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3 years ago

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In sunlight, a vertical yardstick casts a 1 ft shadow at the same time that a nearby tree casts a 15 ft shadow. How tall is the

tree?

2 answers:

nadya68 [22]3 years ago

7 0

To answer this specific problem, the tree is 45 feet tall. I am hoping that this answer has satisfied your query and it will be able to help you, and if you would like, feel free to ask another question.

joja [24]3 years ago

3 0

Answer:

Tree is 45 ft tall.

Step-by-step explanation:

In the figure attached AB is the tree and CD is the yardstick.

Shadow of tree AB is BO = 15 ft and shadow of yardstick is CO.

since length of a yardstick is = 1 yard or 3 ft.

Now we know that ΔABO and ΔDCO are similar.(since ∠A = ∠D and ∠B = ∠C = 90° so AA property proving triangles similar)

Therefore $\frac{AB}{CD}=\frac{OB}{OC}$

By putting the values of AB and CD

$\frac{x}{3}=\frac{15}{1}$

x = 3×15 = 45 ft.

Therefore the height of the tree is 45 ft.

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Crank

Option D: $f(x)=-2(x+2)(x-4)$ is the function

Explanation:

Let the general form of quadratic equation be $y=a x^{2}+b x+c$

The function passes through the intercepts $(-2,0)$ and $(4,0)$ and also passes though the point $(-1,10)$

Substituting the points $(-2,0)$ , $(4,0)$ and $(-1,10)$ in the equation $y=a x^{2}+b x+c$ , we get,

$4a -2b+c=0$ -----------(1)

$16a +4b+c=0$ ----------(2)

$a-b+c=10$ -----------(3)

Subtracting (1) and (2), we get,

$\ \ 4a -2b+c=0\\ 16a +4b+c=0\\\---------\\ \ \ -12a-6b=0$ -----------(4)

Subtracting (2) and (3), we get,

$16a +4b+c=0\\\ \ a \ \ - \ \ b \ +c=10\\---------\\15a+5b=-10$ ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

$-60a-30b=0\\\ 90a+30b=-60\\--------\\30a=-60\\\ \ a=-2$

Thus, the value of a is $a=-2$

Substituting $a=-2$ in equation (4), we get,

$\begin{aligned}-12 a+6 b &=0 \\-12(-2)-6 b &=0 \\ 24-6 b &=0 \\ 24 &=6 b \\ 4 &=b \end{aligned}$

Thus, the value of b is $b=4$

Now, substituting the value of a and b in equation (1), we have,

$\begin{aligned} 4 a-2 b+c &=0 \\ 4(-2)-2(4)+c &=0 \\-8-8+c &=0 \\ c &=16 \end{aligned}$

Thus, the value of c is $c=16$

Now, substituting the value of a,b and c in the general formula $y=a x^{2}+b x+c$ , we get,

$y=-2x^{2} +4x+16$

Taking out the common term as -2 we get,

$y=-2(x^{2} -2x-8)$

Factoring , we get,

$y=-2(x+2)(x-4)$

Thus, the function is $f(x)=-2(x+2)(x-4)$

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3 years ago

234/341 in simplest form?

Natali5045456 [20]

Answer:

0.686 (approximately)

Step-by-step explanation:

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3 years ago

We measure the diameters for a random sample of 25 oak trees in a neighbourhood. Diameters of oak trees in the neighbourhood fol

jarptica [38.1K]

Answer:

The required confidence inteval = 94.9%.

Step-by-step explanation:

Confidence interval: Mean ± Margin of error

Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).

i.e. Mean + Margin of error = 42.969 (i)

Mean - Margin of error = 36.191 (ii)

Adding (i) and (ii), we get

$2Mean =79.16\\\\\Rightarrow\ Mean= 39.58$

Margin of error = 42.969-39.58 [from (i)]

= 3.389

Margin of error = $t^* \dfrac{\sigma}{\sqrt{n}}$

here n= 25 $, \ \sigma=8.25$

i.e.

$3.389=t^*\dfrac{8.25}{5}\\\\\Rightarrow\ t^* = \dfrac{3.389}{1.65}\\\\\Rightarrow\ t^* =2.0539 \$

Using excel function 1-TDIST.2T(2.054,24)

The required confidence inteval = 94.9%.

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3 years ago

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Andru [333]

Answer:

0.234

Step-by-step explanation:

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r-ruslan [8.4K]

Answer:

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Step-by-step explanation:

(3x^2-2)(3x^2+3)

expand to remove the bracket

9x^4 + 9x^2 -6x^2 - 6

9x^4 + 3x^2- 6

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3 years ago