Find dy/dx and d^2y/dx^2. For which values of t is the curve concave upward? x = t^3 + 1, y = t^2 - t

Answers

Answer 1

The denominator is always positive (9t^3), the curve is concave upward for all t ≠ 0.

How to find dy/dx for the parametric equation?

To find dy/dx and d^2y/dx^2 for the parametric equations x = t^3 + 1 and y = t^2 - t, and determine for which values of t the curve is concave upward, follow these steps:

. Differentiate x and y with respect to t:
dx/dt = 3t^2 (from x = t^3 + 1)
dy/dt = 2t - 1 (from y = t^2 - t)

. Find dy/dx by dividing dy/dt by dx/dt:
dy/dx = (2t - 1) / (3t^2)

. Find the second derivative, d^2y/dx^2, by differentiating dy/dx with respect to t and then dividing by dx/dt:
d(dy/dx)/dt = (2 - 0) / (6t) = 2 / (6t) = 1 / (3t)
d^2y/dx^2 = (d(dy/dx)/dt) / (dx/dt) = (1 / (3t)) / (3t^2) = 1 / (9t^3)

. To find where the curve is concave upward, determine the values of t for which d^2y/dx^2 > 0:
1 / (9t^3) > 0

Since the denominator is always positive (9t^3), the curve is concave upward for all t ≠ 0.
So, the content loaded Find dy/dx and d^2y/dx^2 are dy/dx = (2t - 1) / (3t^2) and d^2y/dx^2 = 1 / (9t^3), respectively. For which values of t is the curve concave upward? The curve is concave upward for all t ≠ 0.

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Related Questions

(13x+2)(5x-7)(3x-4) slover for x

Answers

Answer:

x=-.43

Step-by-step explanation:

13x+2 5x-7 3x-4

21x+2-7-4

21x-9

x=-.428

what does the dml compiler do relational algebra

Answers

The DML Compiler translates Data Manipulation Language (DML) queries into Relational Algebra operations to be used by the Relational Database Management System (RDBMS).

The DML Compiler starts by parsing the query to determine which operations are needed. It then builds an Abstract Syntax Tree (AST) which is a hierarchical representation of the query. Next, the DML Compiler will perform semantic analysis on the AST to ensure that all operations are valid and the query is valid. After the semantic analysis has been done, the DML Compiler will then translate the AST into Relational Algebra operations, which are a collection of mathematical rules used to manipulate data in a relational database. Finally, the DML Compiler will generate an executable code and send it to the RDBMS to be executed. The result of the query is then returned to the user.

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sum and product of two irrational numbers is irrational give examples. please answer me fast i am waiting​

Answers

Answer:

π+π/∞+∞/√∞+∛∞

Step-by-step explanation:

which represents the slope of a line that is parallel to a line with a slope of -2

Answers

Answer:

One with a slope of -2 and different y-intercept

e.g. y = -2x + 3

What does a sign with a reflective orange triangle with a red border on each of the three sides warn you of

Answers

This triangle is warning you to slow down and be prepared to stop. It indicates that a railroad crossing is ahead and you should proceed with caution.

This sign is warning you that a railroad crossing is ahead, and you should proceed with caution. The triangle shape is reflective orange with a red border on each of the three sides. This sign indicates that you should slow down and be prepared to stop as a train may be approaching. You should also look both ways for any oncoming trains before continuing to cross the tracks. Additionally, you should never try to drive around a lowered crossing gate and never cross the tracks until you are sure that it is safe to do so. Always obey the signs and signals at railroad crossings and never take any chances when it comes to safety. Following these rules will help to ensure that everyone stays safe when crossing railroad tracks.

the complete question is : What does a sign with a reflective orange triangle with a red border on each of the three sides warn you off ?

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The sign with a reflective orange triangle with a red border on each of the three sides warn you of Slow moving vehicles.

Here we have to find the reason behind sign with a reflective orange triangle with a red border on each of the three sides.

Basically this type of sign are look like a warning triangle which is also an equilateral  triangle of around 600mm in size made of red reflective material. Where it can be put on the side of the road by anyone to warn other drivers of a breakdown or crash ahead.

And it must also said that the reflective orange triangle on the rear of a vehicle means it is traveling 35 mph or less. And here you may see this sign on road maintenance equipment, farm vehicles, or horse- drawn wagons.

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Which measure would you use to describe central tendency for qualitative data?.

Answers

When describing the central tendency for qualitative data, the measure that is commonly used is the mode.

Unlike quantitative data, where measures such as the mean or median can be used to describe central tendency, qualitative data consists of categories or labels rather than numerical values.

Therefore, the mode is the most appropriate measure for central tendency in this context.

The mode can be useful in summarizing qualitative data by identifying the most common category or response. It provides insight into the most prevalent characteristic or attribute among the data, allowing for a better understanding of the distribution and patterns within the dataset.


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\(\frac{1}{4}w-3\ \textless \ 3\)

Answers

Answer:

x<24

I believe

Step-by-step explanation:

Use trig ratios to find both missing sides. Show your work

Use trig ratios to find both missing sides. Show your work

Answers

The missing side of the right triangle is as follows:

a = 22.7 units

b = 10.6 units

How to find the side of a right triangle?

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides a and b can be found using trigonometric ratios as follows:

Hence,

sin 25 = opposite / hypotenuse

sin 25° = b / 25

cross multiply

b = 25 sin 25

b = 25 × 0.42261826174

b = 10.5654565435

b = 10.6 units

cos 25 = adjacent / hypotenuse

cos 25 = a / 25

cross multiply

a = 25 cos 25

a = 22.6576946759

a = 22.7 units

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please help due tomorrow?!?!

please help due tomorrow?!?!

Answers

Answer:

t = 0.0475p

Step-by-step explanation:

From the options provided, the answer would be ...

t = 0.0475p

Lets say Tonia's paycheck is 25,000 she needs to pay 5% of this to her 401k, meaning she should have 95% left

25,000 * 0.95 = 23,750

Now, 5% of this remainder goes to income tax which would be...

23,750 * 0.05 = 1,187.5

Now if we use the formula and plug in 25,000 for p which is Tonia's paycheck we see that we get the same income tax amount. Therefore, we know it is the correct formula.

t = 0.0475 * 25000

t = 1,187.5

what is the probability of correctly choosing (in any order) 4 numbers that match 4 randomly selected balls from a bucket of 35 balls with the different numbers 1 to 35 on them? please enter your answer as a fraction.

Answers

The probability of correctly choosing 4 numbers that match 4 randomly selected balls from a bucket of 35 balls is 1/52360.

To calculate the probability of correctly choosing 4 numbers that match 4 randomly selected balls from a bucket of 35 balls with different numbers from 1 to 35, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

Since there are 35 balls in the bucket, the total number of possible outcomes is given by the combination formula:

nCr = n! / [(n-r)! * r!]

In this case, we need to choose 4 balls out of 35, so the total number of possible outcomes is:

35C4 = 35! / [(35-4)! * 4!]

Number of favorable outcomes:

We want to choose 4 numbers that match the 4 randomly selected balls. Since there are 4 balls that need to match, we can consider this as choosing all 4 numbers correctly.

There is only 1 way to choose all 4 numbers correctly.

Therefore, the number of favorable outcomes is 1.

Probability:

The probability of an event is given by the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is:

Probability = 1 / 35C4

Now, let's calculate the probability:

35C4 = 35! / [(35-4)! * 4!]

= (35 * 34 * 33 * 32) / (4 * 3 * 2 * 1)

= 52360

Probability = 1 / 52360

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thanks for helping with the last one....a few more please help

thanks for helping with the last one....a few more please help

Answers

i’m not 100% sure but my best guess would be
6.A
7.A
8.C
9.C
10.D

(b) how many people would you need to interview to be 73% sure that at least seven of these people can read and write (are not illiterate)? (enter the smallest number of people needed to be at least 73% sure.)

Answers

0.3193 is the probability of your 73% surity that at least seven of these people can read and write ( are not illiterate ).

What is probability ?

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. A probability is a number between 0 and 1, where 1 indicates certainty and 0 indicates impossibility of the event.

Calculation

p = 0.73

q = 1 - p = 1 - 0.73 = 0.27

n = 8

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X > 7) = (8 C 7) * 0.737 * (0.37)8-7  +(8 C 8) * 0.738 * (0.37)8-8

              =  0.238624 + 0.080646

Probability = 0.3193  

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The parallelogram PQRS has vertices P (-2, 3), Q (1, 4), R (2, 6) and S (- 1, 5). Find the coordinates of the point of intersection of the diagonals.

Answers

Call the intersection of 2 diagonal lines as I(a;b)
=> I is the midpoint of the diagonal PR
<=> a= (-2+2)/2. And. b=(3+6)/2
<=> a=0. And. b= 9/2
=> I(0;9/2)

2. A 4-oz. steak contains 700 mg of potassium. It is recommended for the average person to consume at least 3,500mg of potassium a day. If you ate a 10-oz. steak for dinner, what percent of your daily value of potassium did youeat?

Answers

We know that 4 oz of steak contains 700 mg of potassium. We want to know how many mg of potassium a 10 oz steak has. The bigger the steak the more potassium it has, so it is a directly proportional relationship. We can apply a rule of three to find the value we want as shown below:

\(\frac{4}{10}\frac{\text{ oz}}{\text{ oz}}=\frac{700}{x}\frac{\text{ mg}}{\text{ mg}}\)

Since hte relationship is proportional we don't need to invert any of the fractions. The first step is to cross multiply and then solve for x.

\(\begin{gathered} 4\cdot x=10\cdot700 \\ 4\cdot x=7000 \\ x=\frac{7000}{4} \\ x=1750\text{ mg} \end{gathered}\)

A 10 oz steak contains 1750 mg of potassium. We want to know how many percent of the daily value we consumed by eating that steak. To do that we can create another rule of three as shown below:

\(\frac{1750}{3500}\frac{\text{ mg}}{\text{ mg}}=\frac{x}{100}\frac{\text{ \%}}{\text{ \%}}\)\(\begin{gathered} 3500\cdot x=1750\cdot100 \\ 3500\cdot x=175000 \\ x=\frac{175000}{3500} \\ x=50\text{ \%} \end{gathered}\)

We ate 50 % of the daily value of potassium recommended.

Help me please with this question

Help me please with this question

Answers

The distance between the two points (2, 6) and (7, -6) will be 13 units.

What is the distance between two points?

Let one point be (x, y) and another point be (h, k). Then the distance between the points will be

D² = (x - h)² + (y - k)²

A right triangle with the two points forming the hypotenuse. The two points are given below.

(2, 6) and (7, -6)

Then the distance between the points (2, 6) and (7, -6) will be given as,

D² = (7 - 2)² + (-6 - 6)²

D² = 5² + (-12)²

D² = 25 + 144

D² = 169

D = 13 units

The distance between the two points (2, 6) and (7, -6) will be 13 units.

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in a regression output in spss, r 2 represents: a. the coefficient of determination. b. the estimated slope of the regression line. c. the independent variable. d. the dependent variable.

Answers

The answer to the question is (a) the coefficient of determination.

Does R-squared measure the goodness of fit?

The coefficient of determination, denoted as R-squared (R²), represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It is a statistical measure that indicates the goodness of fit of the regression line to the observed data. R-squared ranges from 0 to 1, where 0 indicates no linear relationship between the variables, and 1 indicates a perfect fit. In simpler terms, R-squared tells us how well the independent variable(s) can predict the dependent variable. It is commonly used to evaluate the strength and reliability of a regression model and understand the percentage of variability in the dependent variable that can be accounted for by the independent variable(s). #spj11

R-squared to assess the goodness of fit in a regression model. It quantifies the proportion of the dependent variable's variability that can be explained by the independent variable(s). R-squared ranges from 0 to 1, with higher values indicating a better fit. Is R-squared an indicator of the regression line's accuracy? Understand how R-squared provides insights into the relationship between variables and helps evaluate the predictive power of your model.

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The cost of each ticket at the carnival was $0.25. Li bought $7.50 worth of tickets. How many tickets did she buy?
help me please

Answers

She bought 30 tickets. Just do 7.50 divide 0.25.

Someone please help me right now its important

Someone please help me right now its important

Answers

The actual distance between the two city is,

⇒ 204 miles

We have to given that,

Montraie is planning to drive from City X to City Y.

And, The scale drawing shows the distance between the two cities with a scale of 1/4 inch = 17 miles.

Since, The distanced for the scale drawing is,

⇒ 3 inches

Hence, The actual distance between the two city is,

⇒ 1/4 inches = 17 miles

⇒ 3 inches = 17 × 4 × 3

⇒ 3 inches = 204 miles

Therefore, The actual distance between the two city is,

⇒ 3 inches = 204 miles

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How do I graph h(x) = 4|x+4| +3

How do I graph h(x) = 4|x+4| +3

Answers

Answer:

Move the point on the diagonal to (1,4) then move the vertex 4 units left and 3 units upwards

Step-by-step explanation:

David is performing the following construction. Based on the markings that are present, what construction is he performing?


O Bisecting an angle


O Bisecting a line segment


O Copying an angle


O Copying a line segment



Will mark brainiest

Answers

The correct answer is Option A. Bisecting an angle

David is performing the construction of bisecting an angle. In geometry, the concept of bisecting refers to dividing a line segment or an angle into two equal parts. A line segment is a part of a line that is defined by two endpoints, whereas an angle is the measure of the space between two intersecting lines. It is measured in degrees.

The process of bisecting an angle is done by following these steps:

Step 1: Place the compass at the vertex of the angle

Step 2: Draw an arc that intersects both the sides of the angle.

Step 3: Without changing the radius of the compass, draw another arc that intersects the first arc.

Step 4: Draw a line that passes through the vertex of the angle and the point of intersection of the two arcs.

This line will bisect the angle in half.

In the given figure, David is performing the construction of bisecting an angle.

Hence, the correct answer is Option A. Bisecting an angle. Always remember to measure the angle first before bisecting it.

Two geometrically similar jugs have volumes of 1000 cm3and 512 cm3.They have circular bases. The diameter of the base of the larger jug is 9 cm.

Answers

Complete Question

Two geometrically similar jugs have volumes of 1000 cm³and 512 cm³.They have circular bases. The diameter of the base of the larger jug is 9 cm.

Calculate the diameter of the smaller jug.

Answer:

7.2 cm

Step-by-step explanation:

To solve the above question,we have the proportion

Smaller volume/ Larger volume = (Smaller diameter/ Larger diameter)³

We are to find the smaller diameter

Hence our formula is give as

Cube root(Smaller volume/ Larger volume)= Smaller diameter/ Larger diameter

=cube root( 512/1000) = x/9

= 8/10 = x/9

Cross Multiply

10x = 8 × 9

10x = 72

x = 72/10

x = 7.2cm

Therefore, the diameter of the second jug is 7.2 cm

The Chess Club has 24 members, 14 girls and 10 boys. What is the ratio of
girls to boys in the Chess Club?
A. 3:4
O B. 7:5
O C. 5:7

Answers

Answer: I think it would be 7:5 because half of 14=7 and half of 10=5. by the way, are you good at algebra II by any chance? if so can you help me out in return for me helping you out please?

Which table of values corresponds to the graph below?

On a coordinate plane, a line goes through points (0, negative 2) and (2, 0).

Answers

The table of values corresponding to the linear function that goes through (0, -2) and (2,0) is has points (x,y) in the following format:

(x, x - 2).

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line goes through (0,-2), hence the y-intercept is b = -2. The slope is given by:

m = (0 - (-2))/(2 - 0) = 2/2 = 1.

Hence the equation is:

y = x - 2.

Thus the points on the table are related as follows:

(x, x - 2).

For example

x  f(x)

0  -2

1   -1

2   0

3   1

4   2

5   3

And so on...

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PLEASE HELP
Let f(x) = 4x + 3 and g(x) = -2x + 5. Find.(f.g)(5)
a. 23
b. -17
c. -41
d. -5

Answers

Answer:

After solving we get (f.g)(5)=-115

But the correct option is not given in the question.

Step-by-step explanation:

We are given:

\(f(x) = 4x+3\\g(x)=-2x+5\)

We need to find (f.g)(5)

First we will multiply f and g to find (f.g) i.e

\((f.g)(x)= f(x) \times g(x)\\(f.g)(x) = (4x + 3)(-2x + 5)\\(f.g)(x)=4x(-2x+5)+3(-2x+5)\\(f.g)(x)=-8x^2+20x-6x+15\\(f.g)(x)=-8x^2+14x+15\\\)

Now putting x=5

\((f.g)(x)=-8x^2+14x+15\\Put \ x=5\\(f.g)(5)=-8(5)^2+14(5)+15\\(f.g)(5)=-8(25)+70+15\\(f.g)(5)=-200+70+15\\(f.g)(5)=-115\)

So, after solving we get (f.g)(5)=-115

But the correct option is not given in the question.

Please answer with a detailed and long explanation

Please answer with a detailed and long explanation

Answers

Answer:

The volume of Cone B is twice the volume of Cone A.

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h  where r is the radius and h is the height.

Cone A

d = diameter

r = radius

h = height

V = 1/3 pi r^2 h

Cone B

The diameter is double the diameter of A.

2d  so the radius is 2r

The height is half the height of A.

1/2 h

Substitute into the equation for volume.

V = 1/3 pi ( 2r)^2 (1/2 h)

V = 1/3 pi (4r^2) (1/2h)

V = 1/3 pi 2r^2 h

The volume of Cone B is twice the volume of Cone A.

Answer:

Cone B has a greater volume.

Step-by-step explanation:

Cone B has the greatest volume.

The volume of a cone is calculated using the following formula:

\(\boxed{\bold{\tt{Volume\: of\:cone = \frac{1}{3}\pi*r^2h}}}\)

where:

π is a mathematical constant approximately equal to 3.14 r is the radius of the coneh is the height of the cone

For Cone A.

\(\boxed{\bold{\tt{Volume\: of\:cone\: (A)= \frac{1}{3}\pi*r^2h}}}\)

For Cone B

In this case, the radius of Cone B is double the radius of Cone A, and the height of Cone B is half the height of Cone A. This means:

radius(r)=2r

height(h)= \(\tt{\frac{1}{2}*\frac{h}{2}}\)

\(\boxed{\bold{\tt{Volume\: of\:cone\: (B)= \frac{1}{3}\pi*(2r)^2*\frac{h}{2}}}}\)

\(\boxed{\bold{\tt{Volume \: of\:cone (B)= 2*\frac{1}{3}\pi*r^2h}}}\)

\(\boxed{\bold{\tt{Volume(B) =2*Volume\: of\:cone(A)}}}\)

Since the volume of cone B is twice the volume of Cone A.

Therefore, Cone B has a greater volume.

A factory makes phones cases using 8 cutting machines.each machine can cut 4 cases every 15 seconds.if 25% of the machines are removed for maintenance,then how many fewer cases per minute will the remaining machines cut when compared to the number of cases per minute all 8 machines cut ?

Answers

There are 8 cutting machines and each machine can cut 4 cases every 15 seconds, or 16 cases per minute (4 cases/15 seconds x 60 seconds/minute = 16 cases/minute). Therefore, all 8 machines can cut a total of 8 x 16 = 128 cases per minute.

If 25% of the machines are removed for maintenance, then 2 machines (25% of 8) will be taken out of service. This leaves 6 machines to continue cutting phone cases.

The 6 remaining machines can cut 6 x 16 = 96 cases per minute (since each machine still cuts 16 cases per minute). Therefore, the 6 remaining machines cut 128 - 96 = 32 fewer cases per minute than all 8 machines together.

So the answer is that the remaining machines cut 32 fewer cases per minute when compared to the number of cases per minute all 8 machines cut.

ILL GIVE BRAINIEST TO PERSON WHO ANSWERS CORRECTLY

ILL GIVE BRAINIEST TO PERSON WHO ANSWERS CORRECTLY

Answers

Observe the graph .

There is a coordinate lies on y axis It's (0,3)

Y intercept=3

More:-

Slope intercept form

y=mx+b

Where

m=slopeb=y intercept

PLEASE HELP :/ Write an equation that represents the transformations formed by the following items:

PLEASE HELP :/ Write an equation that represents the transformations formed by the following items:

Answers

Answer:

I have no idea.

but I need points sorry

According to Hooke's Law, the distance that a spring will stretch varies
proportionally to the amount of weight added to it. If a spring is stretched
0.8 inches by a 40-lb weight, how many inches will it be stretched by a 25-lb
weight?

Answers

The 25-lb weight stretched by 0.2 inches.

According to the question, Hooke's law states that the spring can be stretched directly with a force F. Therefore, the expression for the Hooke's law can be written as: F(Force) = extension(d). constant(k)

If a spring is stretched 0.8 inches by 40-lb weight:

40 = 0.8k ⇒k = 50

Now: the stretched inches be:

25 = 50d ⇒ d = 0.2 inches

Hence, the 25-lb weight stretched by 0.2 inches.

What is Hooke's law?

The Hooke's law states that the force produced by the spring is directly proportional to the weight of the spring. And the work done can be done either in the form of stretching or compressing.

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a car travels 30m in 2 minutes whats the speed​

Answers

Answer:

15

Step-by-step explanation:

speed is distance over time so its 30 devided by 2

Other Questions
Which of the following statement is not true for binomial distribution. (Related to Checkpoint 5.4)(Present-value comparison)You are offered $100,000 today or $300,000 in 13years.Assuming that you can earn 11 percent on your money, which should you choose?If you are offered $300,000 in 13 years and you can earn 11 percent on your money, what is the present value of $300,000? Calculate the total deformation in a 25ft long, 4 in. diameter steel bar hanger that supports a 390 kip load. This bar is also subjected to a change in temperature from 140F before loading to 10F after loading, calculate the change in length due to temperature change. (Esteel =30106psi, and =0.0000065 in/in F) Calculate the total deformation in a 25ft long, 4 in. diameter steel bar hanger that supports a 390 kip load. This bar is also subjected to a change in temperature from 140F before loading to 10F after loading, calculate the change in length due to the load. (Estew =30106p si, and = 0.0000065 in/ in FJ Answer: Question 3 Calculate the ttal deformation in a 25ft long, 4 in. diameter steel bar hanger that supports a 390 kip load. This bar is also subjected to a change in temperature from 140F before loading to 10F after loading, calculate the total change in length due to the combined thermal and mechanical. (E steel =30106psi, and =0.0000065 in/in F ) A 120ft. Iong, 2 in. diameter steel rod is expected to fail at 80,000 psi. If a safety factor of 2 is Question 5 A 120ft. long, 2in. diameter steel rod is expected to fail at 80,000psi, If a safety factor of 2 is required what would be the total elongation at the maximum allowable load. ( Esteel =30106p si) 17 POINTS HELP I GIVE BRAINLIEST A line is defined by the equation y = negative x + 3. Which shows the graph of this line?On a coordinate plane, a line goes through points (0, 3) and (3, 0).On a coordinate plane, a line goes through points (0, negative 3) and (0, 3).On a coordinate plane, a line goes through points (0, 0) and (2, 6).On a coordinate plane, a line goes through points (negative 2, 6) and (0, 0). the radius of the base of a cylinder is 7cm and height is 8cm find the volume and surface area of the solid cylinder Many nucleophilic addition reaction of aldehydes and ketones arecatalyzed by acid or base. Bases catalyze hydration by:a. Making the cabonyl more electrophilicb. Shifting the equilibrium of the reactionc. Making the carbonyl less electrophilicd. Converting the water to hydroxide ion, a much betternucleophile The function f(x) = x ^ 2 graphed on a coordinate grid. Lauren wants to graph g(x) = (x + 2) ^ 2 + 3 on the same grid. Which of these will be used to correctly obtain g(x) ? When the United States Constitution was written, which compromise was reached by the authors to gain the support of the states with small populations?a. Congress would consist of both a House of Representatives and a Senateb. The President would be selected by the direct vote of the peoplec. Five enslaved persons would be counted as three free persons for taxationd. Exported goods could not be taxed, but imported could be taxed 6.1.4: Functions with parameters and return values. Write a function ComputeNum that takes one integer parameter and returns 7 times the parameter. Ex: ComputeNum(3) returns 21.#include using namespace std;/* Your code goes here */int main() {int input;int result;cin >> input;result = ComputeNum(input);cout Question Which expression can be used to represent the volume of this prism? Responses 21 4 units 21 4 units 3 11 units 3 11 units 7 7 units 7 7 units 10 4 units 10 4 units A rectangular prism made up of unit cubes. There are 4 layers, and each layer is 3 units long and 7 units wide. Find the area of a circle with a diameter of 16 units. Exact Area:Approx Area (use 3.14 for pi):Approx Area (use 22/7 for pi): Find the area of a regular octagon with an apothem equal to 6.7 this is for advanced math In need help i am doing grade improvements Shelby purchases her college books for the upcoming semester. She has to pay $98 for a biology book, $38 for a used poetry book, and $74 for a trigonometry textbook. If the sales tax rate is 7.5%, how much tax will Shelby pay?pls help i will brainliest If the reaction quotient (Q) is smaller than the equilibrium constant (K) for a reaction then which way will the reaction proceed? a. The reaction is at equilibrium and the reaction will proceed at equal rates in the reverse and forward direction. b. The reaction will proceed to the right (products side) c. The reaction equation is required to answer this question d. The reaction will proceed to the left( reactants side) releases hormones that increase the rate of cellular respiration throughout the body For those fluent in Spanish please help 1. There are two small rectangles in this picture that make one large rectangle. Howcouldyoufind the area of the large rectangle?10My thoughts/workspace35What is the area of the large rectangle?units? Which of the linear equations below is derived from thefollowing table of values? HELP ME