43. Find an equation of the tangent line to the curve [tex]y=10^{x}[/tex] at the point (1,10)

Answers

Answer 1

Answer:

23x-y=13

Step-by-step explanation:

we need to find the derivative with respect to x

In(y) =In(10^x)

In(y)=xIn(10)

now we have to take the derivative with respect to x

Therefore, y'=yIn(10)

where y'=10^xIn(10), Chain rule!

note: First derivative function always give us the gradient value when x value is substituted in

Therefore, at x=1, our gradient will be m= 10^1In(10)

Gradient m=23.0 to the nearest tenth

Finding the equation of the line

y-y1=m(x-x1)

y-10=23(x-1)

y-10=23x-23

y-23x=-23+10

y - 23x = -13

so, the equation of the line tangent line is

23x - y =13


Related Questions

Shen needs to read 2 novels each month
Let N be the number of novels Shen needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Shen needs to read in 13 months.

Answers

Answer:

Equation: N = 2M, Shen needs to read 26 novels in 13 months

Step-by-step explanation:

Given : Shen needs to read 2 novels each month.

i.e. In One month , the number of novels read by Shen = 2

Let N be the number of novels Shen needs to read in M months.

Then , N = 2 M

Thus , the equation relating N to M : N = 2 M

If Number of months = 13 , then put M = 13 in the above equations , we get

N = 2(13) = 26

Hence, the number of novels he read in 13 months = 26.

The ordered pair ( 15,12 ) means that ? pounds of beans cost $ ?.​

Answers

Answer:

15 pounds of beans costs 12 dollars

Step-by-step explanation:

(15,12)  Means 15 pounds of beans costs 12 dollars

The first coordinate is the x value which is pounds and the second coordinate is the y value which is dollars

Answer:

Step-by-step explanation:

5y^3 – 4y – 1


Leading term:


Leading coefficient:


Constant term:

Answers

Answer:

See below for answers and explanations

Step-by-step explanation:

The leading term is the term with the highest degree, in this case, 5y³

The leading coefficient is the number in front of the leading term, 5

The constant term is a term with no variables contained, in this case, -1

Solve this quadratic equation by completing the square.
x2 + 4x = 15
O A. x= -4 = 19
B. X=-4 + 115
OC. =-24 119
O D. x= -2 + 15

Answers

Answer:

C

Step-by-step explanation:

I need help in solving a math problem.

Answers

Negative value has least value.


I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

Step-by-step explanation:

Solve x2 − 90 = 0. If necessary, round to the nearest hundredth.
8100
±9.49
There is no solution as you cannot take the square root of a negative number.
±180

Answers

Answer:

Option B, [tex]x =[/tex] ± [tex]9.49[/tex]

Step-by-step explanation:

Step 1:  Add 90 to both sides

[tex]x^2 - 90 = 0[/tex]

[tex]x^2 - 90 + 90 = 0 + 90[/tex]

[tex]x^2 = 90[/tex]

Step 2:  Square root both sides

[tex]\sqrt{x^2} = \sqrt{90}[/tex]

[tex]x =[/tex] ± [tex]9.49[/tex]

Answer: Option B, [tex]x =[/tex] ± [tex]9.49[/tex]

What translation is shown below?



1 unit down
3 units up
1 unit up
3 units down

Answers

Step-by-step explanation:

3 units down

(-1,3)- (-1,0) 3 units down in y coordinate

and so on

Find the sum of the first 40 terms of the arithmetic sequence.
14, 4, -6, -16, -26, -36

Answers

Answer:

-7240

Step-by-step explanation:

The nth term is -10n + 24.

So the combination of the first and second term would be (-10+24)+(-10x2+24) and this would continue for the first 40 terms so the 24s would add up to 24x40=960. Meanwhile, the -10s would keep adding up so it would be -10-20-30-40.... which you can simplify by making it -10(1+2+3+4) all the way to 40 to make the calculation easier... u can further simplify by making 41 = one pair of numbers so 40+1, 39+2 until you get 21+20 so ur left with -10(20 pairs of 41) so -10(20x41) = -10(820)= -8200.

Add this to your initial 960 so

-8200 +960 = -7240

Hope this helps

Please need now! A. Compute for the average speed Average Speed = distance travelled time taken 1. A bus travels a distance of 300 km in 5 hours 2. Ajet travels 4.000 km in 8 hours 3. An athlete 10 km in 2 hours 4. A hiker travels 50 km in 2.5 hours 5. A biker travels 45 km in 5 hours B. Solve for the time taken to travel (Time = distance travelled + average speed 6. A motorcycle rider iraveis 150 km at 25 km/h. 7. A close van travels 288 km at 72 km/hr. 8. A jogger runs 20 km at 4km/hr. 9. A delivery truck travels 204 km at 68 km/hr. 10. A bird travels 210 km at 42 km/hr. C. Solve for the distance Distance = Average Speed x Time taken) 11. A racing motorbike travels at the speed of 122 km/hr for 1.5 hrs. 12. Mr. Garcia travels by car at 100 km/hs for 2 hours 13. A biker travels 45 km/hrs for 1.5 hrs. 14. Jianna runs 300 m/hrs for 2 hours 15. A carabao walking at a speed of 12 km/hr for 2 hours D. Circle the letter of the correct answer. 16. An airplane took 5 hours flying from point of origin to point of distination. If the total distance for flight 2000 kilometers, how fast was the plane travelled per hour? a. 400 km b. 300 km C. 250 km a. 200 km 17. A family went on an outing. They traveled for 3 hours at an average speed of 72 kilometers an hour. How far was their outing? a. 24 km b. 75 km c. 216 km d. 226km​

Answers

Answer:

Step-by-step explanation:

1. 60                    11. 33  km

2. 500            12. 200 km

3. 5                       13. 67.5 km

4. 20                       14.  600 km

5. 9                   15. 30 km

                                          16. a.400 km

6. 2                                      17. c. 216 km

7. 4

8.5

9. 3

10.5

I’m confused on this please help

Answers

When you reflect a point or a shape across an axis, you are basically flipping it to the other side. So let’s say you have point (-1,2). This point after the reflection would be (1,2).

So.. (x,y) —> (-x, y)

The second option. Hope this helps!

URGENT PLEASE HELP asap

Answers

Answer:

4x-4 < -76

Step-by-step explanation:

Four times a number (x), minus 4, is less than -76.

Answer:

x is less than —18

Step-by-step explanation:

Check out the attached photo

2. What is the coefficient of x in the expression 3 + 6x = 10y?

Answers

Answer:

6

Step-by-step explanation:

3 is a constanty is not xThe coefficient is the number attached to x, which is 6 in this case

Which statement describes the solutions of this equation?

Answers

Answer:

  C.  The equation has two valid solutions

Step-by-step explanation:

A rational equation like this is often solved by "cross-multiplying" to eliminate the fractions. When we do that, we get ...

  4(2x+10) = x(3x+1) . . . . . . . multiply both sides by (3x+1)(2x+10)

  3x² -7x -40 = 0 . . . . . . . . . . rearrange to standard form

  3x² -15x +8x -40 = 0 . . . . . . separate -7 into factors of 3(-40)

  3x(x -5) +8(x -5) = 0 . . . . . factor pairs of terms

  (3x +8)(x -5) = 0 . . . . . . . finish factoring

The zeros of these factors are not zeros of the original denominators, so neither of the solutions these give is extraneous.

  3x +8 = 0   ⇒   x = -8/3

  x -5 = 0   ⇒   x = 5

IM A LIL LOST CAN SOMEBODY SOLVE THE EQUATION

Answers

Step-by-step explanation:

It's just asking you to rewrite it in vertex form. Which would be

[tex](x + 10) ^{2} - 4[/tex]

The longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of the triangle.

Answers

Answer:

9,12,15

Step-by-step explanation:

I just looked at the different pythagorean triples and saw which set has a difference of 6 between the largest and smallest and a difference of 3 between the first and second one.

Here are the first few pythagorean triples:

3,4,5

6,8,10

7,24,25

5,12,13

9,12,15 - This is our answer

Hope this helped and brainliest please

Solve |2x+5| =15

Need help please!!!

Answers

Answer:

applying absolute law

if |u|=a, a>0 then u=a or u=-a

2x+5=15 or 2x+5=-15

2x=15-5 or 2x=-15-5

2x=10 or 2x=-20

x=5 or x= -10

A pet store has 150
150
goldfish and betta fish altogether.
The ratio of goldfish to betta fish is 2:3
2:3
.

How many goldfish does the pet store have?

Answers

Answer:

60

Step-by-step explanation:

hope this helps loves x

Answer:

Step-by-step explanation:

60

Big

Bubble

Hub

Be

Jack has a mask collection of 500 masks. He keeps 235 of the masks on his wall. What percentage of Jack's mask collection does he keep on his wall?

Answers

Answer:

47%

Step-by-step explanation:

First we need to find the ratio of masks on Jack's wall to the total number of masks, which is 235/500. Now we need to make the denominator 100 in order to find the percentage by dividing the numerator and denominator by 5 to get 47/100. Therefore the percentage of Jack's mask collection that is on his wall is 47%.

Use the symbols <,> or = to compare the decimals 56.72 and 5.672

Answers

Answer:

>

Step-by-step explanation:

its because 56.72 is greater than 5.672

Answer:

56.72 > 5.672

Step-by-step explanation:

> means greater than

< means less than

so 56.72 is greater than (>) 5.672

Directions Write Each Equation In Slope-Intercept Form Then Graph The Problem Is X+5y=-15

Answers

Answer:

y = -x/5 - 3

Step-by-step explanation:

Slope intercept form: y = mx + b

x + 5y = -15

5y = -15 - x

y = -15/5 -x/5

y = -x/5 - 3

BRAINLIEST please if this helped!

HELP ME OUT PLS!!!!!!!!!!!!!

Solve for x

A) -30

B) - 6

C) 6

D) 30​

Answers

Answer:

what about this 0=20

Step-by-step explanation:

so x=2 right there for

(-3)2+6=(2)-24

-6+6=4-24

0=20

The answer is choice C (6)

-3x+6=2x-24

Subtract both sides by 2x and 6

-3x-2x=-6-24

Combine like terms

-5x=-30

Divide both sides by -5

X=6

29. Mr. Ignado gave 4 orange erasers and 5 green erasers to each of the
20 students in his class. How many erasers did Mr. Ignado give to his
students?

Answers

One hundred and eighty erasers

Is 16+4 and 2(2w+8) equivalent?

Answers

Answer:

Below!

Step-by-step explanation:

Let us consider that 16 + 4 and 2(2w+8) are equal. Then;

⇒ 16 + 4 = 2(2w + 8)

This equation can be solved in two ways. Listed below!

Method 1:

Let's simplify the left-hand-side of the equation.

⇒ 20 = 2(2w + 8)

Then, divide "2" both sides of the equation to open the parentheses.

⇒ 20/2 = 2(2w + 8)/2⇒ 10 = (2w + 8)⇒ 10 = 2w + 8

Subtract 8 to both sides of the equation to isolate the variable (w) and it's coefficient.

⇒ 10 - 8 = 2w⇒ 2 = 2w

Finally, divide 2 to both sides of the equation to isolate the variable (w).

⇒ w = 1

Therefore, 16 + 4 and 2(2w + 8) can be equal if the value of "w" is 1.

Method 2:

Let's simplify the left-hand-side of the equation.

⇒ 20 = 2(2w + 8)

Then, simplify the distributive property to open the parentheses.

⇒ 20 = 2(2w + 8)⇒ 20 = 4w + 16

Subtract 16 to both sides of the equation to isolate the variable and it's coefficient.

⇒ 20 - 16 = 4w + 16 - 16⇒ 4 = 4w

Finally, divide 4 to both sides of the equation to isolate the variable (w).

⇒ 4/4 = 4w/4⇒ w = 1

As said in method 1, 16 + 4 and 2(2w + 8) can be equal if the value of "w" is 1.

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

3.56 you little silly dum dum girl

Answer:

A. 3.56

Step-by-step explanation:

I didnt take his answer my big brain knew the answer.

If you walk 37 feet north and then 67 feet east, how far,
in a straight line, will you be from your starting point?
Round your answer to the nearest whole foot.

Answers

Answer:

76.54 ft

Step-by-step explanation:

Pythagorean theorem

37^2 + 67^2  = d^2

d = 76.54 ft

How do you write 0.54 in words?

Answers

Answer:

Step-by-step explanation; zero point fittyfour

Answer:

you can say fifty four hundredths, or simpler, zero point fifty four, or even simpler, zero point five four ( I recommend fifty four hundredths)

There are 2 triangles and 6 circles. What is the simplest ratio of triangles to circles?

Answers

Hi!

We are asked to find the ratio.

A ratio is a relationship/comparison between two or more numbers based on their numerical value.

We know that, for every 2 triangles there are 6 circles. We can set up our ratio to look like this:

[tex]\cfrac{2}{6}[/tex]

---

(NOTE: there are many different ways to write ratios, including: "x:y", "x to y", or "x/y")

---

The question asks us to write it in simplest form. The fraction [tex]\cfrac{2}{6}[/tex] is NOT in simplest form. It can be simplified to:

[tex]\cfrac{1}{3}[/tex]

This is the ratio in simplest form.

For another example, see:

https://brainly.com/question/24266834

The prism below is made of cubes which measure 1/4 of a foot on one side what is the Volume?
A: 5/2 cubic ft
B: 9 cubic ft
C: 9/16 cubic ft
D: 36 cubic ft

Answers

Answer:

htrtrheherh

Step-by-step explanation:

Mrs. Chang's class built a platform for use in a school play. What is the
volume of the platform?

PLEASE HELP!

Answers

Answer:

Total Platform = 128 ft^3

Step-by-step explanation:

Volume = Length * Width * Height

Left Volume: 2 ft * 4 ft * 3 ft = 24 ft^3

Mid Volume: 4 ft * 4 ft * 5 ft = 80 ft^3

Right Volume: 2 ft * 4 ft * 3 ft = 24 ft^3

Total Volume = 24 ft^3 + 80 ft^3 + 24 ft^3 = 128 ft^3

Answer:

v = [tex]108^{3}[/tex]

Step-by-step explanation:

I'd start with breaking the platform into two parts, the long flat rectangle and then the bit on top. You'll have to add these together at the end!

_________________

So part one: the long piece

formula: v = lwh

dimensions: 12, 3, 2

plug in: v = 12 * 3 * 2

solve: v = 72^3

_________________

part two: smaller rectangle on top ::

formula: v = lwh

dimensions: 4, 3, 3

plug in: v = 4 * 3 * 3

solve:v = 36*3

__________________

now, we add for the total of the entire shape!

final answer: 72 + 36 = 108^3

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