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sveticcg [70]
3 years ago
7

62. Height Kirsten places her surveyor's telescope on the top of

Mathematics
1 answer:
Solnce55 [7]3 years ago
4 0

Answer:

21 feet

Step-by-step explanation:

Given :

Height of the tripod above the ground = 5 ft

Elevation = 8°

Distance of the tree from the tripod = 120 ft

Therefore from the figure, we can find the height of the tress as:

$\tan 8 ^\circ = \frac{BC}{AB}$

$0.1405  = \frac{BC}{120}$

∴  BC ≈ 16

Therefore, CE = BC+BE

                        = 16 + 5

                        = 21

Therefore the height of the tree is 21 feet.

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
3 years ago
Trisha is making two sides of hamburgers 0.5 pounds and 0.25 pounds how many of each size of hamburgers could she make with 3.75
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Answer:

for 0.5 pounds size, we have 7.5

for 0.25 pounds size, we have 15

Step-by-step explanation:

Here, we want to calculate the number of each hamburger size that could be made

for 0.5 pounds size, we have that;

3.75/0.5 = 7.5

for 0.25 pounds, we have;

3.75/0.25 = 15

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3 years ago
A beekeeper pours honey into jars. Each large jar holds 18 ounces of honey. Each small jar holds 12 ounces of honey. The beekeep
viktelen [127]

Answer:

1,100 ounces because 20 × 30 + 10 × 50 = 1,100

Step-by-step explanation:

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X + y = 4<br> y = -x + 4
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Answer:

Infinite Solutions

Step-by-step explanation:

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2 years ago
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