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frez [133]
3 years ago
9

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 3 (*sqaure root sign*) t (20 − t), [0,

20]
Mathematics
1 answer:
mafiozo [28]3 years ago
5 0

9514 1404 393

Answer:

  • maximum: 15∛5 ≈ 25.6496392002
  • minimum: 0

Step-by-step explanation:

The minimum will be found at the ends of the interval, where f(t) = 0.

The maximum is found in the middle of the interval, where f'(t) = 0.

  f(t)=\sqrt[3]{t}(20-t)\\\\f'(t)=\dfrac{20-t}{3\sqrt[3]{t^2}}-\sqrt[3]{t}=\sqrt[3]{t}\left(\dfrac{4(5-t)}{3t}\right)

This derivative is zero when the numerator is zero, at t=5. The function is a maximum at that point. The value there is ...

  f(5) = (∛5)(20-5) = 15∛5

The absolute maximum on the interval is 15∛5 at t=5.

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The measures of complementary angles have a sum of 90 degrees.Angle A and angle B are complimentary, and their measures have a d
777dan777 [17]

Answer:

The measure of the angles are 55° and 35°

Step-by-step explanation:

Sum of two angles that are complement of each other are 90.

The angles are A and B, so we can write:

A + B = 90

Also,

The difference is 20. Let A be the greater of them, so we can write equation 2 as:

A - B = 20

Now, we add up both equations, eliminate B and solve for A first:

A + B = 90

A - B = 20

---------------

2A = 90 + 20

2A = 110

A = 110/2

A = 55

And now the measure of B:

A + B = 90

55 + B = 90

B = 90 - 55

B = 35

5 0
3 years ago
Please help with these quick
drek231 [11]
To determine whether 10a-10c are true or false, you first need to know how to find the volume of the shoebox and the volume of the crate.

The equation for volume is l × w × h where l is the length, w is the width, and h is the height.

So, the volume of the shoebox is

V = l × w × h
V = 12 × 6 × 4
V = 288 cubic inches.

To find the volume of the crate, we simply multiply the volume of one shoebox by 20, as the crate holds 20 shoeboxes.

228 × 20 = 4560 cubic inches.

10a. Each shoebox has a volume of 22 cubic inches. <span>False. The volume is 228 cubic inches.

</span>10b. Each crate has a volume of about 440 cubic inches. <span>False. The volume of each crate is 4560 cubic inches.</span><span>

</span>10c. If the crate could hold 27 shoeboxes, the volume of the crate would be about 7,776 cubic inches.

For this one, let's do some more math. Since we figured out the volume of a crate holding 20 shoeboxes is 4560 cubic inches, let's do the same thing to find the volume of a crate holding 27 shoeboxes.

228 × 27 = 6156 cubic inches.

<span>False. The volume of a crate holding 27 shoeboxes would be 6156 cubic inches.

</span>11 part A:

Each term above describes the term below, but the term below doesn't necessarily describe the term above.

The choice of terms is : <span>trapezoid</span>, <span>triangle</span>, <span>rhombus</span>, <span>parallelogram</span>

Before we do anything else, let's define our terms, as well as the ones used in the diagram.

Trapezoid - A four sided shape with a pair opposite parallel sides.<span>
Triangle - </span>A shape with three sides.<span>
Rhombus - </span>A shape with four equal straight sides<span>.
Parallelogram - </span>A quadrilateral with two sets of parallel sides.<span>
Quadrilateral - </span>A four-sided shape with four angles.<span>
Square - </span>A four-sided shape with all four sides the same length, and all four angles are the same size.

The first term is quadrilateral. From this, we can determine that the term <span>triangle</span> won't be used at all, as it's a three-sided figure, whereas a <span>quadrilateral</span> is a four-sided figure. This leaves <span>trapezoid, rhombus, </span>and <span>parallelogram </span>as our terms.

A <span>trapezoid </span>is a <span>quadrilateral</span>, because it has four sides, but it can't be a <span>rhombus </span>or <span>parallelogram</span>, so it goes in the first open box.

A parallelogram is a trapezoid, because it has a pair of opposite parallel sides, but it can't be a rhombus, because it doesn't necessarily have all equal sides, so it goes in the second open box.

A rhombus is a parallelogram, because it has two sets of parallel sides, and goes in the third open box.

So, from top box to bottom box, the order the term go is
Quadrilateral
Trapezoid
Parallelogram
Rhombus
Square

3 0
3 years ago
Use the line plot below to
Alinara [238K]
1. There were 11 yards mowed. Each yard is represented by an x on the line plot.
2. The most amount of gas used on any one yard was 5/8 of a gallon. The least amount of gas used was 1/8 of a gallon. The difference is (5/8)-(1/8)= (4/8)= 1/2 gallon
7 0
3 years ago
Determine the standard form of the equation for the circle with center (h,k) = (-5 ½) and radius r =1
wariber [46]
Asuuing yo meant (h,k)=(-5,1/2)

equation is (x-h)^2+(y-k)^2=r^2
(h,k) is center and r=radious
given that (h,k)=(-5,1/2) and r=1
h=-5
k=1/2

(x-(-5))^2+(y- \frac{1}{2} )^2=1^2
(x+5)^2+(y- \frac{1}{2} )^2=1
if you wanted us to expand
x²+y^2+10x-y+25.25=1
8 0
3 years ago
I can’t find answers to this question. Please help.
dlinn [17]

Answer:

Did you try looking it up

Step-by-step explanation:

sorry If I am wrong and don't forget to make me brainliest

3 0
3 years ago
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