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3 years ago

What is the measure of angle BAC? Round to the nearest whole degree.

Mathematics

1 answer:

Deffense [45]3 years ago

6 0

The answer would be 70 degrees.

In order to find this answer, we must first look at the cos value of an angle. The unknown angle here gives us an adjacent side of 3.4 and a hypotenuse of 10. Thus, we can use the following with cos.

Cos(A) = 3.4/10 or Cos(A) = .34

As a result, we can then use the arccos function to find the answer.

acrcos(.34) = A

70.12 = A

Then when we round, we'd get 70.

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A little girl kicks a soccer ball. It goes 10 feet and comes back to her. How is this possible?

Elanso [62]

She is standing in front of a wall which is 10 feet away when she kicks the ball and it hits the wall and comes back to her by the virtue of Newton's third Law of motion! She kicks the ball into the air vertically above her and the ball rises to 10 feet and then comes back to her by the virtue of gravity!

8 0

1 year ago

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2 years ago

Which ordered pairs lie on the graph of the exponential function f(x)=-3(x-1)+2

Whitepunk [10]

Answer:

(-1,2), (1,1), (0,0), (4,-25)

Step-by-step explanation:

Hope this helps!!

4 0

2 years ago

Last questions, plz help

Goryan [66]

Answer:

9. $a_n=7+6n$

10. $a_n=a_{n-1}+7$

Step-by-step explanation:

9. Given the sequence

$13, 19, 25, ...$

In this sequence,

$a_1=13\\ \\a_2=19\\ \\a_3=25\\ \\...$

Note that

$a_2-a_1=19-13=6\\ \\a_3-a_2=25-19=6,$

then the common difference in this sequence is $d=6$

You have

$a_1=13\\ \\d=6,$

then the explicit formula is

$a_n=a_1+(n-1)d\\ \\a_n=13+(n-1)\cdot 6\\ \\a_n=13+6n-6\\ \\a_n=7+6n$

10. Given the sequence

$-10,-3, 4, 11, ...$

In this sequence,

$a_1=-10\\ \\a_2=-3\\ \\a_3=4\\ \\a_4=11\\ \\...$

Note that

$a_2-a_1=-10-(-3)=-10+3=-7\\ \\a_3-a_2=-3-4=-7\\ \\a_4-a_3=11-4=7,$

then the common difference in this sequence is $d=7$

You have

$a_1=-10\\ \\d=7,$

then the recursive formula is

$a_n=a_{n-1}+d\\ \\a_n=a_{n-1}+7$

5 0

3 years ago

* Let S = Span {(2,-1, 1), (3, 1, 1), (1, 2, 0)}. (i) Calculate the dimension of S.

Sholpan [36]

The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.

Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars $c_1,c_2,c_3$ (not all zero) such that

$c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)$

which leads to the system of linear equations,

$\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}$

From the third equation, we have $c_1=-c_2$ , and substituting this into the second equation gives

$-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3$

and in turn, $c_1=c_3$ . Substituting these into the first equation gives

$2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0$

which tells us that any value of $c_3$ will work. If $c_3 = t$ , then $c_1=t$ and $c_2 = -t$ . Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.

Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.

3 0

1 year ago