Find the points on the curve given below, where the tangent is horizontal. (round the answers to three decimal places.) y = 7 x 3 + 6 x 2 - 8 x + 7
To find the points where the tangent is horizontal on the given curve, find the values of x for which the derivative is zero.
Explanation:To find the points on the given curve where the tangent is horizontal, we need to find the values of x for which the derivative of the curve is equal to zero. This is because the derivative represents the slope of the tangent line. Setting the derivative equal to zero and solving for x will give us the x-coordinates of the points.
The given curve is y = 7x³ + 6x² - 8x + 7. To find the derivative of this curve, we use the power rule of differentiation. The derivative is dy/dx = 21x^2 + 12x - 8.
Setting dy/dx equal to zero, we have 21x² + 12x - 8 = 0. To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Using this formula, we can find the values of x that make the derivative equal to zero.
Keywords: curve, tangent, horizontal, derivative, quadratic equation
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Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
Andrew ate 1/3 of a pumpkin pie. sarah ate 1/6 of the pie. how much pie is left?
Geometry
The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.
The sum of two numbers is 30 the difference of the two numbers is 4 what is the lesser number?
The lesser number is 13 and the bigger number is 17.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The sum of two numbers is 30 the difference between the two numbers is 4. Let the number be x and y where x > y. Then the equations will be
x + y = 30 ...1
x - y = 4 ...2
Add both equations, then we have
2x = 34
x = 17
Then the other number will be
17 + y = 30
y = 30 - 17
y = 13
The lesser number is 13 and the bigger number is 17.
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What are the steps for using a compass and straightedge to construct the bisector of ∠G?
Drag the steps and drop them in order from start to finish.
A. Use the straightedge to draw GK−→−.
B. Place the point of the compass on point H and draw an arc in the interior of the angle.
C. Place the point of the compass on point G and draw an arc that intersects the sides of ∠G. Label the points of intersection as points H and J.
D. Without changing the opening of the compass, place the point of the compass on point J and draw another arc in the interior of the angle.
E. Label the intersection of the arcs in the interior of the angle as point K.
Answer:
C, B, D, E, A.
Step-by-step explanation:
the scale of a map is 1 cm :50 mi. Determine the distance between two cities that are
4.2 cm apart on the map
The actual distance between two cities that are 4.2 cm apart on a map with a scale of 1 cm : 50 mi is 210 miles. The distance was calculated using a direct proportion based on the map's scale.
Explanation:To determine the actual distance between two cities that are 4.2 cm apart on a map with a scale of 1 cm : 50 mi, you can use the following method:
First, understand that the scale means for every 1 cm on the map, the actual distance is 50 miles. Therefore, you can set up a direct proportion to solve for the actual distance.
Scale of map: 1 cm : 50 mi
Distance on map: 4.2 cm
Setting up the proportion, we get:
1 cm / 50 mi = 4.2 cm / x miNow, solve for 'x' which represents the actual distance between the two cities.
x = (4.2 cm × 50 mi) / 1 cmx = 210 miThe actual distance between the two cities is 210 miles.
A spinner is numbered 1 through 5 is spun 3 times. What is the probability of spinning a number less than 3, then a number greater than 3, and then the number 3? Write your answer as a decimal. Do not round.
2m= p-q/r
solve for p
Answer: The required solution for p is [tex]p=2mr+q.[/tex]
Step-by-step explanation: We are given to solve the following equation for the variable p :
[tex]2m=\dfrac{p-q}{r}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for p, we must take p on one side of the equation and all other terms on the other side.
From equation (i), we get
[tex]2m=\dfrac{p-q}{r}\\\\\Rightarrow 2mr=p-q~~~~~~~~~~~~~~[\textup{Cross-multiplication}]\\\\\Rightarrow p=2mr+q.[/tex]
Thus, the required solution for p is [tex]p=2mr+q.[/tex]
Mark earns $400 a week plus 5% commission on all sales. Which inequality represents s, what mark's sales must be in order for him to earn at least $700 for the week?
Eight subtracted from five times a number is -138. what is the number?
Answer:
8-5n= -138
You add 8 to each side
5n= -130
Divide by 5 on each side
n = -26
Step-by-step explanation:
Tanya planted seedlings in her garden over the weekend. The instructions that came with the seedlings stated that they need to be planted 0.2 meters apart. Tanya has a measuring tape that has values in centimeters. Help Tanya convert meters to centimeters.
Answer:
20 centimeters apart.
Step-by-step explanation:
Tanya planted seedlings in her garden over the weekend.
The instructions that came with the seedlings stated that they need to be planted 0.2 meters apart.
Tanya has a measuring tape that has values in centimeters.
As we know 1 meter = 100 centimeters
therefore, 0.2 meter = 0.2 × 100 = 20 centimeters
So Tanya need to be planted 20 centimeters apart.
Determine whether the lines l1 and l2 are parallel perpendicular or neither
The lines l1 and l2 are perpendicular to each other. They form a 270° angle which means they form three right angles. Hence they are indeed perpendicular due to the fact they intersect at a point if one line is extended by 180°.
Explanation:In this case, we are asked to determine if the lines l1 and l2 are parallel, perpendicular or neither. One critical information presented is that the two lines are perpendicular and form a 270° angle between each other.
Typically, when two lines are perpendicular, they form a right angle, which is 90°. However, a 270° angle suggests they make three right angles, meaning they do not directly intersect at a right angle, but do meet at a point if you extend one line 180° further. Hence, they are indeed perpendicular.
So, although it might seem a bit unusual, based on this information, the lines l1 and l2 are perpendicular to each other.
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Michael and Jacob are standing on two docks that are 20 miles apart. They are watching a ship that is out in the ocean. The angle between the dock and the line connecting Michael and the ship is 48°, and the angle between the other dock and the line connecting Jacob and the ship is 37°.
If the ship can travel to either dock, which dock would be closest? Explain your answer.
A.) Michael’s dock would be closer because the angle opposite is smaller.
B.) Jacob’s dock would be closer because the angle opposite is smaller.
C.) Michael’s dock would be closer because the docks are 20 miles apart.
D.) Jacob’s dock would be closer because the docks are 20 miles apart.
Based on the basic principles of trigonometry, the ship would be closer to Jacob's dock because the dock's angle is smaller.
Explanation:The question is asking which dock, Michael's or Jacob's, would be closer to the ship based on angles given. In the world of mathematics and specifically trigonometry, larger angles in a triangle usually indicate longer sides opposite that angle. This is because the length of the side of a triangle is directly proportional to sine of its opposite angle.
In this case, the angle between the dock and the line connecting Michael and the ship is given as 48° which is larger than the angle for Jacob (37°). When applying the basic principles of trigonometry, this tells us that the distance from the ship to Michael's dock would be greater than the one to Jacob's. Therefore, the ship would be closer to Jacob's dock. So, the answer is B: Jacob's dock would be closer because the angle opposite is smaller.
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Which decimal number is equal to 2/3 ?
A. 0.6
B. 0.66
C. 0.6
D. 0.67
The answer should be B.
Decimal number equal to 2/3 is 0.67.
What is a Decimal and fractional Numbers?
Decimal numbers include those numbers which have a whole number and the fractional part separated by a decimal point. Example -
2.33, 4.55, 5.6
A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. Example -
2/5, 5/6, 7/9
We have a fraction 2/3.
The decimal number equal to 2/3 is 0.67.
Hence, decimal number equal to 2/3 is 0.67.
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I NEED MATH HELP, QUICK! PLEASE HELP ME!
The graph of the equation y = 3x + 4 is shown. Determine the value of y for the point
(-1, y).
To find the value of y for the point (-1, y) in the equation y = 3x + 4, plug in -1 for x and solve: y = -3 + 4, which simplifies to y = 1. Thus, the value of y is 1.
The student needs to determine the value of y when x is -1 for the equation y = 3x + 4. To find y, we substitute -1 in place of x and solve the equation:
y = 3(-1) + 4
y = -3 + 4
y = 1
Therefore, the value of y for the point (-1, y) is 1.
Solve for x: 3|x - 3| + 2 = 14
A) no solutions
B) X = -1, x = 8.3
C) x = 0, x = 7
D) x = -1, x = 7
.6 divded by 3.66 show work
0.16393442623 tha should be it
una aproximacion por truncamiento del numero 4,56789 es 4,56 .hallar el error absoluto y el error relativo
Dan the detective looked for a number. he found a two-digit number less than 50. the sum of its digits was 12. their different was 4. what number did da find
What number would u add to complete the square ? x^2+22x=9
The sum of two numbers is 66 . the larger number is eight more than the smaller number. what are the numbers?
iana started to evaluate the function f(x) = 2x2 – 3x + 7 for the input value 2.
f(x) = 2(2)2 – 3(2) + 7
= 2(4) – 3(2) + 7
What is the value of the function when x = 2?
9
10
16
17
Answer:
f(2) = 9.
Step-by-step explanation:
Given : f(x) = 2x² – 3x + 7.
To find : What is the value of the function when x = 2.
Solution : We have given that f(x) = 2x² – 3x + 7.
For, x = 2
f(2) = 2(2)² – 3(2) + 7.
f(2) = 2 *4 -6 +7
f(2) = 8 - 6 +7.
f(2) = 2 +7
f(2) = 9.
Therefore, f(2) = 9.
Solve this math problem: a bag of coins contains nickels, dimes, and quarters. there are a total of 21 coins in the bag, and the total amount of money in the bag is $3.00. there is one more dime than there are nickels. how many dimes, nickels, and quarters are in the bag?
Answer: There are 6 nickels, 7 dimes and 8 quarters in the bag.
Step-by-step explanation: Given that the bag contains coins of nickels, dimes and quarters. There are total 21 coins in the bag and number of dimes is one more than the number of nickels.
Let 'x' be the number of nickels in the bag.
So, number of dimes will be (x+1) and number of quarters will be (21-x-x-1) i.e., (20-2x).
Since there are total $3.00 amount of money in the bag, so
[tex]0.05x+0.10(x+1)+0.25(20-2x)=3\\\\\Rightarrow\dfrac{x}{20}+\dfrac{x+1}{10}+\dfrac{20-2x}{4}=3\\\\\Rightarrow \dfrac{x+2x+2+100-10x}{20}=3\\\\\Rightarrow -7x+102=60\\\\\Rightarrow 7x=42\\\\\Rightarrow x=6.[/tex]
Therefore, number of nickels = 6, number of dimes = 6+1 = 7 and number of quarters = 20-2×6 = 8.
Thus, there are 6 nickels, 7 dimes and 8 quarters in the bag.
Please help me with these !!! ❤️❤️ I need it thank youuu!
7x+y=13 y=2x-0.5 elim
A recipe calls for 1 1/2 cups of flour,but you only have 2/3 of a cup.How much more flour do you need?
Your answer would be 5/6
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which inequality best represents the following situation: A driver is on the highway, with a speed limit of 70 miles per hour, and is not breaking the law?
What is the product 4.6(-5.2)
Final answer:
The product of 4.6 and -5.2 is 20.12.
Explanation:
The product of 4.6 and -5.2 is calculated by multiplying the two numbers together. To do this, we can use the following steps:
Multiply the whole numbers: 4 * 5 = 20Multiply the decimal parts: 0.6 * 0.2 = 0.12Add the results: 20 + 0.12 = 20.12Therefore, the product of 4.6 and -5.2 is 20.12.
enter the correct word and unit of measurement to complete the conversion
1 nanosecond = one ___
of a __
Answer:
1 nanosecond = 1 billionth of a second
Step-by-step explanation:
A nanosecond (ns) is an SI unit of time equal to one billionth of a second, that is, 1⁄1 000 000 000 of a second, or 10^−9 seconds. The term combines the prefix nano- with the basic unit for one-sixtieth of a minute. A nanosecond is equal to 1000 picoseconds or 1⁄1000 microsecond.