

4x + 6 = 0

This gives

4x = -6

Divide by 4

x = -1.5

Substitute x = -1.5 in y = 2x^2 + 6x + 3

y = 2(-1.5)^2 + 6(-1.5) + 3

Evaluate

y = -1.5

This means that the function y = 2x^2 + 6x + 3 has a vertex of (-1.5,-1.5)

See attachment for the graph of y = 2x^2 + 6x + 3

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Answer:

x=9

Step-by-step explanation:

since the triangles are similar, the sides are all in proportion. This means that:

[tex] \frac{uw}{eg} = \frac{uv}{fg} [/tex]

Now we can just sub in the sides:

[tex] \frac{91}{13} = \frac{56}{x - 1} [/tex]

simplify the first fraction

[tex] \frac{7}{1} = \frac{56}{x - 1} [/tex]

Now we can cross multiply

56=7(x-1)

56=7x-7

63=7x

Therefore:

×=9

Using linear function concepts, it is found that the correct option is:

B. l, ll and lll only

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

If the slope is positive.

If the slope is negative:

In this problem, the equation is:

[tex]6x - 3y = - 9[/tex]

Placing it into the standard format:

[tex]3y = 6x + 9[/tex]

[tex]y = \frac{6}{3}x + \frac{9}{3}[/tex]

[tex]y = 2x + 3[/tex]

Both slope and intercept are positive, hence, quadrants I, II and III, option B.

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Answer:

36

Step-by-step explanation:

Any triangle have 180 degrees in total.

So 60 + 84 + angle M = 180

144 + angle M = 180

180 - 144 = angle M

angle = 36

Answer:

3 1/5

Step-by-step explanation:

The improper fraction 16/5 is called improper because the top number(the numerator) is bigger than the bottom number(the denominator) we "fix" this by dividing and creating a mixed number (it is called mixed because there is a whole part and a fraction part):

As 16÷5 >>> doing this division gives you 3 wholes and 1/5 leftover. We write this as

3 1/5 (in handwriting the three is big and the 1/5 is a fraction, it is the mixed number they are asking you for)

Answer:

Step-by-step explanation:

Let "n" be the second odd number in the sequence

(n - 2) + n + (n + 2) + (n + 4) + (n + 6) = 135

                                              5n + 10 = 135

                                                      5n = 125

                                                        n = 25

23 + 25 + 27 + 29 + 31 = 135

Answer:

12195508,42

Step-by-step explanation:

An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.

Therefore,

Assume that each year has 52 weeks: then compounding occurs.

n = 52 × 80n

times and the rate for each compounding is

[tex]$i=\frac{5.8 \%}{52}=\frac{0.058}{52}$[/tex]

If the original deposit amount is

PV

then the future value

FV

is equal to

[tex]$$F V=P V \cdot(1+i)^n=P V \cdot\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}$$[/tex]

We know the future value (which is given as $ 102,393.44), so calculating the present value is simple:

[tex]P V=F \frac{V}{(1+i)^n}=\frac{\$ 102,393.44}{\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}}[/tex]

The simplest way to compute this is to use a calculator:

[tex]$P V \approx \$ 991.45 .$$[/tex]

We can simplify this expression with great precision just for fun. It is well known that

[tex]$\left(1+\frac{1}{n}\right)^n \rightarrow e$[/tex]

which easily implies that

[tex]$\left(1+\frac{a}{n}\right)^n \rightarrow e^a$[/tex]

Here,

[tex]$$\left(1+\frac{0.058}{52}\right)^{52 \cdot 80}=\left(\left(1+\frac{0.058}{52}\right)^{52}\right)^{80} \approx\left(e^{0.058}\right)^{80}=e^{0.058 .80}=e^{4.64}[/tex]

That is, [tex]P V \approx F V e^{-4.64}$.[/tex]

Hence, An account has $102,393.44 after 80 years of 5.8% compounded monthly interest. The initial deposit was around $991.45.

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Answer:

Step-by-step explanation:

A relation is only a function if ALL the x-values (the first number in the pairs) ONLY have one partner.

Check that -1

At first that -1 is paired up with a 5 in the ordered pair (-1, 5) but then later... that -1 is down there hanging out with a 1 in the last ordered pair (-1, 1).

This means that this relation (all the pairs lumped together) is NOT a function. Just because of that -1 pairing up with more that one partner.

Answer: please calculate the answer.

Step-by-step explanation:\\ Bro use this formula (sum of all numbers of the question) \ no. of seen numbers.

Arithmetic mean = ( 24+124+243+...) \ 12

Answer:

Wind speed = 40 km/hr

Speed of the plane in still air = 280km/hr

Step-by-step explanation:

Formula to use

Distance = Rate multiplied by Time

D = R × T

Speed of the plane in still air = a

Speed of the wind = b

Plane with the wind (tailwind) is a + b where the time = 3hours

Plane against the wind is a - b, where the time = 4hours

This would give us 2 equations

3 × (a+ b) = 960

3a + 3b = 960 ...... Equation 1

4 × (a- b) = 960

4a - 4b = 960 ........ Equation 2

Solve this like you would with system of equations:

We solve the equation using elimination method.

Mulitply equation 1 by 4 and equation 2 by -3

4 × (3a + 3b = 960)

12a + 12b = 3840 ..... Equation 4

-3 × (4a- 4b = 960)

-12a + 12b= -2880 ........ Equation 5

Therefore we have

12a + 12b = 3840 ..... Equation 4

-12a + 12b= -2880 ........ Equation 5

24b = 960

b = 960÷ 24

b = 40

Wind Speed = 40km/hr

To find the speed of air, we use equation 2

4a - 4b = 960 ........ Equation 2

Substituting 40 which is wind of speed for b in equation 2 we would have

4a - 4(40) = 960

4a - 160 = 960

4a = 960 + 160

4a = 1120

a = 1120 ÷ 4

a = 280

The speed of the small plane in still air is 280 km/hr

The set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1, which is the correct answer that would be an option (C).

An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.

Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)}

According to option (A),

The set of ordered pairs is {(1, 2), (3, 2), (4, 3)}

This represents ƒ -3,

According to option (B),

The set of ordered pairs is {(2,1), (3, 2), (4, 3)}

This represents ƒ -2,

According to option (C),

The set of ordered pairs is {(2, 1), (2, 3), (3, 4)}

This represents ƒ -1,

Thus, the set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1.

Hence, the correct answer would be option (C).

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Answer: 1 1/3 miles

Step-by-step explanation:

Since we know that an hour is 60 minutes, and 60 divided by 15 = 4, then we can multiply 1/3 times 4 to get the total number of miles in 60 minutes.

1/3 X 4 = 4/3

4/3 = 1 1/3

Therefore, the answer is 1 1/3 miles.

Therefore, in an hour, a person will walk 4/3 mile.

Hoped this helped.

[tex]BrainiacUser1357[/tex]