–4
2
32
Evaluating the function,f(x) = –2x² – 3x + 5 for x = -3, we would have: f(-3) = -4. (option B).
To evaluate a function, plug in the given value of the input (x) and simplify.
Thus:
f(x) = –2x² – 3x + 5
Substitute x = -3 into the function
f(-3) = –2(-3)² – 3(-3) + 5
f(-3) = -2(9) + 9 + 5
f(-3) = -4
Therefore, evaluating the function,f(x) = –2x² – 3x + 5 for x = -3, we would have: f(-3) = -4. (option B).
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Answer:
The correct answer is -4.
Step-by-step explanation:
have a good day yall
Using mathematical operations, we know that 76 is not a reasonable answer and 174 songs in actuality can be downloaded.
So, the number of songs Coleton can download more are:
More songs that can be downloaded:
So, 174 more songs can be downloaded.
Therefore, using mathematical operations, we know that 76 is not a reasonable answer and 174 songs in actuality can be downloaded.
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Answer:
No 76 is not a reasonable answer. 174 is a reasonable answer.
Step-by-step explanation:
76×4=304
304+304=608
375×4=1500
174×4=696
696×4=2784
(a) A + B: The result is -4i - 6j, with a magnitude of 2√13 and a direction angle of arctan(3/2).
(b) A - B: The result is -2i + 6j, with a magnitude of 2√10 and a direction angle of arctan(-3).
The given vectors are:
B = -i - 4j
A = -3i - 2j
(a) A + B:
To add two vectors,
Simply add their corresponding components.
So, A + B = (-3i - 2j) + (-i - 4j)
Combining the i-components, we get:
-3i - i = -4i.
And combining the j-components, we get:
-2j - 4j = -6j.
Therefore, A + B = -4i - 6j.
To find the magnitude of A + B,
Use the Pythagorean theorem:
|A + B| = ,
Where x is the magnitude of the i-component and y is the magnitude of the j-component.
In this case,
x = -4 and y = -6,
So: |A + B| =
|A + B| = 2√13
To find the direction angle of A + B,
Use the arctan function:
θ = arctan(y / x),
Where y is the j-component and x is the i-component.
In this case,
x = -4 and y = -6,
so: θ = arctan(-6 / -4)
θ = arctan(3/2)
Therefore, the magnitude of A + B is 2√13 and the direction angle is arctan(3/2).
(b) A - B:
To subtract two vectors,
Subtract their corresponding components.
So, A - B = (-3i - 2j) - (-i - 4j).
Combining the i-components, we get:
-3i + i = -2i.
And combining the j-components, we get:
-2j - (-4j) = 2j + 4j = 6j.
Therefore, A - B = -2i + 6j.
To find the magnitude of A - B,
Use the Pythagorean theorem:
,
Where x is the magnitude of the i-component and y is the magnitude of the j-component.
In this case,
x = -2 and y = 6,
so:
|A - B| = 2√10
To find the direction angle of A - B,
Use the arctan function:
θ = arctan(y / x),
Where y is the j-component and x is the i-component.
In this case, x = -2 and y = 6,
so:
θ = arctan(6 / -2)
θ = arctan(-3)
Therefore,
The magnitude of A - B is 2√10 and the direction angle is arctan(-3).
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The complete question is:
For vectors B =−i −4j and A =−3i −2j ,
Calculate (a) A + B and its magnitude and direction angle, and (b) A − B and its magnitude and direction angle.
The resulting vectors after adding and subtracting vectors A and B are A + B = -4i - 6j with a magnitude of 7.21 and A - B = -2i + 2j with a magnitude of 2.83. The direction angle for the vectors are calculated using arctan of the absolute value of the components' ratios.
For vectors B = -i - 4j and A = -3i - 2j, you first need to add and subtract these vectors component-wise to get the resulting vectors. Addition gives A + B = -i + (-3i) + -4j + (-2j) = -4i - 6j, whereas subtraction gives A - B = -3i - (-i) + -2j - (-4j) = -2i + 2j.
The magnitude of a vector is calculated by the Pythagorean theorem: (magnitude of A+B) = sqrt((-4)^2 + (-6)^2) = 7.21 and (magnitude of A-B) = sqrt((-2)^2 + 2^2) = 2.83.
The direction angle is found using arctan(|Ay / Ax|), but adjustment must be made depending on the quadrant of the resulting vector. In conclusion, (a) A + B = -4i - 6j, |A + B| = 7.21, angle = arctan(6/4), and (b) A - B = -2i + 2j, |A - B|= 2.83, angle = arctan(2/2).
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2nd coin is tossed 250 times so that P(heads) = 0.25.
3rd coin is tossed 16 times and gives P(tails) = 9/16
4th coin is tossed 25,000 times and gives 12,505 heads.
Answer:
109
Step-by-step explanation:
3^2=9 -10^2=100