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3 years ago

6

In the standard x,y plane, a circle has a radius 6 and center (7, 3). The circle intersects the x-axis at (a, 0) and (b, 0). Wha

t is the value of a + b?

1 answer:

arsen [322]3 years ago

4 0

Answer: The required value of a+b is 14.

Step-by-step explanation: Given that in the standard xy plane, a circle has a radius 6 and center (7, 3).

The circle intersects the x-axis at (a, 0) and (b, 0).

We are to find the value of a+b.

We know that

the standard equation of a circle with center at (h, k) and radius r units is given by

$(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

For the given circle, we have

(h, k) = (7, 3) and r = 6 units.

So, from equation (i), we get

$(x-7)^2+(y-3)^2=6^2\\\\\Rightarrow (x-7)^2+(y-3)^2=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Since the circle (ii) passes through the points (a, 0) and (b, 0), so let the point be denoted by (c, 0), then we have

$(c-7)^2+(0-3)^2=36\\\\\Rightarrow (c-7)^2+9=36\\\\\Rightarrow (c-7)^2=27\\\\\Rightarrow c-7=\pm3\sqrt3~~~~~~~~~~~~~~~~~~~~~~[\textup{Taking square root on both sides}]\\\\\Rightarrow c=7\pm3\sqrt3$

Therefore, we get

$a=7+3\sqrt3,\\\\b=7-3\sqrt3.$

That is,

$a+b=(7+3\sqrt3)+(7-3\sqrt3)=14.$

Thus, the required value of a+b is 14.

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Each small box has 12 granola bars and each large box has 30 granola bars. The camp bought 2 more large boxes than small boxes,

sweet-ann [11.9K]

Answer:

The camp Purchased 2 small boxes and 4 large boxes.

Step-by-step explanation:

Let Number of Small box purchased be x.

Now Given:

The camp bought 2 more large boxes than small boxes.

Hence Number of large box purchased = $x+2$

Also Given:

Total Number of Granola bars = 144

Now Each small box has 12 granola bars and each large box has 30 granola bars.

Hence Total Number of Granola bars is equal to sum of number of granola bars in each small box multiplied by number of small box and number of granola bars in each large box multiplied by number of larger box.

Hence equation can be framed as.

$12x+30(x+2)=144$

Now we will use distributive property to solve the same we get;

$12x+30x+30\times2 =144$

Now Using multiplication propert we get;

$12x+30x+60=144$

Now Combining like terms we get;

$12x+30x=144-60\\$

Now By using Addition and Subtraction property we get;

$42x=84$

Now Using Division property we get;

$\frac{42x}{42}=\frac{84}{42}\\\\x=2$

Number of Small boxes purchased = 2

Number of Large boxes purchased = $x+2=2+2=4$

Hence The camp Purchased 2 small boxes and 4 large boxes.

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3 years ago

Diameter of sphere is 8cm it is beaten and drawn out to a diameter of 2 mm find length of wire

m_a_m_a [10]

<span>Diameter of the sphere = 8 cm. Therefore, the radius of the sphere = 8/2 = 4 cm Volume of the sphere = 4/3 * 22/7 * 3 * 3 * 3 cu. cm. The sphere is beaten and drawn into a wire, the wire is cylinder of the diameter = 0.2 cm Area of the base of the cylinder = pi * r2 = 22/7 * 0.2 * 0.2 sq. cm volume of the wire = pi * r2 * I = 22/7 * 0.2 * 0.2 * 1 Therefore, 22/7 * 0.2 * 0.2 * I = 4/3 * 22/7 * 4 * 4 * 4 Therefore I = 4/3 * 22/7 * 4 * 4 * 4 * 7/22 * 1/0.04 I = 256/3 * 1/0.04 I = 2113 cm</span>

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4 years ago

Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2X - 3Y = 6 at X = 3

Shtirlitz [24]

so these two lines intersect at x = 3 hmmmm what's the y-coordinate of the second line at that point?

$\bf 2x-3y=6\implies \stackrel{\textit{using x = 3}}{2(3)-3y=6}\implies 6-3y=6\implies -3y=0\implies y=0$

so the y-coordinate of that second line is 0, so the point there is (3, 0) then.

so the first line is, a line that has a slope of 2 and passes through (3, 0).

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=2(x-3)\implies y=2x-6$

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3 years ago

33. Suppose that the scores on a statewide standardized test are normally distributed with a mean of 78 and a standard deviation

tino4ka555 [31]

Given the scores on a statewide standardized test are normally distributed

Mean = μ = 78

Standard deviation = σ = 3

Normalize the data using the z-score by using the following formula and chart:

$z=\frac{x-\mu}{\sigma}$

Estimate the percentage of scores of the following cases:

(a) between 75 and 81

so, the z-score for the given numbers will be:

$\begin{gathered} 75\rightarrow z=\frac{75-78}{3}=\frac{-3}{3}=-1 \\ 81\rightarrow z=\frac{81-78}{3}=\frac{3}{3}=1 \end{gathered}$

As shown, the percentage when (-1 < z < 1) = 68%

(b) above 87

$87\rightarrow z=\frac{87-78}{3}=\frac{9}{3}=3$

The percentage when (z > 3) = 0.5%

(c) below 72

$72\rightarrow z=\frac{72-78}{3}=\frac{-6}{3}=-2$

The percentage when (z < -2) = 0.5 + 2 = 2.5%

(d) between 75 and 84

$\begin{gathered} 75\rightarrow z=\frac{75-78}{3}=-\frac{3}{3}=-1 \\ 84\rightarrow z=\frac{84-78}{3}=\frac{6}{3}=2 \end{gathered}$

The percentage when ( -1 < z < 2 ) = 68 + 13.5 = 81.5%

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1 year ago

Please help me! No links as answers please. Find the expected value: Tim wins $3 if a coin toss shows heads or $2 if it shows ta

amm1812

The answer and the expected value is $2.50

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3 years ago