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3 years ago

Identify all the functions that have a greater rate of change and the function represented in the graph

Mathematics

2 answers:

Anna007 [38]3 years ago

6 0

Answer:

A. C. E. would be the correct answers

Step-by-step explanation:

Damm [24]3 years ago

3 0

A. C. E. Lol I got you gta

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A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides

ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

=(15-2x)(10-2x)x cubic inches

=(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ , here a=12, b= -100 and c=15

$x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}$

$\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}$

$\Rightarrow x=0.1528,8.18$

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, $V''|_{x=0.1528}=24(0.1528)-100$

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

4 0

3 years ago

In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.

ankoles [38]

<h2>Answer:</h2>

$\boxed{\overline{MN}=37.96}$

<h2>Step-by-step explanation:</h2>

For a better understanding of this problem, see the figure below. Our goal is to find $\overline{MN}$ . Since:

$\angle MRS=\angle MQP=90^{\circ} \\ \\ \overline{MQ}=\overline{MR}=30mm$

and $\overline{MN}$ is a common side both for ΔMRN and ΔMQN, then by SAS postulate, these two triangles are congruent and:

$\overline{RN}=\overline{QN}$

By Pythagorean theorem, for triangle NQP:

$\overline{QN}=\sqrt{\overline{NP}^2+\overline{QP}^2} \\ \\ \overline{QN}=\sqrt{10^2+21^2} \\ \\ \overline{QN}=\sqrt{541}$

Applying Pythagorean theorem again, but for triangle MQN:

$\overline{MN}=\sqrt{\overline{MQ}^2+\overline{QN}^2} \\ \\ \overline{MN}=\sqrt{30^2+(\sqrt{541})^2} \\ \\ \boxed{\overline{MN}=37.96}$

3 0

3 years ago

Kate walks half a mile to the library how many yards does she walk

Crank

Theres 1760 yards in a mile so divide that by 2.
answer is 880

5 0

3 years ago

Read 2 more answers

Janie bought 8 apples and 6 bananas. Each apple costs $0.80, and each banana cost $.60. Answer an expression representing the to

Pavel [41]

A: apples
b: bananas

Your expression could be:

$0.80a + $0.60b = $10.00

----

$0.80 ( 8 ) + $0.60 ( 6 ) = $10.00
$6.40 + 3.60 = $10.00
$10.00 = $10.00
✔

3 0

3 years ago

Andrea put 2 quarts of water and 1 1/2 cups of lemon juice in a pitcher. How many total liquids are in the pitcher

gizmo_the_mogwai [7]

Key: 1 quart = 4 cups

So two quarts would equal 8 cups...So we add...

8 + 1 1/2 = 9 1/2

9 1/2 is the total. ^^

4 0

3 years ago