Given:
The vector
[tex]v=<-3,8>[/tex]Required:
To find the unit vector u with the same direction.
Explanation:
Unit formula is the vector is divided by its magnitude.
Now the magnitude of v is,
[tex]\begin{gathered} mag.v=\sqrt{(-3)^2+8^2} \\ =\sqrt{9+64} \\ =\sqrt{73} \end{gathered}[/tex]Now the unit vector is,
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Final Answer:
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]The volume of cylinder is 504 pi cm^(3) & height is 14cm Find the curved surface area 8 total surface area.
The Solution:
The correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Given that the volume of a cylinder with height 14cm is
[tex]504\pi cm^3[/tex]We are required to find the curved surface area and the total surface area of the cylinder.
Step 1:
We shall find the radius (r) of the cylinder by using the formula below:
[tex]V=\pi r^2h[/tex]In this case,
[tex]\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]504\pi=\pi r^2\times14[/tex]Finding the value of r by first dividing both sides, we get
[tex]\begin{gathered} \frac{504\pi}{14\pi}=r^2 \\ \\ r^2=36 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{r^2}\text{ =}\sqrt[]{36} \\ \\ r=6\operatorname{cm} \end{gathered}[/tex]Step 2:
We shall find the curved surface area by using the formula below:
[tex]\text{CSA}=2\pi rh[/tex]Where
[tex]\begin{gathered} \text{ CSA=curved surface area=?} \\ h=14\operatorname{cm} \\ r=6\operatorname{cm} \end{gathered}[/tex]Substituting these values in the formula above, we have
[tex]\text{CSA}=2\times6\times14\times\pi=168\pi=527.788\approx527.79cm^2[/tex]Step 3:
We shall find the total surface area by using the formula below:
[tex]\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh[/tex]Where
TSA= total surface area and all other parameters are as defined earlier on.
Substituting in the formula, we get
[tex]\text{TSA}=(2\pi\times6^2)+(2\pi\times6\times14)=72\pi+168\pi[/tex][tex]\text{TSA}=240\pi=753.982\approx753.98cm^2[/tex]Therefore, the correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
please help me solve this no tutor can ahelp me
Solution:
Since the confidence interval width is inversely proportional to n , the answer is the smallest n.
CORRECT OPTION: 36
Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680Find the probabilities.P (X>45,500)
A square has side length (2x+3). The perimeter is 60cm. Find the length of one side in centimetres
As given by the question
There are given that the side length is (2x+3) and perimeter is 60 cm.
Now,
From the formula of perimeter:
[tex]\text{Perimeter =4}\times side[/tex]So,
[tex]\begin{gathered} \text{Perimeter =4}\times side \\ 60=4\times(2x+3) \\ 60=8x+12 \\ 8x=60-12 \\ 8x=48 \\ x=\frac{48}{8} \\ x=6 \end{gathered}[/tex]Then,
Put the value of x into the given side length (2x+3)
So,
[tex]\begin{gathered} 2x+3=2\times6+3 \\ =12+3 \\ =15 \end{gathered}[/tex]Hence, the one side of length is 15 cm.
Consider the following equation find the X- and y- Intercepts, if possible
Answer:
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Explanation:
The x-intercept is the point where the graph crosses the x-axis, so to find the x-intercept, we need to replace y = 0 on the given equation and solve for x
y - 2x = 1
0 - 2x = 1
-2x = 1
-2x/(-2) = 1/(-2)
x = -1/2
Then, the x-intercept is (-1/2, 0)
The y-intercept can be calculated replacing x = 0 and solving for y, so
y - 2x = 1
y - 2(0) = 1
y - 0 = 1
y = 1
Then, the y-intercept is (0, 1)
Therefore, the answers are
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Which equation could be represented by the number line? O A. -5 + 7 = 2 O.B. -3+(-4)= -7 O C. 4+ (-7)=-3 O D.7+(-6) = 1 SURAT E PREVIOUS
C. 4 + (-7) = -3
C. 4 + (-7) = -3 could represent by the number line because no other equation has reflected the lines' displacement of 7 grid from a certain point going to the left which is equivalent to -7.
The rest of the choices is not a possible equation to the line.
A. -5 + 7 = Displacement of 7 Grid to the Right from Point -5
B. -3 - 4 = Displacement of 4 Grid to the Left from Point -3
D. 7 - 6 = Displacement of 6 Grid to the Left from Point 7
A store is having a " 15 % off sale on perfume . You have a coupon for 50 % off any perfume . What is the final price , in dollars , of a $ 30 bottle of perfume ? If necessary round your answer to the nearest cent .
ANSWER
$12.75
EXPLANATION
The store is selling the perfumes at 15% off the original price, so if a bottle of perfume costs $30, then they are selling it at,
[tex]30\cdot\frac{100-15}{100}=30\cdot\frac{85}{100}=30\cdot0.85=25.50[/tex]But you also have a coupon for 50% off, so you get to buy the perfume at half that price,
[tex]25.50\cdot\frac{50}{100}=25.50\cdot0.5=12.75[/tex]Hence, the final price of the perfume is $12.75.
Use the functions f(x) = 8x + 11 and g(x) = 4x² + 7x - 2 to evaluate the following:a. f(8) =b. f(-8)=c. g(6) =d. g(-7)=e. g(a) =
Given:
f(x) = 8x + 11
g(x) = 4x² + 7x - 2
We are asked to evaluate using the following:
(a) f(8)
f(8) = 8(8) + 11
f(8) = 64 + 11
f(8) = 75
(b) f(-8)
f(-8) = 8(-8) + 11
f(-8) = -64 + 11
f(-8) = -53
(c) g(6)
g(6) = 4(6)² + 7(6) - 2
g(6) = 4(36) + 42 - 2
g(6) = 144 + 42 - 2
g(6) = 184
(d) g(-7)
g(-7) = 4(-7)² + 7(-7) - 2
g(-7) = 4(49) - 49 - 2
g(-7) = 196 - 49 - 2
g(-7) = 145
(e) g(a)
g(a) = 4(a)² + 7(a) - 2
g(a) = 4a² + 7a - 2
Open the image attached belowProve that:sec n/(tan n + cot n) = sin n
Given:
We are required to prove:
[tex]\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ = sin}\theta[/tex]From the left-hand side:
[tex]\begin{gathered} =\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ } \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}\text{ + }\frac{\cos \theta}{\sin \theta}} \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin ^2\theta+cos^2\theta}{\sin \theta\cos \theta}} \\ \end{gathered}[/tex]From standard trigonometric identity, we have:
[tex]\sin ^2\theta+cos^2\theta\text{ = 1}[/tex]Substituting we have:
[tex]\begin{gathered} =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{1}{\sin \theta\cos \theta}} \\ =\text{ }\frac{\sin \theta\cos \theta}{\cos \theta} \\ =\text{ sin }\theta\text{ (Right-hand side)} \end{gathered}[/tex]247474647447x4747474747
Answer:
1174879639277360520909 in exact form
or
in decimal form 1.17487963 x 10^21
Step-by-step explanation:
You might need: Calculator
Write the equation for a parabola with a focus at (-6,0) and a directrix at x = -2.
x=
y² = -8(x - 4), which is the required equation of the parabola.
What are a parabola's focus and directrix ?All points in a plane that are equally spaced out from a given point and a given line make up a parabola.
The line is known as the directrix, and the point is known as the parabola's focus.
A parabola's axis of symmetry is perpendicular to the directrix, which does not touch the parabola.
The focus of the parabola is F(-6,0) and its directrix is the line x=−2 i.e., x+2=0
Let P(x,y) be any point in the plane of directrix and focus, and MP be the perpendicular distance from P to the directrix,then P lies on parabola if FP=MP
⇒(x+6)²+(y−0)² = ∣x+2∣÷1
⇒x² + 12x+36+y² = x² +4x +4
⇒y² + 8x = -32
⇒y² = - 8x - 32
⇒y² = -8(x - 4)
⇒ y² = -8(x - 4), which is the required equation of the parabola.
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If two lines intersect to form a right angle, then they are
..(perpendicular, parallel, obtuse
the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. what is the best point estimate for the mean monthly water bill for all residents of the local apartmemt complex?
From the information given, the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. The best estimate for the mean monthly water bill is the sample mean. Since 137 dollars is the sample mean, the correct answer is 137
I have 4 questions I need help with This is first question number 2
We have the next function that models the Australian GDP since 1960 :
[tex]G(i)=1806x(1.037)^t[/tex]Where t is the number of years since 1960.
a)If we are in the year 1960, it means t=0
Therefore:
[tex]G(t)=1806x(1.037)^1[/tex][tex]G(0)=1806x(1.037)^0[/tex][tex]G(0)=1806[/tex]b)Now, we need to find the Australia capita in 1963.
This means t=3
Therefore:
[tex]G(t)=1806x(1.037)^t[/tex][tex]G(3)=1806x(1.037)^3[/tex][tex]G(3)=2013.974721[/tex]c) We need to find when the function is equal to 100,000.
Therefore we equal the function G(t)=100,000.
Then:
[tex]1806x(1.037)^t=1000000[/tex]Solve for t:
Divide both sides by 1806:
[tex]\frac{1806x(1.037)^t}{1806}=\frac{100000}{1806}[/tex][tex](1.037)^t=\frac{50000}{903}[/tex]Add Ln for each side:
[tex]\ln (1.037)^t=in(\frac{50000}{903})[/tex][tex]t\ln (1.037)=in(\frac{50000}{903})[/tex]Then:
[tex]t=\frac{in(\frac{50000}{903})}{\ln (1.037)}[/tex][tex]t=110.48286[/tex]Rounded to the nearest year:
[tex]t=110[/tex]Therefore: 1960 +110 = 2070
On 2070 the Austranlian GDP reaches 100,000 USD
2.) On the first night of a concert, Fish Ticket Outlet collected $67,200 on the sale of 1600 lawn
seats and 2400 reserved seats. On the second night, the outlet collected $73,200 by selling
2000 lawn seats and 2400 reserved seats. Solve the system of equations to determine the cost
of each type of seat.
Answer:
L=$15
R=$18
Step-by-step explanation:
i cant really explain the work
A person standing 306 feet from the base of a church observed the angle of elevation to the church’s steeple to be 20°. How tall is the church. Give answer to the nearest whole number
Solution
- The solution steps are given below:
[tex]\begin{gathered} \text{ Applying SOHCAHTOA, we have:} \\ \frac{h}{306}=\tan20 \\ h=306\tan20 \\ \\ h=111.374...ft\approx111ft\text{ \lparen To the nearest whole number\rparen} \end{gathered}[/tex]Final Answer
111 ft
there are 3 members on a hockey team (including all goalie) at the end of a hockey game each member if the team shakes hands with each member of the opposing team. how many handshakes occur?
Two cyclists, 108 miles apart, start riding toward each other at the same time. One cycles 2 times asfast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
Initial distance: 108 miles
We know that they start riding toward each other, and one of them is 2 times as fast as the other. Then, if the speed of the slowest is v, the speed of the faster cyclist is 2v. The combined speed is:
[tex]v_T=v+2v=3v[/tex]The speed and the distance are related by the equation:
[tex]V=\frac{D}{t}[/tex]They meet 4 hours later, thus:
[tex]\begin{gathered} D=108 \\ t=4 \end{gathered}[/tex]Finally, using the previous equation:
[tex]\begin{gathered} 3v=\frac{108}{4} \\ \Rightarrow v=9\text{ mi/h} \end{gathered}[/tex]The speed of the faster cyclist (2v) is 18 mi/h.
if you copy a page on a machine at 60%, you should get a similar copy of the page. What is the corresponding setting to obtain the original from the copy? The corresponding setting to obtain the original from the copy is _______%
Answer:
The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Explanation:
Let c and x represent the copy and original respectively;
[tex]c=60\text{\% of x}[/tex]making x the subject of formula;
[tex]\begin{gathered} c=0.6x \\ x=\frac{c}{0.6} \\ x=1\frac{2}{3}c \\ in\text{ percentage;} \\ x=1\frac{2}{3}c\times100\text{\%} \\ x=166.67\text{\% of c} \end{gathered}[/tex]Therefore, The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]bridget is growing seven plants for her science project. here are the heights of the plants after four weeks. what is the mode?
Given the data:
Plant Height(Cm)
1 9
2 10
3 10
4 6
5 9
6 7
7 10
The mode of a data set is the value that occurs most frequently.
From the data above, the height that occurs most frequently is 10 cm.
Therefore, the mode is 10.
ANSWER:
What is the equation, in slope-intercept form, of a line that passes through the points(-8,5) and (6,5)?
Given the points (-8,5) and (6,5), we can find the equation of the line first by finding the slope with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(-8,5) \\ (x_2,y_2)=(6,5) \\ \Rightarrow m=\frac{5-5}{6-(-8)}=\frac{0}{6+8}=0 \\ m=0 \end{gathered}[/tex]since the slope is m = 0, we have that the line is a horizontal line that goes through the points (-8,5) and (6,6), then, the equation of the line is:
[tex]y=5[/tex]in slope-intercept form the equation would be:
[tex]y=0x+5[/tex]The first part of the function rule for the values in the table below is Y equals X over two. What is the complete function rule?
Given:
The tabular representation having different values of x and y.
Required:
The relation between x and y.
Explanation:
When x = 6 and y = 2,
[tex]y\text{ = }\frac{6}{2}\text{ = 3 }\Rightarrow\text{ 3 - 1 = 2 = x}[/tex]When x = 8 and y = 3,
[tex]y\text{ = }\frac{8}{2}\text{ = 4 }\Rightarrow\text{ 4-1 = 3}[/tex]When x = 10 and y = 4,
[tex]undefined[/tex]The length of a rectangle is 2 inches more than its width.If P represents the perimeter of the rectangle, then its width is:oAB.O4Ос. РOD.P-2 별O E, PA
Given:
a.) The length of a rectangle is 2 inches more than its width.
Since the length of a rectangle is 2 inches more than its width, we can say that,
Width = W
Length = L = W + 2
Determine the width with respect to its Perimeter, we get:
[tex]\text{ Perimeter = P}[/tex][tex]\text{ P = 2W + 2L}[/tex][tex]\text{ P = 2W + 2(W + 2)}[/tex][tex]\text{ P = 2W + 2W + }4[/tex][tex]\text{ P = 4W + }4[/tex][tex]\text{ P - 4 = 4W}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = }\frac{\text{4W}}{4}[/tex][tex]\text{ }\frac{\text{P - 4}}{4}\text{ = W}[/tex]Therefore, the answer is D.
The directions for a weed spray concentrate state that 3 tablespoons of the concentrate should be mixed with 4 gallons of water. How many tablespoons of concentrate need to be mixed with 5 gallons of water?
The given information is:
- 3 tablespoons of the concentrate should be mixed with 4 gallons of water.
The ratio of tablespoons to gallons of water is:
[tex]\frac{3\text{ tablespoons}}{4\text{ gallons of water}}[/tex]Then, we can apply proportions to find how many tablespoons of concentrate need to be mixed with 5 gallons of water, so:
[tex]\begin{gathered} \frac{3}{4}=\frac{x}{5} \\ Isolate\text{ x} \\ x=\frac{5*3}{4} \\ x=\frac{15}{4} \\ x=3.75\text{ tablespoons} \end{gathered}[/tex]It is needed 3.75 tablespoons of the concentrate.
Compute P(7,4)
From probability and statistics
The resultant answer from computing P(7,4) from probability and statistics is 840.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.So, P(7,4):
This is a permutation and can be calculated as:
ₙPₓ= n! / (n - x)!Here, n = 7 and x = 4Put the values in the given formula:
P(7, 4) = 7! / (7 - 4)!P(7, 4) = 7! / 3!P(7, 4) = 840Therefore, the resultant answer from computing P(7,4) from probability and statistics is 840.
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Can't help me??
x/4 - 9 = 7
solve the equation... use transposing method
The Answer Is x = 64.
Explanation.x/4 - 9 = 7
x/4 = 7 + 9
x/4 = 16
x = 16 × 4
x = 64
_________________
Class: High School
Lesson: Equation
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
Answer:
x = 64
Step-by-step explanation:
x/4 - 9 =7
Step 1: Add 9 to both sides
x/4 - 9 + 9 = 7 + 9
x/4 = 16
Step 2: Multiply right side by 4
x/4= 16 x 4
x = 64
Step 3: Prove your x-value
64/4 = 16 - 9 = 7
64/4 - 9 = 7
So x = 64
PS: Please make brainliest.
Determine the system of inequalities that represents the shaded area .
For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]Subtract. Write fractions in simplest form. 12/7 - (-2/9) =
You have to subtract the fractions:
[tex]\frac{12}{7}-(-\frac{2}{9})[/tex]You have to subtract a negative number, as you can see in the expression, both negatives values are together. This situation is called a "double negative" when you subtract a negative value, both minus signs cancel each other and turn into a plus sign:
[tex]\frac{12}{7}+\frac{2}{9}[/tex]Now to add both fractions you have to find a common denominator for both of them. The fractions have denominators 7 and 9, the least common dneominator between these two numbers is the product of their multiplication:
7*9=63
Using this value you have to convert both fractions so that they have the same denominator 63,
For the first fraction 12/7 multiply both values by 9:
[tex]\frac{12\cdot9}{7\cdot9}=\frac{108}{63}[/tex]For the second fraction 2/9 multiply both values by 7:
[tex]\frac{2\cdot7}{9\cdot7}=\frac{14}{63}[/tex]Now you can add both fractions:
[tex]\frac{108}{63}+\frac{14}{63}=\frac{108+14}{63}=\frac{122}{63}[/tex]Write equation for graph ?
The equation for parabolic graphed function is y = [tex]-3x^{2} -24x-45[/tex].
What is parabola graph?
Parabola graph depicts a U-shaped curve drawn for a quadratic function. In Mathematics, a parabola is one of the conic sections, which is formed by the intersection of a right circular cone by a plane surface. It is a symmetrical plane U-shaped curve. A parabola graph whose equation is in the form of f(x) = ax2+bx+c is the standard form of a parabola.
The given graph has 2 intercept at x axis x = -3, x = -5
y = a (x+3) (x+5)
using the intercept (-4, 3)
3 = a (-4 +3)(-4+5)
3 = a (-1)(1)
a =-3
y = -3(x+3)(x+5)
y = -3 [x(x+5) +3(x+5)]
y = [tex]-3x^{2}-24x-45[/tex]
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Shaun deposits $3,000 into an account that has an rate of 2.9% compounded continuously. How much is in the account after 2 years and 9 months?
The formula for finding amount in an investment that involves compound interest is
[tex]A=Pe^{it}[/tex]Where
A is the future value
P is the present value
i is the interest rate
t is the time in years
e is a constant for natural value
From the question, it can be found that
[tex]\begin{gathered} P=\text{ \$3000} \\ i=2\frac{9}{12}years=2\frac{3}{4}years=2.75years \end{gathered}[/tex][tex]\begin{gathered} e=2.7183 \\ i=2.9\text{ \%=}\frac{2.9}{100}=0.029 \end{gathered}[/tex]Let us substitute all the given into the formula as below
[tex]A=3000\times e^{0.29\times2.75}[/tex][tex]\begin{gathered} A=3000\times2.21999586 \\ A=6659.987581 \end{gathered}[/tex]Hence, the amount in the account after 2 years and 9 months is $6659.99
