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Llana [10]
3 years ago
9

The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given

f (0) = 7, find the absolute minimum value of f (x) over the interval [–3, 0].
A. 0
B. 2.5
C. 4.5
D. 11.5

Mathematics
1 answer:
ivolga24 [154]3 years ago
4 0

Answer:

B

Step-by-step explanation:

f(0) - f(-3) = area under f'(x) from x=0 to x=3.

We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.

A = 1/2 b h

A = 1/2 (3) (3)

A = 4.5

f(0) - f(-3) = 4.5

Since f(0) = 7:

7 - f(-3) = 4.5

f(-3) = 7 - 4.5

f(-3) = 2.5

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a^2 + b^2 = c^2

In this case we're looking for C

so

(3)^2 +  b^2 = (6)^2

9 + b^2 = 36

b^2 = 36-9

√b^2 = √27

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4 0
3 years ago
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A=444 b=213. 4÷a×b= can you help me plz
Lelechka [254]
First, let's input "a" and "b" into the equation:
(Don't forget to put brackets around the inputted numbers to show you are inputting "a" and "b")

<span>4 ÷ a × b = </span>4 ÷ (444) x (213)

Now we can solve!
 
               = 1.918
               = ~ 2

Hope this helps!
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5 0
3 years ago
Square pyramid is made up of a base with a side length of 10 inches and faces that are triangles with a height of 12 inches what
Nataly [62]

The surface area of the square pyramid is 360 in²

Explanation:

Given that the side length is 10 inches.

The height of the pyramid is 12 inches.

We need to determine the surface area of the pyramid.

The surface area of the pyramid is given by

SA=s^2+2sl

Where s is the side length and l is the slant height.

The slant height can be determined using the formula,

l=\sqrt{h^2+b^2}

where h = 12 and b=\frac{s}{2} =5

Substituting these values in the formula, we get,

l=\sqrt{12^2+5^2}

 =\sqrt{144+25}

l=\sqrt{169}

l=13

Thus, the slant height is l=13

Now, we shall find the surface area of the pyramid.

Substituting l=13 and s=10 in the formula SA=s^2+2sl, we get,

SA=10^2+2(10)(13)

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SA=360 \ in^2

Thus, the surface area of the square pyramid is 360 in²

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4 years ago
What polynomail is this<br> 2x-6
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Its bionmails love
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A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local b
IrinaK [193]

Answer:

a. [ 0.454,0.51]

b. 599.472 ~ 600

Step-by-step explanation:

a)

Confidence Interval For Proportion

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))

x = Mean

n = Sample Size

a = 1 - (Confidence Level/100)

Za/2 = Z-table value

CI = Confidence Interval

Mean(x)=410

Sample Size(n)=850

Sample proportion = x/n =0.482

Confidence Interval = [ 0.482 ±Z a/2 ( Sqrt ( 0.482*0.518) /850)]

= [ 0.482 - 1.645* Sqrt(0) , 0.482 + 1.65* Sqrt(0) ]

= [ 0.454,0.51]

b)

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.05 is = 1.96

Samle Proportion = 0.482

ME = 0.04

n = ( 1.96 / 0.04 )^2 * 0.482*0.518

= 599.472 ~ 600

8 0
3 years ago
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