Mathematics High School

Find the value for k for which y= 2x+k is a tangent to the curve y=2x^2-3 and determine the point of intersection

Answers

Answer 1

Answers:

k = -3.5

Intersection point is (0.5, -2.5)

================================================

Explanation:

Apply the derivative to y=2x^2-3 and you should get dy/dx = 4x

The derivative helps determine the slope of the tangent at any point on the curve.

The slope of the tangent line y = 2x+k is 2.

We want the slope of the tangent to be 2, so we'll replace the dy/dx with 2 and solve for x.

dy/dx = 4x

2 = 4x

x = 2/4

x = 0.5

Plug this into the curve's original equation.

y = 2x^2 - 3

y = 2(0.5)^2 - 3

y = -2.5

Therefore, the tangent line y = 2x+k and the curve y = 2x^2-3 intersect at the point (0.5, -2.5). This is the point of tangency.

We'll use the coordinates of this point to determine k.

y = 2x+k

-2.5 = 2(0.5) + k

-2.5 = 1 + k

k = -2.5-1

k = -3.5

Visual verification is shown below. I used GeoGebra to make the graph, but you could use any other tool you prefer (such as Desmos).

Find The Value For K For Which Y= 2x+k Is A Tangent To The Curve Y=2x^2-3 And Determine The Point Of

Related Questions

i don’t understand how to find x to solve.

Answers

Answer:

X + 3

Step-by-step explanation:

There is no definite working. The first container is what I call the base because everything is a little above the first container, X. They are basically asking you what is the total of the four jars bigger than X. In other words how many steps more to climb before the top floor while you are on the first step. So then you add the other numbers like 0.5 etc which will give you X +3. Hope it helps.

Review the steps of the proof of the identity
At which step was an error made?
sin (A-3) - COSA.
= A.
step 1
step 2
3п
sin
step 3
step 4
Step 1: = sinAcos
3 п
2
-
COSAsin
n ()
Step 2: = (sinA)(0) + COSA( - 1)
Step 3: = (sinA)(0) + (1) (COSA)
Step 4: = 0 + COSA
Step 5: Cos A

Answers

Answer:

step 2

and then step 3 : the error neutralized the error of step 2

Step-by-step explanation:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

and because

sin(-b) = -sin(b)

cos(-b) = cos(b)

we have

sin(a - b) = sin(a)cos(-b) + cos(a)sin(-b) =

= sin(a)cos(b) - cos(a)sin(b)

3pi/2 = 270° or -90°.

sin(3pi/2) = sin(270) = sin(-90) = -1

that means, it is the full radius straight down from the center of the circle.

cos(3pi/2) = cos(270) = cos(-90) = cos(90) = 0

so, step 1 is correct :

sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2) =

= sin(A)×0 - cos(A)×(-1) (correct step 2)

but as we see, the provided step 2 is incorrect.

it should have been the indicated

sin(A)×0 - cos(A)×(-1)

and NOT the provided

sin(A)×0 + cos(A)×(-1)

step 3 based on the erroneous step 2 should then have been

sin(A)×0 - (1)cos(A)

but instead another error with the sign was made that neutralized the error of step 2 and we got after this second mistake by pure chance the overall correct step 3

sin(A)×0 + (1)cos(A)

so, again, the first error was made in step 2.

but technically, there was also a consecutive error made in step 3 to bring everything back to the correct approach.

This figure is divided into triangles. What fraction of the figure is each triangle?

Answers

Answer:

a) 1/8

Step-by-step explanation:

There are 8 triangle in that shape. So, the fraction will be 1/8. Hence, option (a) is the correct answer.

The answer is 1/8 because there is 8 triangles

whats the answer for this? 0.5x=24

Answers

The answer for the expression 0.5x=24 will be x=48

What is a linear equation?

The linear equation is defined as the equation having a degree of one or the power of the variable will be one. Linear equation shows the staright line on the graph.

here the given equation is:-

0.5x=24

We can write 0.5 in fraction as 1/2

1/2x=24

x=48

Hence the answer for the expression 0.5x=24 will be x=48

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Question
Consider the diagram.

A triangle with interior angles labeled w degrees, x degrees, and y degrees. A ray extends to the left on the top side of the triangle to create an exterior angle labeled z degrees.

Which equations are true? Select all true equations.

Answers

Answer: 1, 2, 5

Step-by-step explanation:

The first equation is true because angles in a triangle add to 180 degrees.

The second equation is true because both sides equal 180 degrees (left hand side is a straight angle, right hand side is the sum of angles in a triangle)

The third equation is not true because z = 180 - y, and 180-y+w+z is not 180.

The fourth equation is not true because z=180-y, and 180-y=w+y is not always true.

The fifth equation is true by the exterior angle theorem.

• A. All real numbers
• B. All real numbers except 2
• C. All real numbers except -6
• D. All real numbers except -6 and 2

Answers

Answer:

Option C

Step-by-step explanation:

you cancel the whole parentheses.

So you know, x+6 can't equal to 0.

that's why there is a choice that is all real numbers but not -6.

Answer:

A. All real numbers

Step-by-step explanation:

Given

(x - 2)(x + 6)/7(x + 6) = (x - 2)/7

On cross multiplying,

(x - 2)(x + 6)(7) = (x - 2)(x + 6)(7)LHS = RHSThis means on applying any value for x, both sides will be equalHence, the correct option is A

write the ratio in the simplest form 40kg : 480g

Answers

Answer: 1kg : 12g

Step-by-step explanation: Ratio in the simplest form is to divide both numbers by the greatest factor.

40 divided by 40 is 1

480 divided by 40 is 12

The answer is 1 kg : 12g

least to greatest:
1.11, 1 1/10, the square root of 3, 1.73, 1 2/5

Answers

Answer:

least to greatest:

1 1/10, 1.11, 1 2/5, 1.73, the square root of 3

Step-by-step explanation:

1 1/10 = 1.10

1.11 = 1.11

1 2/5 = 1.4

1.73 = 1.73

the square root of 3 is approximately 1.732

Samin can run 5 kilometers in 30 minutes. Assuming she keeps a constant pace, how many kilometers can she run in 45 minutes

Answers

Answer:

7.5 kilometres

Step-by-step explanation:

In 30 minutes she ran 5 kilometres.

We know that 30 + 15 = 45, so we can divide the minutes and kilometres by 2.

So 30 divided by 2= 15 minutes.

And 5 kilometres divided by 2= 2.5 kilometres.

Now we just add the two distances, as we know that the minutes make 45.

2.5 + 5 = 7.5.

I hope this helps, have a lovely day.

The speed is the distance covered by an object at a particular time. The distance covered by Saima in 45 minutes is 7.5 km.

What is speed?

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given Samin can run 5 kilometres in 30 minutes. Therefore, the speed of Samin will be,

Speed = 5km/30min = 5/30 km per minute

The distance covered by Saima in 45 minutes will be equal to

Distance = 5/30 × 45 = 7.5 km

Hence, The distance covered by Saima in 45 minutes is 7.5 km.

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The diameter of a circle is 12 centimeters. What is the circle's area?

Answers

BEST ANSWER :

CIRCLE

solve for area

A = 113.1 cm^2

d diameter = 12 cm.

Answer:

Area of circle = π r^2

Step-by-step explanation:

Diameter = 12
Radius = 12/2
= 6
Area = π x 6^2
= π x 36
= 113.04

therefore the area of the circle is 113.04

I NEED HELP! ASAP, THIS IS SO HARD AND MY BRAIN HURTS, IF U HELP ME WITH OTHER QUESTIONS LIKE THIS ILL GIVE U 50+ POINTS

Answers

Answer:

24.3

Step-by-step explanation:

We need to follow the order of operations PEMDAS:

ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)

Carry out the operation in the parentheses first:

3³ + 14.7 ÷ 7 - (1.2 × 4)

⇒ 3³ + 14.7 ÷ 7 - 4.8

Now the exponent:

⇒ 3³ + 14.7 ÷ 7 - 4.8

⇒ (3 × 3 × 3) + 14.7 ÷ 7 - 4.8

⇒ 27 + 14.7 ÷ 7 - 4.8

Now, the division (there is no multiplication):

⇒ 27 + 14.7 ÷ 7 - 4.8

⇒ 27 + 2.1 - 4.8

Finally, carry out the addition and subtraction (from left to right)

⇒ 27 + 2.1 - 4.8

⇒ 29.1 - 4.8

⇒ 24.3

A rectangular stained glass window is made up of identical triangular parts as pictured below. 24 triangles are connected to have a height of 36 inches and a width of 48 inches. every 2 triangles combine to form a rectangle. what is the area of the shaded triangular section? 18 square inches 36 square inches 72 square inches 144 square inches

Answers

The area of the shaded triangular section of the stained glass window is 72 square inches.

What is the area of the shaded triangular section?

The first step is to determine the dimensions of each rectangle that makes up the stained glass window.

Length of one rectangle = length of the window / number of rectangles along the length

36/4 = 9 inches

Width of one rectangle = width of the window / number of rectangles along the width

48/3 = 16 inches

Area of the shaded triangular section = 1/2 x area of one rectangle

1/2 ( length x width)

1/2 x (16 x 9) = 72 square inches.

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Answer:

144

Step-by-step explanation:

i took the test

Graph the two sides of the equation 2* – 2.5 = 2x +0.7. Zoom in a few times for added accuracy, and use the pointer tool to approximate the intersection. Then, find the value of x at the point (or points) of intersection.

Answers

By graphing both functions, we will see that there are two intersections at (-1.41, -2.12) and (3.28, 7.27).

How to solve the equation graphically?

Here we must solve:

[tex]2^x - 2.5 = 2x + 0.7[/tex]

To do it, we can graph the functions:

[tex]y = 2^x - 2.5\\\\y = 2x + 0.7[/tex]

And see where do the curves intersect.

The graph can be seen below, in there we can see two intersections.

One at (-1.41, -2.12) and (3.28, 7.27).

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how much larger is 8 x 10^8 than 2 x 10^5

Answers

Answer:

799800000 larger

Step-by-step explanation:

8 × (10 × 8) = 8000000002 × (10 × 5) = 200000

So . . Subtract

800000000 - 200000 = 799800000

Answer: 799800000

Step-by-step explanation: For 8 x 10^8, do 10 x 10 x 10 10 x 10 x 10 10 x 10 to get 100,000,000 and x 8 is 800,000,000

For 2 x 10^5 do 10^5 ( 10 x 10 x 10 x 10 x 10) which is 100,000 and then x 2 is 200,000

Then subtract.

800,000,000 - 200,000 is 799800000

Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.

Answers

The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

How to categorize the situations?

For a situation to be fair, the probability of every outcome must be equal.

Using the above definition, we can now analyze each option

Situation 1

Letters = 26

P(Vowel) = 5/26

P(Consonant) = 21/26

Both probabilities are not equal.

Hence, this situation is not fair

Situation 2

Participants = 4

P(Each) = 1/4

All probabilities are equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

Cousins = 5

P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

Numbers = 5 i.e. 2 to 6

P(Prime) = 3/5

P(Composite) = 4/6

Both probabilities are not equal.

Hence, this situation is not fair

Situation 5

Roommates = 5

Cards = 5

Aces = 4

P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

Answers

8π is the circumference

Need help!
Y=-2x^2-4x+6

Answers

Answer: (1, 0) , (-3, 0)

Step-by-step explanation:

I used an app. T-e-e-h-e-e

In the figure above, the shaded triangle is bounded by the y-axis, the line y=6, and the line y=2/3x. What is the area, in square units, of the shaded triangle?

Answers

Answer:

84.9

Step-by-step explanation:

Can you please help me with 12 please? I will give an brainlist

Answers

Answer:

[tex]x+(\frac{1}{2} x + 12) =[/tex] number of postcards Simone has now

Step-by-step explanation:

x = the number of postcards in Simone's collection

Simone bought 12 more than half the number of postcards in her collection.

So Simone bought half her collection ( [tex]\frac{1}{2} *x = \frac{1}{2} x[/tex] ) plus 12 more postcards.

[tex](\frac{1}{2}x +12)[/tex] = number of postcards Simone bought

Write an expression to show how many pstcards she has now.

[tex]x+(\frac{1}{2} x + 12) =[/tex] number of postcards Simone has now

Let she has p no of postcards before .

She bought 12 more than the half of p

p/2+12

Currently she has

p+p/2+123p/2+12(3p+24)/2 postcards

Mamadou surveyed 500 of his students in his school about their favorite color students could choose between blue and red 390 students said their favorite color was red what percentage of the surveyed students said they favorite color was red

Answers

Answer:

78%

Step-by-step explanation:

a percentage is equivalent to a number over 100.

43% is 43/100

72% is 72/100

87% is 87/100

etc.

to find the percentage of students who said their favorite color is red, we need to set up a cross-multiplication equation

390/500 = ?/100

390 times 100 is 39000

39000/500 = 78

78% of the students said their favorite color is red

give brainliest please!

hope this helps :)

Determine the identity. Show all steps.

Answers

Step-by-step explanation:

[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}=1-\frac{1}{\csc \left(x\right)}[/tex]

[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}[/tex]

[tex]=1-\sin \left(x\right)[/tex]

⇒ [tex]\sin \left(x\right)=\frac{1}{\csc \left(x\right)}[/tex]

[tex]=1-\frac{1}{\csc \left(x\right)}[/tex]

Julianna is making a rectangular garden in her backyard. She has plotted three of the corners on the coordinate plane.

Answers

A. (5,8)
B. Length 13 width 7
C. Yes because the perimeter is only 40 ft and she has 45 ft of fencing

2x+4 (2x+7)= 3(2x+4)
solve x

Answers

given:

[tex]2x + 4(2 x + 7) = 3(2x + 4)[/tex]

to find:

solve the ( x ).

solution:

[tex]2x + 4(2x + 7) = 3(2x + 4)[/tex]

[tex]2x + 8x + 28 = 6x + 12[/tex]

[tex]10x + 28 = 6x + 12[/tex]

[tex]4x + 28 = 12[/tex]

[tex]4x = - 16[/tex]

[tex]x = - 4[/tex]

2x+4(2x+7)= 3(2x+4)

2x+8x+28=6x + 12

10x+28=6x + 12

4x+28=12

4x= -16

x=-4

A scale drawing of a rectangular park had a scale of 1 cm = 100 m. What is the actual area of the park in meters squared?

Answers

Answer: 606,900 square meters

Explanation:

5.1 cm on paper corresponds to 5.1*100 = 510 meters in real life due to the scale 1 cm = 100 m.

11.9 cm on paper corresponds to 11.9*100 = 1190 meters in real life.

The 5.1 cm by 11.9 cm rectangle on paper corresponds to the real life counterpart of 510 meters by 1190 meters.

The actual area of the real life park is length*width = 510*1190 = 606,900 square meters

if a shoelace drawer is 12.49 inches and a paperclip drawer is 4.579 inches about how many inches wider is the shoelace drawer than the paperclip drawer

Answers

The shoelace drawer is 7.911 inches wider than the paperclip drawer.

Measurement difference between two drawers

The height of shoelace drawer is = 12.49 inches

The height of paperclip drawer is = 4.579 inches

Therefore the measurement difference between the two drawer is = 12.49 inches - 4.579 inches

= 7.911 inches

Therefore, the shoelace drawer is 7.911 inches wider than the paperclip drawer.

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does anyone live in the concord, NC area? I need to get out of this place TwT

Answers

that's tuff you live in NC

solve the equation 3x^2-x-3=0 to the nearest tenth

Answers

Answer:

You use the quadartic foruala for this problem your fanial anwers is

x=1 + or - radical 37 / 6.

1+ radical 37 over 6 =1.180460422

To the nearest tenth =1.2

1-radical 37 over 6= -0.8471270884

To the nearest tenth=-0.8

I need help with writing the number as a decimal.
The question is
Two hundred thirty eight and forty-nine thousandths

Answers

Answer: 0.23849

Step-by-step explanation:

0.23849

2 is tenth

3 is hundredth

8 is thousandth

4 is ten thousandth

9 is hundred thousandth

5,200,000×(8.3×10^2)−(3.1×10^8) in scientific notation, need it quick

Answers

Step-by-step explanation:

5,200,000 = 5.2 × 10⁶

so, we have

(5.2 × 10⁶) × (8.3 × 10²) - (3.1 × 10⁸)

(5.2 × 8.3 × 10⁸) - (3.1 × 10⁸)

(43.16 × 10⁸) - (3.1 × 10⁸) = 40.06 × 10⁸ = 4.006 × 10⁹

Which of the following fall between 12 and 13?

Answers

I don’t see any answer choices so I would think 12.5

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