Crater Lake Oregon is a roughly circular lake. The lake basin formed about 7000 years ago when the top of a volcano exploded in an immense explosion. Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2). Find the coordinates of the center of the lake.

Answers

Answer 1

Answer: To solve the problem we must find the equation of the circumference of the form:
(Xa) ² + (Yb) ² = r²
They do not give us the center or the radio, but we have 3 points.
With the points H (-4,1), G (-2, -3) and C (5, -2) we find 3 equations
1) (-4-a) ² + (1-b) ² = r²
2) (-2-a) ² + (-3-b) ² = r ²
3) (5-a) ² + (-2-b) ² = r ²
Now we have a system of 3 equations with 3 unknowns: r, a, b
When solving the system we have to:
r = 5
a = 1
b = 1
Therefore, the center of the circumference of the lake is the point (a, b)
That is, the point (1,1)

Answer 2

Answer:

Answer:

The coordinates of the center of the lake are $((-1)/(3),(-4)/(3))$ .

Step-by-step explanation:

It is given that Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2).

If we joint these points, then we get a triangle and the center of a triangle is known as centroid.

The formula for centroid of a triangle is

$Centroid=((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3))$

The centroid of the triangle H(-4,1), G(-2,-3), and C(5,-2) is

$Centroid=((-4-2+5)/(3),(1-3-2)/(3))$

$Centroid=((-1)/(3),(-4)/(3))$

Therefore the coordinates of the center of the lake are $((-1)/(3),(-4)/(3))$ .

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Miles and Nick each separately apply for and receive loans worth $5,000 apiece. Miles has a very good credit score, so his loan has an APR of 7.75%, compounded monthly. Nick’s credit score is rather low, so his loan has an APR of 13.10% interest, compounded monthly. If both of them repay their loans over a four year period, making equal monthly payments based on their own loan, how much more will Nick have paid than Miles? (Round all dollar values to the nearest cent.) a.$619.68 b.$267.50 c.$1,609.57 d.$1,070.00

Answers

Answer:

Ans. Nick paid $619.68 more than Miles (exactly $619.54). So the answer is A)

Step-by-step explanation:

Hi, first we need to find the equal monthly payments for both, Miles and Nick, for that, we need to find the effective monthly rate (because the payments are going to be made monthly), also, we need to convert that 4 year period into months. After doing all that, we need to use the following equation and solve for "A".

$Present Value=(A((1+r)^(n) -1))/(r(1+r)^(n) )$

Where:

A= monthly payments

r= rate of interest (for Miles is 0.075/12=0.006458 and Nick 0.131/12=0.010916)

n= number of periodic payments (both are 4*12=48 months)

First, let´s find out how much money Miles has to pay every month.

$5,000=(A((1+0.00645833)^(48) -1))/(0.00645833(1+0.00645833)^(48) )$

$5,000=A(41.1594758)$

$A=121.48$

So, Miles has to pay $121.48 every month, for 48 months, that is a total of $5,830.98 (121.48*48=5,830.98)

Now, let´s do Nick

$5,000=(A((1+0.01091667)^(48) -1))/(0.01091667(1+0.01091667)^(48) )$

$5,000=A(37.2063189)$

$A=134.39$

So, Nick has to pay $134.39 every month, for 48 months, that is a total of $6,450.52 (134.39*48=6,450.52)

The difference is 6,450.52- 5,830.98=619.54

Means that Nick has to pay $619.54 more than Miles. To your answers, the closest is A) $619.68.

Best of luck

Miles:7.75% (0.0775) x 5,000 = $387.5 x 4 = $1550 (over four year period)Nick:13.10% (0.131) x 5,000 = $655 x 4 = $2620$2620 - $1550 = $1,070 (rounded to nearest cent)So the answer is D.

Ace_santiagoFigure TUVW ≌ figure TꞌꞌUꞌꞌVꞌꞌWꞌꞌ.

Which sequence of transformations was performed on figure TUVW to produce figure TꞌꞌUꞌꞌVꞌꞌWꞌꞌ?

A.
TUVW was reflected across the x-axis and then rotated 270° clockwise about the origin.

B.
TUVW was translated 3 units to the left and 2 units down and then reflected across the x-axis.

C.
TUVW was rotated 90° counterclockwise about the origin and then translated 4 units to the right.

D.
TUVW was translated 2 units right and 3 units up and then reflected across the y-axis.

Answers

The right answer for the question that is being asked and shown above is that: "C. TUVW was rotated 90° counterclockwise about the origin and then translated 4 units to the right." This is the sequence of transformations was performed on figure TUVW to produce figure TꞌꞌUꞌꞌVꞌꞌWꞌꞌ

to meet building codes, a building must have a roof no taller than 96 feet.an architect is designing an office building with an 18 3/4 foot ground floor, and 11 ft. 8 inch upper floors. How many floors , including ground floor, can the building have?

Answers

$96ft-18(3)/(4)ft=77(1)/(4)ft\n\n11ft\ 8in=11(8)/(12)ft=11(2)/(3)ft\n\n77(1)/(4):11(2)/(3)=(309)/(4):(35)/(3)=(309)/(4)\cdot(3)/(35)=(927)/(140)=6(87)/(140)\n\nAnswer:ground\ floor\ and\ 6\ upper\ floors.$

Help the image says it all

Answers

Answer:

use distance formula and solve it

Step-by-step explanation:

this formula is in co ordinate geometry class 10 ncert book

Answer:

5 sqrt(10) square units

Step-by-step explanation:

The coordinates of the points A, B, and C are (-6,-2), (2,-8), and (-4,-6), respectively.

To find the area of a triangle, we can use the following formula:

Area of a triangle = 1/2 * base * height

We can use the distance formula to find the length of the base, which is AB:

$d(A,B) = sqrt((x2 - x1)^2 + (y2 - y1)^2)$

Substituting the coordinates of A and B, we get:

$d(A,B) = sqrt((2 - (-6))^2 + (-8 - (-2))^2) = sqrt(64 + 36) = 10$

Now, we need to find the height of the triangle. The height of a triangle is the perpendicular distance from a vertex to the opposite base. In this case, we can draw a perpendicular line from C to AB:

[Image of triangle ABC with line segment CD drawn perpendicular to AB]

The length of CD is the height of the triangle. We can use the distance formula to find the length of CD:

$d(C,D) = sqrt(((-7) - (-4))^2 + (-5) - (-6))^2) = sqrt(9 + 1) = sqrt(10) \n$

Now, we can find the area of the triangle:

Area of triangle ABC = 1/2 * base * height = 1/2 * 10 * sqrt(10) = 5 * sqrt(10)

Therefore, the area of triangle ABC is 5 square roots of 10 square units.

NOTEIFYOUFINDTHISANSWERUSEFULLINANYWAYTHENPLEASECONSIDERGIVE5STARTANDNOTFORGETTOMAEKASBRAINIST.THISSMALLSTEPSEEMSEASYBUTHAVEAGREATIMPACTONSOMEONE.

The sum of the first 10 terms of an arithmetic sequence is 235 and thesum of the second 10 terms is 735. Find the first term and the common

difference.

Answers

If the sum of the first 10 terms of an arithmetic sequence is 235 and the sum of the second 10 terms is 735. The first term of the arithmetic sequence is -21.5 and the common difference is 10.