You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height.The shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees, This forms a right triangle.
a. What is the measure of the other acute angle?
b. What is the height of the tree?
c. You are standing at the end of the tree's shadow and want to take a picture of the tree but your camera can only focus at distance less than 500 feet. When you hold the camera to take the picture it is 5 feet above the ground. What is the distance from the end of the shadow to the top of the tree?
d. Can you take a clear picture of the top of the tree from where you are standing?
e. How many total tiles will be needed to complete the job?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

given that You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height.

the shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees, This forms a right triangle.

a) Other acute angle is 90-35 = 55 degrees

b) Height of the tree = 500 tan 35 =350.104 feet

c) Here height would be reduced to 350.104 - 5 = 345.104 feet.

Hence distance adjusted= 354.104 cot 35=492.8596 feet.

d) Yes because this is less than 500 feet.

e) height of 5 feet itself is sufficient here

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In a certain country, the life expectancy of a woman born in 1995 was 80.2 years. Between 1995 and 2005, the life expectancy increased 0.4 year every 5 years.

Answers

The Equation of life expectancy is x- 0.4(2) = 80.2.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

The life expectancy of a woman born in 1995 was 80.2 years.

The life expectancy increased 0.4 year every 5 years.

So, from 1995 to 2005 there are two times the life expectancy increase.

let the lifeexpectancy by x.

Thus, the equation is

x- 0.4(2) = 80.2

Learn more about Equation here:

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Answer:

a. L - 0.4(2)= 80.2 or L - 80.2 = 0.4(2) or 80.2 + 0.4(2) = L

b. No; The equations must be equivalent. They may look different, but all equations can be rewritten as L= 80.2 + 0.4(2).

Step-by-step explanation:

Students plan to pay back half the debt now though fundraising, and the rest after the harvest. Write an equation to represent the debt they will repay through fundraising. Use a negative integer to show debt. Use "D" to represent the debt that will be repaid by through fundraising

Answers

Answer:

D = $(-d)/(-2)$

Step-by-step explanation:

The amount of money that the students will pay back with the fundraiser (D) would be half of the current debt (d) since debt is represented as a negative but the fundraiser needs to be a positive since it is money gained we would divide by -2

D = $(-d)/(-2)$

This equation shows the debt that will be repaid through the fundraiser which would be exactly half of the current debt.

Find the x-intercept of the parabola with vertex (6,27) and y-intercept (0,-81)

Answers

The vertex form of the equation of a parabola with the vertex (h,k):
$y=a(x-h)^2+k$

The parabola has the vertex at (6,27).
$y=a(x-6)^2+27$

The y-intercept is (0,-81).
$x=0, \ y=-81 \n\Downarrow \n-81=a(0-6)^2+27 \n-81=a(-6)^2+27 \n-81=36a+27 \n-81-27=36a \n-108=36a \n(-108)/(36)=a \na=-3$

The equation of the parabola is:
$y=-3(x-6)^2+27$

y=0 at the x-intercepts.
$0=-3(x-6)^2+27 \n-27=-3(x-6)^2 \n(-27)/(-3)=(x-6)^2 \n9=(x-6)^2 \n√(9)=√((x-6)^2) \n3=|x-6| \nx-6=3 \ \lor \ x-6=-3 \nx=3+6 \ \lor \ x=-3+6 \nx=9 \ \lor \ x=3$

The x-intercepts are x=3 and x=9.

A swimmer dives to 65 feet below the surface of the ocean. Write the integer that represents the depth of the dive

Answers

Answer:

The integer is -65

Step-by-step explanation:

Hope that helps

Answer:The integer is -65

Pick a product that might be packaged in the shape of a rectangular prism.Surface Area: S.A.=2lw+2wh+2lh
Volume: V=lwh

Choose an appropriate length, width, and height for your package so that it can fit the product you are shipping. Using these dimensions, what is the ratio of surface area to volume?

Answers

Let us assume the following units of measure:
Length = 10 inches
Width = 5 inches
Height = 8 inches

Surface area = 2lw + 2wh + 2lh
S.A = 2(10in * 5in) + 2(5in * 8in) + 2(10in * 8in)
S.A = 2(50in²) + 2(40in² + 2(80in²)
S.A = 100in² + 80in² + 160in²
S.A = 340 in²

Volume = lwh
V = 10 in * 5 in * 8 in
V = 400 in³

ratio of the surface area to volume?
340 in² / 400 in³ = 34 / 40 in = 17/20 in

Answer:

Product: Iphone 6s plus box

W= 3in L= 6in H= 3in

And then use the surface area equation ( SA = 2lw + 2wh + 2lh)

To get your volume use the equation ( V = lwh)

And then divide those two SA / V and you get your ratio

Task 1 complete!!

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Step-by-step explanation:

Ian has a yardstick with marks for every tenth of an inch. Which could be the most accurate measurement of his height using the yardstick

Answers

yardstick
1 yard=3 feet
1 foot=12 inches
1 yard=3 times 12 inches=36 inches

the most acurate measurement would be to the 10th of an inch exg 5 feet 3inches and 1/10th inch

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