A plane flying horizontally at an altitude of 2 miles and a speed of 430 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station. (Round your answer to the nearest whole number.)
Answers
The rate at which the distance from the plane to the station is increasing is 430 miles per hour.
Altitude of the plane from the radar station = 2 miles
Speed of the plane = 430 miles per hour
Total distance of the plane from the radar station = 5 miles
Let us assume that the radar station is at point O and the plane is at point P. We can now form a right-angled triangle OPA with altitude AP of 2 miles, OP as x (horizontal distance of plane from the radar station), and OA as 5 miles which is the hypotenuse. Thus we can say that:
OA² = AP² + OP²
Here, we need to find the rate at which the distance from the plane to the station is increasing i.e. we need to find dOP/dt when OP = 5 miles.
Differentiating both sides w.r.t time t we get:
2OA(dOA/dt) = 2AP(dAP/dt) + 2OP(dOP/dt)
Now when OP = 5 miles, using Pythagoras theorem, we get:
5² = 2² + x²=> x = 5 miles
And, OA = 5 miles, AP = 2 miles
Differentiating once more w.r.t time t, we get:
d(OA²)/dt = d(AP²)/dt + d(OP²)/dt
We know that OA is constant (5 miles), and thus d(OA²)/dt = 0 And, AP is also constant, d(AP²)/dt = 0
And thus we get:
2OP(dOP/dt) = 2(x)(430)dOP/dt = x(430/OP)dOP/dt = (5)(430/5) = 430 miles per hour
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Related Questions
A. 124ft
B. 125ft
C. 126ft
D. 123ft
Answers
Answer:
\( \sqrt{950} \)
Step-by-step explanation:
3800=4(x^2)
x^2=950
who ever answer all these questions will get brilliantist and 5 stars
Answers
Answer:
Step-by-step explanation:
Answer:
A. Because 4:5 and 8:10 are equivalent because
4:5 are already in the lowest term
8 and 10 are can simplify by 2 ensure that you know how to lowest term
8 ÷ 2 = 4 and 10 ÷ 2 = 5 Overall it equals to 4:5
B. Because 18:3 and 6:1 are equivalent because
6:1 are already in the lowest term
18 and 3 are can simplify by 3 ensure that you know how to lowest term
18 ÷ 3 = 6 and 3 ÷ 3 = 1 Overall it equals to 6:1
C. Because 2:7 and 10,000:35,000 are equivalent because
2:7 are already in the lowest term
10,000 and 35,000 are can simplify by 5,000 ensure that you know how to lowest term
10,000 ÷ 5,000 = 2 and 35,000 ÷ 5,000 = 7 Overall it equals to 2:7
Explain why 6:4 and 18:8 are not equal
18 and 8 are can simplify by 2 ensure that you know how to lowest term
18 ÷ 2 = 9 and 8 ÷ 2 = 2 Overall it equals to 9:2 not in 6:4
Explain why 3:6 and 6:3 are not equivalent
3:6 can also represent 6:3 just if you reverse it
3 and 6 are can simplify by 3 ensure that you know how to lowest term
3 ÷ 3 = 1 and 6 ÷ 3 = 2 Overall it equals to 1:2
The diagram represents
9:15 but you can simplify this ratio
9 and 15 are can simplify by 3 ensure that you know how to lowest term
9 ÷ 3 = 3 and 15 ÷ 3 = 5 Overall it equals to 3:5
In fruits
A. For every 4 apples there are 3 oranges
B. The ratio of bananas to oranges is 6:3
C. The ratio of apples to bananas is 4 to 6
D. For every 1 orange there are 2 bananas
Mr. Bulky’s Candy Emporium sells all candy items for $0.60 per ounce. Penny and Ruth each bought several different types of candy.
Answers
Answer: what’s the rest of the question? You didn’t provide enough data…✨
Step-by-step explanation:
Please Help 100 POINTS!!!
Answers
Answer:
B
Step-by-step explanation:
Answer:
B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)
Step-by-step explanation:
hat is the speed of a car that takes 1.5 hours to travel 75 kilometers? _
Answers
Answer: Velocity
=
Displacement
Time
Explanation:
75 km = 75000 m
1.5 hours = 5400 sec
Applying the formula
Velocity
=
75000 m
5400 s
=
13.89 m/s
Step-by-step explanation:
Answer:
Speed= 50 km/h
Step-by-step explanation:
S=d/t
s=75km/1.5h
s=50km/h
A triangle has a perimeter of 13 and one side of
length 3. If the lengths of the other two sides are
equal, what is the length of each of them?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Answers
Answer:
(B) 5Step-by-step explanation:
A triangle has a perimeter of 13 and one side of
length 3. If the lengths of the other two sides are
equal, what is the length of each of them?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
having two equal sides is isosceles, remove the known angle from the perimeter and divide by two
(13 - 3) : 2 =
10 : 2 = 5
--------------------
check
5 + 5 + 3 = 13
the answer is good
The length of another side of the triangle will be 5 so option (B) will be correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
Let's say the length of the other sides are x
So,
Perimeter = sum of all sides
13 = x + x + 3
2x + 3 = 13
2x = 10
x = 5
Hence "The length of another side of the triangle will be 5 so".
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6. what are the two most generic and widely used valuation multiples?
Answers
The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.
1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.
A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.
2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).
The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.
The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.
Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.
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Jessica opened a savings account with $40.00.
She is going to add $20 per week over the twelve weeks of summer. She will close the account when the summer is over.
Which expression would be an appropriate domain for this situation?
Answers
Check the picture below.
so for the equation y = 40 + 20x, what's an appropriate domain? or namely, what could be some valid values for "x"?
well, Jessica is going to put in 20 bucks only for 12 weeks, so whatever "x" is going to be, is must be from 0 to 12, or in interval notation [0 , 12].
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. He believes that the mean income is $28.4, and the standard deviation is known to be $6.6. How large of a sample would be required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.56
Answers
To estimate the mean per capita income for a major city in California with an error of at most $0.56 at the 85% confidence level, the economist needs to determine the required sample size.
To calculate the required sample size, we can use the formula: \(n = \left(\frac{{Z \cdot \sigma}}{{E}}\right)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level (in this case, for 85% confidence level, \(Z \approx 1.44\)), \(\sigma\) is the known standard deviation (\$6.6), and \(E\) is the desired margin of error (\$0.56). Plugging in the values, we have \(n = \left(\frac{{1.44 \cdot 6.6}}{{0.56}}\right)^2 \approx 52\). Therefore, a sample size of approximately 52 would be required to estimate the mean per capita income with an error of at most $0.56 at the 85% confidence level.
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Complete the proof of the Law of Sines/Cosines.
Given triangle ABC with altitude segment AD labeled x. Angles ADB and CDB are _____1._____ by the definition of altitudes, making triangle ABD and triangle BCD right triangles. Using the trigonometric ratios sine of B equals x over c and sine of C equals x over b. Multiplying to isolate x in both equations gives x = _____2._____ and x = b ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by bc gives: sine of B over b equals sine of C over c.
Answer choices:
1. altitudes
2. b ⋅ sinB
3. b ⋅ sinB = c ⋅ sinC
1. right angles
2. b ⋅ sinB
3. b ⋅ sinB =c ⋅ sinB
1. altitudes
2. c ⋅ sinB
3. c ⋅ sinB = b ⋅ sinC
1. right angles
2. c ⋅ sinB
3. c ⋅ sinB = b ⋅ sinC
Answers
Corrected Question:
Complete the proof of the Law of Sines/Cosines.
Given triangle ABC with altitude segment AD labeled x. Angles ADB and CDA are _____1._____ by the definition of altitudes, making triangle ABD and triangle ACD right triangles. Using the trigonometric ratios sine of B equals x over c and sine of C equals x over b. Multiplying to isolate x in both equations gives x = _____2._____ and x = b ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by bc gives: sine of B over b equals sine of C over c.
Answer:
(1) right angles
(2) c sin B
(3) c sin B = b sin C
Step-by-step explanation:
As shown in the diagram attached to this response,
(i) the given triangle is ABC with altitude segment AD labeled as x,
(ii) side AB is labeled as c, side AC is labeled as b, and
(iii) angles ADB and CDA are right angles by definition of altitudes.
(iv) Therefore, triangle ABD and CDA are right-angled triangles.
(v) Now, using trigonometric ratios, sine of B equals x over c. i.e
sin B = \(\frac{x}{c}\) --------(i)
(vi) Also, sine of C equals x over b. i.e
sin C = \(\frac{x}{b}\) ------------(ii)
(vii) Multiplying to isolate x in both equations gives;
x = c sin B [from equation (i)] ------------(iii)
x = b sin C [from equation (ii)] -----------(iv)
(viii) We know that x = x by the reflective property. i.e x in equation (iii) is equal to x in equation (iv). By substitution property, this becomes,
c sin B = b sin C -----------------(v)
(ix) Dividing each side of the equation in equation (v) by bc gives: sine of B over b equals sine of C over c i.e
\(\frac{csinB}{bc} = \frac{bsinC}{bc}\)
\(\frac{sinB}{b} = \frac{sinC}{c}\) [This is the sine rule]
Let V={(a,b)∣a,b∈R}. Define the following operations of V : vector addition: (a,b)+(c,d)=(a+c,b+d) scalar multiplication: λ(a,b)={
(0,0)
(λa,
λ
b
)
if λ=0
if λ
=0
Is V a vector space over R ?
Answers
Yes, V is a vector space over R.
To prove this, we need to show that V satisfies the 10 axioms of a vector space.
1. Closure under addition: For any vectors (a,b) and (c,d) in V, the sum (a+c, b+d) is also in V.
2. Associativity of addition: (a,b) + [(c,d) + (e,f)] = [(a,b) + (c,d)] + (e,f)
3. Commutativity of addition: (a,b) + (c,d) = (c,d) + (a,b)
4. Existence of additive identity: There exists a vector (0,0) such that (a,b) + (0,0) = (a,b) for any vector (a,b) in V.
5. Existence of additive inverse: For any vector (a,b) in V, there exists a vector (-a,-b) such that (a,b) + (-a,-b) = (0,0).
6. Closure under scalar multiplication: For any scalar λ and vector (a,b) in V, λ(a,b) is also in V.
7. Distributivity of scalar multiplication with respect to vector addition: λ[(a,b) + (c,d)] = λ(a,b) + λ(c,d)
8. Distributivity of scalar multiplication with respect to scalar addition: (λ + μ)(a,b) = λ(a,b) + μ(a,b)
9. Associativity of scalar multiplication: (λμ)(a,b) = λ(μ(a,b))
10. Identity element of scalar multiplication: 1(a,b) = (a,b)
Since V satisfies all these axioms, it is a vector space over R.
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The shaded part of the diagram below shows the top surface of an engine part.
5
Diagram not drawn to scale
The measurements taken by a motor engineer are:
• reflex angle BÔC = 240°,
• AO=OD= 6 cm,
• BO=OC=3 cm.
The top surface of the engine part is to be painted.
The paint costs 15p per cm².
75
Using = 3, calculate how much it costs to paint the top surface of 20 engine parts.
Give your answer in pounds.
(1 mark)
Answers
Answer:
To calculate the cost of painting the top surface of 20 engine parts, we need to find the surface area of one engine part and then multiply it by 20.
To find the surface area, we need to find the length of the curved surface. We can do this by using the Pythagorean theorem to find AB and then use that to find the circumference of the curved surface.
AB^2 = BO^2 + AO^2 = 9 + 36 = 45
AB = sqrt(45) = 3 sqrt(5)
Circumference = 2 * pi * AB = 2 * pi * 3 sqrt(5) = 6 pi sqrt(5)
Using the fact that the reflex angle BÔC is 240 degrees, we can find the length of the curved surface:
240° / 360° = 2/3 of the circumference
Curved surface length = 2/3 * 6 pi sqrt(5) = 4 pi sqrt(5)
Finally, we can find the surface area of one engine part:
Surface area = (2 * 6 * 3) + (4 pi sqrt(5) * 6) = 36 + (24 pi sqrt(5))
To paint 20 engine parts, the cost would be:
20 * surface area * 15p = 20 * 36 + 20 * 24 pi sqrt(5) * 15p = 720 + (24 * 20 * 15 * pi * sqrt(5)) p = 720 + 720 pi sqrt(5) p
Since 1 pound is equal to 100 pence, the cost in pounds would be:
720 + 720 * pi * sqrt(5) / 100 = 720 + 720 * 0.177 / 100 = 720 + 1.264
So, the cost to paint the top surface of 20 engine parts would be 721.264 pounds.
which of the following is the correct graph of the linear equation below? y+2=1/5(x+1)
Answers
Answer:
Step-by-step explanation:
This almost should be reported. But here is the graph you are looking for.
It has to have a y intercept of about -2 and an x intercept of 9.
L is the circle with the equation x²+y²=9
full question in photo :)
Answers
The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;
a) a = 2
b = -2
c = 4
What is the general equation of a circle?The general equation of a circle is; (x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The coordinates of the radius of the circle
The specified equation of a circle is; x² + y² = 9
The coordinates of the center of the circle, is therefore, O = (0, 0)
a) The coordinates of the points P and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)
((3·√3)/4)/(3/2) = (√3)/2
The specified form of the gradient is; (√3)/a, therefore;
(√3)/a = (√3)/2
a = 2
The value of a is 2
b) The gradient of the tangent to a line that has a gradient of m is -1/m
The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)
The form of the gradient of the tangent at P is b/(√3), therefore;
-2/(√3) = b/(√3)
b = -2
The value of b is; -2
c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates
Slope of the tangent = -2/(√3)
((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)
((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3
(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4
Therefore; c = 4
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find the domain of f(x)=sec(2x)
Answers
Answer:
*Refer the image attached
Step-by-step explanation:
*Refer the image attached
How many solutions does this equation have?
4v = -6 + 5v
no solution
one solution
infinitely many solutions
Submit
4
Answers
Answer:
One Solution
Step-by-step explanation:
v can only equal 6
Just think that there can be as many solutions as the highest power of the variable
Here it’s 1
Thus no of solutions is 1
PLEASE HELP I CANT MISS ANY MORE QUESTIONS
Andrea has a bag of marbles. Without looking in the bag,
she selects a marble, records its color, and puts it back in
the bag. All marbles are equally likely to be chosen. She
performs the process 50 times. In the 50 trials, she records
the following colors of marbles from the bag.
Number of times a purple marble was chosen 24
Number of times a pink marble was chosen 11
Number of times a yellow marble was chosen 15
Based on the data Andrea collected, what is the estimated probability, in
simplest form, of choosing a purple marble from the bag?
A. 50/24
B. 48/50
C. 12/100
D. 12/25
Answers
Answer:12/100
Step-by-step explanat
Answer:
D. 12/25
Step-by-step explanation:
find the percentage of students that scored higher than 75.5. round your answer to the nearest percent.
Answers
Approximately 14 percentage of the values are higher than 95.5.
From the figure we have the following frequencies for each class
Class Frequency
_______________________
70.5-75.5 13
75.5-80.5 7
80.5-85.5 6
85.5-90.5 10
90.5-95.5 19
95.5-100.5 9
________________________
Total 64
Based on the given frequency distribution, we can determine the percentage of values higher than 95.5.
The total number of values is 64, and the frequency of values higher than 95.5 is 9. To calculate the percentage, we divide the frequency by the total number of values and multiply by 100.
Percentage = (Frequency of values higher than 95.5 / Total number of values) * 100
Percentage = (9 / 64) * 100
Percentage ≈ 14.06%
Therefore, approximately 14% of the values are higher than 95.5.
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Complete Question:
The following histogram shows the exam scores for a Prealgebra class. Use this histogram to answer the questions.
Find the percentage of students that scored higher than 75.5. round your answer to the nearest percent.
please answer to this fast !!
Answers
To gain 10% profit, the shopkeeper must offer a 8.33% discount on the market price.
What is the profit ?Profit is the difference between the total revenue and total cost of a business. It is an important measure of the success of a business, as it shows how much money the business is making from its operations. Profit is usually expressed as a percentage of the total revenue. It is also known as "net income" or "net profit" and is the amount of money left over after all expenses, including taxes, have been paid. Profit is important because it allows a business to reinvest in itself, expand, and grow. It can also be used to pay dividends to shareholders, increase wages, and cover other expenses.
To gain 10% profit, the shopkeeper must offer a 8.33% discount on the market price. This is because if the shopkeeper was gaining 20% before, a 10% discount would reduce the profit he is making to 10%.
Lets 20% gain = $20
Then market price be = 120/100 = $120
10% gain = $110
Discount = $120 - $110
= $10
Discount % = 10/120
= 0.083
= 8.33%
Thus, To gain 10% profit, the shopkeeper must offer a 8.33% discount on the market price.
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Gary has 9 quarts of paint. If He Uses Half How Much gallons will he have.
Answers
Answer:
1.125 gallons
Step-by-step explanation:
The first thing you do here is convert 9 quarts to gallons. To convert from quarts to gallons you dvide by 4. So 9/4=2.25.
The next thing you do is divide this number by two to achieve your answer
2.25/2=1.125
So the final answer you would be after using half of his paint Gary is left with 1.125 gallons of paint
what is 83,74.21 written on expend form
Answers
8000 + 300 + 70 + 4 + 0.2 + 0.01
Find the least squares solution of the system Ax = b.
A =
1 1 1 1 1 −1
0 2 −1
2 1 0
0 2 1
b =
1 0
1
−1
0
Expert Answer
Answers
To find the least squares solution of the system Ax = b, we first need to find the pseudoinverse of A (denoted as A+). Then, we can use the formula x = A+ b to find the least squares solution.
To find the pseudoinverse of A, we can use the Moore-Penrose inverse formula:
A+ = (A^T A)^-1 A^T
where A^T is the transpose of A.
Using this formula, we get:
A^T A =
1 0 3 0
0 10 1 4
3 1 2 2
0 4 2 2
0 0 0 6
1 -1 0 0
Taking the inverse of A^T A, we get:
(A^T A)^-1 =
0.0447 -0.0206 0.0358 -0.0323 -0.0171 0.0478
-0.0206 0.0111 -0.0115 0.0074 0.0035 -0.0155
0.0358 -0.0115 0.0505 -0.0395 -0.0125 0.0383
-0.0323 0.0074 -0.0395 0.0356 0.0082 -0.0295
-0.0171 0.0035 -0.0125 0.0082 0.0068 -0.0099
0.0478 -0.0155 0.0383 -0.0295 -0.0099 0.0451
Multiplying A^T and b, we get:
A^T b =
1
1
-1
-1
1
-2
Using the formula x = A+ b, we get:
x =
0.2
0.1
-0.6
Therefore, the least squares solution of the system Ax = b is:
x = (0.2, 0.1, -0.6)
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13.
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=(x-1)(4x+2)-4x^(2)
A.
linear function
linear term: 7x
constant term: –4
B.
linear function
linear term: -2x
constant term: –2
C.
quadratic function
quadratic term: -4x^(2)
linear term: -2x
constant term: –2
D.
quadratic function
quadratic term: 4x^(2)
linear term: 7x
constant term: –4
Answers
Answer:
B.
linear function
linear term: -2x
constant term: –2
Step-by-step explanation:
Find the degree of the equation to determine if linear.
Linear
Find the constant of variation.
y
doesn't vary directly with
x
Hello,
Multiplying (x-1) by (4x+2) the term in x² is x*4x=4x².
If we substract 4x² the term of y in x² will be 0.
The function is not quadratic.
Since 4x*(-1)+2*x=-2x (product of terms in x) : the function is thus linear.
Constant term is -1*2=-2
f(x) = (3x+2)(-6x-3) Use the FOIL method to multiply out the factors: f(x) = -18x2 - 9x - 12x -6 Combine like terms: f(x) = -18x2 -21x - 6
The function is quadratic ax^2+bx+c. ax^2=quadratic.
bx=linear.
c=constant.
If I use the distributive property to simplify the expression: 2(6y - 3), I should
the factor of 2 outside the parentheses by each of the terms inside the
parentheses.
Multiply
Divide
Subtract
Add
Answers
Answer:
multiply the factor 2 with each term inside the parentheses
write the expression using exponents. a⋅a⋅c⋅c =
Answers
The expression when expressed in its exponent is a²+c²
how to express a number in exponent form?In mathematics, we should understand that exponent tell the power to which a number is raise.
It shows the number of times a number multiplies itself to get the certain member.
The given expression is a*a*c*.
Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.
Here a appeared twice a*a=a²
And c appeared twice that is c*c=c²
Combining the two exponents together we have that
a²+c²
In conclusion, the exponent of a*a*a*a is a²+c²
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why did the girl wear glasses during math class
Answers
Answer:
Because she found it improves division.
Step-by-step explanation:
a) Convert 7BEC2 F16 to decimal. b) Convert 111010110110101.11010111012 to octal. c) Convert F6AF59 16 to octal. d) Convert 179.75 to hexadecimal. e) Using 2's complement, perform the following subtraction: 10001012−101101112 f) Using 1's complement, perform the follqwing subtraction: 101010102−1101101012
Answers
101010102 − 1101101012 using 1's complement is equal to 25610.
a) Converting 7BEC2F16 to decimal
7BEC2F16 = 286720 + 2816 + 14 + 0.765625 + 0.05859375 + 0.00034375
= 289610.82422
Therefore, 7BEC2F16 in decimal is 289610.82422.
b) Converting 111010110110101.11010111012 to octal
111010110110101.11010111012
= 1655.6561
Therefore, the given binary number is 111010110110101.11010111012 in octal form is 1655.6561.
c) Converting F6AF5916 to octal
F6AF5916 = 771655
Therefore, F6AF5916 in octal form is 771655.
d) Converting 179.75 to hexadecimal
17910 = B3116
0.7510 = C16
Therefore, 179.75 in hexadecimal form is B3C.
e) Subtracting 10001012 from 101101112 using 2's complement
10001012 − 101101112
= 10111000
Therefore, 10001012 − 101101112 using 2's complement is equal to 18410.
f) Subtracting 101010102 from 1101101012 using 1's complement
101010102 − 1101101012
= 100000000
Therefore, 101010102 − 1101101012 using 1's complement is equal to 25610.
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The function g is defined by g(x) = x² + bx, where b is a constant. If the line tangent to the graph of g at x = -1 is parallel to the line that contains the points (0, -2) and (3, 4), what is the value of b?
Answers
Answer:
b = 4.
Step-by-step explanation:
To find the value of b, we can use the fact that the line tangent to the graph of g at x = -1 is parallel to the line that contains the points (0, -2) and (3, 4).
The equation of the line tangent to the graph of g at x = -1 is of the form y = m(x - (-1)) + g(-1), where m is the slope of the line. The slope of the line is given by the derivative of g at x = -1, which is given by g'(-1).
The equation of the line that contains the points (0, -2) and (3, 4) is given by y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is given by the rise over the run between the two points, which is (4 - (-2))/(3 - 0) = 6/3 = 2. The y-intercept is the y-coordinate of the point where the line crosses the y-axis, which is -2.
Thus, the equation of the line that contains the points (0, -2) and (3, 4) is y = 2x - 2.
Since the line tangent to the graph of g at x = -1 is parallel to this line, they have the same slope, which is 2. Therefore, g'(-1) = 2.
The derivative of g(x) = x^2 + bx is given by g'(x) = 2x + b. Setting x = -1, we find that g'(-1) = 2(-1) + b = -2 + b = 2. Solving for b, we find that b = 4.
Therefore, the value of b is b = 4.
you are starting a small cupcake business. the expenses in the first month costs $155. you plan to charge $3.50 per cupcake. you would like to have a profit of atleast $250. write and solve an inequality that represents the number of cupcakes, c, that you need to sell
Answers
Determine the equation of the line that passes through (-8,9) and (2,-6)
Express you answer as a fraction in lowest terms.
Answers
The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.
We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.
Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.
Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.
The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.
Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.
Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.
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