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3 years ago

The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)2 + (y + 12)2 = 172

1 answer:

defon3 years ago

3 0

Hello :
an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =4 and b = -12
 the length of the radius is : r = √172

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The cost of a unit is made up of $6.25 material cost, $4.75 labour cost, and $3.25 overhead. What is the ratio that exists betwe

blsea [12.9K]

Answer:

The ratio that exist between this three elements are 25 : 19 : 13.

Step-by-step explanation:

Ratio compares one thing to another. Ratios indicate the comparison of the size of a number to another . One trick about ratio is that you can multiply or divide the ratios by same number. For example the ratio of boy to girls can be represented as 3 : 4. If you multiply the ratios by 2 you will get the ratio 6 : 8 and it still represent the same ratios of boys to girls. Ratios can be written as a fraction for example 3/4 for our example.

The cost of the unit is made up of $6.25 , $4.75 and $3.25.

$6.25 $4.75 $3.25 . Let us multiply by 100 to remove the decimals.

625 : 475 : 325 . Now let simplify the ratios by dividing through by 25.

625/25 : 475/25 : 325/25 . The simplest ratios can be written as follows

The ratios are 25 : 19 : 13.

6 0

3 years ago

Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

Dima020 [189]

Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

$\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)$

$\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)$

respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

$\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt$

where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

$=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt$

$=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6$

6 0

3 years ago

The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.

coldgirl [10]

Answer:

Solution given:

Since the given triangle is isosceles and right angled triangle

perpendicular [p]=base[b]=x

hypotenuse [h]=6

we have

by using Pythagoras law

p²+b²=h²

x²+x²=6²

2x²=36

x²=36/2

x²=18

x= $\sqrt{18}$

x= $\bold{3\sqrt{2}}$

6 0

3 years ago

Jordan throws a ball from a cliff 12 feet above the ground with an initial velocity of 32 feet per second. In the following func

lbvjy [14]

Answer:

Your answer will be the third function

Step-by-step explanation:

The base function you need to know is h(t)= 1/2at^2

Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12

8 0

2 years ago

A scatterplot is used to display data for a runner where x is the number of miles run, and y is the time, in minutes, that it ta

larisa [96]

The interpretation of y = 9.5x is that: (a) For each 1 minute, the runner ran 9.5 miles.

<h3>How to interpret the equation?</h3>

The equation of the line of best fit is given as:

y = 9.5x

Divide both sides by x

9.5 = y/x

From the question, we have:

x ⇒ number of miles run
y ⇒ time

This means that:

9.5 = number of miles run/time

Hence, the interpretation of y = 9.5x is that: (a) For each 1 minute, the runner ran 9.5 miles.