16. The height, h, in feet of an object above the ground is given by h = -16t² +64t+190, t≥0, where t is the time in seconds. a) b) c) d) When will the object be 218 feet above the ground? When will it strike the ground? Will the object reach a height of 300 feet above the ground? Find the maximum height of the object and the time it will take.
Answers
the maximum height is 254 feet.
Answer:
a) 0.5 seconds and 3.5 seconds.
b) 5.98 seconds (2 d.p.)
c) No.
d) 254 feet at 2 seconds.
Step-by-step explanation:
Given equation:
[tex]h=-16t^2+64t+190, \quad t \geq 0[/tex]
where:
h is the height (in feet).t is the time (in seconds).Part aTo calculate when the object will be 218 feet above the ground, substitute h = 218 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 218\\-16t^2+64t+190-218& = 0\\-16t^2+64t-28 & = 0\\-4(4t^2-16t+7) & = 0\\4t^2-16t+7 & = 0\\4t^2-14t-2t+7 &=0\\2t(2t-7)-1(2t-7)&=0\\(2t-1)(2t-7)&=0\\\implies 2t-1&=0\implies t=\dfrac{1}{2}\\\implies 2t-7&=0 \implies t=\dfrac{7}{2}\end{aligned}[/tex]
Therefore, the object will be 218 feet about the ground at 0.5 seconds and 3.5 seconds.
Part bThe object strikes the ground when h is zero. Therefore, substitute h = 0 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 0\\-2(8t^2-32t-95) & = 0\\8t^2-32t-95 & = 0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(-95)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024+3040} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{4064} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot 254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4 \sqrt{254} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{254} }{4}[/tex]
As t ≥ 0,
[tex]\implies t=\dfrac{8+ \sqrt{254} }{4}\quad \sf only.[/tex]
[tex]\implies t=5.98 \sf \; s \; (2 d.p.)[/tex]
Therefore, the object strikes the ground at 5.98 seconds (2 d.p.).
Part c
To find if the object will reach a height of 300 feet above the ground, substitute h = 300 into the equation and solve for t:
[tex]\begin{aligned}\implies -16t^2+64t+190 & = 300\\-16t^2+64t+190-300 & =0\\-16t^2+64t-110 & =0\\-2(8t^2-32t+55) & =0\\8t^2-32t+55& =0\end{aligned}[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(55)} }{2(8)}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{1024-1760} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{-736} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot -1 \cdot 46} }{16}[/tex]
[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{-1} \sqrt{ 46}}{16}[/tex]
[tex]\implies t=\dfrac{32 \pm 4i\sqrt{ 46} }{16}[/tex]
[tex]\implies t=\dfrac{8\pm \sqrt{ 46} \;i}{4}[/tex]
Therefore, as t is a complex number, the object will not reach a height of 300 feet.
Part dThe maximum height the object can reach is the y-coordinate of the vertex.
Find the x-coordinate of the vertex and substitute this into the equation to find the maximum height.
[tex]\textsf{$x$-coordinate of the vertex}: \quad x=-\dfrac{b}{2a}[/tex]
[tex]\implies \textsf{$x$-coordinate of the vertex}=-\dfrac{64}{2(-16)}=-\dfrac{64}{-32}=2[/tex]
Substitute t = 2 into the equation:
[tex]\begin{aligned}t=2 \implies h(2)&=-16(2)^2+64(2)+190\\&=-16(4)+128+190\\&=-64+128+190\\&=64+190\\&=254\end{aligned}[/tex]
Therefore, the maximum height of the object is 254 feet.
It takes 2 seconds for the object to reach its maximum height.
Related Questions
Helppppp!!!! Please!!
Answers
n > 39/4 is value of quartic equation.
What does quartic equation mean?
A fourth-degree equation, often known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.
For a quadratic ax² + bx +c , the sign of its determinant, given by
Δ = b²- 4ac
"determines" the nature of its roots. In particular, if Δ<0 , then the quadratic has two distinct non-real roots.
Now, we have
3z² - 9z = n - 3
3z² - 9z - (n - 3) = 0
with determinant
Δ = (-9)² - 4 .3( n - 3 ) = 117 - 12n
Solve for such that Δ < 0
Δ = 117 - 12n < 0 ⇒ 12n > 117
n > 117/12
n > 39/4
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Write a two-column proof.
4. Given: AB EF
AC DF
Prove: ABC ~ FED
Please help
Answers
Explanation:
The following is a proof that ∆ABC ~ ∆FED.
Statement . . . . Reason1. AB║EF, AC║FD . . . . given
2. ∠BCA ≅ ∠EDF . . . . alternate exterior angles theorem
3. ∠ABC ≅ ∠FED . . . . alternate interior angles theorem
4. ∆ABC ~ ∆FED . . . . AA similarity postulate
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (0, 5) and point (3, -1) rounded to the nearest tenth?
Answers
The distance between the points is 6.7 units
What is distance?The distance between two points is the number of points between them
How to determine the distance?The points are given as
(0, 5) and (3, -1)
The distance formula is given as
d = √(x2 - x1)^2 + (y2 - y1)^2
Substitute the given points in the above distance formula
So, we have
d = √(0 - 3)^2 + (5 + 1)^2
Evaluate the difference and the sum
d = √(-3)^2 + 6^2
Evaluate the exponents
d = √9 + 36
Evaluate the sum
d = √45
This gives
d = 6.7
Hence, the distance is 6.7 units
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What is the end behavior of the polynomial function?
Drag the choices into the boxes to correctly describe the end behavior of the function.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
f(x)=6x9−6x4−6 f(x)=−3x4−6x+4x−5
Answers
The end behavior of each function is given as follows:
f(x) = 6x^9 - 6x^4 - 4, as x -> -∞, f(x) -> -∞ and as x -> ∞, f(x) -> ∞.f(x) = -3x^4 - 6x + 4x - 5, as x -> -∞, f(x) -> -∞ and as x -> ∞, f(x) -> -∞.End behavior of a functionThe end behavior of a function is given by the limits of the function as x goes to infinity, both negative and positive infinity, giving how the function behaves to the left and to the right of the graph.
For a polynomial function, only the term with the highest exponent is considered for the calculation of the limit, which is a standard rule for limits when x goes to infinity.
The first function is given by:
f(x) = 6x^9 - 6x^4 - 4.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ x^9 = (-∞)^9 = -∞.lim x -> ∞ x^9 = (∞)^9 = ∞.The second function is given by:
f(x) = -3x^4 - 6x + 4x - 5.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ -x^4 = -(-∞)^4 = -∞.lim x -> ∞ -x^4 = -(∞)^4 = -∞.A similar problem, also about the end behavior of a function, is presented at https://brainly.com/question/28884735
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Sydney purchased a $50.00 gift for a baby shower. She uses a coupon that offers 20% off. How much will Sidney spend on the gift after the coupon?
Answers
From the scenario, the following are the pieces of information being given:
Price of Gift = $50
Discount Coupon used = 20% Off
Let's compute how much will Sidney spend on the gift after the coupon.
Step 1: Let's determine the equivalent amount of the discount.
[tex]\text{ Amount to be Discounted = Price of Gift x }\frac{Percentage\text{ of Discount}}{100}[/tex][tex]\text{ = \$50 x }\frac{20}{100}\text{ = \$50 x 0.20}[/tex][tex]\text{ = \$10}[/tex]Step 2: Let's deduct the equivalent amount of 20% to the actual price of the gift.
[tex]\text{ = \$50 - \$10}[/tex][tex]\text{ = \$40}[/tex]Therefore, Sydney will spend $40 on the gift after the coupon.
I BEG YOU FOR HELP!!! Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answers
Answer:
Step-by-step explanation:
The triangles are congruent because they follow the SSS triangle congruence postulate. As the SSS postulate says that all 3 sides of one triangle are congruent to another triangle's sides, these triangles shown have all three of their sides congruent to each other.
Answer: I am no sure but the only way to decide whether a pair of triangles are congruent would be to measure all of the sides and angles, and these triangles do not look the same so I would say that these tringles are not congruent.
Step-by-step explanation:
Simplify the expression by first transforming the radical to exponential form. Leave the answer in exact form as a radical or a power, not as a decimal approximation.
Answers
Answer:
[tex]\textsf{Radical form}: \quad \sqrt[4]{2}\\\\\textsf{Exponent form}: \quad 2^{\frac{1}{4}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{8} \div \sqrt[4]{32}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies 8^{\frac{1}{2}} \div 32^{\frac{1}{4}}[/tex]
Rewrite 8 as 2³ and 32 as 2⁵:
[tex]\implies (2^3)^{\frac{1}{2}} \div (2^5)^{\frac{1}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{\frac{3}{2}} \div 2^{\frac{5}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \div a^c=a^{b-c}:[/tex]
[tex]\implies 2^{\frac{3}{2}-\frac{5}{4}}[/tex]
[tex]\implies 2^{\frac{6}{4}-\frac{5}{4}}[/tex]
[tex]\implies 2^{\frac{1}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \sqrt[4]{2}[/tex]
jamals lawn is shaped like a square with an area of 224.9 ft2. which measurement is closest to the side length of his lawn in feet?
Answers
Given:
Area of the square shaped lawn = 224.9 ft²
A square has all four side lengths equal.
To find the side length of this lawn, use the formula for area of a square below:
[tex]\text{Area = }L^2[/tex]Take the square root of both sides to find the sile length L:
[tex]\begin{gathered} \sqrt[]{Area\text{ }}=\sqrt[]{L^2} \\ \\ \sqrt[]{Area}\text{ = L} \\ \\ \sqrt[]{224.9}\text{ = L} \\ \\ 14.99\text{ ft = L} \end{gathered}[/tex]Therefore, the measurement that is closest to the side length in feet is 15 ft
ANSWER:
15 ft
It took 12 men 5 hours to build an airstrip. Working at the same rate, how many additional men could have been hired in order for the job to have taken 1 hour less?
A) Two
B) Three
C) Four
D) Six
Answers
Answer:
B
Step-by-step explanation:
hello the question is if it took 12 men 5 hours to build an age is working at the same rate how many additional men could have been hired in order for the job to have taken 1 hour less ok so we have to find that how many extra may be required to complete the job for a strip 1 hour less than five hours that is 4 hours ok bye have to complete the airstrip in 4 hours and they have to find that how many experiment we have to required for that we will assume that let extra number of number of extra man bhi X show the number of men when we are finishing in it in 4 hours would be 12 + X ok
would be the number of men now and time required would be equal to 1 hour less than 5 hours that is 4 hours ok no from the given data we can say that one cares if strip x 12 men and fibres ok so all vacancy job correct so vacancy job per man are would be 1 divided by 12 in 25 this is the job or the amount of a strip that is completed when
one man works for one hour ok so this is the amount of the job that is done for men power and we have we have this number of men that are not want working and the number of hours that their working for so for one job we will need for one job would be best job per man per hour into number of men into number of hour ok and we have 1 equal to number of Doberman per Rs 1 by 2 11 25 and number of men we have already know that 12 + 6 is the number of men that we will require 12 + X number
forces were less than 5 that is 44 4312 so it would give us 12 + X / 3515 1 to 15 of this site it would give us 12 + X equal to 15 which implies X is equals to 15 - 12 and X is equals to 3 significant required 3 more men to complete the job in Porus dancer is 3 which is given is be in the question make you
Determine if the line passing through A(7,5) and B(-14, -9) is parallel, or perpendicular to the line passing through C(0,1) and D(4, -5).
Answers
To solve this problem, we will use the two pair of points to find the slope of the equation of each line. Then, by comparing these slopes, we can determine either if they are perpendicular or parallel.
Slope calculations
To calcula the slopes, given the pairs of points, we are going to use the following formula: Given points (a,b) and (c,d) the slope of the line that passes through them is given by the formula
[tex]m=\frac{d\text{ - b}}{c\text{ -a}}=\frac{b\text{ - d}}{a\text{ -c}}[/tex]Let us calculate first the slope of the line that passes through the points (7,5) and (-14,-9). In this case, we have a=7,b=5,c=-14 and d=-9. So we get
[tex]m=\frac{5\text{ - (-9)}}{7\text{ - (-14)}}=\frac{14}{21}=\frac{2\cdot7}{3\cdot7}=\frac{2}{3}[/tex]Now, let us calculate the slope of the line that passes through the points (0,1) and (4,-5). In this case, we have a=0,b=1,c=4 and d=-5. So we get
[tex]m=\frac{1\text{ -(-5)}}{0\text{ - 4}}=\frac{6}{\text{ -4}}=\text{ -}\frac{3\cdot2}{2\cdot2}=\text{ -}\frac{3}{2}[/tex]Slope comparison
Now, we compare the slopes to determine if the lines are perpendicular or parallel. Recall that two lines are parallel if they have the same slope and they are perpendicular if the product of their slopes is -1. From our calculations, we can see that the slopes are not equal. Let us confirm that they are perpendicular. To do so, we multiply both slopes. So we get
[tex]\frac{2}{3}\cdot(\text{ -}\frac{3}{2})=\text{ -1}[/tex]Since their product is -1, this confirms that both lines are perpendicular.
Which answer choice shows two hundred and two thousandths?A) 200.02B) 200.202C) 202.02D) 202.002
Answers
Given
two hundred two and two thousandths.
Answer
202.002
Option D is correct
I need help with problem 7.Use the figure to find the values of x, y, and z that makes triangle DEF similar to triangle GHF.
Answers
ANSWER
• x = 12
,• y = 16
,• z = 7
EXPLANATION
Because the triangles are similar, we have that:
• The ratio between corresponding sides is constant:
[tex]\frac{DE}{GH}=\frac{EF}{GF}=\frac{DF}{HF}[/tex]• Corresponding angles are congruent:
[tex]\begin{gathered} \angle D\cong\angle H \\ \angle E\cong\angle G \\ \angle F\cong\angle F \end{gathered}[/tex]We know that the measure of angle E is 16°, so the measure of angle G must be the same because they are congruent,
[tex]16\degree=2(x-4)\degree[/tex]With this equation, we can find x. First, divide both sides by 2,
[tex]\begin{gathered} \frac{16}{2}=\frac{2(x-4)}{2} \\ \\ 8=x-4 \end{gathered}[/tex]And then, add 4 to both sides,
[tex]\begin{gathered} 8+4=x-4+4 \\ \\ 12=x \end{gathered}[/tex]Hence, x = 12.
Now we know that the length of side EF is,
[tex]EF=x-5=12-5=7[/tex]To find y and z, we will use the proportions we got at the top of this explanation,
[tex]\frac{DE}{GH}=\frac{EF}{GF}=\frac{DF}{HF}[/tex]Replace with the known values and the expressions with y and z,
[tex]\frac{25}{6z+8}=\frac{7}{14}=\frac{24}{3y}[/tex]With the first two, we can find z,
[tex]\frac{25}{6z+8}=\frac{7}{14}[/tex]Simplify the right side,
[tex]\frac{25}{6z+8}=\frac{1}{2}[/tex]Rise both sides to the exponent -1 - i.e. flip both sides of the equation,
[tex]\frac{6z+8}{25}=2[/tex]Multiply both sides by 25,
[tex]\begin{gathered} 25\cdot\frac{(6z+8)}{25}=2\cdot25 \\ \\ 6z+8=50 \end{gathered}[/tex]Subtract 8 from both sides,
[tex]\begin{gathered} 6z+8-8=50-8 \\ 6z=42 \end{gathered}[/tex]And divide both sides by 6,
[tex]\begin{gathered} \frac{6z}{6}=\frac{42}{6} \\ \\ z=7 \end{gathered}[/tex]Hence, z = 7.
Finally, with the last two proportions, we can find y,
[tex]\frac{7}{14}=\frac{24}{3y}[/tex]The first two steps are the same we did to find z: simplify the left side and flip both sides,
[tex]2=\frac{3y}{24}[/tex]Multiply both sides by 24,
[tex]\begin{gathered} 24\cdot2=24\cdot\frac{3y}{24} \\ \\ 48=3y \end{gathered}[/tex]And divide both sides by 3,
[tex]\begin{gathered} \frac{48}{3}=\frac{3y}{3} \\ \\ 16=y \end{gathered}[/tex]Hence, y = 16.
Which of the expressions are equivalent to the one below? Check all that apply.
( 15 • 3) - 20
Answers
Answer:
I don't know your answer choices but...
Step-by-step explanation:
( 15 • 3) - 20 is equal to:
45-20
25
(5)(3)(3)-20
1. m/ASN = 63°
m/GSN =
Answers
The measure of angle ∠GSN is 27°.
What do we mean by angles?An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as the sides of an angle.So, a measure of ∠GSN:
The given angle ASG is 90° (Given)∠ASN = 63°Then, ∠GSN will be:
∠ASN + ∠GSN = ∠ASG63 + ∠GSN = 90∠GSN = 90 - 63∠GSN = 27°Therefore, the measure of angle ∠GSN is 27°.
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HELP!!
Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 58 degrees, angle B labeled 44 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
136°
102°
78°
58
Answers
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle m∠K is 102° so option (B) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
Triangle is a very common figure to deal with in our daily life.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠A + m∠B + m∠C = 180°
m∠C = 180° - 58° - 44°
m∠C = 78°.
The exterior angle of C = 180- 78 = 102°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to m∠K is 102°".
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Answer:
136
Using the exterior angle theorem,
Step-by-step explanation:
A right triangle has an area of 54 ft2 and a hypotenuse of 25 ft long. What are the lengths of its other two sides?
Answers
By theorem we have the following:
[tex]h^2=a^2+b^2[/tex]And, we are given:
[tex]A=\frac{a\cdot b}{2}\Rightarrow2A=a\cdot b[/tex]Then:
[tex]\Rightarrow4A^2=a^2b^2\Rightarrow4A^2=a^2(h^2-a^2)[/tex][tex]\Rightarrow a^4-h^2a^2+4A^2=0[/tex]Now, we replace h and A:
[tex]a^4-(25)^2a^2+4(54)^2=0[/tex]And solve for a:
[tex]a^4-625a^2+11664=0[/tex]Then, the possible values for a are:
[tex]a=\begin{cases}a_1=-\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_2=\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_3=\frac{\sqrt[]{409}}{2}-\frac{29}{2} \\ a_4=\frac{29}{2}+\frac{\sqrt[]{409}}{2} \\ \end{cases}[/tex]We can see that a1, and a2 are not solutions, therefore a2 and a4 are.
So, the two possible b sides are then:
[tex]b_2=\sqrt[]{25^2-(\frac{29}{2}-\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_2\approx24.99[/tex]and:
[tex]b_4=\sqrt[^{}]{25^2-(\frac{29}{2}+\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_{4\approx}15.50[/tex]So, the lengths of the two sides can be:
a = 4.38 and b = 24.99
or
a = 24.61 and b = 15.50
Given z1 = 5(cos 240° + isin 240°) and z2 = 15(cos 135° + isin 135°), what is the product of z1 and z2?
Answers
By multiplying z1 and z2, we get:
[tex]\begin{gathered} z1\times z2=5(cos240+isin240)15(cos135+isin135) \\ z1\times z2=75(cos240+isin240)(cos135+isin135) \end{gathered}[/tex]Applying the distributive property:
[tex]\begin{gathered} z1\times z2=75(cos240+\imaginaryI s\imaginaryI n240)(cos135+\imaginaryI s\imaginaryI n135) \\ z1\times z2=75(cos240\times cos135+cos240\times isin135+\mathrm{i}s\mathrm{i}n240\times cos135+\imaginaryI s\imaginaryI n240\times\imaginaryI s\imaginaryI n135) \\ z\times1z\times2=75(cos240\times cos135+cos240\times\imaginaryI s\imaginaryI n135+\imaginaryI s\imaginaryI n240\times cos135-s\imaginaryI n240\times s\imaginaryI n135) \end{gathered}[/tex]In order to simplify this, we can use the following trigonometric identities:
[tex]\begin{gathered} sin(\alpha+\beta)=sin(\alpha)cos(\beta)+cos(\alpha)sin(\beta) \\ cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta) \end{gathered}[/tex]By taking β as 135 and α as 240, we can write:
[tex]\begin{gathered} is\imaginaryI n(240+135)=isin(375)=is\imaginaryI n(240)s\imaginaryI n(135)+icos(240)s\imaginaryI n(135) \\ cos(240+135)=cos(375)=cos(240)cos(135)-s\imaginaryI n(240)s\imaginaryI n(135) \end{gathered}[/tex]Then, by grouping some terms of the expression, we get:
[tex]z\times1z\times2=75(cos(375)+isin(375))[/tex]375° is equivalent to 15° (375 - 360 = 15), then the product of z1 and z2 can be finally written as:
[tex]z1\times z2=75(cos(15)+\imaginaryI s\imaginaryI n(15))[/tex]Then, option A is the correct answer
write a point slope equation for the line that has a slope 5and passes the point (6,22).
Answers
Solution:
The general equation of a line of slope m passing through a point A is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ (x_1,y_1)\text{ is the coordinate of the point A through which the line passes through} \end{gathered}[/tex]Given that the line has a slope of 5, and passes through the (6, 22), we have
[tex]\begin{gathered} m=5 \\ x_1=6 \\ y_1=22 \end{gathered}[/tex]thus,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-22=5(x-6) \end{gathered}[/tex]Hence, the point-slope equation for the line is expressed as
[tex]y-22=5(x-6)[/tex]
Please help me with my calculus homework, only question 3****
Answers
I would start by stating the Fundamental Theorem of Calculus which states that;
If a function f is continuous on a closed interval [a,b] and F is an antiderivative of f on the interval [a,b], then
[tex]\int ^b_af(x)dx=F(b)-F(a)\text{ }[/tex]Let
[tex]\begin{gathered} f(x)=x^3-6x^{} \\ F(x)=\int f(x)dx=\int (x^3-6x)dx \end{gathered}[/tex]Recall that;
[tex]\int x^n=\frac{x^{n+1}}{n+1},n\ne-1[/tex]That implies that,
[tex]F(x)=\int (x^3-6x)dx=\int x^3dx-\int 6xdx=\frac{x^4}{4}-6(\frac{x^2}{2})=\frac{x^4}{4}-3x^2+C[/tex]Applying the Fundamental Theorem of Calculus, where a=0, b=3
[tex]\begin{gathered} \int ^3_0(x^3-6x)dx=F(3)-F(0) \\ F(3)=\frac{3^4}{4}-3(3)^2+C=\frac{81}{4}-27+C=-\frac{27}{4}+C \\ F(0)=\frac{0^4}{4}-3(0)^2+C=C \\ \Rightarrow\int ^3_0(x^3-6x)dx=-\frac{27}{4}+C-C=-\frac{27}{4} \end{gathered}[/tex]So the answer is -27/4
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 8.4% compounded monthly.
Answers
The desired monthly yield at the retirement time will be equal to $565,714.28.
Compound Interest may be defined as the interest earned by the bank on the basis of principle and also accumulated interest which increases exponentially and not linearly with respect to time. In calculating compound interest, the amount earned at the end of first year becomes principle for the next year and so on. Compound interest can be calculated, annually, half-yearly or quarterly etc.
Time for which work is planned = 40 years, Principle = $4500 and APR = 8.4% = 0.084/12 = 0.007.
The value of n = 12 × 25 = 300
The amount can be calculated by the formula A = P/r [1 - (1 + r) ⁻ⁿ]
A = (4500/0.007) [1 - (1 + 0.007) ⁻³⁰⁰]
A = 642,857.14 [1 - 0.12]
A = 642,857.14 × 0.88
A = $565,714.28 which is required amount.
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Complete Question:
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 8.4% compounded monthly. What monthly deposits are required to achieve the desired monthly yield at retirement?
please help with this practice question thank you
Answers
Answer:
Formula for slope of line is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
First, identify the coordinates of the two points shown on the graph.
First coordinate is (0,-1) and second coordinate is (3,1).
After that, find the slope of the line using the formula.
Slope = (1-(-1))÷(3-0)
= 2/3
Which number line shows all the values of x that make the inequality - 3x +1 <7 true?A2-5-4--3-2-10123B.5in-4-3-2-1012.34С5-5-4-3-2-1012345D-4-3-2.12345
Answers
First let's solve the given inequality:-
[tex]\begin{gathered} -3x+1<7 \\ -3x<6 \\ x>-2 \end{gathered}[/tex]So the correct option is (D).
These two equations look very similar at first. What is the difference in how you would solve them?
`\frac{x-2}{3}=5` `\frac{x}{3}-2=5`
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The difference in how we would solve them is that there is a different order of steps.
We are given two equations.The two equations look similar, but there is a different order of steps in order to solve them.The first equation is :(x-2)/3 = 5Multiply both the sides by 3.x-2 = 15Add 2 on both sides.x = 17Hence, the solution of the first equation is x = 17.The second equation is :(x/3)-2 = 5Add 2 on both sides.x/3 = 7Multiply both the sides by 3.x = 21Hence, the solution of the second equation is x = 21.To learn more about equations, visit :
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which variable has a set of zero pairs as a coefficients? (x or y)2x + 3y=20-2x + y=4
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Answer:
The variable that has a set of zero pairs as a coefficients is;
[tex]x[/tex]Explanation:
We want to find the variable that has a set of zero pairs as a coefficients.
Zero pair is a pair of number that sum up to give zero.
Given the system of equation;
[tex]\begin{gathered} 2x+3y=20 \\ -2x+y=4 \end{gathered}[/tex]The pair of coefficient of x is;
[tex]\begin{gathered} 2\text{ and -2} \\ 2+-2=2-2=0 \end{gathered}[/tex]The pair of coefficient of y is;
[tex]\begin{gathered} 3\text{ and 1} \\ 3+1=4 \end{gathered}[/tex]So, since the coefficient of x sum up to give zero.
The variable that has a set of zero pairs as a coefficients is;
[tex]x[/tex]13. Write an equation of the line that passes through the points (-7, 6) and (3, -4 )in slope-
intercept form.
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Answer:
Firstly we need to find the gradient of give two points as follows;
M= y
Answer:
Answer: y = -x - 1
Step-by-step explanation:
- Consider a straight line passing through (x, y) from the origin (0, 0). That line with a positive gradient of m and meets at a point (0, c) [y-intercept]
- It has a general equation as below;
[tex]{ \rm{y = mx + c}} \\ [/tex]
- So, consider the line given in our question; Let's find its slope m first;
[tex]{ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]
- From the points given in the question, (-7, 6) and (3, -4)
x_1 is -7x_2 is 3y_1 is 6y_2 is -4[tex]{ \rm{m = \frac{ - 4 - 6}{3 - ( - 7)} }} \\ \\ { \rm{m = \frac{ - 10}{10} }} \\ \\ { \underline{ \rm{ \: m = - 1 \: }}}[/tex]
- Therefore, our equation so far is y = -x + c. Our line has a negative slope that means it slants from top to bottom, its origin is its y-intercept
- Consider point (3, -4);
[tex]{ \rm{y = - x + c}} \\ { \rm{ - 4 = - 3 + c}} \\ { \rm{c = - 1}}[/tex]
- y-intercept is -1
hence equation is y = -x - 1
[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]
4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 simplify help
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The simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]
In the given question, it is given
We know the simplification property of the division of numbers as,
Division in exponential form
[tex]\frac{a^{x} }{a^{y} }[/tex] = [tex]a^{x-y}[/tex] , and
Multiplication in exponential form
[tex]a^{x} . a^{y}[/tex] = [tex]a^{x+y}[/tex]
Similarly, we'll apply the same property to solve this question,
[tex]4^{5+3+2+3 + ( -2 -1 -2)}[/tex]
[tex]4^{5+3+2+3 - ( 2 + 1 + 2)}[/tex]
[tex]4^{13 - 5}[/tex]
[tex]4^{8}[/tex]
Hence, the simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]
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2^3= 8 is equivalent to log, C = D.cand D
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we have
2^3= 8
Applying log both sides
log(2^3)=log(8)
Apply property of log
3log(2)=log(8)
therefore
C=3 and D=log(8)
A true-false test contains 11 questions. In how many different ways can this test be completed. (Assume we don't care about our scores.)Your answer is :
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Let's suppose that 1 = TRUE and 0 = FALSE, we want to find how many combinations we can do with 11 zeros and ones, in fact, it's:
[tex]\begin{gathered} \text{ 000 0000 0000} \\ \text{ 000 0000 0001} \\ \text{ 000 0000 0010} \\ \text{ 000 0000 0011} \\ ... \\ \text{ 111 1111 1111} \end{gathered}[/tex]To evaluate the number of combinations we can do:
[tex]C=2^{11}[/tex]2 because we can pick 2 different options (true or false) and 11 because it's the number of questions, then
[tex]\begin{gathered} C=2^{11} \\ \\ C=2048 \end{gathered}[/tex]We have 2048 different ways that this test can be completed.
What is the slope of the line passing through (3, 0) and (4, 0) ?
A) 0
B) 3/4
C) 4/3
D) Undefined
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[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{0-0}{4-1} \\m=\frac{0}{1} \\m=0[/tex]
⇒0 divided by any number is 0
OPTION A IS THE ANSWER.
Answer:
A
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 0 ) and (x₂, y₂ ) = (4, 0 )
m = [tex]\frac{0-0}{4-3}[/tex] = [tex]\frac{0}{1}[/tex] = 0
mr. Morales mix for 4 4/5 pound of macaroni and cheese and brings it to the 5th grade party. the kids ate 3/4 of the total amount that mr. Morales brought. he took the rest home then gave 3/4 of a pound of the macaroni and cheese to Mr. kang the next day. how many pounds of macaroni and cheese is left over for mr. Morales to eat
Answers
Convert the Mixed number to an Improper fraction:
- Multiply the Whole number by the denominator.
- Add the product to the numerator.
- Use the same denominator.
Then:
[tex]4\frac{4}{5}=\frac{(4)(5)+4}{5}=\frac{20+4}{5}=\frac{24}{5}[/tex]Then, the total amount of macaroni and cheese Mr. Morales brought was:
[tex]\frac{24}{5}lb[/tex]After the kids ate macaronis and cheese, the amount he took home was:
[tex]\frac{24}{5}lb-(\frac{24}{5}lb)(\frac{3}{4})=\frac{6}{5}lb[/tex]After he gave some macaroni and cheese to Mr. Kang the next day, the amount of macaroni and cheese (in pounds) left for mr. Morales to eat, is the following:
[tex]\frac{6}{5}lb-(\frac{6}{5}lb)(\frac{3}{4})=\frac{3}{10}lb[/tex]The answer is:
[tex]\frac{3}{10}lb[/tex]