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gizmo_the_mogwai [7]
3 years ago
11

a tree casts a 26 ft shadow. a boy standing nearby casts a 10 foot shadow, forming similar triangles. his height is 4 ft. how ta

ll is the tree
Mathematics
1 answer:
andrezito [222]3 years ago
6 0

Answer:

he would be 22 ft smaller than the tree

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Hector deposited $90 in a savings account earning 10% interest, compounded annually. to the nearest cent how much interest will
Tcecarenko [31]

Answer:

$117

Step-by-step explanation:

$90*10= $9

1 year is $9 interest, which is increase.

$9*3=$27

So than you add $27 and $90 and get $117

8 0
3 years ago
A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin
Natalija [7]

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2}   or  \frac{30-21.21 }{2}\\ = \frac{51.21 }{2}   or  \frac{8.79}{2}\\ = 25.605 or 4.395

x ≅ 25.61 or 4.4

V = (30 - 2x)(16 - 2x)x

Substituting the values of x into L and B, we have )x

L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22

B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22

Since L and B cannot be negative, we use the other value for x = 4.4, So

L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2

B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2

So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³

3 0
3 years ago
There are four times as many girls in a chemistry class as there are boys. if there are 45 students in the class, how many boys
puteri [66]
In order to determine the number of boys in the class, first, we set-up an algebraic equation. Let x = number of boys in the class. The equation is then: x + 4x = 45. This is because the number of girls is 4 times greater than the number of boys. After solving the algebraic equation, it is then determined that there are 9 boys in the Chemistry class.   
4 0
3 years ago
Write 3.25 as a mixed number in simplest form.
snow_tiger [21]
3.25 can be re-written as;
=3+0.25
Converting the decimal to a fraction gives;
3+\frac{25}{100}
=Simplify the fraction;
3+\frac{1}{4}
The final answer is;
3\frac{1}{4}

4 0
3 years ago
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14K gold hoop earrings are on sale for 50 cents off. They normally sell for $75.00 a pair. How much did Elizabeth save on 2 pair
KonstantinChe [14]

Answer: $1

Step-by-step explanation:

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