The Golden Gate, located in San Francisco, California , is the tallest bridge in the world, with its tower extending 746 feet above the water and the floor of the bridge extending 220 feet above water. Notice that the supporting cables of the Golden Gate Bridge approximate the shape of a parabola. This parabola can be modeled by the quadratic function y = 0.00012x2 + 6, where x represents the distance form the axis of symmetry and y represents the height of the cables. The related quadratic equation is 0.00012x2 +6 = 0. Calculate the value of the discriminant
Answers
a. -0.00056
b. -0.00288
c. -0.00126
d. -0.00078
The discriminant formula for a quadratic function is: ax^2+bx+c,b^2−4ac, where a=0.00012, b=0, and c=6
Substituting these values and solving the given discriminant formula, the value of the discriminant is therefore B. -0.00288.
ax^2+bx+c,
and the discriminant formula is expressed as:
b^2−4ac,
where for this equation the values of the coefficients are:
a=0.00012, b=0, and c=6
Substituting these values to the discriminant formula will yield to a value of -0.00288.
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In right triangle XYZ, _X and Z are complementary angles and cos(x)is 11. What is sin(Z)?
9
OA.
B. 1/2
11
mus 网。
C.
20
9
20
11
D.
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Answers
Answer:
A
Step-by-step explanation:
Using the cofunction identity
cos(90 - x) = sinx , or
sin(angle) = cos(complement of angle)
x and z are complementary angles , x + z = 90 , then
sinz = cosx =
Final answer:
In right triangle XYZ, if X and Z are complementary and cos(X) is 11, sin(Z) should be 11 as well. Nevertheless, the cosine of an angle in a standard triangle can't exceed 1 in absolute value, suggesting an error in the provided data.
Explanation:
In a right triangle, if two angles are complementary, their sum equals 90 degrees. In the case of right triangle XYZ, angles X and Z are complementary. This means that angle Z is the complement of angle X. In trigonometry, the sine of an angle is equal to the cosine of its complement.
Therefore, sin(Z) = cos(X).
Given that cos(X) is 11, it follows that sin(Z) is also 11. However, it is essential to point out that the cosine of an angle can't exceed 1 in absolute value in a standard triangle, so there might be a misprint or misunderstanding in the problem. If cos(X) falls within a valid range, then sin(Z) should equal cos(X).
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3/8 or 0.38.
Can you tell me how to work it out?please!
Answers
Answers
Final answer:
The interest earned on a $5000 deposit with a simple interest rate of 2.5% for one year is $125.
Explanation:
To calculate the interest earned on a savings account, you can use the formula: Interest = Principal × Interest Rate × Time. In this case, the principal (amount deposited) is $5000, the interest rate is 2.5% (or 0.025 as a decimal), and the time is 1 year. Plugging in these values, we get:
Interest = $5000 × 0.025 × 1 = $125.
Therefore, you will earn $125 in interest on your $5000 deposit after one year.
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Answers
Answer:
To determine if two lines are parallel or perpendicular, we need to examine their slopes.
First, let's rearrange the second equation, x+y=-5, to slope-intercept form (y = mx + b):
y = -x - 5
In this form, we can see that the slope of the second line is -1.
The first equation, y=x-8, is already in slope-intercept form, y = mx + b, where the slope is 1.
Comparing the slopes, we can see that the slopes of the two lines are different. The slope of the first line is 1, and the slope of the second line is -1.
Since the slopes are not equal, the lines are not parallel.
Now, let's determine if the lines are perpendicular:
Two lines are perpendicular if the product of their slopes is -1.
The slope of the first line is 1, and the slope of the second line is -1.
Since 1 * -1 = -1, the product of the slopes is -1.
Therefore, the lines y = x - 8 and x + y = -5 are perpendicular.
Step-by-step explanation:
Answer: Perpendicular
Step-by-step explanation:
Our task is to identify if these lines are parallel or not. The lines are :
A good move would be to write these two equations in the same format. The easiest one is slope-intercept. Equation 1 is already in this form, but the second one isn't.
To write the second equation in slope-intercept, all we need to do is subtract x from both sides, and we get:
Now, switch the terms:
The slope of the first line is 1, and the slope of the second line is -1.
They can't be parallel, since their slopes are not the same. For them to be perpendicular, their slopes should be negative reciprocals of each other.
Is -1 the negative inverse of 1? Yes.
∴ The lines are perpendicular.
Answers
Answer:
0.9533
Step-by-step explanation:
(a) Probability that a randomly selected woman's height is less than 65 inches:
Using the z-score formula:
�
=
�
−
�
�
Z=
σ
X−μ
Where:
�
X = 65 inches
�
μ = 64.3 inches
�
σ = 2.7 inches
�
=
65
−
64.3
2.7
≈
0.2593
Z=
2.7
65−64.3
≈0.2593
Now, find the probability associated with this z-score, which is approximately 0.6010 (rounded to four decimal places).
(b) Probability that the mean height of 43 randomly selected women is less than 65 inches:
Using the Central Limit Theorem:
�
μ (mean of the sample means) remains 64.3 inches.
�
sample mean
σ
sample mean
(standard deviation of the sample means) is calculated as
2.7
43
≈
0.4115
43
2.7
≈0.4115.
Now, find the z-score for a sample mean of 65 inches:
�
=
65
−
64.3
0.4115
≈
1.6924
Z=
0.4115
65−64.3
≈1.6924
The probability associated with this z-score is approximately 0.9533 (rounded to four decimal places).