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Tanya [424]
3 years ago
10

Let f be the function given by f(x) = x+4(x−1)(x+3) on the closed interval [−5,5]. On which closed interval is the function f gu

aranteed by the Extreme Value Theorem to have an absolute maximum and an absolute minimum?
Mathematics
1 answer:
Vlad [161]3 years ago
6 0

Answer:

Step-by-step explanation:

f(x)=x+4(x^2+2x-3)=4x^2+9x-12

f'(x)=8x+9

f'(x)=0,gives x=-9/8

f(-5)=-5+4(-5-1)(-5+3)=-5+4*-6*-2=43

f(-9/8)=-9/8+4(-9/8-1)(-9/8+3)

=-9/8+4*-17/8*15/8

=-9/8-255/16

=-273/16=-17 1/16

f(5)=4*5^2+9*5-12=100+45-12=133

absolute maximum=133

absolute minimum=-17 1/16

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If Jane has 3 3/4 dozen boxes of envelopes, and she ordered 11 1/2 dozen more, how many dozen boxes will she have in all?
Debora [2.8K]
Hi there:-)

She has=3+3/4=15/4
She ordered=11+1/2=23/2
Now how many she has in all
(15/4)+(23/2)=15 1/4 ...answer

15 1/4 means 15+1/4=15.25

Hope it helps
3 0
3 years ago
Read 2 more answers
A white square quilt has a purple square in the center.the side length of the purple square is (x-5) inches and the width of the
ankoles [38]
Area of quilt, Q= 60^2\, in^2=3600\,in^2
Area of purple square, P = (x-5)^2\, in^2
Area of white area 
= Q-P
= 3600-(x-5)^2\, in^2
=3600-x^2+10x-25\, in^2
=3575-x^2+10x\, in^2
4 0
3 years ago
The larger of two supplementary angles is 6 less than 5 times the smaller. Find the measure of the two angles.
zimovet [89]

Answer:

Step-by-step explanation:

Let the two angles be x and y

Then: y = 5x - 6

And x + y = 180° (the of supplementary angle is 180°)

Putting y = 5x - 6

x + 5x - 6 = 180

6x = 180 + 6

6x = 186

x = 186/6

x = 31°

And y = 5x - 6

y = 5(31) - 6

y = 155 - 6

y = 149°

The angles are 31° and 149°

6 0
3 years ago
Solve for x.<br> Need help, Thank you!!<br> Also, i need explanation.
babunello [35]

Answer:

7.) x = 12

9.) x = 4

Step-by-step explanation:

7.) Angle Y and Angle X both add up to 180

=> 40 + 12x - 4 = 180

=> 36 + 12x = 180

=> 12x = 180 - 36

=> 12x = 144

=> x = 12

9.) Angle W and Angle X add up to 180

=> 145 + (-1) + 9x = 180

=> 144 + 9x = 180

=> 9x = 180 - 144

=> 9x = 36

=> x = 36 / 9

=> x = 4

Hope this helps!

4 0
2 years ago
A sea turtle swims at a speed of 27 kilometers per hour. A girl swims 14 decimeters per second. 1 m = 10 dm 1000 m = 1 km How mu
insens350 [35]
The sea turtle's speed is
v_{t} = (27 \, \frac{km}{h} )*(1000 \, \frac{m}{km} )*( \frac{1}{60} \, \frac{h}{min} ) = 450 \, \frac{m}{min}

The girl's speed is
v_{g} = (14 \, \frac{dm}{s} )*( \frac{1}{10} \, \frac{m}{dm} )*(60 \, \frac{s}{min} ) = 84 \, \frac{m}{min}

The ratio of the turtle's speed to that of the girl is
\frac{v_{t}}{v_{g}} = \frac{450}{84} =5.357

Answer: 5.36 faster  (nearest hundredth)


4 0
3 years ago
Read 2 more answers
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