Use the table and diagram to answer this question. (I attached the picture)

Mathematics

1 answer:

iragen [17]4 years ago

3 0

We have a right triangle with two of the legs known (7 and 4). The hypotenuse is unknown. Because of this, we will use the tangent trigonometric function.

Tangent of an angle is equal to the ratio of the opposite and adjacent sides
tan(angle) = opposite/adjacent

Divide those two sides to get
opposite/adjacent = 7/4 = 1.75

Look through the table and see which value in the "tan(x)" column is closest to 1.75, and that happens to be 1.7321. It is in the bottom row corresponding to 60 degrees.

So the final answer is choice D) 60 degrees

Note: it turns out that the angle theta is roughly 60.2551187 degrees

You might be interested in

Use the given transformation to evaluate the integral. (15x + 15y) dA R , where R is the parallelogram with vertices (−1, 4), (1

MA_775_DIABLO [31]

Answer:

$\int_R 15x+15y dA = \frac{8}{16875}$

Step-by-step explanation:

Recall the following: x = 15u+15v, y = -60u+15v. So, x-y = 75u. Then u = (x-y)/75. 4x+y = 75v. Then v = (4x+y)/75.

We will see how this transformation maps the region R to a new region in the u-v domain. To do so, we will see where the transformation maps the vertices of the region.

(-1,4) -> ((-1-4)/75,(4(-1)+4)/75) = (-1/15, 0)

(1,-4)->(1/15,0)

(3,-2)->(1/15,2/15)

(1,6)->(-1/15,2/15)

That is, the new region in the u-v domain is a rectangle where $\frac{-1}{15}\leq u \leq \frac{1}{15}, 0\leq v \leq \frac{2}{15}$ .

We will calculate the jacobian of the change variables. That is

$\left |\begin{matrix} \frac{du}{dx}& \frac{du}{dy}\\ \frac{dv}{dx}& \frac{dv}{dy}\end{matrix}\right|$ (we are calculating the determinant of this matrix). The matrix is

$\left |\begin{matrix} \frac{1}{75}& \frac{-1}{75}\\ \frac{4}{75}& \frac{1}{75}\end{matrix}\right|=(\frac{1}{75^2})(1+4) = \frac{1}{15\cdot 75}$ (the in-between calculations are omitted).

We will, finally, do the calculations.

Recall that

$15x+15y = 15(15u+15v) + 15(-60u+15v) = (15^2-15\cdot 60 )u+2\cdot 15^2v = 15^2(-3)u+2\cdot 15^2 v$

We will use the change of variables theorem. So,

$\int_R 15x+15y dA = \int_{\frac{-1}{15}}^{\frac{1}{15}}\int_{0}^{\frac{2}{15}} 15^2(-3)u+2\cdot 15^2 v \cdot (\frac{1}{15^2\cdot 5}) dv du = \int_{\frac{-1}{15}}^{\frac{1}{15}}\int_{0}^{\frac{2}{15}}\frac{-3}{5}u+\frac{2}{5}v dvdu$

This si because we are expressing the original integral in the new variables. We must multiply by the jacobian to guarantee that the change of variables doesn't affect the value of the integral. Then,

$\int_{\frac{-1}{15}}^{\frac{1}{15}}\int_{0}^{\frac{2}{15}}\frac{-3}{5}u+\frac{2}{5}v dvdu = \int_{\frac{-1}{15}}^{\frac{1}{15}}\frac{-3}{5}u\cdot \frac{2}{15} + \frac{2}{5}\cdot \left.\frac{v^2}{2}\right|_{0}^{\frac{2}{15}}du = \frac{-3}{5}\left.\frac{u^2}{2}\right|_{\frac{-1}{15}}^{\frac{1}{15}}\cdot \frac{2}{15} + \frac{2}{5}\cdot \left.\frac{v^2}{2}\right|_{0}^{\frac{2}{15}} = \frac{8}{16875}$

5 0

4 years ago

A quilt maker is creating a design of a sailboat. she needs exactly the same amount of fabric for the sail as she needs for the

valina [46]

The shape of sail is triangle
The shape of the boat is trapezoid
Fabric needed for sail = fabric needed for boat
which mean ;
                      the area of triangle = the area of trapezoid

the area of triangle = 0.5 * base * height
base = bottom sail = 10 and height = 10
∴ the area of triangle = 0.5 * 10 * 10 = 50 ⇒⇒⇒⇒⇒(1)

the area of trapezoid = 0.5 * (b₁ +b₂) * h
b₁ = long base
b₂ = short base = 10 cm.
h = height = 4 cm.
∴ the area of trapezoid = 0.5 (b₁ + 10 ) * 4 ⇒⇒⇒⇒ (2)

Equating (1) and (2)
∴ 0.5 (b₁ + 10 ) * 4 = 50
    b₁ + 10 = 25
    b₁ = 15

∴ <span>The length of the long base of the trapezoid = 15 cm.

The correct answer is option (C)
</span>

5 0

3 years ago

Read 2 more answers

Hello do you know what 80÷1000=

SOVA2 [1]

Answer: 0.08 if you meant what you said if you meant a thousand divided by 80 then your answer is 12.5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Select the correct equations.

Verizon [17]