Answer:
Eight hundred and eighty, and nineteen hundredths,
Explanation:
In the decimal number 880.19, the place value of the digits is given below:
The decimal number written in words will be:
Eight hundred and eighty, and nineteen hundredths.
Now cos⁻¹(0.7) is about 45.6°, that's on the first quadrant.
keep in mind that the inverse cosine function has a range of [0, 180°], so any angles it will spit out, will be on either the I quadrant where cosine is positive or the II quadrant, where cosine is negative.
however, 45.6° has a twin, she's at the IV quadrant, where cosine is also positive, and that'd be 360° - 45.6°, or 314.4°.
now, those are the first two, but we have been only working on the [0, 360°] range.... but we can simply go around the circle many times over up to 720° or 72000000000° if we so wish, so let's go just one more time around the circle to find the other fellows.
360° + 45.6° is a full circle and 45.6° more, that will give us the other angle, also in the first quadrant, but after a full cycle, at 405.6°.
then to find her twin on the IV quadrant, we simply keep on going, and that'd be at 360° + 360° - 45.6°, 674.4°.
and you can keep on going around the circle, but only four are needed this time only.
Answer:
- x = arcsin(√20.5 -3√2) +2kπ . . . k any integer
- x = π - arcsin(√20.5 -3√2) +2kπ . . . k any integer
Step-by-step explanation:
Add √(82) -3sin(x) to both sides to get ...
2sin(x) = √82 -√72
Now, divide by 2 and find the arcsine:
sin(x) = (√82 -√72)/2
x = arcsin((√82 -√72)/2)
Of course, the supplement of this angle is also a solution, along with all the aliases of these angles.
___
In degrees, the solutions are approximately 16.562° and 163.438° and integer multiples of 360° added to these.
Answer: Daniel bought 3 apples and 7 bananas.
Step-by-step explanation:
Let x represent the number of apples that Daniel bought.
Let y represent the number of bananas that Daniel bought.
He bought a total of 10 apples and bananas altogether. This means that
x + y = 10
Daniel and his children went into a grocery store and he bought $10.15 worth of apples and bananas. Each apple costs $1.75 and each banana costs $0.70. This means that
1.75x + 0.7y = 10.15 - - - - - - - - - - - 1
Substituting x = 10 - y into equation 1, it becomes
1.75(10 - y) + 0.7y = 10.15
17.5 - 1.75y + 0.7y = 10.15
- 1.75y + 0.7y = 10.15 - 17.5
- 1.05y = - 7.35
y = - 7.35/- 1.05
y = 7
x = 10 - y = 10 - 7
x = 3
EZ!
Let's say each box costs $X and each program costs $Y
Thus, Mike's family spent:
$(5X+3Y)
or
$41
Sean's family spent
$(3X+2Y)
or
$26
This yields us a system of two equations:
5x+3y=41
3x+2y=26
<span>5x+3y=41
</span>2y=26-3x
<span>5x+3y=41
</span><span>y=13-1.5x
</span>
5x+3(13-1.5x)=41
y=13-1.5x
5x+39-4.5x=41
<span>y=13-1.5x
</span>
0.5x+39=41
<span>y=13-1.5x
</span>
0.5x=2
<span>y=13-1.5x
</span>
x=4
<span>y=13-1.5x
</span>
x=4
<span>y=7
</span>
Each box costs $4 and each program costs $7
