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My interpretation of the wording is:

. . . .21e4x

y = ---------

. . . . . .x

From here, just take the derivative, using the quotient rule:

y' = 21* [4e3x * ex * x - 1 * e4x] / x2

= 21 * [e4x](4x - 1) / x2

When x=1

y = 21e4

At x=1, gradient = 63e4

Point gradient formula gives:

y - 21e4 = 63e4 * (x - 1)

y = 63e4x - 42e4

That should be the answer.

Q: How to find the equation of the line tangent to the graph of y is equal to 21 times e with an exponent of 4x divided by x at the point x is equal to 1 and you need the slope and what y is equal to?

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No, it does not.

0.0024

10

It is Y.

The left hand side of the equation in the question is 42 * 2 + 16 / 2 * 4 This equals 16*2 + 16/2*4 = 32 + 32 = 64 which does not equal 10.

Related questions

No, it does not.

the tangent of an angle is equal to the length of the opposite side from the angle divided by the length of the side adjacent to the angle.

The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.

0.0024

The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X. The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.

10

It is Y.

tan(pi/3) = tan (60 degrees) = 1.732 which is square root of 3

The left hand side of the equation in the question is 42 * 2 + 16 / 2 * 4 This equals 16*2 + 16/2*4 = 32 + 32 = 64 which does not equal 10.

If it doesn't have an equal sign, then it's an expression, not an equation. The expression 7x2x is quadratic, because it equals 14x², and something is quadratic if it contains the squared exponent ².

Any number with an exponent of zero is equal to one. 60 = 1

No, it is not. To be correct, the expression requires parenthesis, which are missing.