(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?
Answers
The height of the javelin is given by
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Here, x is the horizontal distance from the point at which the javelin is thrown.
a)
When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:
[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]Thus, the height of the javelin when it was thrown is 6 ft.
b)
When the javelin strikes the ground the value of h(x) is zero.
Find the value of x when h(x) is zero.
[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]Now, the roots of the equation are x = 160.74 and x = -0.74.
The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.
Related Questions
Find the equation of the line with the given properties. Express the equation in general form or slope-intercept form.
Answers
To asnwer this questions we need to remember that two lines are perpendicular if and only if their slopes fullfil:
[tex]m_1m_2=-1[/tex]Now to find the slope of the line
[tex]-7x+y=43[/tex]we write it in slope-intercept form y=mx+b:
[tex]\begin{gathered} -7x+y=43 \\ y=7x+43 \end{gathered}[/tex]from this form we conclude that this line has slope 7.
Now we plug this value in the condition of perpendicularity and solve for the slope of the line we are looking for:
[tex]\begin{gathered} 7m=-1 \\ m=-\frac{1}{7} \end{gathered}[/tex]Once we hace the slope of the line we are looking for we plug it in the equation of a line that passes through the point (x1,y1) and has slope m:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values we know we have that:
[tex]\begin{gathered} y-(-7)=-\frac{1}{7}(x-(-7)) \\ y+7=-\frac{1}{7}(x+7) \\ y+7=-\frac{1}{7}x-1 \\ y=-\frac{1}{7}x-8 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-\frac{1}{7}x-8[/tex]I’ve been working on these similar questions but coming to this question. I found myself being stuck.
Answers
Solution:
If the variation in pressure is P pounds per square inch, then the Loudness L in decibels is;
[tex]L=20\log _{10}(121.3P)[/tex]When L=115 decibels;
[tex]\begin{gathered} 115=20\log _{10}(121.3P) \\ \text{Divide both sides by 20;} \\ \frac{115}{20}=\frac{20\log_{10}(121.3P)}{20} \\ \log _{10}(121.3P)=5.75 \end{gathered}[/tex]But from the logarithmic law, we have;
[tex]\log _ba=c\leftrightarrow a=b^c[/tex]Thus,
[tex]\begin{gathered} \log _{10}(121.3P)=5.75 \\ 121.3P=10^{5.75} \\ 121.3P=562341.33 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by 121.3;} \\ \frac{121.3P}{121.3}=\frac{562341.33}{121.3} \\ P\cong4635.95 \end{gathered}[/tex]FINAL ANSWER:
[tex]4636.0\text{ pounds per square inch.}[/tex]Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–8x+2
Answers
We have to calculate the zeros of the function with the quadratic formula.
[tex]f(x)=x^2-8x+2[/tex][tex]\begin{gathered} x=\frac{-(-8)}{2\cdot1}\pm\frac{\sqrt[]{(-8)^2-4\cdot1\cdot2}}{2\cdot1}=\frac{8}{2}\pm\frac{\sqrt[]{64-8}}{2}=4\pm\frac{\sqrt[]{56}}{2}=4\pm\sqrt[]{\frac{56}{4}}=4\pm\sqrt[]{14} \\ \\ x_1=4+\sqrt[]{14}\approx4+3.742=7.742 \\ x_2=4-\sqrt[]{14}\approx4-3.742=0.258 \end{gathered}[/tex]The roots are x1=7.742 and x2=0.258, both reals., both
The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 10. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 62.
Answers
we are given
mean=42
Std=10
if the mean=42 + std =10 42+10=52
if the mean=42 - std=10 42-10=32
Rule -- 68-95-99.7
68% of the measures are within 1 standard deviation of the mean.
42+10=52
95% are within 2.
42+20=62
99.7% are within 3.
42+30=72
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
we are ask for the porcentage of request between 42-62 (between the mean and 2+std)
62 is two standard deviations above the mean.
Of the 50% of the measures below the mean, 95% are between 42 and 62, so
0.95(50)=47.5
The approximate percentage of light bulb replacement requests numbering between 42 and 62 is of 47.5%
Find the volume of the figure round to the nearest 10th if needed
Answers
Given: A triangular prism with base 6ft,height of triangle is 8 ft and height of prism is 12ft
Find : the volume of the prism.
Explanation: the volume of the triangular prism is equal to area of the base triangle times height of the prism.
[tex]\begin{gathered} =\frac{(8\times6)\times12}{2} \\ =288\text{ ft}^3 \end{gathered}[/tex]final answer: the volume of the rectangular prism is
[tex]288ft^3[/tex]Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3
Answers
Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex](x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]Answer:
• Slope: -5/2
,• y-intercept: 3
The correct answer is option B
Missed this day of class and have no idea how to solve this last problem on my homework
Answers
From the given expression
a) The linear system of a matrix form is
[tex](AX=B)[/tex]The linear system of the given matrix will be
[tex]\begin{gathered} 2x+y+z-4w=3 \\ x+2y+0z-7w=-7 \\ -x+0y+oz+w=10 \\ 0x+0y-z+3w=-9 \end{gathered}[/tex]b) The entries in A of the matrix is
[tex]\begin{gathered} \text{For }a_{22}=2 \\ a_{32}=0 \\ a_{43}=-1 \\ a_{55}\text{ is undefined} \end{gathered}[/tex]c) The dimensions of A, X and B are
[tex]\begin{gathered} A\mathrm{}X=B \\ \begin{bmatrix}{2} & 1 & {1} & -4 \\ {1} & {2} & {0} & {-7} \\ {-1} & {0} & {0} & {1} \\ {0} & {0} & {-1} & {3}\end{bmatrix}\begin{bmatrix}x{} & {} & {} & {} \\ {}y & {} & {} & {} \\ {}z & {} & {} & {} \\ {}w & {} & {} & {}\end{bmatrix}=\begin{bmatrix}3{} & {} & {} & {} \\ {}-7 & {} & {} & {} \\ {}10 & {} & {} & {} \\ {}-9 & {} & {} & {}\end{bmatrix} \end{gathered}[/tex]See photo for problem
Answers
The distance, x, from one corner to another corner three corners away is 4. 70cm
The distance, y, from one corner to another corner two corners away is 4. 07cm
How to determine the valueIt is important to note that the image shown is a hexagon and each of the interior angles of a hexagon has a value of 120 degrees
Also note that the have the trigonometric identities;
sinecosinetangentcotangentsecantcosecantUsing the cosine identity, we have;
sin θ = adjacent/ hypotenuse
substitute the values
cos 60 = 2.35/x
cross multiply
x = 2. 35/cos 60
x = 2. 35/ 0. 5
x = 4. 7 cm
Then, we have,
sin 60 = y/ 4. 7
y = sin 60 × 4.7
y = 0. 8660 × 4. 7
y = 4. 07cm
Hence, the values are 4. 7cm and 4. 07cm
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the four faced of a rectangular pyrimid below are painted yellow. how many square feet will be painted
Answers
The number of square feet to be painted is equal to the surface area of the four face painted yellow.
Total Surface Area (TSA) =
[tex]4(\frac{1}{2}bh)[/tex]By Pythagoras Theorem,
[tex]\begin{gathered} h^2+1.5^2=5^2 \\ h^2=5^2-1.5^2 \\ h=\sqrt[]{25-2.25}\text{ =}\sqrt[]{22.75}=4.7697\text{ fe}et \end{gathered}[/tex]Write the equation of the circle given the following graph.
Answers
Given:
Equation of a circle on a graph with center(3, -2).
To find:
Equation of a circle.
Explanation:
General eqution of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Solution:
From the graph, we can see that center is (3, -2) and radius equal 3.
So, equation of a circle is
[tex](x-3)^2+(y+2)^2=3^2[/tex]Hence, this is the equation of a circle.
Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Construct the probability distribution and histogram of the random variable Z.
Answers
ANSWER and EXPLANATION
Let R represent the number of red balls.
Let B represent the number of blue balls.
There are four possible outcomes when the balls are picked:
[tex]\lbrace RR,RB,BR,BB\rbrace[/tex]We have that Z is the random variable that represents the number of blue balls.
This implies that the possible values of Z are:
To construct the probability distribution, we have to find the probabilities of each of the outcomes:
[tex]\begin{gathered} P(RR)=\frac{5}{11}*\frac{4}{10}=\frac{2}{11} \\ P(RB)=\frac{5}{11}*\frac{6}{10}=\frac{3}{11} \\ P(BR)=\frac{5}{11}*\frac{6}{10}=\frac{3}{11} \\ P(BB)=\frac{6}{11}*\frac{5}{10}=\frac{3}{11} \end{gathered}[/tex]Hence, the probabilities for the possible outcomes of the random variable are:
[tex]\begin{gathered} P(Z=0)=\frac{2}{11} \\ P(Z=1)=\frac{3}{11}+\frac{3}{11}=\frac{6}{11} \\ P(Z=2)=\frac{3}{11} \end{gathered}[/tex]Therefore, the probability distribution is:
Now, let us plot the histogram:
That is the answer.
A bicycle wheel is 63 centimeters from top to bottom . When the wheel goes all the way around one time , the bicycle travels 198 centimeters . How can this information be used to estimate the value of pi
Answers
Given :
A bicycle wheel is 63 centimeters from top to bottom .
So, the diameter of the wheel = 63 cm
When the wheel goes all the way around one time , the bicycle travels 198 centimeters .
So, the circumference of the circle = 198 cm
The circumference of the circle of diameter = d will be :
[tex]\pi\cdot d[/tex]So,
[tex]\begin{gathered} \pi\cdot63=198 \\ \\ \pi=\frac{198}{63}=\frac{22}{7} \end{gathered}[/tex]10 Zara writes a sequence of five numbers. The first number is 2. The last number is 18. Her rule is to add the same amount each time. Write the missing numbers. 2,____ ,_____,______, 18
Answers
If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
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Find the area of each figure. Round to the nearest 10th if necessary.
Answers
1.
First, divide the figure into 3 different figures.
Find the area of each figure, and then add them:
A1 is a rectangle:
Area of a rectangle: Lenght x width
A1 = 8 x 5.3 = 42.4 in2
A2 is also a rectangle:
Lenght = 4
width = 8 - 5.3 = 2.7
A2 = 4 x 2.7 = 10.8 in2
A3 is a triangle:
Area of a triangle = (base x height) / 2
base = 2.7
Height = 8-4 = 4
A3= ( 2.7 x 4 ) / 2 = 5.4 in2
Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2
Answer = 58.6 in2
Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB=10 feet, and BE and BD trident angle ABC, what is the perimeter of the deck area to the right of the beam of light ?PART 1: what others angles or sides of triangle BDC can you label given that side AB is 10 feet, BE and BD trisect angle ABC? Label the diagram accordingly, and explain your reasoning
Answers
Part 1
The labelled disgram is shown below.
We would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Considering triangle ABE
Sin 60 = 10/BE
BE = 10/Sin60 = 11.55
tan60 =10/AE
AE = 10/tan60 = 5.77
Part 1
Side DC of triangle BDC = 10 feet(opposite sides of a rectangle are congruent)
angle DBC = 30 degrees because BE and BD trisect angle ABC. 90/3 = 30
The sum of the angles in a triangle is 180 degrees. Thus,
angle DBC + angle DCB + angle BDC = 180
30 + 90 + angle BDC = 180
angle BDC = 180 = 180 - (30 + 90 = 180 - 120
angle BDC = 60
Sin 30 = CD/BD = 10/BD
BD = 10/Sin30
BD = 20
tan 30 = DC/BC = 10/BC
BC = 10/tan30
BC = 17.32
Perimeter of deck area to the right of the beam of light = perimeter of triangle BDC
= BD + DC + BC
= 20 + 10 + 17.32
Perimeter = 47.32 feet
Ashlynn is trying a low-carbohydrate diet. She would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:460 < 2x + 10 and 2x + 10 < 660Solve for x in the inequality, and explain what the answer represents
Answers
To find:
The value of x.
Solution:
The given compound inequalities are 460 < 2x + 10 and 2x + 10 < 660. Solve each separately to get the interval in which the value of x lies.
[tex]\begin{gathered} 460<2x+10 \\ 460-10<2x \\ 450<2x \\ 225225 \end{gathered}[/tex][tex]\begin{gathered} 2x+10<660 \\ 2x<650 \\ x<325 \end{gathered}[/tex]So, from the above calculation, we have obtained that x is greater than 225 and less than 325. So, the answer is (225, 325).
The answer represents that the amount of carbs is between 225 grams and 325 grams.
You need a shelf for a small space in your house, so you make a measurement with your meter stick and head to the store. Once there, you find that the dimension of the shelves you want is given in cm.If your space measured 0.9 m, and the shelves at the store measure 30 cm, answer the following questions:1) How many meters wide is the shelf you want to buy?
Answers
We will have the following:
[tex]0.9m=90cm[/tex]So, the number of shelves you need is 3.
Thus, the shelves you can buy are 0.3 m long each.
Ava graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options.Ava’s graph is a vertical translation of f(x) = x^2.Victor’s graph is a vertical translation of f(x) = x^2.Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.Victor’s graph moved 4 units from f(x) = x^2 in a positive direction.Ava’s graph has a y-intercept of 4.
Answers
Given,
Ava graphs the function h(x) = x^2 + 4.
Victor graphs the function g(x) = (x + 4)^2.
Required:
Check the correct statement about graph.
The graph of Ava and vector function is:
Here, victor graph was represented by blue curve and ava graph by green curve.
For first statement,
Ava’s graph is a vertical translated by 4 units.
Hence, statement is true.
For second statement,
The graph of victor is not vertically translated.
Hence, statement is false.
For statement three,
The curve of the Ava graph is moved 4 unit up in the positive direction. It is in y axis. Hence, statement is true.
For statement forth,
The curve of the victor graph is moved to negative direction not positive. Hence, statement is false.
For statement fifth,
The graph of Ava has the y intercept at 4. So, statement is correct.
Hence, option A (Ava’s graph is a vertical translation of f(x) = x^2), option C (Ava’s graph moved 4 units from f(x) = x^2 in a positive direction) and option E (Ava’s graph has a y-intercept of 4.) is true.
does (51, 58) make the equation y =x -7 true?
Answers
The objective is to verify whether the point (51,58) maes the equation y=x-7.
Substitute the values of x and y coordinate in the given equation.
[tex]\begin{gathered} y=x-7 \\ y-x=-7 \\ 58-51=-7 \\ 7=-7 \end{gathered}[/tex]Since, LHS is not equal to RHS.
Thus, the coordinate (51,58) does not make the equation y=x-7.
Hence the answer is NO.
how would I solve and what would the answer be?
Answers
Given that:
f(x) = |x| and g(x) = x + 6
[tex](f\circ g)(x)=|x+6|[/tex]and
[tex](g\circ f)(x)=|x|+6[/tex]find the other binomial p squared -13 p +36 =(p-9)
Answers
To find the other factor of the polynomial
[tex]p^2-13p+36[/tex]We need to find two integers which multiplication gives 36 and addition is -13.
This integers would be -9 and -4, then we have
[tex]p^2-13p+36=p^2-9p-4p+36[/tex]now we factor the right term using common factors:
[tex]\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}[/tex]Hence:
[tex]p^2-9p-4p=(p-9)(p-4)[/tex]Therefore, the other binomial we are looking for is (p-4).
how do I graph the line with the given slope m and y-intercept b.
m=5/3,b=-4
Answers
y=(5/3)x+4
I am aware that the slope is "big," m = - 5 /3, and that the yy-intercept is "left(0, 4), right" (0,4). The final graph of the line should be declining when viewed from left to right because the slope is negative.
y = mx+c
how to draw this graph?
step 1: Plot the given equation's yy-intercept, which is left(0,4right), first (0,4).
On the xy axis, the position (0,4) .
step2: Use the slope largem = -5 /3
m= 5/3
to locate a different point using the y-intercept b as a guide. The slope instructs us to move 3 units to the right after dropping down 5 units.
To find the opposite spot, start at (0,4) and go 5 units down and 3 units to the right.
Step 3: Make a line that goes through all of the points.
Create a line that joins the coordinates (0,4) and (3,5)
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3A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed.Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents ofMississippl would purchase the new product. Identify a problem with the study.The conclusion is based on a small sample.
Answers
The main problem of the research conducted is the number of participants who polled for the new product. If we want to conduct a study that represents a state, the number of participants must be close as possible to the total population of the state. Of course, 24 participants is very small sample size when we compare it to the population of the state, which means we cannot easily conclude that 50% of the residents would like to purchase the new product based on just 24 participants.
Answer: a. The conclusion is based on a small sample
The vertex of the parabola below is at the point
Answers
SOLUTION
The equation of a parabola in a vertex form is given
since the parabola is on the x-axis.
[tex]\begin{gathered} x=a(y-h)^2+k \\ \text{Where } \\ \text{Vertex}=(h,k) \end{gathered}[/tex]From the diagram given, we have
[tex]\text{vertex}=(-4,-2)[/tex]Substituting into the formula above, we have
[tex]\begin{gathered} x=a(y-h)^2+k \\ h=-4,k=-2 \end{gathered}[/tex]We have
[tex]\begin{gathered} x=(y-(-2)^2-4 \\ x=(y+2)^2-4 \end{gathered}[/tex]Since the parabola is a reflection from the parent function, then
[tex]a=-2[/tex]The equation of the parabola becomes
[tex]x=-2(y+2)^2-4[/tex]Answer; x = -2(y + 2)^2-4
Draw the graph of the line that is parallel to Y -3 = 1/3(x+2) and goes through the point (1, 7)
Answers
Explanation:
We are required to draw the graph of the line that is parallel to y-3=1/3(x+2) and goes through the point (1, 7).
Given the equation of the line:
[tex]y-3=\frac{1}{3}(x+2)[/tex]Compare the equation with the slope-point form of a line:
[tex]$$y-y_1=m(x-x_1)$$[/tex]• The slope of the line, m=1/3
,• In addition, the line goes through the point (1,7)
Substitute these values into the point-slope form given above:
[tex]y-7=\frac{1}{3}(x-1)[/tex]Finally, graph the line by looking for another point in addition to point (1,7):
When x=-2
[tex]\begin{gathered} y-7=\frac{1}{3}(x-1) \\ y-7=\frac{1}{3}(-2-1) \\ y-7=\frac{1}{3}(-3) \\ y-7=-1 \\ y=-1+7 \\ y=6 \\ \implies(-2,6) \end{gathered}[/tex]Join the points (1, 7) and (-2, 6) to plot the line.
Answer:
The graph showing the two points is attached below:
Note:
For comparison purposes and to show that the two lines are parallel, the other graph is added below:
Triangle Inequality TheoremDetermine if a triangle can be formed with the given lengths. If so, classify the triangle by its angle.YESorNO
Answers
Given:-
[tex]7,20,12[/tex]To find:-
Wheather the given sides form a valid triangle.
So now let,
[tex]A=7,B=20,C=12[/tex]To check we use the condition,
[tex]A+B>C,B+C>A,C+A>B[/tex]Substituting the values we get,
[tex]7+20>12,20+12>7,12+7>20[/tex]In the above condition 12+7>20 is wrong.
So the condition fails and the given sides doesnt form a triangle.
Compare f(0) and g(0)f(0) is <, =, or > to g(0)
Answers
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
When finding the height of a triangle, you need to find the equation of the lineperpendicular to the base of the triangle that passes through the vertex opposite thebase and then find the point of the intersection of the base and the perpendicular line. True Or False?
Answers
EXPLANATION:
Given;
We are given the step by step procedure to find the height of a triangle.
Required;
We are required to determine if the step by step solution is true or false.
Solution/Explanation;
When finding the height of a triangle, we may use the Pythagoras theorem or we may use trigonometric ratios for right angled triangles.
Note that the Pythagoras' theorem is also used only for right angled triangles and one of the three sides will be the height of the triangle.
When required to calculate the the height of a triangle given a line perpendicular to the base (that is, at a 90 degree angle with the base), and passing through the vertex opposite the base, the triangle can be effectively split into two parts along the perpendicular and the perpendicular line will then become the height. Also depending on the amount of information available, we may use the Pythagoras' theorem (if the other two sides are given). Alternatively we may use the trigonometric ratios if one other side and one of the angles is given.
Therefore,
ANSWER:
FALSE
Open the image attached belowProve that:sec n/(tan n + cot n) = sin n
Answers
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]