0.3(5x - 1.5) = 7.5 x= ?

Determine the value of life g(x)=4x+k is a tangent to f(x)=-x^2+8x+20

vivado [14]

Answer:

k=16

Step-by-step explanation:

So the tangent line is

$4x + k$

and it tangent to function

${x}^{2} + 8x + 20$

Since the slope of the tangent line is 4, this means the derivative of f(x) is 4 but first let find the derivative of

${x}^{2} + 8x + 20$

Use the Sum Rule,

$\frac{d}{dx} {x}^{2} + \frac{d}{dx} 8x + \frac{d}{dx} 20$

Use the Power Rule and we get

$2x + 8$

Set this equal to 4

$2x + 8 = 4$

$2x = - 4$

$x = - 2$

So at x=-2, the slope of the tangent line is 4.

Plug -2 in the orginal function, and we get

${ - 2}^{2} + 8( - 2) + 20 = 8$

So the point must pass through -2,8 with a slope of 4.

$y - 8 = 4(x + 2)$

$y - 8 = 4x + 8$

$y = 4x + 16$

So the value of k is 16.

4 0

2 years ago

PLS HELP, 50 POINTS!!!

Sedaia [141]

Answer:

Part A: From 0 to 2 seconds, the height of the water balloon increases from 60 to 75 feet, therefore the water balloon's height is increasing during the interval [0,2]

Part B: From 2 to 4 seconds, the height of the water balloon stays the same at 75 feet, therefore the water balloon's height is the same during the interval [2,4] From 10 to 12 seconds, the height of the water balloon stays the same at 0 feet, therefore the water balloon's height is the same during the interval [10,12] From 12 to 14 seconds, the height of the water balloon stays the same at 0 feet, therefore the water balloon's height is the same during the interval [12,14]

Part C: The interval, [4,6] of the domain is when the water ballon's height decreases the fastest. The interval [4,6] decreases by 35 feet. The two other intervals that decrease are [6,8] and [8,10] which both have the same slope. They decrease by 20 feet. Therefore, this helps us conclude that the interval [4,6] decreases the fastest because 35 feet is a more significant decrease than 20 feet.

Part D: I predict that the height of the water balloon at 16 seconds is 0 feet. This is because at 10-14 seconds, the water balloon's height is 0 feet. In read-world situations, if the water balloon is on the ground which is 0 feet, it stays on the ground due to gravity.

Step-by-step explanation:

I hope this helps! I also do not know if it is all correct but I did research and everything so hopefully it is correct! Good luck!

8 0

3 years ago

Read 2 more answers

Drag the items to complete the sentences about the end behavior of the exponential function graphed.

zalisa [80]

Answer:

as x --> oo, f(x) = oo (infinite)

as x -- -oo, f(x) = 3

5 0

3 years ago

Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Beth can read 3 pa

Mama L [17]

Answer:

3x + 16 = 2x + 26

-2x -2x

x + 16 = 26

- 16 - 16

x = 10 min

3(10) + 16

46

2(10) + 26

46

Both read 46

4 0

3 years ago

A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the plate, including t

vredina [299]

You're looking for the extreme values of $x^2+3y^2+13x$ subject to the constraint $x^2+y^2\le1$ .

The target function has partial derivatives (set equal to 0)

$\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2$

$\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0$

so there is only one critical point at $\left(-\dfrac{13}2,0\right)$ . But this point does not fall in the region $x^2+y^2\le1$ . There are no extreme values in the region of interest, so we check the boundary.