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allsm [11]
3 years ago
8

Find the maximum value or minimum value for the function f(x) = 0.15(x + 1)² - 3.

Mathematics
1 answer:
il63 [147K]3 years ago
7 0

Answer:

The minimum value for  f(x) = 0.15(x + 1)^2 - 3 is -3.

Step-by-step explanation:

Given function is f(x) = 0.15(x + 1)^2 - 3

We need to find the maximum value or the minimum value for the function.

Now, differentiate f(x) = 0.15(x + 1)^2 - 3  w.r.t x.

f'(x) =\frac{d}{dx}(0.15(x + 1)^2 - 3)\\f'(x)=\frac{d}{dx}(0.15(x+1)^2-\frac{d}{dx}(3)\\

f'(x)=2\times 0.15(x+1)\frac{d}{dx}(x+1)-0\\f'(x)=0.3(x+1)(1)\\f'(x)=0.3(x+1)

Now, we will equate f'(x)=0 to find critical point.

0.3(x+1)=0\\x=-1

Plug this critical point in to the function f(x) = 0.15(x + 1)^2 - 3  we get,

f(-1) = 0.15(-1 + 1)^2 - 3\\f(-1)=-3

Also, f''(x)=0.3 which is positive, We have minimum value.

So, the minimum value for  f(x) = 0.15(x + 1)^2 - 3 is -3.

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Answer:

638

Step-by-step explanation:

1. Isolate the variable 881 = k - (-243)

                                  -243         -243

2. combine like terms 881 - 243 = k

3. answer 638

5 0
2 years ago
A number increased by two thirds of the number
Artyom0805 [142]

Answer:

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Gary deposits $1,500 into each of two savings accounts. Account I earns 5% annual simple interest. Account II earns 5% interest
hodyreva [135]

Answer:

  • $3623.26

Step-by-step explanation:

<u>Given</u>

  • Each deposit = $1500
  • Interest rate= 5%
  • Time = 4 years
  • Compound number = annual

<u>Simple interest account</u>

  • B = 1500*(1 + 4*0.05) = 1500*1.2 = $1800

<u>Compound interest account</u>

  • B = 1500*(1 + 0.05)^4 = $1823.26

<u>Total balance</u>

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7 0
3 years ago
5. If Amber decides to mail copies of her photos to the 45 residents of her grandmother’s assisted living facility, the new func
pav-90 [236]

Answer: please find the answer in the explanation

Step-by-step explanation:

From the information given from the question, the initial function representing her photo sharing is:

F(x) = 3(4)^2

F(x) = 3 × 16 = 48 photos

Then the new graph has an upward shift ( translation) of 45 units

The new function representing her photo sharing is:

F(x) = 3(4)^2 + 45

F(x) = 48 + 45

F(x) = 93 photos.

8 0
3 years ago
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Figure RHOM is a rhombus. and are the diagonals of the rhombus, as well as angle bisectors of the vertex angles, and they create
Ganezh [65]

Answer:

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Step-by-step explanation:

It is given that RHOM is a Rhombus

Also ΔHOM, ΔMHR, ΔRHO and ΔOMR are isosceles triangles

Let us take ΔMSR and ΔRSH

∠MRS =∠HRS            ( since it is given that the diagonal RO bisects ∠R)

∠RMS =∠RHS     ( since Δ MRH is isosceles triangle )

RS = RS        ( common side )

By AAS congruency rule ΔMSR ≅ ΔHSR

so we have

∠MSR=∠RSH  ( corresponding parts of congruent triangles are congruent)

also we have

∠MSR +∠RSH =180°   ( supplementary angles)

∠MSR +∠MSR=180°          ( since ∠MSR=∠RSH)

2∠MSR= 180°

∠MSR =90°

Hence ∠MSR is right angle


6 0
3 years ago
Read 2 more answers
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