The solution according to the given question is provided below in the explanation segment.
According to the question,
The cost of drilling x feet is:
[tex]c(x) = f(x) \ dollars[/tex]
(a) [tex]f'(x) = \frac{df(x)}{dx} \ \frac{dollars}{feet}[/tex]
(b) Throughout the practical terms,
[tex]f'(x)[/tex] represents how many dollars its going to cost one feet.
(c) [tex]f'(x)[/tex] is positive,
The cost of drilling increases as "x" feet increases.
(d) The cost of drilling an additional foot at 300 feet will be [tex]f'(x) \Delta \ x[/tex]
here,
[tex]\Delta x =0[/tex][tex]f'(300) =1000[/tex]then,
= [tex]1000\times 1[/tex]
= [tex]1000 \ dollars[/tex]
If you want drill 1 more feet at 300 feet, its going to cost 100 dollars in one.
Thus the above answer is correct.
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There is a sales tax of $22 on an item that costs $272 before tax. The sales tax on a second item is $19.25. How much does the second item cost before tax?
The sales tax rate was calculated based on the information of the first item, and we found it to be approximately 8.09%. Using this tax rate, the pre-tax price of the second item, on which the sales tax was $19.25, was found to be approximately $237.85.
Explanation:To solve this problem, we first need to determine the percentage rate of the sales tax based on the first item. Given that a sales tax of $22 was applied to an item that cost $272 before tax, we can calculate the tax rate as follows: (22/272)*100 = 8.09%. This indicates that the tax rate is approximately 8.09%.
Next, if we assume that the sales tax rate is the same for the second item, we can calculate the pre-tax price of this item. Given that the sales tax on the second item is $19.25, the price of the item before tax can be calculated as follows: 19.25/0.0809 = $237.85 approximately. Therefore, the second item costs about $237.85 before tax.
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what it is the original price of a new board game that cost $31.25 after a 15% discount
What is the lowest degree that a polynomial can have and explain.
which number is greater than -24
(A) -42
(B) -27
(C) -16 (my answer **)
(D) -30
q^2 + 11qr + 18t^2
x^2 - 14xy - 15y^2
Solve the system by using substitution
6x+y=12
4x+6y=(-8)
Mia soccer practice started at 3:15 p.m. and ended at 4:10 p.m. how long was Mia soccer practice.
The price of a t-shirt is $50. If you buy 4 shirts, you will get 10% discount. How much do you have to pay if you buy 8 shirts?
100-8301>7320<8393+939=?
find the length of the missing side of the right triangle. side is 8 bottom is 15 A. 289 B. 17 C. 23. D. 4.79
General Idea:
Pythagorean theorem states that in a right triangle, if side of triangle is given by ' a ', bottom of the triangle is given by ' b ' and hypotenuse of triangle is given by ' c', then Sum of squares of a and b is equal to the square of hypotenuse.
[tex] a^{2} \; +\; b^{2}\; =\; c^{2} [/tex]
Applying the Concept:
[tex] Given\\Side\;of\;triangle\;(a)\; =\; 8\\ Bottom\;of\;triangle\;(b)=15\\ \\ To\; Find\\Hyptotenuse\;(c)\\ \\ a^{2}+b^{2}=c^{2}\\ 8^2+15^2=c^2\\ \\ 64+225=c^2\\ \\ 289=c^2\\ \\ c^2=289\\ Taking \; Square\;root\;on\;both\;sides\\ \\ \sqrt{c^2}=\sqrt{289} \\ \\ c=17 [/tex]
Conclusion:
The length of the missing side of the right triangle, when side 8 & bottom 15 is 17. The correct answer is option B!!
solve for f
d=16ef^2
Here are a bunch of CORRECT answers. Your answer is in the first pic. I got number 3 wrong, but it still showed the correct answer.
Please show me the work thank you
Can someone help me with number 5
Estimating square roots
Last year, the tree in Pedro's front yard was 5 feet tall. This year, the tree is 2 feet less than the height of Pedro's house. Pedro's house is 17 feet tall. How tall is the tree?
When responding to this question, please justify/explain your answer. You may use words, numbers and/or symbols to answer your question. Please write in COMPLETE sentences.
The tree is 15 feet tall
The tree in Pedro's front yard was 5 ft tall last year.
This year, the tree is 2 feet less than the height of Pedro's house.
let
the height of the tree = x
Therefore,
height of the house = 17 feet
17 - 2 = x
x = 15 ft
Therefore, the tree is 15 feet tall
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The tree in Pedro's front yard is currently 15 feet tall, which is 2 feet shorter than the height of Pedro's 17 feet tall house.
Explanation:Last year, the tree in Pedro's front yard was 5 feet tall. This year, the tree is 2 feet shorter than the height of Pedro's house. If Pedro's house is 17 feet tall, we need to calculate the tree's current height by subtracting 2 feet from the height of the house. Therefore, the tree's current height would be 17 feet - 2 feet = 15 feet tall.
Quadrilateral ABCD is inscribed in a circle. What’s the measure of angle B
simplify 2d(3) expression
Final answer:
The expression 2d(3) is simplified by multiplying 2 by 3, yielding 6, and then by d, resulting in 6d.
Explanation:
To simplify the expression 2d(3), you simply need to multiply the variable d by the number 2 and then multiply the result by the number inside the parentheses, which is 3. This is straightforward multiplication, similar to the distributive property used in algebra to simplify expressions.
The simplified form of the expression is found by multiplying 2 by 3, giving us 6, and then multiplying that result by d. Hence, 2d(3) simplifies to 6d.
to prepare for competitions your swimming coach required you to swim 8 lengths in the pool you swam 10 lenghts what percent of the required practice did you swim
6 friends go out for dinner and order from a menu of 8 different sandwiches. What is the probability that at least 2 of the group order the same sandwich?
Please help. Find the value of each variable. If your answer is not an integer, express it in simplest radical form.
solve on the interval [0, 2pi) : 3 sec x -2 = 1
The equation 3sec (x) -2 = 1 solved on the interval is x = 0
How to solve the equation on the intervalFrom the question, we have the following parameters that can be used in our computation:
3sec (x) -2 = 1
Express sec(x) as 1/cos(x)
So, we have
3 * (1 / cos (x)) - 2 = 1
Add 2 to both sides
3 * (1 / cos (x)) = 1 + 2
Evaluate the like terms
3 (1 / cos (x)) = 3
Divide through by 3
(1 / cos (x)) = 3/3
So, we have
cos (x) = 1
Take the arc cos of both sides
x = 2nπ
On the interval [0, 2π), we have x = 0
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Angle Q measures 30 degrees. If angle Q is rotated 15 degrees, what is the measure of angle Q'? 30 degrees 45 degrees 150 degrees 180 degrees
After rotating angle Q, which initially measures 30 degrees, by 15 degrees, the new angle Q' measures 45 degrees.
When we talk about rotating an angle, we are referring to moving the angle around its vertex through a specified measure. If we have angle Q which measures 30 degrees and we rotate it by 15 degrees, we are effectively adding 15 degrees to the original angle. Thus, the measure of angle Q' will be 30 degrees plus 15 degrees which equals 45 degrees. Rotations do not change the original angle but instead give us a new angle based on the original position plus the rotation.
Which of the following quadratic equations has the solution set (1/2,5)? Select all that apply
(x+1/2)(x-5)=0
(x-5)(2x-1)=0
(x+5)(2x-1)=0
(-2x+1)(-x+5)=0
(x+1/2)(x+5)=0
(-2x+1)(x-5)=0
-2x+6y=12 in graph ???
Maria invested $2000 in an account that earns 4.5% interest , compounded annually. The formula for compound interest is A(t) =P(1+l)×
How much did Maria have in the account after 5 years ?
A. $10,450.00
B. $2492.36
C. $2450.00
D. $12,819.47
Answer:
B. $2492.36
Step-by-step explanation:
We are given the formula for compound interest,
[tex]A(t)=p(1+i)^x[/tex] where p is the amount of principal, i is the interest rate and x is the number of years.
In our problem, p is 2000, i = 4.5% = 4.5/100 = 0.045, and x is 5:
[tex]A(t)=2000(1+0.045)^x\\\\A(5)=2000(1.045)^5\approx 2492.36[/tex]
Maria will have [tex]\$\ 2492.36[/tex] in her account after [tex]5[/tex] years.
What is compound interest ?Compound interest is the interest which is received on the principal and the previous interest.
Amount [tex]=P(1+\frac{R}{100})^t[/tex]
We have,
Invested principal [tex]=\$2000[/tex]
Compound interest Rate [tex]=4.5\%[/tex]
Time of investment [tex]=5[/tex] years
So,
Using the above mentioned formula;
Amount [tex]=P(1+\frac{R}{100})^t[/tex]
[tex]=2000(1+\frac{4.5}{100})^5[/tex]
[tex]=2000(1+\frac{9}{200})^5[/tex]
[tex]=2000\ *\ (\frac{209}{200})^5[/tex]
Amount [tex]=\$\ 2492.36[/tex]
So, Amount in Maria's account is [tex]\$\ 2492.36[/tex].
Hence, we can say that Maria will have [tex]\$\ 2492.36[/tex] in her account after [tex]5[/tex] years.
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Can someone please help me find the arc length ?
Find the perimeter and area of the polygon enclosed by points
If you use your office computer 40 hours per week, and do not unplug the computer when it is not in use, how much carbon dioxide is produced from the “vampire energy” used by the computer in one year?
Final answer:
A computer that uses 4W of power during 'vampire' mode over weekends throughout a year produces approximately 4.992 kg of CO2 annually. This is calculated by multiplying the total hours in vampire mode by the power consumption and then by the CO2 emission factor for electricity.
Explanation:
To calculate the amount of carbon dioxide produced from the vampire energy used by a computer that is not unplugged, we first have to establish the power consumption while in 'vampire' mode. The power consumed by the computer's LED when it is turned off but not unplugged is stated to be about 4 watts (W).
A year has 52 weeks, and each weekend amounts to 60 hours of the computer being in 'vampire' mode. To find the total number of hours in a year this mode occurs, we multiply 60 hours by 52, which gives us 3,120 hours of energy consumption annually when the computer is in 'standby' mode.
Next, to convert the total power consumed in watts to kilowatt-hours (kWh), we divide the power in watts by 1,000 (since 1 kW = 1,000 W), and then multiply by the total hours per year.
The carbon dioxide emissions can be estimated using an average emission factor for electricity production. For example, if we assume that the emission factor is about 0.4 kilograms of CO2 per kWh (which varies based on local energy sources), we can calculate the total emissions for the computer's vampire energy consumption.
Calculations: 4 W ÷ 1,000 = 0.004 kW
0.004 kW × 3,120 hours/year = 12.48 kWh/year
12.48 kWh/year × 0.4 kg CO2/kWh = 4.992 kg CO2/year
Therefore, the computer produces approximately 4.992 kg of CO2 annually from vampire energy when not unplugged over weekends.
The area of a parallelogram is 60 feet the height 5 feet how long is the base
jeff pizza is cut into 8 equal pieces. he eats 1/2 of it. Samantha says he ate 2/8 of the pizza. how did she get the answer?
Answer:
4/8
Step-by-step explanation: