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Sidana [21]
3 years ago
6

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

Mathematics
1 answer:
vfiekz [6]3 years ago
6 0

Answer:

x=5.3

Step-by-step explanation:

.3(5x-1.5)=7.5

1.5x-.45=7.5

1.5x=7.95

x=5.3

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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.

Parameterize the boundary of x^2+y^2\le1 by

x=\cos u

y=\sin u

with 0\le u. Then t(x,y) can be considered a function of u alone:

t(x,y)=t(\cos u,\sin u)=T(u)

T(u)=\cos^2u+3\sin^2u+13\cos u

T(u)=3+13\cos u-2\cos^2u

T(u) has critical points where T'(u)=0:

T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0

(1)\quad\sin u=0\implies u=0,u=\pi

(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4

but |\cos u|\le1 for all u, so this case yields nothing important.

At these critical points, we have temperatures of

T(0)=14

T(\pi)=-12

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

4 0
3 years ago
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