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djyliett [7]
1 year ago
13

Find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1

Mathematics
1 answer:
kicyunya [14]1 year ago
6 0

Given:

f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1

To find:

The correct function.

Explanation:

Let us consider the function given in option D.

f(x)=\frac{x^2}{2}-4x+5

Differentiating with respect to x we get,

\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}

Substituting x = 2 in the function f(x), we get

\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}

Therefore, the given conditions are satisfied.

So, the function is,

f(x)=\frac{x^{2}}{2}-4x+5

Final answer: Option D

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Multiply. (3.5x10^-5) (3x10^-10) express your answer in scientific notation.​
Len [333]

Answer:

5.69034 × 1011

Step-by-step explanation:

Decimal  

1234000000

Scientific Notation  

1.234 x 10^9

×10^  

9

1st Number  

1.234

×10^  

9

Operation  

2nd Number  

5.678

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11

3 0
3 years ago
What is the hourly utilization rate of each resource if the bottleneck(s) work nonstop during a 10-hour day?
Bess [88]

Answer:

100%

Step-by-step explanation:

Utilization rate =

Hours worked / total working hours per day

Since the bottle works nonstop during a 10-hour day, it worked 10 hours

Utilization rate in percentage = (10/10)×100%

= 100%

6 0
3 years ago
Help me please. Find the measures of CAD and DAE
VladimirAG [237]

well, we know the "sum" of both angles is 90°, notice the rectangle in the corner, so we can say that the angles are simply complementary angles, thus

\left( \cfrac{3}{2}x+20 \right)+2x=90\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{3}{2}x+20 + 2x \right)=2(90)} \\\\\\ 3x+40+4x=180\implies 7x+40=180\implies 7x=140\implies x=\cfrac{140}{7} \\\\\\ x = 20~\hfill \stackrel{\measuredangle CAD}{\cfrac{3}{2}20+20\implies 50}\qquad\qquad \stackrel{\measuredangle DAE}{2(20)\implies 40}

8 0
2 years ago
Dilate by a scale<br> factor of 1/2<br> AL<br> D
Firdavs [7]

Answer:

The image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

  • D' (0, 1)
  • L' (1/2, 5/2) or L'(0.5, 2.5)
  • W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

Step-by-step explanation:

Given the triangle ΔDLW withe the vertices

  • D(0, 2)
  • L(1, 5)
  • W(5, 4)

As the scale factor 1/2 < 0, thus the image triangle will be smaller than the original triangle.

The rule of dilation is given by

Dilation: (x, y)  →  (1/2x, 1/2y), centered at (0, 0)

D(0, 2)  → D' (1/2x, 1/2y) → D' (1/2(0), 1/2(2)) = D' (0, 1)

L(1, 5)  → L'(1/2x, 1/2y) →  L'(1/2(1), 1/2(5)) = L' (1/2, 5/2)

W(5, 4)  → W'(1/2x, 1/2y) →  W'(1/2(5), 1/2(4)) = W' (5/2, 2)

Therefore, the image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

  • D' (0, 1)
  • L' (1/2, 5/2) or L'(0.5, 2.5)
  • W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

7 0
3 years ago
Definition: A word or phrase used to show division in a word problem.
myrzilka [38]
I think the word is "each". im not very sure.


8 0
3 years ago
Read 2 more answers
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