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3 years ago

Rounding to the nearest dollar?

1 answer:

7 0

If you have for example
19.90$ you round it as 20
if u have 19.05 you have it as 19 only because its not near to the next number to it

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Determine which of the following sets of side lengths represents the side lengths of a right triangle. select all that apply.

Igoryamba

Know about the following topics. 1. Converse of Pythagorean Theorem. 2. 45-45-90 Right Triangles. 3. 30-60-90 Right Triangles. 4. Tangent Ratio. 5. Sine Ratio. 6. ... Check to see whether the side lengthssatisfy the equation c2. = a2 + b2. (√113)2 = 72 + 82. 113 = 49 + 64. 113 = 113 ✓. 7. 8. √113 ? ? The triangle is a.

5 0

4 years ago

Read 2 more answers

Your company is introducing a fruit drink packaged in an aluminum box with a square

solong [7]

Answer:

See explanation

Step-by-step explanation:

Let x in be the base side length and y in be the height of the box. Since the base is a square, we have

$S=x^2\Rightarrow x=\sqrt{S}$

The volume of the box is

$V=S\cdot y\\ \\36=Sy\Rightarrow y=\dfrac{36}{S}$

The surface area of the box is

$SA=2x^2+4xy\\ \\SA(S)=2S+4\cdot \sqrt{S}\cdot \dfrac{36}{S}=2S+\dfrac{144}{\sqrt{S}}$

The graph of the function SA(S) is shown in attached diagram.

Find the derivative of this function:

$SA'(S)=(2S+144S^{-\frac{1}{2}})'=2-\dfrac{1}{2}\cdot 144\cdot S^{-\frac{1}{2}-1}=2-\dfrac{72}{S\sqrt{S}}$

Equate this derivative to 0:

$2-\dfrac{72}{S\sqrt{S}}=0\\ \\2S\sqrt{S}=72\\ \\S\sqrt{S}=36\\ \\S^{\frac{3}{2}}=6^2\\ \\S=6^{\frac{4}{3}}$

So, the dimensions that produce a minimum surface area for this aluminum box are:

$x=\sqrt{6^{\frac{4}{3}}}=6^{\frac{2}{3}} \ in\\ \\y=\dfrac{6^2}{6^{\frac{4}{3}}}=6^{\frac{2}{3}}\ in.$

4 0

3 years ago

Mr. Parker's farm borders a river. He buys 1,000 ft of fencing

Gelneren [198K]

When one side of a quadrilateral is not to be fenced (ex. a river, as in this case), the optimal fencing to maximize the area is always to use half the fencing for the length, and one-fourth for each of the two widths

A) For 1000 ft of fencing which is to be used to cover 1 length and 2 widths:
L = 1000/2 = 500, and W = 1000/4 = 250. The optimal dimensions will be 250 x 500 ft.

B) This will result in an area of 250*500 = 125,000 sq. ft.

8 0

4 years ago

What are the common factors of 14 and 30

Lesechka [4]

1, 2, 7, 14.
Would be your answer

3 0

3 years ago

Help me! With number 9 and 10

bekas [8.4K]

9 is 82 blue v-necks and 43 red crew necks. 10 is for one angle it's 56 and fornthe other it is 34. For the first one, let a = blue v-necks and b = red crew necks. Then we have a system of equations: a + b = 125(total amount of shirts) and 7.95a + 8.95b = 1036.75(cost of shirts times how many shirts sold is the profit they got). Multiplyig the top equation by 8.95 we get 8.95a + 8.95b = 1118.75. Subtract that from the second and we get (8.95 - 7.95)a + (8.95 - 8.95)b = 82. The b is gone from that zero and a is being multiplied by one so that means a = 82. Plugging that into a + b = 125 and we get 82 + b = 125 ∴ b = 43. For the second question, since two angles are complementary, we can say ∠A = 90° - ∠B Then its says ∠A = 2∠B - 12. So putting the second ∠A def. into the first equation we get 2∠B - 12 = 90° - ∠B. Adding ∠B to both sides we get 3∠B -12 = 90°. Then adding 12 to both sides we get 3∠B = 102°. Divide by three and you get ∠B = 34 ∴ ∠A = 56.

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4 years ago