The equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].
What is the general equation for the circle?The general equation of the circle is [tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex].
Where, (h, k) is the center and r is the radius of the circle.
Let the equation of the circle be
[tex](x-h)^{2} +(y-k)^{2} =r^{2}..(i)[/tex]
According to the given question.
The center of the circle is (-8, 15).
⇒ (h, k) = (-8, 15)
And, the circle is passing through origin i.e. (0, 0).
Since, the center of the circle is (-8, 15).
So, the equation (i) can be written as
[tex](x-(-8))^{2} +(y - 15)^{2} = r^{2}[/tex]
Also, the circle is passing through (0, 0).
Therefore,
[tex](0+8)^{2} +(0-15)^{2} = r^{2}[/tex]
[tex]\implies 64+ 225 = r^{2} \\\implies 289 = r^{2} \\\implies r=\sqrt{289} \\\implies r = 17[/tex]
So, the radius of the circle is 17 unit and its center is (-8, 15).
Therefore, the equation of the circle is
[tex](x+8)^{2} +(y-15)^{2} = 289[/tex]
Hence, the equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].
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Which set of side lengths is a Pythagorean triple?
1)1,3, 10
2)4,5,9
3)9, 40, 41
4)16, 30, 44
[tex]\huge{\boxed{\text{3) \bf{9, 40, 41}}}}[/tex]
A Pythagorean triple is a set of three numbers where [tex]a^2 + b^2 = c^2[/tex].
Trying 1:
[tex]1^2+3^2=10^2[/tex]
[tex]1+9=100[/tex]
[tex]10=100[/tex]
Incorrect.
Trying 2:
[tex]4^2+5^2=9^2[/tex]
[tex]16+25=81[/tex]
[tex]41=81[/tex]
Incorrect.
Trying 3:
[tex]9^2+40^2=41^2[/tex]
[tex]81+1600=1681[/tex]
[tex]1681=1681[/tex]
Correct!
Trying 4: (unnecessary, but practice is good)
[tex]16^2+30^2=44^2[/tex]
[tex]256+900=1936[/tex]
[tex]1156=1936[/tex]
Incorrect.
What would be a common mistake when solving this problem? 3(x-3) <3
Answer:
Incorrectly distributing the 3 and (x-3).
Step-by-step explanation:
A common mistake when solving 3(x-3) <3 would be incorrectly distributing the 3 and (x-3).
A rectangle is enlarged by a factor of 6 that originally has the area of 20in squared. What is the area of the enlarged rectangle?
A: 120in squared
B: 720in squared
C: 2,400in squared
D: 14,400in squared
Answer:
The person on top is wrong the answer is 14,400 in.² or D
Step-by-step explanation:
The correct option is B. 720in squared. The area of the rectangle, when enlarged by a factor of 6, scales by the square of 6, resulting in an enlarged area of 720 square inches.
To determine the area of a rectangle after it has been enlarged by a factor, we need to understand how area scales with respect to the linear dimensions. When a shape is enlarged by a factor, the area scales by the square of that factor.
Given:
→ Original area = 20 square inches
→ Enlargement factor = 6
Steps to Find the Enlarged Area:
→ Calculate the scaling factor for the area:
= 6²
= 36.
→ Multiply the original area by this scaling factor:
= 20 in² * 36
= 720 in².
Therefore, the area of the enlarged rectangle is 720 square inches, which corresponds to answer choice B.
WILL GIVE BRAINLEIST NEED TO TURN IN BY 9 P.M. PLS HURRY SUPER EASYIdentify the equation that does not belong with the other three. Explain your reasoning.
A. 6+x=9 B. 15=x+12 C. x+9=11 D. 7+x=10
Answer:
C. x + 9 = 11
Step-by-step explanation:
We are trying to identify which of the equations does not match with the others. In this case, solve for x in each equation:
Option A):
6 + x = 9
Subtract 6 from both sides:
6 (-6) + x = 9 (-6)
x = 9 - 6
x = 3
Option B):
15 = x + 12
Subtract 12 from both sides:
15 (-12) = x + 12 (-12)
15 - 12 = x
x = 3
Option C):
x + 9 = 11
Subtract 9 from both sides:
x + 9 (-9) = 11 (-9)
x = 11 - 9
x = 2
Option D):
7 + x = 10
Subtract 7 from both sides:
x + 7 (-7) = 10 (-7)
x = 10 - 7
x = 3
---------------------------------------------------------------------------------------------------------
As you can tell, all the equations end with x = 3 as there answers except C. x+9=11, making (C) your answer.
~
Jason deposits $5 into his savings account twice a week for 6 weeks. How much money will he have saved after 6 weeks?
Let s stand for the amount of money saved.
Equation:
How much money did he save?
Show your work.
First person who answers gets to be followed and marked brainliest.
Answer:
$60
The equation is x(5(2))=s or x(10)=s when x = number of weeks
Step-by-step explanation:
For 6 weeks, all you have to do is plug in the 6 where the x is.
6(5(2)) = s
6(10) = s
60 = s
or
6(10) = s
60 = s
2. Write and solve an equation to find the value of x.
3.8, 4.2, 5.3, x; mean 4.8
Answer:
5.9
Step-by-step explanation:
The mean means arithmetic average (some people just say average here).
The average of 4 numbers is the sum of those 4 numbers divided by the number of numbers which is 4 in this case.
So we have this formula:
[tex]\frac{3.8+4.2+5.3+x}{4}=4.8[/tex]
Multiply both sides by 4:
[tex]3.8+4.2+5.3+x=4(4.8)[/tex]
Simplify:
[tex]13.3+x=19.2[/tex]
Subtract 13.3 on both sides:
[tex]x=19.2-13.3[/tex]
Simplify:
[tex]x=5.9[/tex]
Complete the equation ....
URGENT NEED HELP ON THIS PROBLEM ASAP!!!
Answer:
h(x) = 7 * (9/7) ^x
Step-by-step explanation:
h(x) = a b^x
When x=0 h(x) = 7
7 = a * b^0
7 = a *1
7 =a
Rewriting the equation
h(x) = 7 b^x
Let x=1
9 = 7 * b^1
9 = 7 * b
Divide each side by 7
9/7 =7b/7
9/7 =b
h(x) = 7 * (9/7) ^x
Can u help me solve this
Explanation:
Rewrite the left side in terms of sine and cosine, then rearrange.
[tex](1+\tan^2{A})+(1+\dfrac{1}{\tan^2{A}})=\dfrac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\dfrac{\sin^2{A}}{\cos^2{A}})+(1+\dfrac{\cos^2{A}}{\sin^2{A}})=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\dfrac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\dfrac{1}{\cos^2{A}}+\dfrac{1}{\sin^2{A}}=\\\\\dfrac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\dfrac{1}{(\sin^2{A})(1-\sin^2{A})}=\dfrac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}[/tex]
Find the domain the function graphed below. Express in interval notation.
Domain:
The domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.
What are the domain and range of a function?• Domain is the set of values for which the given function is defined.
• Range is the set of all values which the given function can output.
What is the domain of the given function?Since the dark point of the function show that is the beginning of the function therefore the function will be defined from that point to all values of x but will not be defined at the point where there is a blank dot, also, the function is defined till the line is drawn.
Thus, the domain of the function will be,
Domain: [-1,2]-{2}
Hence, the domain of the function can be written as [-1,2]-{2}, therefore the function is defined from -1 to 2 except 2.
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For the function y=-3+ cos (x + 4)], what is the minimum value?
Answer:
-4 is the mimumum of y=-3+cos(x+4)
Step-by-step explanation:
The minimum value of y=cos(x) is -1.
The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.
The minimum value of y=-3+cos(x+4) is -3-1 which is -4. This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. W(3,3) V(3,4) U(5,4) Rotation: 90∘ counterclockwise about the origin. W′( , ) V′( , ) U′( , )
Answer:
W'(-3,3) V'(-4,3) U'(-4,5)
Step-by-step explanation:
The mapping for 90 degrees counterclockwise rotation is;
[tex](x,y)\to (-y,x)[/tex]
The given points have coordinates: W(3,3) V(3,4) U(5,4)
[tex](x,y)\to (-y,x)[/tex]
This implies that:
[tex]W(3,3)\to W'(-3,3)[/tex]
[tex]V(3,4)\to V'(-4,3)[/tex]
[tex]U(5,4)\to U'(-4,5)[/tex]
The required points of the image are:
W'(-3,3) V'(-4,3) U'(-4,5)
1. A plane flew 3,200 miles in 5 hours.
How fast was it flying?
Use the formula d = rt.
Answer:
640 miles per hour.
Step-by-step explanation:
I calculated this by 3200/5
Is this appropriate?
Find f(-2) for f(x) = 2 • 3 ^x
А. -18
B. 2/9
C. 1/18 D. -36
Answer:
2/9
Step-by-step explanation:
We have [tex]f(x)=2 \cdot 3^x[/tex] and are asked to find [tex]f(-2)[/tex].
[tex]f(-2)[/tex] means to replace x with -2 and evaluate the expression named f.
Let's do that:
[tex]f(x)=2 \cdot 3^x[/tex]
[tex]f(-2)=2 \cdot 3^{-2}[/tex]
[tex]f(-2)=2 \cdot \frac{1}{3^2}[/tex]
[tex]f(-2)=2 \cdot \frac{1}{9}[/tex]
[tex]f(-2)=\frac{2}{9}[/tex]
Answer:
2/9
Step-by-step explanation:
Given:
[tex]f(x)=2*3^x[/tex][tex]f(-2)[/tex]We'd substitute x with -2:
[tex]2 *3^{-2}[/tex]
Using order of operations, we'd solve the exponent first:
[tex]3^{-2}=.111[/tex](repeating)
Multiply by 2:
.111(repeating) * 2 = 2/9
Our answer is 2/9
Evan has an exam worth fifteen percent of his grade. He has an overall grade of 84.7 percent. The exam has 40 questions. How many questions does he need to get right in order to pass with an overall grade of 70?
Answer:
He needs to get 1 right
Step-by-step explanation:
1/40 is equal to .025. This means the other 39/40 incorrect ones are worth .975(97.5%). If we multiply the .975 by the 15 percent of his overall grade, we get 14.625. When you subtract this from the overall grade, you get 70.075, which is just above a 70%.
For this case we have that the general qualification is 70, of it Evan has accumulated 84.7%. Making a rule of three:
70 ----------> 100%
x -------------> 84.7%
Where "x" represents the rating that Evan has accumulated:
[tex]x = \frac {84.7 * 70} {100}\\x = 59.29\\70-59.29 = 10.71[/tex]
Evan is missing 10.71 to get 70.
In percentage, we have to:
100% -84.7% = 15.3%
Now we have that the exam represents 15% of the grade, this is divided into 40 questions.
It is observed that Evan must correctly answer the 40 questions of the exam, so he would get 15%. Even so, it would lack a 0.3% note to reach 70.
Answer:
He must answer the 40 questions correctly.
6. A square is inscribed in a circle. The sic
length of the square is 4 centimeters,
Calculate the area of the shaded region.
Answer:
9.13 cm^2.
Step-by-step explanation:
The diagonal of the square = the diameter of the circle.
The length of the diagonal = 4√2 cm (because we have a 45-45-90 triangle), so the radius of the circle is half of this = 2√2 cm.
The area of the shaded part = area of the circle - area of the square
= π (2√2)^2 - 4^2
= 25.13 - 16
= 9.13 cm^2.
Can anyone show me how to do this or do it for me ill give brainlist
Answer: x^2-6x-8
Step-by-step explanation:
Step 1 : Factor - x^3-11x^2+22x+40: (x-5)(x^2-6x-8)/(x-5)
Step 2 : Divide, which should give you x^2-6x-8
7. How much 6% solution can you make by diluting 350 mL of a 15% solution
Answer:
We know that the formula to mix chemical solutions is: C1V1 = C2V2
where C represents the concentration of the solute, and V represents volume in milliliters or ml.
In this case, we have:
0.06V1 = 0.15×350
Solving for 'V1' we have:
V1 = (0.15×350)/0.06 = 52.5/0.06 = 875
Therefre I can make 875 mL of a 6% solution by diluting 350 mL of a 15% solution.
A large map of the United States uses a scale of $2 \text{ cm} = 2.5\text{ km}$. On the map, the distance between two cities is 1 meter. What is the actual distance between the two cities (in kilometers)? PLZ ANSWER NOW CORRECTLY FAST ILL GIVE 40 POINTSS!!!!!!! PLZZZZZZZZZZZZZZZZZZZZZ
Answer: (AoPS)
125
Step-by-step explanation:
A distance of 1 meter is 50 times 2 cm, so the actual distance between the two cities is 50 times 2.5 km, which is 125 km.
To find the actual distance between two cities on a map given a scale, convert the map distance to real-world distance using the scale ratio.
The actual distance between two cities on the map can be calculated as follows:
Given scale: 2 cm = 2.5 kmDistance on the map: 1 meterConvert meters to centimeters (1 meter = 100 cm)Use the scale to convert centimeters on the map to kilometers in realitySo, the actual distance between the two cities is 1.25 kilometers.
Parallelogram FGHJ was dilated and translated to form
similar parallelogram F'G'H'J'.
What is the scale factor of the dilation?
Answer: The required scale factor of the dilation is 4.
Step-by-step explanation: Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.
We are to find the scale factor of the dilation.
From the graph, we note that
JH = 2 units and J'H' = 8 units.
We know that
[tex]\textup{Scale factor of dilation}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the correponding side of the original figure}}.[/tex]
Therefore, the scale factor of the given dilation is
[tex]S=\dfrac{J'H'}{JH}\\\\\\\Rightarrow S=\dfrac{8}{2}\\\\\Rightarrow S=4.[/tex]
Thus, the required scale factor of the dilation is 4.
Answer:
4 on edge
Step-by-step explanation:
Suppose a life insurance policy costs $24 for the first unit of coverage and then $6 for each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage. What will 10 units of coverage cost?
Answer:
C(x) =24+6(z-1) where z is the total of units sold.
Therefore if z=10 units, the answer is: C(x)=24+6(10-1)
Or 24+6(9)
Or $78
Step-by-step explanation:
Answer:
10 Units would cost $78
Step-by-step explanation:
We will be using the following equation to solve this problem
[tex]C(x) = 24+6(x-1)[/tex]
Where x will be the amount of units of coverage that are sold. The equation subtracts 1 from the amount of units sold (since the first unit costs $24) and multiplies that by $6 which is the cost per unit. Then it adds $24 to that, which gives us the total cost.
Since we sold 10 units of coverage we plug that into the equation
[tex]C(10) = 24+6(10-1)[/tex]
[tex]C(10) = 24+6(9)[/tex]
[tex]C(10) = 24+54[/tex]
[tex]C(10) = 78[/tex]
So 10 units of coverage sold would cost $78
Find the solution(s) to 2x2 – 5x – 3 = 0.
Answer:
x = - [tex]\frac{1}{2}[/tex], x = 3
Step-by-step explanation:
Given
2x² - 5x - 3 = 0 ← in standard form
Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 3 = - 6 and sum = - 5
The factors are - 6 and + 1
Use these factors to split the x- term
2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term
(x - 3)(2x + 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
x - 3 = 0 ⇒ x = 3
PLEASE HELP 30 POINTS!! AND BRAINLIEST ASAP
What is an equation of the line that is perpendicular to 3x+y=−5 and passes through the point (3, −7) ?
Enter your equation in the box.
Answer:
y = 1/3x -8
Step-by-step explanation:
3x+y=−5
First we need to get the equation in slope intercept form to find the slope
Subtract 3x from each side
3x-3x+y=-3x−5
y = -3x-5
The slope is -3
We want a line perpendicular. Perpendicualr lines have slopes that are the negative reciprocal. Take the negative reciprocal
m new = - (1/-3) = 1/3
The slope of the new line is 1/3
We have the slope (1/3) and a point (3,-7)
We can use the point slope form for the equation of a line
y-y1 = m(x-x1)
y--7 = 1/3 (x-3)
y+7 = 1/3 (x-3)
or if we want the slope intercept form
Distribute
y+7 = 1/3x -1
Subtract 7 from each side
y+7-7 = 1/3x -1-7
y = 1/3x -8
• Which of the following equations represents a line that is perpendicular to
y = --4x+9 and passes through the point, (4, 5)?
A. y = -4x+4
B. y = 1/4x+5
C. y = 1/4x+4
D. y = 1/4x+6
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 9 ← is in slope- intercept form
with slope m = - 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (4, 5) into the partial equation
5 = 1 + c ⇒ c = 5 - 1 = 4
y = [tex]\frac{1}{4}[/tex] x + 4 ← equation of perpendicular line → C
Twenty-seven less than twice a number is -1
Answer: 13
Step-by-step explanation:
2x-27=-1
2x=26
X=13
The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given,
Twenty-seven less than twice a number is -1
Let's say that number is x.
Twice of x = 2x
27 less will be 2x - 27
It is equal to -1.
2x - 27 = -1
2x = -1 + 27
2x = 26
x = 13
Hence "The expression of the given mathematical phrase Twenty-seven less than twice a number is -1 is 2x - 27 = -1 and that number will be 13".
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Since 2002, the number of a telephone company’s customers using a landline has been decreasing by 10% per year. Which of these statements are correct? Select all that apply.
1. To find the number of landline customers in 2004, you can multiply the number of landline customers in 2002 by 0.81.
2. To find the number of landline customers in 2004, you can subtract the product of 0.2 and the number of landline customers in 2002 from the number of landline customers in 2002.
3. To find the number of landline customers in 2003, you can multiply the number of landline customers in 2002 by 0.9
4. To find the number of landline customers in 2003, you can subtract the product of 0.1 and number of landline customers in 2002 from the number of landline customers in 2002.
1 and 3 I believe are the correct answers
Answer:
Option 1 , Option 3 and Option 4 are correct.
Step-by-step explanation:
Number of customers using landlines decreases 10% per year.
Let x be the umber of customers using landlines in 2002.
⇒ Number of customer using landlines in 2003 = [tex]x-\frac{10}{100}\times x[/tex]
= [tex]x-0.1x[/tex]
= 0.9x
Number of customers using landlines in 2004 = [tex]0.9x-\frac{10}{100}\times 0.9x[/tex]
= [tex]0.9x-0.1\times0.9x[/tex]
= [tex]0.9x-0.09x[/tex]
= [tex]0.81x[/tex]
Therefore, from this Option 1 , Option 3 and Option 4 are correct.
The graph of f(t) = 5•2^t shows the value of a rare coin in year t What is the
meaning of the yintercept?
Answer:
D.
Step-by-step explanation:
The y-intercept is where the graph crosses the y-axis.
It crosses the y-axis at (0,5).
The graph is of f(t)=5*2^t where t is the number of years and the value of f(t) is the value of that coin after t years.
So we have (0,5) is on the graph of f which means f(0)=5.
f(0)=5 means at t=0 years the value of the coin is $5.
As per the y-intercept of a function, when the coin was purchased, the value of it was $5.
What is the y-intercept of a function?"The y-intercepts are points where the graph of a function crosses or touches the y-axis of the Cartesian Plane. "
The given function is
[tex]f(t)=5(2^{t})[/tex]
As per the graph of the given function, it starts from the point (0, 5).
Hence, it cuts the y-axis at point (0, 5).
Therefore, at the time of purchasing the coin, the value of the coin was at $5.
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What is the value of sec
in the triangle below?
41 ft
9 ft
40 ft
Answer:
C
Step-by-step explanation:
[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } \\ \\ \sec( \alpha ) = \frac{1}{ \frac{ad}{hip} } \\ \\ \sec( \alpha ) = \frac{hip}{ad} \\ \\ \sec( \alpha ) = \frac{41}{40} [/tex]
The value of the secθ is 41/40.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The diagram shows the right-angled triangle.
The sides of the right-angled triangle are
Hypotenuse side = 41 ft
Opposite side = 9 ft
Adjacent side = 40 ft
The value of secθ is
[tex]sec \theta =\frac{1}{cos \theta}[/tex]
where, [tex]cos \theta =\frac{adjacent}{hypotenuse}[/tex]
⇒ [tex]sec \theta =\frac{hypotenuse}{adjacent}[/tex]
⇒ [tex]sec \theta =\frac{41}{40}[/tex]
Hence we can conclude that the value of the secθ is 41/40.
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A car is traveling at a rate of 99 kilometers per hour. What is the car's rate in meters per second? How many meters will the car travel in 10 seconds? Do not
round your answers.
Answer:
27.5 m/s
275 m
Step-by-step explanation:
99 km/hr × (1000 m / km) × (1 hr / 3600 s) = 27.5 m/s
Distance = rate × time
d = 27.5 m/s × 10 s
d = 275 m
For f(x) = 2x+1 and g(x) = x2 - 7, find (f+9)(x).
Answer:
[tex]\large\boxed{(f+g)(x)=x^2+2x-6}[/tex]
Step-by-step explanation:
[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\(f+g)(x)=(2x+1)+(x^2-7)=2x+1+x^2-7=x^2+2x-6[/tex]
PG¯¯¯¯¯¯¯¯=9 in. The radius of the circle is 41 inches. Find the length of CT¯¯¯¯¯¯¯.
A. 40
B. 9
C. 80
D. not enough information
See the attached picture for the solution.
Answer:
Option: C is the correct answer.
C. 80
Step-by-step explanation:
PG=9 in. The radius of the circle is 41 inches.
We know that the side CT is given by:
CT=CS+ST
The side CS is calculated by using the Pythagorean Theorem in ΔCSP
i.e.
[tex]CP^2=CS^2+SP^2\\\\i.e.\\\\[/tex]
as CP is the radius of the circle
and SP=PG=9 in.
i.e.
[tex]41^2=9^2+CS^2\\\\i.e.\\\\1681=81+CS^2\\\\i.e.\\\\CS^2=1681-81\\\\i.e.\\\\CS^2=1600\\\\i.e.\\\\CS=40\ units[/tex]
and
similarly in right angled triangle ΔPST
we have:
[tex]TP^2=ST^2+PS^2\\\\i.e.\\\\41^2=9^2+ST^2\\\\i.e.\\\\ST=40\ units[/tex]
Hence,
[tex]CT=CS+ST\\\\i.e.\\\\CT=40+40\\\\i.e.\\\\CT=80\ in.[/tex]