Pi is a mathematical term that has a numerical value of 3.14 how would this number be written in expanded form.

An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The hei

MatroZZZ [7]

Title:

<h2>Check the explanation.</h2>

Step-by-step explanation:

The standard form of an ellipse is $\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1$ .

The span of the river is 20 meters. As per the given condition, y-axis will pass through the middle point of the river. That is why, the value of a will be $\frac{20}{2} = 10$ .

Since the height of the arc is 6, the value of b is 6.

The equation of the arc will become $\frac{x^2}{{10}^2} + \frac{y^2}{6^2} = 1$ .

8 0

4 years ago

The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to

Harman [31]

*attachment contains the omitted graph

Answer:

$y = -\frac{4}{3}x + 9$

Step-by-step explanation:

The equation that represents the path of the swimmer to the shoreline can be represented in the slope-intercept form, given as $y = mx + b$ .

Where,

Slope (m) = the negative reciprocal of the slope of the shoreline, since it is perpendicular to it = ??

y-intercept (b) = ??

Find the slope of the shoreline using, (0, 1) and (4, 4):

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{4 - 0} = \frac{3}{4}$ .

Since the slope of the shoreline is ¾. The slope of the path of the swimmer would be the negative reciprocal of ¾.

The negative reciprocal of ¾ = -⁴/3.

The slope of the swimmer's path = -⁴/3.

Using the coordinate of the point of the swimmer (6, 1), and the slope of the path, we can find b, the y-intercept of the path.

Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.

Thus:

1 = (-⁴/3)(6) + b

1 = -8 + b

Add 8 to both sides

1 + 8 = b

9 = b

b = 9

Substitute m = -⁴/3 and b = 9 into y = mx + b.

✅The equation that represents the path would be:

$y = -\frac{4}{3}x + 9$

8 0

3 years ago

A farmer charges $6 for 4 pounds of tomatoes. Which

Paha777 [63]

Answer:

The correct option is C) $d= 1.5p$

Step-by-step explanation:

Consider the provided information.

A farmer charges $6 for 4 pounds of tomatoes.

First find the unit rate as shown below:

$\frac{6}{4}=1.5$

Therefore, the cost of 1 pound of tomatoes is $1.5

let d represents the dollars he should charge and p represent the pounds of tomatoes farmer sold.

Thus the required equation is $d=1.5p$

Hence, the correct option is C) $d= 1.5p$

4 0

3 years ago

A)none <br> B)7<br> C)6i<br> D)I-6<br> E) - square of 7<br> ( look at the picture better)

Anika [276]

The correct answer is A). None

Step-by-step explanation:

The given quadratic polynomial has 3 roots and some of roots are x= $\sqrt{7}$ and x=6+i

It is necessary to note that one of the roots is a complex number and root of complex number always in pair of the conjugate to each other.

Since x=6+i

Conjugate of (6+i) is (6-i)

<em>Therefore, (6-i) is 3rd required root of a polynomial </em>

<em>The correct answer is A). None</em>

4 0

4 years ago

A number, n, is multiplied by -7/8. The product is -0.5. What is the value of n?

Yuki888 [10]

Answer: A.n = 4/7

have:

$n.\frac{-7}{8} =-0.5\\\\n.\frac{-7}{8}=\frac{-1}{2}\\\\n=\frac{-1}{2}:\frac{-7}{8}=\frac{4}{7}$

Step-by-step explanation:

3 0

3 years ago