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3 years ago

At what point of the curve y = cosh(x) does the tangent have slope 3?

Mathematics

1 answer:

Rus_ich [418]3 years ago

3 0

Answer:

(1.82, 3.17)

Step-by-step explanation:

Given the curve:

y = cosh(x)

we need that the tangent has slope 3. The tangent of a curve in a given point is found with its derivative.

dy/dx = sinh(x) = 3

From the plot of sinh(x), we get:

x ≈ 1.82

Replacing into cosh(x), we get:

y = cosh(1.82) ≈ 3.17

Then, at point (1.82, 3.17) the tangent is 3

You might be interested in

The 7-digit numbers 74A52B1 and 326AB4C are each multiples of 3. Which of the following could be the value C?

lbvjy [14]

74A52B1 and 326AB4C are multiples of 3.....That means if we divide them by 3, we should get a whole number.

Lets assume A=1 and B=1,
So,
74A52B1 becomes 7415211

Now, lets divide it by 3.
7415211 / 3 = 2471737

Since we got a whole number as a quotient, we can safely say that A=1 and B=1.

∴ The second number 326AB4C becomes 326114C.

Now, lets assume C = 1.
So,
326114C becomes 3261141.
Now,
lets divide it by 3.

3261141 / 3 = 1087047

Since we got a whole number as a quotient, C = 1

∴The value of C is 1. So, answer choice A is correct.

6 0

3 years ago

The length of a rectangle is 15ft greater than the width. The area is 100 square ft. Find the length and the Width.

gogolik [260]

Step-by-step explanation:

so let's say that the width is x then the length is x+15

and the area of a square is length times width

x(x+15)=100

x^2+15x-100=0

(x+20)(x-5)=0

x=5 or x=-20 but a side length can't be negative so x would equal 5

Length=x+15 with 5 as x

Length=20

Width=5

Hope that helps :)

7 0

3 years ago

Read 2 more answers

Write -7.5 as a common fraction.

Alina [70]

Answer:

-15/2 (or -7 1/2)

Step-by-step explanation:

-7.5 is equal to -75/10.

When you simplify it, you get:

-15/2 which simplifies to -7 1/2

4 0

3 years ago

The circle described by the equation <img src="https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%20%2B%28y%2B4%29%5E%7B2%7D%3D9" id="T

ElenaW [278]

Answer:

The point at which center of the image circle located is (-2, -3) so second option is correct.

Step-by-step explanation:

Given equation of circle is:

$(x-3)^{2} + (y+4)^{2} = 9$ (i)

The general equation of circle is mentioned below,

$(x-h)^{2} + (y-k)^{2} = r^{2}$ (ii)

Here 'r' represents the radius of the circle and (h,k) shown the center of the circle.

By comparing equation (i) and equation (ii), we get

r^2 = 9

r = 3

$(x-3)^{2} = (x-h)^{2}$

$(x-3) = (x-h)$

$h = 3$

$(y+4)^{2} = (y-k)^{2}$

$(y+4) = (y-k)$

$k = -4$

So the center of given circle is (h,k) = (3,-4)

Also, the circle is translated 5 units left, that is towards the -x-axis. Therefore h = 3 - 5 = -2

Also, the circle is translated 1 unit up, that is towards the +y-axis. Therefore k = -4 + 1 = -3

Hence, the point at which center of the image circle located is (-2, -3) so second option is correct.

6 0

3 years ago

Read 2 more answers

Salama makes fruit baskets with oranges and bananas.

vovangra [49]

The ratio for problem is:

oranges : bananas = 9 : 6 or oranges : bananas = 6 : 4

Solution:

Given that, Salama makes fruit baskets with oranges and bananas

She uses between 8 and 16 oranges and bananas in a ratio of 3 oranges to 2 bananas

Given ratio is:

Ratio of orange to bananas = 3 : 2

They add up to 5 fruits, so some possible values are 5, 10, 15 , 20, 25, etc

But we need a value between 8 and 16 oranges and bananas

So we can choose 15 or 10

Now let us choose 15 and solve

Let the oranges be 3x

Let the bananas be 2x

Therefore,

3x + 2x = 15

5x = 15

x = 3

Thus oranges = 3x = 3(3) = 9

Bananas = 2x = 2(3) = 6

Thus the ratio for problem is:

oranges : bananas = 9 : 6

Similarly solve for 10

3x + 2x = 10

5x = 10

x = 2

Thus oranges = 3x = 3(2) = 6

Bananas = 2x = 2(2) = 4

Thus the ratio for problem is:

oranges : bananas = 6 : 4

8 0

3 years ago